# GW190521—The big one

GW190521 is a huge discovery—it a gravitational wave signal from the coalescence of two black holes to form one about $140 M_\odot$ (where our Sun has a mass of $1 M_\odot$). That is the largest black hole we have yet discovered with gravitational waves. It is the first definitive discovery of an intermediate-mass black hole. It is also a puzzle, as it is a mystery how its source could form…

#### How big can a black hole be?

Anything can become a black hole if it is squeezed enough [bonus note]: you just need to pack enough stuff into a small enough space (just like when taking a Ryanair flight). In practice, most stuff is stiff enough to push back against squeezing to avoid becoming a black hole. It’s only when you get the core of a star about somewhere between $2.1 M_\odot$ and $3 M_\odot$ that gravity becomes strong enough to collapse things down to a black hole [bonus note]. Above this threshold, can we have a black hole of any size?

The biggest black holes are found in the centres of galaxies. These can be hundreds of thousands to tens of billions the mass of our Sun. Our own Milky Way has a rather moderate $4 \times 10^6 M_\odot$ black hole. These massive (or supermassive) black holes are far bigger than any star. Even Elvis. They therefore couldn’t have formed from a collapsing star. So how did they form? The truth is that we’re not sure. It’s possible that we started with smaller black holes and fed them up, or merged them together, or a mixture of both. These initial seed black holes could have formed from stars, or possibly giant clouds of collapsing gas (which may form $10,000 M_\odot$ black holes). In any case, whatever mechanism created these black holes needs to work quickly, as we know from observations of quasars, that there are massive black holes by the time the Universe is a mere billion years old. To figure out how massive black holes form, we need to discovery their seeds.

The shadow of a black hole reconstructed from the radio observations of the Event Horizon Telescope. The black hole lies at the centre of M87, and is about $6.5 \times 10^9 M_\odot$. Credit: Event Horizon Team

Between stellar-mass black holes and massive black holes should lie intermediate-mass black holes. These are typically defined as having masses between $100 M_\odot$ and $100,000 M_\odot$. Massive black holes should grow from these smaller black holes. However, we have never found one, they are the missing link in the black hole spectrum. There are candidates: ultrabright X-ray sources, or globular clusters with suspiciously moving stars, but none of these is rock solid, and couldn’t be explained another way.  GW190521 changes this, at $142^{+28}_{-16} M_\odot$ the merger remnant is without doubt an intermediate-mass black hole.

This discovery shows that intermediate-mass black holes can form from mergers of smaller black holes. However, this doesn’t yet solve the mystery of how massive black holes are grown; we need observations of larger intermediate-mass black holes for that. We’ll keep searching.

What I find more exciting about GW190521 are the masses of the two black holes that merged. Our analysis gives these as $85^{+21}_{-14} M_\odot$ and $66^{+17}_{-18} M_\odot$. The large black hole masses extremely difficult to explain.

Estimated masses for the two components in the binary $m_1 \geq m_2$. We show results several different waveform models and use the numerical relativity surrogate (NRSur PHM) as our best results. The two-dimensional shows the 90% probability contour. The dotted lines in one-dimensional plots the symmetric 90% credible interval. Part of Figure 1 of the GW190521 Implications Paper.

When you form a black hole from a star, its mass depends upon the mass of of its parent star. More massive stars generally form bigger black holes, but because of all the physics that goes on inside stars, it’s not a simple relationship. One important phenomena in determining the fate of massive stars is pair instability. When the cores of stars become very hot ($\sim 3 \times 10^9~\mathrm{K}$, just slightly less than the temperature of the mozerlla on that first bite of pizza, even though you should know better by now), the photons of light (gamma-rays) bouncing around inside the core become energetic enough to produce pairs of electrons and positrons [bonus note]. For the star, this causes some trouble. Its core is mostly supported by radiation pressure. If photons start disappearing as they are converted to electrons and positrons, then there isn’t as much radiation around, and the star will start to collapse. As it collapses, explosive nuclear reactions are triggered. Pair instability kicks in for stars with helium cores about $30 M_\odot$. If the core is between $30 M_\odot$ and about $65 M_\odot$, the star will blast off its outer layers, possibly repeating the cycle of pair-instability collapse and explosion many times. This results in smaller black holes than you might otherwise expect. For helium cores between $65 M_\odot$ and about $135 M_\odot$, the explosion completely destroys the star, leaving nothing behind. These stars never collapse down to a black hole, and this leaves a gap, predicted to start somewhere between $45 M_\odot$ and $55 M_\odot$.

Remnant (white dwarf, neutron star or black hole) mass $M_\mathrm{rem}$for different initial (zero age main sequence) stellar masses $M_\mathrm{ZAMS}$. This is just for single stars, and ignores all the complicated things that can happen in binaries. The different coloured lines indicate different metallicities $Z$ (higher metallicity stars lose more mass through stellar winds). The two panels are for two different supernova models. The grey bars indicate potential mass gaps: the lower core collapse mass gap (only predicted by the Rapid model) and the upper pair-instability mass gap. The tick marks in the middle are various claimed gravitational-wave source, colour-coded by the total mass of the binary $M_\mathrm{tot}$. Figure 1 of Zevin et al. (2020).

The more massive of GW190521’s black holes sits squarely in the expected pair-instability mass gap. How can we form such a system?

To delve into all the details, we have put together two papers on GW190521. The high mass of the system poses challenges not just for our understanding of astrophysics, but also for our data analysis. Below, I’ll go through what we have discovered.

### The signal

GW190521 was first identified in our online searches about 20 seconds after we took the data. All three of our detectors were online and observing at the time. It was a short bleep of a signal indicating a high mass system. Short signals always make me suspicious as they can easily confused with some types of glitch. The signal was picked up by multiple search algorithms, which generally is a good sign, as they all estimate the background of noise in a slightly different way. However, the estimated false alarm rates were only one per few years. That’s not terribly impressive—it’s the range where things can change as we collect more data. Immediately, checks of the signal began. We have many ways of monitoring our detectors, and experts started running through these. Microphones at Hanford picked up a helicopter overhead a few minutes later, but that’s too far away in time to be related to the signal. The initial checks all looked OK, so we were confident that it was safe to share the candidate detection S190521g.

Visualisations of GW190521. The top panels show whitened data and reconstructed waveforms from the template-free detection algorithm cWB, BayesWave (which reconstructs the signal from sine–Gaussian wavelets), and our parameter estimation code LALInference (which uses binary black hole waveforms). The bottom panels show time–frequency plots: each plot has a different scale as the signal is loudest in LIGO Livingston and hardly noticeable in Virgo. As the signal is so short, we don’t see the usual chirp of a binary coalescence clearly. Figure 1 of the GW190521 Discovery Paper.

After hearing that the initial checks were complete, I went to bed, little knowing the significance of what we had found. The initial estimates for the masses of a binary come from our search pipelines—specifically the pipelines that match signal templates to the data. At high masses, the search template bank doesn’t have many templates, so the best fitting template can be quite a way from the true value. It was only after completing a proper parameter estimation analysis that we get a good idea of the masses and their uncertainties. When these results came in we found that we potentially had something lying smack in the middle of the pair-instability mass gap. That was, if the signal were real.

While initial checks of the signal showed nothing suspicious, we always do more offline checks. For GW190521 there were a few questions that took some digging to understand.

First, the peak of the signal is around 60 Hz. This is also the mains frequency in the US, so there was concern that the signal was contaminated by noise caused by this (which would obviously be shocking). A variety of careful investigations were done subtracting out noise from the mains. In the end, it turns out that this makes negligible difference to the results, which is nice.

Second, there was concern over the shape of the signal. Our template-based search algorithms always look at how well the signal matches the template: if you get a really good match in one frequency range, but not another, then that’s an indicator that you have some random noise rather than a true signal. This consistency test is summarised in a statistic, which should be around 1 if all is OK, and larger if things don’t fit. For the PyCBC algorithm, the value for the Livingston data was about 3. Since the signal was loudest in Livingston, was this cause for alarm? One explanation could be that the template wasn’t a good fit because the templates used by the search don’t include the effects of spin precession. Hence, if you have a signal where spin precession is important, you would expect a bad fit. Checking the consistency with templates which included precession did give better consistency. However, the GstLAL algorithm also used templates without precession, and its consistency test looked fine. Therefore, it couldn’t just be precession. It seems that the key is that there are so few templates in the relevant area for PyCBC’s template bank (GstLAL had things better covered). Hence, it is hard to find a good fitting template. Adding the best fitting template from the GstLAL bank to the PyCBC search leads to it being picked out as the best template too, with a consistency check statistic of 1.7 (not perfect, but not suspicious). I think this highlights the importance of not limiting yourself to only finding what you expect: we need to include the potential for our searches to discover things outside of what we have discovered in the past.

Finally, there was the difference in significance reported by the different search algorithms. In addition to the template-based searches, we also have searches which look for more generic signals without templates [bonus note], instead using the consistency in the data from different detectors to spot signals. Famously, our non-template algorithm coherent WaveBurst (cWB) made the first detection of GW150914 (other algorithms weren’t up-and-running at the time).  Usually, the template searches should do better as they know what they are looking for. This has mostly been the case so far. The exception was GW170729, our previously most massive and lowest significance detection. Generally, you expect searches to disagree more on quiet signals (not too much of an issue for GW190521), as then how they characterise the noise background is more important. We also expect the template searches to lose their advantage for very short signals, when there’s not much for a template to match, and when the coherence check used by cWB comes in especially handy. GW190521 is again found with greatest significance by cWB. In our final searches (using all the data from the first six months of the third observing run), cWB gives a false alarm rate of 1 per 4900 years (pretty darn good—at least a Jammie Wagon Wheel in biscuit terms), GstLAL gives 1 per 829 years (nice—a couple of Fruit Creme biscuits), and PyCBC gives 1 per 0.94 years (not at all exciting—an Iced Gem at best). Should we be suspicious of the difference? Perhaps cWB can pick up on something extra in the signal because actually the source isn’t a quasicircular binary [bonus note] as assumed by our templates? We know that the search templates are missing some features, like the effects of spin precession, and also higher order multipole moments. Seeing how our search algorithms cope finding simulated signals that include these extra bits of physics, we find that similar discrepancies between cWB and GstLAL happen around 8% of the time, while for cWB and PyCBC they happen about 3% of the time. That’s enough to make me go Hmm, but not enough to convince me that we’ve detected a completely new type of signal, one which doesn’t come from a quasicircular binary.

The conclusion from our analysis is that GW190521 is a good-looking gravitational wave signal. We are confident that it is a real detection, even though it is really short. However, we can’t be positive that the source is quasicircular binary. That’s the most likely explanation, and consistent with what we’ve seen, but potentially not the only explanation.

There are other sources for gravitational waves beyond quasicircular binaries. One of the best known would be a supernova explosion. GW190521 is certainly not one of these. For one thing, the signals are much longer and more complicated, and for another, we could really only detect a supernova within our own galaxy, and we probably would have noticed that happen. Another hypothesised search which could produce a nice, short bleep of a signal would be a cosmic string. Vibrations or ripples along a cosmic string can source gravitational waves, and while we don’t know if cosmic strings exist, we do have templates for what these signals should look like. Using these, we can compare how well the data are described by cosmic string signals compared to our quasiciruclar binary templates. We find Bayes factors of about $10^{30}$ in favour of the binary signals, so it’s probably not cosmic strings. Finally, you’ve perhaps noticed that I’ve been writing quasicircular [bonus note] a lot. Part of that is because it’s a cool word (25 points in Scrabble), but also because it’s possible that we have an eccentric binary. These are difficult to model, so we don’t have lots of good templates for them, but when you have a short signal, it is possible that eccentricity could be confused with spin precession. This would lead us to overestimating the distance and underestimating the masses. Initial studies do seem to show that an eccentric signal fits the data well (Romero-Shaw et al. 2020; Gayathri et al. 2020). An eccentric binary is the most probable alternative to a quasicircular binary, but it is pretty improbable. Since eccentricity is lost during inspiral, we would need something to have pumped the eccentricity, which is difficult for a binary so close to merger. I would bet my Oreos on the source being a quasicircular binary.

### The source properties

If we stick with the assumption of a quasicircular binary, what can we tell about the source? We have already covered the component masses of $m_1 = 85^{+21}_{-14} M_\odot$ and $m_2 = 66^{+17}_{-18} M_\odot$, and that the merger remnant is $M_\mathrm{f} = 142^{+28}_{-16} M_\odot$. The plot below shows the final mass as well as the spin, which is $\chi_\mathrm{f} = 0.72^{+0.09}_{-0.12}$. For the black holes formed from the mergers of near equal mass binaries, you’d expect the final spin to be around $0.7$.

Estimated mass $M_\mathrm{f}$ and spin $\chi_\mathrm{f}$ for the final black hole. We show results several different waveform models and use the numerical relativity surrogate (NRSur PHM) as our best results. The two-dimensional shows the 90% probability contour. The dotted lines in one-dimensional plots the symmetric 90% credible interval. The mass is safely above the conventional lower limit to be considered an intermediate-mass black hole. Figure 3 of the GW190521 Implications Paper.

We can also get an estimate of the final spin from the final part of the signal, the ringdown. This is where the black hole settles down to its final state, like me after 6 pm. What is neat about using the ringdown is that we don’t need to assume that the binary was quasicircular, as we only care about the black hole formed at the end. The downside is that we don’t get an estimate of the distance, so we only measure the redshifted final mass $(1+z)M_\mathrm{f}$. Looking at the ringdown, we get lovely consistent results trying ringdown models at different start times and including different higher order multipole moments, and all agree with the analysis of the entire signal using the quasicircular templates.

Estimated redshifted mass $(1+z)M_\mathrm{f}$ and spin $\chi_\mathrm{f}$ for the final black hole. We show results several different insprial–merger–ringdown waveform models, which we use for our standard analysis, as well as ringdown-only waveforms.  They agree nicely. The two-dimensional shows the 90% probability contour. The dotted lines in one-dimensional plots the symmetric 90% credible interval. The mass is safely above the conventional lower limit to be considered an intermediate-mass black hole. Part of Figure 9 of the GW190521 Implications Paper.

Being able to measure the ringdown at all is an achievement. It’s only possible for loud signals from high mass systems. The consistency of the mass and spin estimates is not only a check of the quasicircular analysis. It is much more powerful than that. The ringdown measurements are a test of the black hole nature of the final object. All looks as expected so far. I really want to do this for louder signals in the future.

Returning to the initial binary, what can we say about the spins of the initial black holes? Not much, as it is difficult to extract information from such a short waveform.

The spin components aligned with the orbital angular momentum affect the transition from inspiral, and have a small influence on the final spin. We often quantify the aligned components of the spin in the mass-weighted effective inspiral spin parameter $\chi_\mathrm{eff}$, which goes from $-1$ for both the spins being maximal and antialigned with the orbital angular momentum to $1$ for both spins being maximal and aligned with the orbital angular momentum. We find that $\chi_\mathrm{eff} = 0.08^{+0.27}_{-0.36}$, consistent with no spin, spins antialigned with each other or in the orbital plane. The result is strongly influenced by the assumed prior, we’ve not learnt much from the signal.

The component of the spin in the orbital plane (perpendicular to the orbital angular momentum) control the amount of spin precession. We often quantify this using the effective precession spin parameter $\chi_\mathrm{p}$, which goes from $0$ for no in-plane spin, to $1$ for maximal precession. Precession normally shows up in the modulation of the inspiral signal, so you wouldn’t expect to measure it well from a short signal. However, it can also influence to amplitude of the signal around merger, and we seem to get a bit of information here, which seems to prefer larger $\chi_\mathrm{p}$. We find $\chi_\mathrm{p} = 0.68^{+0.28}_{-0.34}$, but there’s support across the entire range.

Estimated effective inspiral spin $\chi_\mathrm{eff}$ and effective precession spin $\chi_\mathrm{p}$ . We show results several different waveform models and use the numerical relativity surrogate (NRSur PHM) as our best results. The two-dimensional shows the 90% probability contour. The dotted lines in one-dimensional plots the symmetric 90% credible interval. We also show the prior distributions in the one-dimensional plots. Part of Figure 1 of the GW190521 Implications Paper.

Looking at the spins overall, the lack of aligned spin plus the support for in-plane spins means that we prefer misaligned spins. You wouldn’t expect this for two stars which have lived their lives together as a binary, but it wouldn’t be implausible for a dynamically formed binary. A dynamical formation seems plausible to me, but since the spin measurements aren’t too concrete, we can’t really rule too much out [bonus note].

Finally, let’s take a look at the distance to the source. Our analysis gives a luminosity distance of $D_\mathrm{L} 5.3^{+2.4}_{-2.6}~\mathrm{Gpc}$. This makes the source a good contender for the most distant gravitational wave source ever found [bonus note]. It’s actually far enough, that we might want to reconsider our standard approximation that sources are uniformly distributed like $D_\mathrm{L}^2$. This would be OK if sources were uniformly distributed in a non-evolving Universe, but sadly we don’t live in such a thing, and we have to take into account the expansion of the Universe, and the evolution of the galaxies and stars within it. We’ll come back to look at this when we present our catalogue of detections from the first part of the third observing run.

### The astrophysics

#### Exploring the upper mass gap

The location of the upper mass gap is pretty well determined. There are a variety of uncertainties in the input physics, such as the nuclear reaction rate for burning carbon into oxygen, the treatment of convection inside stars or if stars rapidly rotate which can alter the cut-off. No-one has tried varying all these together, but individually you can’t get above about $55 M_\odot$ for your black hole. Allowing for new types of particles (like axions, one of the candidates for dark matter, and possibly the explanation for why teenage boys can smell terrible) can potentially increase the limit to above $70 M_\odot$, but that is extremely speculative (I’d love it if it were true). Sticking to known physics, at face value, it is hard to explain the mass of the primary black hole from our understanding of how stars evolve.

There are potentially ways around the mass gap with help from a star’s environment:

1. Super efficient accretion from a companion star can grow black holes into the mass gap. Then you wouldn’t expect the total mass of the binary to over about $100 M_\odot$, so we’d need to swap out partners in this case.
2. The pair instability originates in the helium core of a star. If we can find a way to grow the envelope of the star, while keeping the core below the threshold for the instability to set in, then the whole thing could collapse down to a mass gap black hole. This could potentially happen if two stars collide after one has already formed its helium core. The other gets disrupted and swells the envelope. This might be expected in stellar clusters. Similarly, a couple of recent papers (Farrell et al. 2020; Kinugawa, Nakamura & Nakano 2020) have also suggested that the first generation of stars, which have few elements other than hydrogen or helium, could also collapse down to black holes in this mass range. The idea here is that these stars lose much less of their envelopes due to stellar winds, so you can end up with what we would otherwise consider an oversized envelope around a core below the pair instability threshold
3. We could have two black holes merge to form a bigger one, and then have the remnant go on to form a new binary. You would need a dense environment for this, somewhere like a globular cluster where it’s easy to find new partners. Ideally, somewhere with a large escape velocity, perhaps a nuclear star cluster, which has a high escape velocity so that it is more difficult for the remnant black hole to get kicked out at any point: gravitational waves give a recoil kick, and close encounters with other objects can also lead to the initial binary getting a kick.
4. Especially good for growing black holes may be if they are embedded in the accretion disc around a supermassive black hole. Then these disc black holes can merge with each other whilst being unlikely to escape the environment. Additionally, they can swallow lots of gas from the surrounding disc to help them grow big and strong.

There is also the potential that we don’t have a black hole formed from stellar collapse, but instead a primordial black hole formed from dense regions in the early Universe. These primordial black holes are a another candidate for dark matter. I like that there are two options for potential dark matter-related formation channels. It’s good to have options.

The difficulty with all of these alternative formation channels is matching the observed rate for GW190521-like systems. It’s not enough for a proposed channel to be able to explain the system’s properties, it also needs to make enough of them for us to have come across one. From our data, we infer that GW190521-like systems have a merger rate density of $0.13^{+0.30}_{-0.11}~\mathrm{Gpc^{-3}\,yr^{-1}}$. Predicted rates for the various formation mechanisms discussed above can be rather uncertain (kind of like how the exact value of a small bag full of Bitcoin is uncertain), so I would like to see more work on this, before picking a most plausible option.

#### Hierarchical mergers

We did do some quantitative analysis for the case of hierarchical mergers of black holes, following the framework outlined in Kimball et al. (2020). This simultaneously fits the mass and spin distribution for the first generation (1g) of black holes formed from stars, and a fraction of hierarchical mergers involving second generation (2g) merger remnants. To calibrate the number of hierarchical mergers, we use globular cluster simulations.

Using our base model, where the 1g+1g population is basically the Model C we used to describe our detections from the first two observing runs, we find that the odds are in favour of GW190521 being a 1g+1g merger. Hierarchical mergers are so rare, that it’s actually more probable that we squish down the inferred masses and have something from the tail of the 1g population.

The rate of hierarchical mergers, however, is very sensitive to the distribution of spins of 1g black holes. Larger spins give bigger kicks (even a spin of 0.1 is enough to mean remnants are hardly ever retained in typical globular clusters). If we add into the mix a fraction of 1g+1g binaries which have 0 spin (motivated by recent simulations), we improve the odds to be roughly even 1g+1g vs 1g+2g, and less common for 2g+2g. Given that we are not taken into account that only a fraction of binaries would be in clusters, which would reduce the odds of a hierarchical merger considerably, this isn’t quite enough to convince me.

However, what if we were to turn up the mass of the cluster? For our globular cluster model, we used $5\times 10^5 M_\odot$, what if we tried $10^8 M_\odot$, more like you would expect for a nuclear star cluster? We shouldn’t really be doing this, as our model is calibrated against globular cluster simulations, and nuclear star clusters have different dynamics, but we can use our results as illustrative. In this case, we find odds of about 1000:1 in favour of hierarchical mergers. This suggests that this option may be a promising one to follow, but we must moderate our results remembering that only a fraction of binaries would form in these dense environments.

The analysis is done using only our first 10 detected binary black hole from our first two observing runs plus GW190521. GW190521 is not the most representative of the third observing run detections (hence why it gets special papers™), so it is not exactly fair to stick it in to the mix to infer the population parameters. We’ll need to redo this analysis when we have the full results of the run to update the results. Having more binaries in the analysis should allow us to more precisely measure the population parameters, so we will be more confident in our results.

### The surprise

After all our investigations, we thought we had examined every aspect of GW190521. However, there’s always one more thing. As we were finishing up the paper, a potential electromagnetic counterpart was announced.

Electromagnetic counterparts are not expected when two black holes merge—black holes are indeed black—however, material around the binary could produce light.

The counterpart was found by the Zwicky Transient Factory. They targeted active galactic nuclei to look for counterparts. These are the bright cores of galaxies where the supermassive black hole is feeding off a surrounding disc. In this case, they hypothesis that the binary had some gas orbiting around it, and when the binary merged, the gravitational wave recoil kick sent the remnant black hole and its orbiting material into the disc of the supermassive black hole. As the orbiting material crashes into the disc it will emit light. Then, once it is blasted away, material from the disc accreting onto the remnant black hole will also emit light. This seems to fit with what was observed, with the later powering the observed emission.

What I think is exciting about this proposal is that active galactic nuclei are one of the channels predicted to produce binaries as massive as GW190521! Therefore, things seem to line up nicely.

The three dimensional localisation for GW190521. The lines indicate the position of the claimed electromagnetic counterpart from around an active galactic nucleus. This location lies at the 70% credible level. Credit: Will Farr

What I think is less certain is if the counterpart is really associated with our gravitational wave source. The observing team estimate that the probability of a chance association is small. However, there is a lot of uncertainty in how active galactic nuclei can flare. The good news is that the remnant black hole may continue to orbit and hit the disc again, leading to another flare. The bad news is that the uncertainty on when this happens is many years, so we don’t know when to look.

Follow-up analyses by Ashton et al. (2020) and Palmese et al. (2021) cast the association as more uncertain. It is difficult to be confident of an association when the localization volume is so large. If we knew that this type of flare had to look exactly like the observed emission, that would help, but we can’t be that certain yet.

Overall, I think we need to observe another similar association before we can be certain what’s going on. I really hope this candidate counterpart encourages people to follow up more binary black holes to look for emission. The unexpected discoveries are often the most rewarding.

### The papers

#### The GW190521 Discovery Paper

Title: GW190521: A binary black hole merger with a total mass of 150 solar masses
Journal:
Physical Review Letters125(10):101102(17)
arXiv: 2009.01075 [gr-qc]
You want to understand the detection of GW190521

This is the paper announcing the gravitational wave detection. It follows our now standard pattern for a detection paper of discussing our instruments and data quality; our detection algorithms and the statistical significance of the search; the inferred properties of the source, and a bit of testing gravity; a check of the reconstruction of the waveform, and then a nice summary looking forward to more discoveries to come.

What is a little different for this paper is that because the signal is so short, we have had to be extra careful in our checks of the detectors’ statuses, the reliability of our detection algorithms, and the assumptions that go into estimating the source properties. If you are sceptical of being able to detect such short signals, I recommend checking out the Supplemental Material for a summary of some of the tests we did.

#### The GW190521 Implications Paper

Title: Properties and astrophysical implications of the 150 solar mass binary black hole merger GW190521
Journal:
Astrophysical Journal Letters; 900(1):L13(27)
arXiv: 2009.01190 [astro-ph.HE]
You want to understand the implications for fundamental physics and astrophysics of the discovery

In this paper we explore the properties of GW190521. We check the robustness of the inferred source properties. For such a short signal, our usual assumption that we have a quasicircular binary is probably the most sensible thing to do, but we can’t be certain, and if this assumption is wrong, then we will have got the properties wrong. Astronomy is hard sometimes. Assuming that our estimates of the properties are correct, we look at potential formation mechanisms. We don’t come to any firm conclusions, but sketch out some of the possibilities. We also look at tests of the black hole nature of the final object in a bit more detail. A few wibbles can sure cause a lot of excitement.

Science summary: GW190521: The most massive black hole collision observed to date
Data release: Gravitational Wave Open Science Center; Parameter estimation results
Rating: 🍰🐋📏🏆

### Bonus notes

#### Minimum black hole mass

The uncertainty in when gravity will take over and squish things down to a black hole is set by the stiffness of neutron star matter. Neutron stars are the densest matter can be, this is the stiffest form of matter, the one most resistant to being crushed down into a black hole. The amount of weight neutron star matter can support is uncertain, so we don’t quite know their maximum mass yet. This made the discovery of GW190814 particularly intriguing. This gravitational wave came from a binary where the less massive component was about $2.6 M_\odot$, exactly in the range where we’d expect the transition between neutron stars and black holes. We can’t tell for certain which it is, but I’ve bet my M&Ms on a black hole.

It’s potentially possible that there are black holes smaller than the maximum neutron star mass which didn’t form from collapsing stars. These are primordial black holes, which formed from overdense regions in the early universe. We don’t know for certain if they do exist, but we are looking.

#### Positrons

Positrons are antielectrons, the antimatter equivalent of electrons. This means that they share identical properties to electrons except that they have opposite charge. Electrons things that the glass is half-empty, positrons think it is half-full. Neutrinos think that the glass is twice as big as it needs to be, but so long as we have a well-mixed cocktail, who cares?

#### Burst searches

In the jargon of LIGO and Virgo, we refer to the non-template detection algorithms as Burst searches, as they are good at spotting bursts of gravitational waves. Burst is not a terribly useful description if you’ve not met it before, so we generally try to avoid this in our papers. A common description is an unmodelled search, to distinguish from the template-based searches which use model waveforms as input. However, it’s not really true that the Burst searches don’t make modelling assumptions about the signal. For example, the cWB algorithm used to look for binaries assumes that the frequency will increase with time (as you would expect for an inspiralling binary). To avoid this, we’ve sometimes describes the search algorithm as weakly modelled, but that’s perhaps no clearer than Burst. For this post, I’ll stick to non-template as a description.

#### Quasicircular

When talking about the orbits of binaries, we might be interested in their eccentricity. Eccentricity is a key tracer of how the binary formed. As binaries emit gravitational waves, they quickly lose their eccentricity, so in general we don’t expect there to be significant eccentricity for the binaries detected by LIGO and Virgo.

An orbit with zero eccentricity should be circular. However, since we have a binary emitting gravitational waves the orbit will be shrinking. As we have an inspiral, if you were to trace out the orbit, it would not be a circle, even though we would describe it as having zero eccentricity. This is particularly noticeable at the end of the inspiral, when we get close to the two objects plunging together. Hence, we describe orbits as quasicircular, which I think sounds rather cute.

The simulation above shows the orbit of an inspiral. Here the spins of the black holes also lead to the precession of the orbit, making it a bit more complicated than you might expect for a something described as circular, but, of course, not at all unexpected for something with a cool name like quasicircular. I also really like how this visualisation shows the event horizons of the two black holes merging.

#### Spin Bayes factors

To try to quantify the support for spin, we quote two Bayes factors. The first is for spin verses no spin. There we find a Bayes factor of about 8.3 in favour of there being spin. That’s not something you’d want to bet against, but for comparison, for GW190412 we found that is it over 400, and for GW151226 it is over a million. I’d expect any statement on spins for GW190521 will depend upon your prior assumptions. The second Bayes factor is in favour of measurable precession. This is not the same as comparing the Bayes factor between perfectly aligned spins (when there would be no precession) and generic, isotropically distributed spins. Instead we are comparing the scenario where we can measure in-plane spins verses the case where there are isotropically distributed but the in-plane spins don’t have any discernible consequences. Here we find a Bayes factor of 11.5 in favour of measurable precession. This makes sense as we do have some information on $\chi_\mathrm{p}$, and would expect an even Bayes factor of 1 if we only got the prior back. It seems we have gained some information about the spins from the signal.

For more on Bayes factors, I would suggest reading Zevin et al. (2020). In particular, this explains why it can make sense here that the Bayes factor for measurable precession is larger than the Bayes factor for there being spin. At first, it might appear odd that we can be more definite that there is precession than any spin at all. However, this is because in comparing spin verses no spin we are hit by the Occam factor—we are adding extra parameters to our model, and we are penalised for this. If the effects of spins are small, so that they are not worth including, we would expect no-spin to win. When looking at the measurability of precession, we have set up the comparison so that there is no Occam factor. We can only win, if waveforms with precession clearly fit the data better, or break even if they make no difference.

#### Economically large

To put a luminosity distance of $5.3~\mathrm{Gpc}$ in context, if you put $1 in a jar ever two weeks over the duration the gravitational wave signal was travelling from its source to us (7.1 billion years, about 1.5 times the age of the Sun), you would end up with about a net worth only 7% less than Jeff Bezos (currently$199.3 billion).

# GW190412—A new flavour of binary black hole

On 1 April 2019 LIGO and Virgo began their third observing run (O3). Never before had we observed using such sensitive gravitational wave detectors. Throughout O3 discoveries came rapidly. Binary black holes are our most common source, and as we built a larger collection we starting to find some unusual systems. GW190412 is our first observation from a binary with two distinctly differently sized black holes. This observation lets us test our predictions for gravitational wave signals in a new way, and is another piece in the puzzle of understanding how binary black holes form.

### The discovery

On 12 April 2019 I awoke to the news that we had a new gravitational wave candidate [bonus note]. The event was picked up by our searches and sent out as a public alert under the name S190412m. The signal is a real beauty. There’s a striking chirp visible in the Livingston data, and a respectable chirp in the Hanford data. You can’t see a chirp in Virgo, the signal-to-noise ratio is only about 4, but this is why we have cunning search algorithms instead of looking at the data by eye. In our final search results, our matched-filter searches (which use templates of gravitational wave signals to comb through the data) GstLAL and PyCBC identified the event with false alarm rates of better than 1 in 100,000 years and 1 in 30,000 years, respectively. Our unmodelled search coherent WaveBurst (which looks for compatible signals in multiple detectors, rather than a specific template) also identified the event with a false alarm rate of better than 1 in 1,000 years. This is a confident detection!

Time–frequency plots for GW190412 as measured by LIGO Hanford, LIGO Livingston and Virgo. The chirp of a binary coalescence is clearer in two LIGO detectors, with the signal being loudest in Livingston. Figure 1 of the GW190412 Discovery Paper.

### Vanilla black holes

Our first gravitational wave detection, GW150914, was amazing. We had never seen a black hole around 30 times the mass of our Sun, and here we had two merging together (which we had also never seen). By the end of our second observing run, we had discovered that GW150914 was not rare! Many of detections consisted of two roughly equal mass black holes around 20 to 40 times the mass of Sun. We now call these systems vanilla binary black holes. They are nice and easy to analyse: we know what to do, and it’s not too difficult. I think that these signals are delicious.

GW190412’s source, however, is different. We estimate that the binary had one black hole $m_1 = 30.1^{+4.6}_{-5.3}$ times the mass of our Sun (quoting the 90% range for parameters), and the other $m_2 = 8.3^{+1.6}_{-0.9}$ times the mass of our Sun. Neither of these masses is too surprising on their own. We know black holes come in these sizes. What is new is the ratio of the masses $q = m_2/m_1 = 0.28^{+0.12}_{-0.07}$ [bonus note]. This is roughly equal to the ratio of filling in a regular Oreo to in a Mega Stuf Oreo. Investigations of connections between Oreos and black hole formation are ongoing. All our previous observations have mass ratios close to 1 or at least with uncertainties stretching all the way to 1. GW190412’s mass ratio is the exception.

Estimated mass ratio $q$ for the two components in the binary and the effective inspiral spin $\chi_\mathrm{eff}$ (a mass-weighted combination of the spins perpendicular to the orbital plane). We show results for two different model waveforms: Phenom PHM and EOB PHM (the PHM stands for precession and higher order multipoles). Systems with unequal masses are difficult to model, so we have some extra uncertainty from the accuracy of our models. The two-dimensional shows the 90% probability contour. The one-dimensional plots show the probability distributions and the the dotted lines mark the central 90%. Figure 2 of the GW190412 Discovery Paper.

The interesting mass ratio has a few awesome implications:

1. We get a really wonderful measurement of the spin of the more massive black hole.
2. We can observe a new feature of the gravitational wave signal (higher order multipole moments).
3. We understand a bit more about the population of binary black holes.

### Spin

Black holes have two important properties: mass (how much the bend spacetime) and spin (how much they swirl spacetime around). The black hole masses are most important for determining what a gravitational wave signal looks like, so we measure the masses pretty well. Spins leave a more subtle imprint, and so are more difficult to measure.

A well measured, and convenient to work with, combination of the two spins is the effective inspiral spin parameter

$\displaystyle \chi_\mathrm{eff} = \frac{m_1 \chi_1 \cos \theta_1 + m_2 \chi_2 \cos \theta_2}{m_1 + m_2}$,

where $\chi_1$ and $\chi_2$ are the spins of the two black holes [bonus note], and $\theta_1$ and $\theta_2$ are the tilts angles measuring the alignment of the spins with the orbital angular momentum. The spins change orientations during the inspiral if they are not perfectly aligned with the orbital angular momentum, which is referred to as precession, but $\chi_\mathrm{eff}$ is roughly constant. It also effects the rate of inspiral, binaries with larger $\chi_\mathrm{eff}$ also merge when they’re a bit closer. For GW190412, we measure $\chi_\mathrm{eff} = 0.25^{+0.08}_{-0.11}$.

This is only the second time we’ve had a definite non-zero measurement of $\chi_\mathrm{eff}$ after GW151226. GW170729 had a reasonable large value, but the uncertainties did stretch to include zero. The measurement of a non-zero $\chi_\mathrm{eff}$ means that we know at least one of the black holes has spin.

The effective inspiral spin parameter $\chi_\mathrm{eff}$ measures the spin components aligned with the orbital angular momentum. To measure the spin components in the orbital plane, we typically use the effective precession spin parameter [bonus note]

$\displaystyle \chi_\mathrm{p} = \max\left\{\chi_1 \sin \theta_1 , \frac{q(4q + 3)}{(4 + 3q)}\chi_2 \sin \theta_2\right\}$.

This characterises how much spin precession we have: 1 means significant in-plane spin and maximal precession, and zero means no in-plane spin and no precession.

For GW190412, we measure $\chi_\mathrm{p} = 0.31^{+0.19}_{-0.16}$. This is the best measurement of $\chi_\mathrm{p}$ so far. It shows that we don’t see strong procession, but also suggests that there is some in-plane spin.

Estimated effective precession spin parameter $\chi_\mathrm{p}$. Results are shown for two different waveform models. To indicate how much (or little) we’ve learnt, the prior probability distribution is shown: the global prior is what we would get if we had learnt nothing, the restricted prior is what we would have after placing cuts on the effective inspiral spin parameter and mass ratio to match our observations. We are definitely getting information on precession from the data. Figure 5 of the GW190412 Discovery Paper.

Now, since we know that the masses are unequal in the binary, the contribution to $\chi_\mathrm{eff}$ is dominated by the spin of the larger black hole, or at least the component of the spin aligned with the orbital angular momentum ($\chi_\mathrm{eff} \approx \chi_1 \cos \theta_1$), and similarly $\chi_\mathrm{p}$ is dominated by the in-place components of the larger black hole’s spin ($\chi_\mathrm{p} \approx \chi_1 \sin \theta_1$). Combining all this information, we can actually get a good measurement of the spin of the bigger black hole. We infer that $\chi_1 = 0.44^{+0.16}_{-0.26}$. This is the first time we’ve really been able to measure an individual spin!

We don’t yet have a really good understanding of the spins black holes are born with. Their spins can increase if they accrete material, but it needs to be a lot of stuff to change it significantly. When we make a few more spin measurements, I’m looking forward to using the information to help figure out the histories of our black holes.

### Higher order multipoles

When calculating gravitational wave signals, we often use spin-weighted spherical harmonics. These are a set of functions, which describe possible patterns on a sphere. Using them, we can describe the amount of gravitational waves emitted in a particular direction. Any gravitational wave signal can be approximated as a sum of the spin-weighted spherical harmonics ${}_{-2}Y_{\ell m}(\vartheta, \phi)$, where we use $\{\vartheta, \phi\}$ as the angles on the sphere, and $(\ell, m)$ specify the harmonic. The majority of the gravitational radiation emitted from a binary is from the $(2, \pm2)$ harmonic, so we usually start with this. Larger values of $\ell$ contribute less and less. For exactly equal mass binaries with non-spinning components, only harmonics with even $\ell$ are non-zero, so really the $(2, \pm2)$ harmonic is all you need. For unequal mass binaries this is not the case. Here odd $\ell$ are important, and harmonics with $\ell = \pm m$ are expected to contribute a significant amount. In previous detection, we’ve not had to worry too much about the harmonics with $\ell > 2$, which we refer to as higher order multipole moments, as they contributed little to the signal. GW190412’s unequal masses mean that they are important here.

During the inspiral, the frequency of the part of the gravitational wave signal corresponding to a given $(\ell, m)$ is $f_{\ell m} \simeq m f_\mathrm{orb}$, where $f_\mathrm{orb}$ is the orbital frequency. Most of the signal is emitted at twice the orbital frequency, but the emission from the higher order multipoles is at higher frequencies. If the $m = 2$ multipole was a music A, then the $m = 3$ multipole would correspond to an E, and if the $m = 2$ multipole was a C, the $m = 3$  would be a G. There’s a family of chirps [bonus note]. For GW190412, we clearly pick out the frequency component at $3 f_\mathrm{orb}$ showing the significance of the $(3,\pm3)$ mode. This shows that the harmonic structure of gravitational waves is as expected [bonus note]. We have observed a perfect fifth, as played by the inspiral of two black holes.

Using waveforms which include higher order multipoles is important to get good measurements of the source’s parameters. We would not get a good measurement of the mass ratio or the distance ($740^{+130}_{-160}~\mathrm{Mpc}$, corresponding to a travel time for the signal of around 2 billion years) using templates calculated using only the $(2,\pm2)$ harmonic.

### The black hole population

GW190412’s source has two unequal mass black holes, unlike our vanilla binary black holes. Does this indicate a new flavour of binary black hole, and what can we learn about how it formed from it’s properties?

After our second observing run, we analysed our family of ten binary black holes to infer what the population looked like. This included fitting for the distribution of mass mass ratios. We assumed that the mass ratios were drawn from a distribution something like $p(q) \propto q^{\beta_q}$ and estimated the value of $\beta_q$. A result of $\beta_q = 0$ would mean that all mass ratios were equally common, while larger values would mean that binaries liked more equal mass binaries. Our analysis preferred larger values of $\beta_q$, making it appear that black holes were picky about their partners. However, with only ten systems, our uncertainties spanned the entire range we’d allowed for $\beta_q$. It was too early to say anything definite about the mass ratio distribution.

If we add in GW190412 to the previous ten observations, we get a much tighter measurement of $\beta_q$, and generally prefer values towards the lower end of what we found previously. Really, we shouldn’t just add in GW190412 when making statements about the entire population, we should fold in everything we saw in our observing run. We’re working on that. For now, consider these as preliminary results which would be similar to those we would have got if the observing run was only a couple of weeks long.

Estimated power-law slope $\beta_q$ for the binary black hole mass ratio distribution $p(q) \propto q^{\beta_q}$. Dotted lines show the results with our first ten detections, and solid lines include GW190412. Results are shown for two different waveform models. Figure 11 of the GW190412 Discovery Paper.

Since most of the other binaries are more equal mass, we can see the effects of folding this information into our analysis of GW190412. Instead of making weak assumptions about what we expect the masses to be (we normally assume uniform prior probability on the masses as redshifted and measured in the detector, as that’s easy to work with), we can use our knowledge of the population. In this case, our prior expectation that we should have something near equal mass does shift the result a little, the 90% upper limit for the mass ratio shifts from $q < 0.37$ to $q < 0.43$, but we see that the mass ratio is still clearly unequal.

Have we detected a new flavour of binary black hole? Should we be lumping in GW190412 with the others, or should it be it’s own category? Going back to our results from the second observing run, we find that we’d expect that in a set of eleven observations that at least one would have a mass ratio as extreme as GW190412 $1.7^{+10.3}_{-1.3}\%$ of the time. Therefore, GW190412 is exceptional, but not completely inconsistent with our previous observations. If we repeat the calculation using the population inferred folding in GW190412, we (unsurprisingly) find it is much less unusual, with such systems being found in a set of eleven observations $25^{+47}_{-17}\%$ of the time. In conclusion, GW190412 is not vanilla, but is possibly raspberry ripple or Neapolitan: there’s still a trace of vanilla in there to connect it to the more usual binaries

Now we’ve compared GW190412 to our previous observations, where does its source fit in with predictions? The two main options for making a merging binary black hole are via isolated evolution, where two stars live their lives together, and dynamical formation, where you have lots of black holes in a dense environment like a globular cluster and two get close enough together to capture each other. Both of these favour more equal mass binaries, with unequal mass binaries like GW190412’s source being rare (but not impossible). Since we’ve only seen one system with such a mass ratio in amongst our detections so far, either channel could possibly explain things. My money is on a mixture.

In case you were curious, calculations from Chase Kimball indicate that GW190412 is not a hierarchical merger with the primary black hole being formed from the merger of two smaller black holes.

Odds of binary black holes being a hierarchical merger verses being original generation binary. 1G indicates first generation black holes formed from the collapse of stars, 2G indicates a black hole formed from the merger of two 1G black holes. These are preliminary results using the GWTC-1 results plus GW!90412. Fig. 15 of Kimball et al. (2020).

As we build up a larger collection of detections, we’ll be able to use our constraints on the population to better understand the relative contributions from the different formation mechanisms, and hence the physics of black hole manufacturing.

### Einstein is not wrong yet

Finally, since GW190412 is beautifully loud and has a respectably long inspiral, we were able to perform our usual tests of general relativity and confirm that all is as predicted.

We performed the inspiral/merger–ringdown consistency test, where we check that parameters inferred from the early, low frequency part of the signal match those from the later, high frequency part. They do.

We also performed the parameterized test, where we we allow different pieces of the signal template vary. We found that all the deviations were consistent with zero, as expected. The results are amongst the tightest we have from a single event, being comparable to results from GW151226 and GW170608. These are the lowest mass binary black holes we’ve observed so far, and so have the longest chirps.

We’ll keep checking for any evidence that Einstein’s theory of gravity is wrong. If Columbo has taught us anything, it is that the guest star is usually guilty. If it’s taught us something else, it’s the importance of a good raincoat. After that, however, it’s taught us the importance of perseverance, and always asking one more thing. Maybe we’ll catch Einstein out eventually.

### Just a taste of what’s to come

GW190412 was observed on the 12th day of O3. There were many detections to follow. Using this data set, we’ll be able to understand the properties of black holes and gravitational waves better than ever before. There are exciting results still being finalised.

Perhaps there will be a salted caramel binary black hole, or even a rocky road flavoured one? We might need to wait for our next observing run in 2021 for sprinkles though.

Title: GW190412: Observation of a binary-black-hole coalescence with asymmetric masses
Journal: Physical Review D; 102(4):043015(29)
arXiv: 2004.08342 [astro-ph.HE]
Science summary: GW190412: The first observation of an unequal-mass black hole merger
Data release: Gravitational Wave Open Science Center
Rating: 🍨🐦🎶🐦🥴

### Bonus notes

#### Sleep

I like sleep. I’d strongly recommend it.

#### Notation

Possibly the greatest dispute in gravitational wave astronomy is the definition of $q$. We pretty much all agree that the larger mass in a binary is $m_1$ and the lesser mass $m_2$. However, there two camps on the mass ratio: those enlightened individuals who define $q = m_2/m_1$, meaning that the mass ratio spans the entirely sensible range of $0 \leq q \leq 1$, and those heretics who define $q = m_1/m_2$, meaning that it cover the ridiculous range of $1 \leq q \leq \infty$. Within LIGO and Virgo, we have now settled on the correct convention. Many lives may have been lost, but I’m sure you’ll agree that it is a sacrifice worth making in the cause of consistent notation.

The second greatest dispute may be what to call the spin magnitudes. In LIGO and Virgo we’ve often used both $\chi$ (the Greek letter chi) and $a$. After a tense negotiation, conflict was happily avoided, and we have settled on $\chi$, with only the minimum amount of bloodshed. If you’re reading some of our older stuff, please bear in mind that we’ve not been consistent about the meaning of these symbols.

#### Effective spins

Sadly, my suggestions to call $\chi_\mathrm{p}$ and $\chi_\mathrm{eff}$ Chip and Dale have not caught on.

#### Hey! Listen!

Here are two model waveforms (made by Florian Wicke and Frank Ohme) consistent with the properties of GW190412, but shifted in frequency by a factor of 25 to make them easier to hear:

Can you tell the difference? I prefer the more proper one with harmonics.

#### Exactly as predicted

The presence of higher order multipole moments, as predicted, could be seen as another win for Einstein’s theory of general relativity. However, we expect the same pattern of emission in any theory, as it’s really set by the geometry of the source. If the frequency were not an integer multiple of the orbital frequency, the gravitational waves would get out of phase with their source, which would not make any sense.

The really cool thing, in my opinion, is that we now how detectors sensitive enough to pick out these subtle details.

# The O2 Catalogue—It goes up to 11

The full results of our second advanced-detector observing run (O2) have now been released—we’re pleased to announce four new gravitational wave signals: GW170729, GW170809, GW170818 and GW170823 [bonus note]. These latest observations are all of binary black hole systems. Together, they bring our total to 10 observations of binary black holes, and 1 of a binary neutron star. With more frequent detections on the horizon with our third observing run due to start early 2019, the era of gravitational wave astronomy is truly here.

The population of black holes and neutron stars observed with gravitational waves and with electromagnetic astronomy. You can play with an interactive version of this plot online.

The new detections are largely consistent with our previous findings. GW170809, GW170818 and GW170823 are all similar to our first detection GW150914. Their black holes have masses around 20 to 40 times the mass of our Sun. I would lump GW170104 and GW170814 into this class too. Although there were models that predicted black holes of these masses, we weren’t sure they existed until our gravitational wave observations. The family of black holes continues out of this range. GW151012, GW151226 and GW170608 fall on the lower mass side. These overlap with the population of black holes previously observed in X-ray binaries. Lower mass systems can’t be detected as far away, so we find fewer of these. On the higher end we have GW170729 [bonus note]. Its source is made up of black holes with masses $50.2^{+16.2}_{-10.2} M_\odot$ and $34.0^{+9.1}_{-10.1} M_\odot$ (where $M_\odot$ is the mass of our Sun). The larger black hole is a contender for the most massive black hole we’ve found in a binary (the other probable contender is GW170823’s source, which has a $39.5^{+11.2}_{-6.7} M_\odot$ black hole). We have a big happy family of black holes!

Of the new detections, GW170729, GW170809 and GW170818 were both observed by the Virgo detector as well as the two LIGO detectors. Virgo joined O2 for an exciting August [bonus note], and we decided that the data at the time of GW170729 were good enough to use too. Unfortunately, Virgo wasn’t observing at the time of GW170823. GW170729 and GW170809 are very quiet in Virgo, you can’t confidently say there is a signal there [bonus note]. However, GW170818 is a clear detection like GW170814. Well done Virgo!

Using the collection of results, we can start understand the physics of these binary systems. We will be summarising our findings in a series of papers. A huge amount of work went into these.

### The papers

#### The O2 Catalogue Paper

Title: GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs
arXiv:
1811.12907 [astro-ph.HE]
Data: Catalogue; Parameter estimation results
Journal: Physical Review X; 9(3):031040(49); 2019
LIGO science summary: GWTC-1: A new catalog of gravitational-wave detections

The paper summarises all our observations of binaries to date. It covers our first and second observing runs (O1 and O2). This is the paper to start with if you want any information. It contains estimates of parameters for all our sources, including updates for previous events. It also contains merger rate estimates for binary neutron stars and binary black holes, and an upper limit for neutron star–black hole binaries. We’re still missing a neutron star–black hole detection to complete the set.

More details: The O2 Catalogue Paper

#### The O2 Populations Paper

Title: Binary black hole population properties inferred from the first and second observing runs of Advanced LIGO and Advanced Virgo
arXiv:
1811.12940 [astro-ph.HE]
Journal: Astrophysical Journal Letters; 882(2):L24(30); 2019
Data: Population inference results
LIGO science summary: Binary black hole properties inferred from O1 and O2

Using our set of ten binary black holes, we can start to make some statistical statements about the population: the distribution of masses, the distribution of spins, the distribution of mergers over cosmic time. With only ten observations, we still have a lot of uncertainty, and can’t make too many definite statements. However, if you were wondering why we don’t see any more black holes more massive than GW170729, even though we can see these out to significant distances, so are we. We infer that almost all stellar-mass black holes have masses less than $45 M_\odot$.

More details: The O2 Populations Paper

### The O2 Catalogue Paper

Synopsis: O2 Catalogue Paper
Read this if: You want the most up-to-date gravitational results
Favourite part: It’s out! We can tell everyone about our FOUR new detections

This is a BIG paper. It covers our first two observing runs and our main searches for coalescing stellar mass binaries. There will be separate papers going into more detail on searches for other gravitational wave signals.

#### The instruments

Gravitational wave detectors are complicated machines. You don’t just take them out of the box and press go. We’ll be slowly improving the sensitivity of our detectors as we commission them over the next few years. O2 marks the best sensitivity achieved to date. The paper gives a brief overview of the detector configurations in O2 for both LIGO detectors, which did differ, and Virgo.

During O2, we realised that one source of noise was beam jitter, disturbances in the shape of the laser beam. This was particularly notable in Hanford, where there was a spot on the one of the optics. Fortunately, we are able to measure the effects of this, and hence subtract out this noise. This has now been done for the whole of O2. It makes a big difference! Derek Davis and TJ Massinger won the first LIGO Laboratory Award for Excellence in Detector Characterization and Calibration™ for implementing this noise subtraction scheme (the award citation almost spilled the beans on our new detections). I’m happy that GW170104 now has an increased signal-to-noise ratio, which means smaller uncertainties on its parameters.

#### The searches

We use three search algorithms in this paper. We have two matched-filter searches (GstLAL and PyCBC). These compare a bank of templates to the data to look for matches. We also use coherent WaveBurst (cWB), which is a search for generic short signals, but here has been tuned to find the characteristic chirp of a binary. Since cWB is more flexible in the signals it can find, it’s slightly less sensitive than the matched-filter searches, but it gives us confidence that we’re not missing things.

The two matched-filter searches both identify all 11 signals with the exception of GW170818, which is only found by GstLAL. This is because PyCBC only flags signals above a threshold in each detector. We’re confident it’s real though, as it is seen in all three detectors, albeit below PyCBC’s threshold in Hanford and Virgo. (PyCBC only looked at signals found in coincident Livingston and Hanford in O2, I suspect they would have found it if they were looking at all three detectors, as that would have let them lower their threshold).

The search pipelines try to distinguish between signal-like features in the data and noise fluctuations. Having multiple detectors is a big help here, although we still need to be careful in checking for correlated noise sources. The background of noise falls off quickly, so there’s a rapid transition between almost-certainly noise to almost-certainly signal. Most of the signals are off the charts in terms of significance, with GW170818, GW151012 and GW170729 being the least significant. GW170729 is found with best significance by cWB, that gives reports a false alarm rate of $1/(50~\mathrm{yr})$.

Cumulative histogram of results from GstLAL (top left), PyCBC (top right) and cWB (bottom). The expected background is shown as the dashed line and the shaded regions give Poisson uncertainties. The search results are shown as the solid red line and named gravitational-wave detections are shown as blue dots. More significant results are further to the right of the plot. Fig. 2 and Fig. 3 of the O2 Catalogue Paper.

The false alarm rate indicates how often you would expect to find something at least as signal like if you were to analyse a stretch of data with the same statistical properties as the data considered, assuming that they is only noise in the data. The false alarm rate does not fold in the probability that there are real gravitational waves occurring at some average rate. Therefore, we need to do an extra layer of inference to work out the probability that something flagged by a search pipeline is a real signal versus is noise.

The results of this calculation is given in Table IV. GW170729 has a 94% probability of being real using the cWB results, 98% using the GstLAL results, but only 52% according to PyCBC. Therefore, if you’re feeling bold, you might, say, only wager the entire economy of the UK on it being real.

We also list the most marginal triggers. These all have probabilities way below being 50% of being real: if you were to add them all up you wouldn’t get a total of 1 real event. (In my professional opinion, they are garbage). However, if you want to check for what we might have missed, these may be a place to start. Some of these can be explained away as instrumental noise, say scattered light. Others show no obvious signs of disturbance, so are probably just some noise fluctuation.

#### The source properties

We give updated parameter estimates for all 11 sources. These use updated estimates of calibration uncertainty (which doesn’t make too much difference), improved estimate of the noise spectrum (which makes some difference to the less well measured parameters like the mass ratio), the cleaned data (which helps for GW170104), and our most currently complete waveform models [bonus note].

This plot shows the masses of the two binary components (you can just make out GW170817 down in the corner). We use the convention that the more massive of the two is $m_1$ and the lighter is $m_2$. We are now really filling in the mass plot! Implications for the population of black holes are discussed in the Populations Paper.

Estimated masses for the two binary objects for each of the events in O1 and O2. From lowest chirp mass (left; red) to highest (right; purple): GW170817 (solid), GW170608 (dashed), GW151226 (solid), GW151012 (dashed), GW170104 (solid), GW170814 (dashed), GW170809 (dashed), GW170818 (dashed), GW150914 (solid), GW170823 (dashed), GW170729 (solid). The contours mark the 90% credible regions. The grey area is excluded from our convention on masses. Part of Fig. 4 of the O2 Catalogue Paper. The mass ratio is $q = m_2/m_1$.

As well as mass, black holes have a spin. For the final black hole formed in the merger, these spins are always around 0.7, with a little more or less depending upon which way the spins of the two initial black holes were pointing. As well as being probably the most most massive, GW170729’s could have the highest final spin! It is a record breaker. It radiated a colossal $4.8^{+1.7}_{-1.7} M_\odot$ worth of energy in gravitational waves [bonus note].

Estimated final masses and spins for each of the binary black hole events in O1 and O2. From lowest chirp mass (left; red–orange) to highest (right; purple): GW170608 (dashed), GW151226 (solid), GW151012 (dashed), GW170104 (solid), GW170814 (dashed), GW170809 (dashed), GW170818 (dashed), GW150914 (solid), GW170823 (dashed), GW170729 (solid). The contours mark the 90% credible regions. Part of Fig. 4 of the O2 Catalogue Paper.

There is considerable uncertainty on the spins as there are hard to measure. The best combination to pin down is the effective inspiral spin parameter $\chi_\mathrm{eff}$. This is a mass weighted combination of the spins which has the most impact on the signal we observe. It could be zero if the spins are misaligned with each other, point in the orbital plane, or are zero. If it is non-zero, then it means that at least one black hole definitely has some spin. GW151226 and GW170729 have $\chi_\mathrm{eff} > 0$ with more than 99% probability. The rest are consistent with zero. The spin distribution for GW170104 has tightened up for GW170104 as its signal-to-noise ratio has increased, and there’s less support for negative $\chi_\mathrm{eff}$, but there’s been no move towards larger positive $\chi_\mathrm{eff}$.

Estimated effective inspiral spin parameters for each of the events in O1 and O2. From lowest chirp mass (left; red) to highest (right; purple): GW170817, GW170608, GW151226, GW151012, GW170104, GW170814, GW170809, GW170818, GW150914, GW170823, GW170729. Part of Fig. 5 of the O2 Catalogue Paper.

For our analysis, we use two different waveform models to check for potential sources of systematic error. They agree pretty well. The spins are where they show most difference (which makes sense, as this is where they differ in terms of formulation). For GW151226, the effective precession waveform IMRPhenomPv2 gives $0.20^{+0.18}_{-0.08}$ and the full precession model gives $0.15^{+0.25}_{-0.11}$ and extends to negative $\chi_\mathrm{eff}$. I panicked a little bit when I first saw this, as GW151226 having a non-zero spin was one of our headline results when first announced. Fortunately, when I worked out the numbers, all our conclusions were safe. The probability of $\chi_\mathrm{eff} < 0$ is less than 1%. In fact, we can now say that at least one spin is greater than $0.28$ at 99% probability compared with $0.2$ previously, because the full precession model likes spins in the orbital plane a bit more. Who says data analysis can’t be thrilling?

Our measurement of $\chi_\mathrm{eff}$ tells us about the part of the spins aligned with the orbital angular momentum, but not in the orbital plane. In general, the in-plane components of the spin are only weakly constrained. We basically only get back the information we put in. The leading order effects of in-plane spins is summarised by the effective precession spin parameter $\chi_\mathrm{p}$. The plot below shows the inferred distributions for $\chi_\mathrm{p}$. The left half for each event shows our results, the right shows our prior after imposed the constraints on spin we get from $\chi_\mathrm{eff}$. We get the most information for GW151226 and GW170814, but even then it’s not much, and we generally cover the entire allowed range of values.

Estimated effective inspiral spin parameters for each of the events in O1 and O2. From lowest chirp mass (left; red) to highest (right; purple): GW170817, GW170608, GW151226, GW151012, GW170104, GW170814, GW170809, GW170818, GW150914, GW170823, GW170729. The left (coloured) part of the plot shows the posterior distribution; the right (white) shows the prior conditioned by the effective inspiral spin parameter constraints. Part of Fig. 5 of the O2 Catalogue Paper.

One final measurement which we can make (albeit with considerable uncertainty) is the distance to the source. The distance influences how loud the signal is (the further away, the quieter it is). This also depends upon the inclination of the source (a binary edge-on is quieter than a binary face-on/off). Therefore, the distance is correlated with the inclination and we end up with some butterfly-like plots. GW170729 is again a record setter. It comes from a luminosity distance of $2.84^{+1.40}_{-1.36}~\mathrm{Gpc}$ away. That means it has travelled across the Universe for $3.2$$6.2$ billion years—it potentially started its journey before the Earth formed!

Estimated luminosity distances and orbital inclinations for each of the events in O1 and O2. From lowest chirp mass (left; red) to highest (right; purple): GW170817 (solid), GW170608 (dashed), GW151226 (solid), GW151012 (dashed), GW170104 (solid), GW170814 (dashed), GW170809 (dashed), GW170818 (dashed), GW150914 (solid), GW170823 (dashed), GW170729 (solid). The contours mark the 90% credible regions.An inclination of zero means that we’re looking face-on along the direction of the total angular momentum, and inclination of $\pi/2$ means we’re looking edge-on perpendicular to the angular momentum. Part of Fig. 7 of the O2 Catalogue Paper.

#### Waveform reconstructions

To check our results, we reconstruct the waveforms from the data to see that they match our expectations for binary black hole waveforms (and there’s not anything extra there). To do this, we use unmodelled analyses which assume that there is a coherent signal in the detectors: we use both cWB and BayesWave. The results agree pretty well. The reconstructions beautifully match our templates when the signal is loud, but, as you might expect, can resolve the quieter details. You’ll also notice the reconstructions sometimes pick up a bit of background noise away from the signal. This gives you and idea of potential fluctuations.

Time–frequency maps and reconstructed signal waveforms for the binary black holes. For each event we show the results from the detector where the signal was loudest. The left panel for each shows the time–frequency spectrogram with the upward-sweeping chip. The right show waveforms: blue the modelled waveforms used to infer parameters (LALInf; top panel); the red wavelet reconstructions (BayesWave; top panel); the black is the maximum-likelihood cWB reconstruction (bottom panel), and the green (bottom panel) shows reconstructions for simulated similar signals. I think the agreement is pretty good! All the data have been whitened as this is how we perform the statistical analysis of our data. Fig. 10 of the O2 Catalogue Paper.

I still think GW170814 looks like a slug. Some people think they look like crocodiles.

We’ll be doing more tests of the consistency of our signals with general relativity in a future paper.

#### Merger rates

Given all our observations now, we can set better limits on the merger rates. Going from the number of detections seen to the number merger out in the Universe depends upon what you assume about the mass distribution of the sources. Therefore, we make a few different assumptions.

For binary black holes, we use (i) a power-law model for the more massive black hole similar to the initial mass function of stars, with a uniform distribution on the mass ratio, and (ii) use uniform-in-logarithmic distribution for both masses. These were designed to bracket the two extremes of potential distributions. With our observations, we’re starting to see that the true distribution is more like the power-law, so I expect we’ll be abandoning these soon. Taking the range of possible values from our calculations, the rate is in the range of $9.7$$101~\mathrm{Gpc^{-3}\,yr^{-1}}$ for black holes between $5 M_\odot$ and $50 M_\odot$ [bonus note].

For binary neutron stars, which are perhaps more interesting astronomers, we use a uniform distribution of masses between $0.8 M_\odot$ and $2.3 M_\odot$, and a Gaussian distribution to match electromagnetic observations. We find that these bracket the range $97$$4440~\mathrm{Gpc^{-3}\,yr^{-1}}$. This larger than are previous range, as we hadn’t considered the Gaussian distribution previously.

90% upper limits for neutron star–black hole binaries. Three black hole masses were tried and two spin distributions. Results are shown for the two matched-filter search algorithms. Fig. 14 of the O2 Catalogue Paper.

Finally, what about neutron star–black holes? Since we don’t have any detections, we can only place an upper limit. This is a maximum of $610~\mathrm{Gpc^{-3}\,yr^{-1}}$. This is about a factor of 2 better than our O1 results, and is starting to get interesting!

We are sure to discover lots more in O3… [bonus note].

### The O2 Populations Paper

Synopsis: O2 Populations Paper
Read this if: You want the best family portrait of binary black holes
Favourite part: A maximum black hole mass?

Each detection is exciting. However, we can squeeze even more science out of our observations by looking at the entire population. Using all 10 of our binary black hole observations, we start to trace out the population of binary black holes. Since we still only have 10, we can’t yet be too definite in our conclusions. Our results give us some things to ponder, while we are waiting for the results of O3. I think now is a good time to start making some predictions.

We look at the distribution of black hole masses, black hole spins, and the redshift (cosmological time) of the mergers. The black hole masses tell us something about how you go from a massive star to a black hole. The spins tell us something about how the binaries form. The redshift tells us something about how these processes change as the Universe evolves. Ideally, we would look at these all together allowing for mixtures of binary black holes formed through different means. Given that we only have a few observations, we stick to a few simple models.

To work out the properties of the population, we perform a hierarchical analysis of our 10 binary black holes. We infer the properties of the individual systems, assuming that they come from a given population, and then see how well that population fits our data compared with a different distribution.

In doing this inference, we account for selection effects. Our detectors are not equally sensitive to all sources. For example, nearby sources produce louder signals and we can’t detect signals that are too far away, so if you didn’t account for this you’d conclude that binary black holes only merged in the nearby Universe. Perhaps less obvious is that we are not equally sensitive to all source masses. More massive binaries produce louder signals, so we can detect these further way than lighter binaries (up to the point where these binaries are so high mass that the signals are too low frequency for us to easily spot). This is why we detect more binary black holes than binary neutron stars, even though there are more binary neutron stars out here in the Universe.

#### Masses

When looking at masses, we try three models of increasing complexity:

• Model A is a simple power law for the mass of the more massive black hole $m_1$. There’s no real reason to expect the masses to follow a power law, but the masses of stars when they form do, and astronomers generally like power laws as they’re friendly, so its a sensible thing to try. We fit for the power-law index. The power law goes from a lower limit of $5 M_\odot$ to an upper limit which we also fit for. The mass of the lighter black hole $m_2$ is assumed to be uniformly distributed between $5 M_\odot$ and the mass of the other black hole.
• Model B is the same power law, but we also allow the lower mass limit to vary from $5 M_\odot$. We don’t have much sensitivity to low masses, so this lower bound is restricted to be above $5 M_\odot$. I’d be interested in exploring lower masses in the future. Additionally, we allow the mass ratio $q = m_2/m_1$ of the black holes to vary, trying $q^{\beta_q}$ instead of Model A’s $q^0$.
• Model C has the same power law, but now with some smoothing at the low-mass end, rather than a sharp turn-on. Additionally, it includes a Gaussian component towards higher masses. This was inspired by the possibility of pulsational pair-instability supernova causing a build up of black holes at certain masses: stars which undergo this lose extra mass, so you’d end up with lower mass black holes than if the stars hadn’t undergone the pulsations. The Gaussian could fit other effects too, for example if there was a secondary formation channel, or just reflect that the pure power law is a bad fit.

In allowing the mass distributions to vary, we find overall rates which match pretty well those we obtain with our main power-law rates calculation included in the O2 Catalogue Paper, higher than with the main uniform-in-log distribution.

The fitted mass distributions are shown in the plot below. The error bars are pretty broad, but I think the models agree on some broad features: there are more light black holes than heavy black holes; the minimum black hole mass is below about $9 M_\odot$, but we can’t place a lower bound on it; the maximum black hole mass is above about $35 M_\odot$ and below about $50 M_\odot$, and we prefer black holes to have more similar masses than different ones. The upper bound on the black hole minimum mass, and the lower bound on the black hole upper mass are set by the smallest and biggest black holes we’ve detected, respectively.

Binary black hole merger rate as a function of the primary mass ($m_1$; top) and mass ratio ($q$; bottom). The solid lines and bands show the medians and 90% intervals. The dashed line shows the posterior predictive distribution: our expectation for future observations averaging over our uncertainties. Fig. 2 of the O2 Populations Paper.

That there does seem to be a drop off at higher masses is interesting. There could be something which stops stars forming black holes in this range. It has been proposed that there is a mass gap due to pair instability supernovae. These explosions completely disrupt their progenitor stars, leaving nothing behind. (I’m not sure if they are accompanied by a flash of green light). You’d expect this to kick for black holes of about $50$$60 M_\odot$. We infer that 99% of merging black holes have masses below $44.0 M_\odot$ with Model A, $41.8 M_\odot$ with Model B, and $41.8 M_\odot$ with Model C. Therefore, our results are not inconsistent with a mass gap. However, we don’t really have enough evidence to be sure.

We can compare how well each of our three models fits the data by looking at their Bayes factors. These naturally incorporate the complexity of the models: models with more parameters (which can be more easily tweaked to match the data) are penalised so that you don’t need to worry about overfitting. We have a preference for Model C. It’s not strong, but I think good evidence that we can’t use a simple power law.

#### Spins

To model the spins:

• For the magnitude, we assume a beta distribution. There’s no reason for this, but these are convenient distributions for things between 0 and 1, which are the limits on black hole spin (0 is nonspinning, 1 is as fast as you can spin). We assume that both spins are drawn from the same distribution.
• For the spin orientations, we use a mix of an isotropic distribution and a Gaussian centred on being aligned with the orbital angular momentum. You’d expect an isotropic distribution if binaries were assembled dynamically, and perhaps something with spins generally aligned with each other if the binary evolved in isolation.

We don’t get any useful information on the mixture fraction. Looking at the spin magnitudes, we have a preference towards smaller spins, but still have support for large spins. The more misaligned spins are, the larger the spin magnitudes can be: for the isotropic distribution, we have support all the way up to maximal values.

Inferred spin magnitude distributions. The left shows results for the parametric distribution, assuming a mixture of almost aligned and isotropic spin, with the median (solid), 50% and 90% intervals shaded, and the posterior predictive distribution as the dashed line. Results are included both for beta distributions which can be singular at 0 and 1, and with these excluded. Model V is a very low spin model shown for comparison. The right shows a binned reconstruction of the distribution for aligned and isotropic distributions, showing the median and 90% intervals. Fig. 8 of the O2 Populations Paper.

Since spins are harder to measure than masses, it is not surprising that we can’t make strong statements yet. If we were to find something with definitely negative $\chi_\mathrm{eff}$, we would be able to deduce that spins can be seriously misaligned.

#### Redshift evolution

As a simple model of evolution over cosmological time, we allow the merger rate to evolve as $(1+z)^\lambda$. That’s right, another power law! Since we’re only sensitive to relatively small redshifts for the masses we detect ($z < 1$), this gives a good approximation to a range of different evolution schemes.

Evolution of the binary black hole merger rate (blue), showing median, 50% and 90% intervals. For comparison, a non-evolving rate calculated using Model B is shown too. Fig. 6 of the O2 Populations Paper.

We find that we prefer evolutions that increase with redshift. There’s an 88% probability that $\lambda > 0$, but we’re still consistent with no evolution. We might expect rate to increase as star formation was higher bach towards $z =2$. If we can measure the time delay between forming stars and black holes merging, we could figure out what happens to these systems in the meantime.

The local merger rate is broadly consistent with what we infer with our non-evolving distributions, but is a little on the lower side.

### Bonus notes

#### Naming

Gravitational waves are named as GW-year-month-day, so our first observation from 14 September 2015 is GW150914. We realise that this convention suffers from a Y2K-style bug, but by the time we hit 2100, we’ll have so many detections we’ll need a new scheme anyway.

Previously, we had a second designation for less significant potential detections. They were LIGO–Virgo Triggers (LVT), the one example being LVT151012. No-one was really happy with this designation, but it stems from us being cautious with our first announcement, and not wishing to appear over bold with claiming we’d seen two gravitational waves when the second wasn’t that certain. Now we’re a bit more confident, and we’ve decided to simplify naming by labelling everything a GW on the understanding that this now includes more uncertain events. Under the old scheme, GW170729 would have been LVT170729. The idea is that the broader community can decide which events they want to consider as real for their own studies. The current condition for being called a GW is that the probability of it being a real astrophysical signal is at least 50%. Our 11 GWs are safely above that limit.

The naming change has hidden the fact that now when we used our improved search pipelines, the significance of GW151012 has increased. It would now be a GW even under the old scheme. Congratulations LVT151012, I always believed in you!

Is it of extraterrestrial origin, or is it just a blurry figure? GW151012: the truth is out there!.

#### Burning bright

We are lacking nicknames for our new events. They came in so fast that we kind of lost track. Ilya Mandel has suggested that GW170729 should be the Tiger, as it happened on the International Tiger Day. Since tigers are the biggest of the big cats, this seems apt.

Carl-Johan Haster argues that LIGO+tiger = Liger. Since ligers are even bigger than tigers, this seems like an excellent case to me! I’d vote for calling the bigger of the two progenitor black holes GW170729-tiger, the smaller GW170729-lion, and the final black hole GW17-729-liger.

Suggestions for other nicknames are welcome, leave your ideas in the comments.

#### August 2017—Something fishy or just Poisson statistics?

The final few weeks of O2 were exhausting. I was trying to write job applications at the time, and each time I sat down to work on my research proposal, my phone went off with another alert. You may be wondering about was special about August. Some have hypothesised that it is because Aaron Zimmerman, my partner for the analysis of GW170104, was on the Parameter Estimation rota to analyse the last few weeks of O2. The legend goes that Aaron is especially lucky as he was bitten by a radioactive Leprechaun. I can neither confirm nor deny this. However, I make a point of playing any lottery numbers suggested by him.

A slightly more mundane explanation is that August was when the detectors were running nice and stably. They were observing for a large fraction of the time. LIGO Livingston reached its best sensitivity at this time, although it was less happy for Hanford. We often quantify the sensitivity of our detectors using their binary neutron star range, the average distance they could see a binary neutron star system with a signal-to-noise ratio of 8. If this increases by a factor of 2, you can see twice as far, which means you survey 8 times the volume. This cubed factor means even small improvements can have a big impact. The LIGO Livingston range peak a little over $100~\mathrm{Mpc}$. We’re targeting at least $120~\mathrm{Mpc}$ for O3, so August 2017 gives an indication of what you can expect.

Binary neutron star range for the instruments across O2. The break around week 3 was for the holidays (We did work Christmas 2015). The break at week 23 was to tune-up the instruments, and clean the mirrors. At week 31 there was an earthquake in Montana, and the Hanford sensitivity didn’t recover by the end of the run. Part of Fig. 1 of the O2 Catalogue Paper.

Of course, in the case of GW170817, we just got lucky.

#### Sign errors

GW170809 was the first event we identified with Virgo after it joined observing. The signal in Virgo is very quiet. We actually got better results when we flipped the sign of the Virgo data. We were just starting to get paranoid when GW170814 came along and showed us that everything was set up right at Virgo. When I get some time, I’d like to investigate how often this type of confusion happens for quiet signals.

#### SEOBNRv3

One of the waveforms, which includes the most complete prescription of the precession of the spins of the black holes, we use in our analysis goes by the technical name of SEOBNRv3. It is extremely computationally expensive. Work has been done to improve that, but this hasn’t been implemented in our reviewed codes yet. We managed to complete an analysis for the GW170104 Discovery Paper, which was a huge effort. I said then to not expect it for all future events. We did it for all the black holes, even for the lowest mass sources which have the longest signals. I was responsible for GW151226 runs (as well as GW170104) and I started these back at the start of the summer. Eve Chase put in a heroic effort to get GW170608 results, we pulled out all the stops for that.

#### Thanksgiving

I have recently enjoyed my first Thanksgiving in the US. I was lucky enough to be hosted for dinner by Shane Larson and his family (and cats). I ate so much I thought I might collapse to a black hole. Apparently, a Thanksgiving dinner can be 3000–4500 calories. That sounds like a lot, but the merger of GW170729 would have emitted about $5 \times 10^{40}$ times more energy. In conclusion, I don’t need to go on a diet.

#### Confession

We cheated a little bit in calculating the rates. Roughly speaking, the merger rate is given by

$\displaystyle R = \frac{N}{\langle VT\rangle}$,

where $N$ is the number of detections and $\langle VT\rangle$ is the amount of volume and time we’ve searched. You expect to detect more events if you increase the sensitivity of the detectors (and hence $V$), or observer for longer (and hence increase $T$). In our calculation, we included GW170608 in $N$, even though it was found outside of standard observing time. Really, we should increase $\langle VT\rangle$ to factor in the extra time outside of standard observing time when we could have made a detection. This is messy to calculate though, as there’s not really a good way to check this. However, it’s only a small fraction of the time (so the extra $T$ should be small), and for much of the sensitivity of the detectors will be poor (so $V$ will be small too). Therefore, we estimated any bias from neglecting this is smaller than our uncertainty from the calibration of the detectors, and not worth worrying about.

#### New sources

We saw our first binary black hole shortly after turning on the Advanced LIGO detectors. We saw our first binary neutron star shortly after turning on the Advanced Virgo detector. My money is therefore on our first neutron star–black hole binary shortly after we turn on the KAGRA detector. Because science…

# GW170817—The papers

After three months (and one binary black hole detection announcement), I finally have time to write about the suite of LIGO–Virgo papers put together to accompany GW170817.

### The papers

There are currently 9 papers in the GW170817 family. Further papers, for example looking at parameter estimation in detail, are in progress. Papers are listed below in order of arXiv posting. My favourite is the GW170817 Discovery Paper. Many of the highlights, especially from the Discovery and Multimessenger Astronomy Papers, are described in my GW170817 announcement post.

Keeping up with all the accompanying observational results is a task not even Sisyphus would envy. I’m sure that the details of these will be debated for a long time to come. I’ve included references to a few below (mostly as [citation notes]), but these are not guaranteed to be complete (I’ll continue to expand these in the future).

#### 0. The GW170817 Discovery Paper

Title: GW170817: Observation of gravitational waves from a binary neutron star inspiral
arXiv:
1710.05832 [gr-qc]
Journal:
Physical Review Letters; 119(16):161101(18); 2017
LIGO science summary:
GW170817: Observation of gravitational waves from a binary neutron star inspiral

This is the paper announcing the gravitational-wave detection. It gives an overview of the properties of the signal, initial estimates of the parameters of the source (see the GW170817 Properties Paper for updates) and the binary neutron star merger rate, as well as an overview of results from the other companion papers.

I was disappointed that “the era of gravitational-wave multi-messenger astronomy has opened with a bang” didn’t make the conclusion of the final draft.

More details: The GW170817 Discovery Paper summary

#### −1. The Multimessenger Astronomy Paper

Title: Multi-messenger observations of a binary neutron star merger
arXiv:
1710.05833 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 848(2):L12(59); 2017
LIGO science summary:
The dawn of multi-messenger astrophysics: observations of a binary neutron star merger

I’ve numbered this paper as −1 as it gives an overview of all the observations—gravitational wave, electromagnetic and neutrino—accompanying GW170817. I feel a little sorry for the neutrino observers, as they’re the only ones not to make a detection. Drawing together the gravitational wave and electromagnetic observations, we can confirm that binary neutron star mergers are the progenitors of (at least some) short gamma-ray bursts and kilonovae.

Do not print this paper, the author list stretches across 23 pages.

More details: The Multimessenger Astronomy Paper summary

#### 1. The GW170817 Gamma-ray Burst Paper

Title: Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A
arXiv:
1710.05834 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 848(2):L13(27); 2017
LIGO science summary:
Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A

Here we bring together the LIGO–Virgo observations of GW170817 and the Fermi and INTEGRAL observations of GRB 170817A. From the spatial and temporal coincidence of the gravitational waves and gamma rays, we establish that the two are associated with each other. There is a 1.7 s time delay between the merger time estimated from gravitational waves and the arrival of the gamma-rays. From this, we make some inferences about the structure of the jet which is the source of the gamma rays. We can also use this to constrain deviations from general relativity, which is cool. Finally, we estimate that there be 0.3–1.7 joint gamma ray–gravitational wave detections per year once our gravitational-wave detectors reach design sensitivity!

More details: The GW170817 Gamma-ray Burst Paper summary

#### 2. The GW170817 Hubble Constant Paper

Title: A gravitational-wave standard siren measurement of the Hubble constant [bonus note]
arXiv:
1710.05835 [astro-ph.CO]
Journal:
Nature; 551(7678):85–88; 2017 [bonus note]
LIGO science summary:
Measuring the expansion of the Universe with gravitational waves

The Hubble constant quantifies the current rate of expansion of the Universe. If you know how far away an object is, and how fast it is moving away (due to the expansion of the Universe, not because it’s on a bus or something, that is important), you can estimate the Hubble constant. Gravitational waves give us an estimate of the distance to the source of GW170817. The observations of the optical transient AT 2017gfo allow us to identify the galaxy NGC 4993 as the host of GW170817’s source. We know the redshift of the galaxy (which indicates how fast its moving). Therefore, putting the two together we can infer the Hubble constant in a completely new way.

More details: The GW170817 Hubble Constant Paper summary

#### 3. The GW170817 Kilonova Paper

Title: Estimating the contribution of dynamical ejecta in the kilonova associated with GW170817
arXiv:
1710.05836 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 850(2):L39(13); 2017
LIGO science summary:
Predicting the aftermath of the neutron star collision that produced GW170817

During the coalescence of two neutron stars, lots of neutron-rich matter gets ejected. This undergoes rapid radioactive decay, which powers a kilonova, an optical transient. The observed signal depends upon the material ejected. Here, we try to use our gravitational-wave measurements to predict the properties of the ejecta ahead of the flurry of observational papers.

More details: The GW170817 Kilonova Paper summary

#### 4. The GW170817 Stochastic Paper

Title: GW170817: Implications for the stochastic gravitational-wave background from compact binary coalescences
arXiv:
1710.05837 [gr-qc]
Journal: Physical Review Letters; 120(9):091101(12); 2018
LIGO science summary: The background symphony of gravitational waves from neutron star and black hole mergers

We can detect signals if they are loud enough, but there will be many quieter ones that we cannot pick out from the noise. These add together to form an overlapping background of signals, a background rumbling in our detectors. We use the inferred rate of binary neutron star mergers to estimate their background. This is smaller than the background from binary black hole mergers (black holes are more massive, so they’re intrinsically louder), but they all add up. It’ll still be a few years before we could detect a background signal.

More details: The GW170817 Stochastic Paper summary

#### 5. The GW170817 Progenitor Paper

Title: On the progenitor of binary neutron star merger GW170817
arXiv:
1710.05838 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 850(2):L40(18); 2017
LIGO science summary:
Making GW170817: neutron stars, supernovae and trick shots (I’d especially recommend reading this one)

We know that GW170817 came from the coalescence of two neutron stars, but where did these neutron stars come from? Here, we combine the parameters inferred from our gravitational-wave measurements, the observed position of AT 2017gfo in NGC 4993 and models for the host galaxy, to estimate properties like the kick imparted to neutron stars during the supernova explosion and how long it took the binary to merge.

More details: The GW170817 Progenitor Paper summary

#### 6. The GW170817 Neutrino Paper

Title: Search for high-energy neutrinos from binary neutron star merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory
arXiv:
1710.05839 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 850(2):L35(18); 2017

This is the search for neutrinos from the source of GW170817. Lots of neutrinos are emitted during the collision, but not enough to be detectable on Earth. Indeed, we don’t find any neutrinos, but we combine results from three experiments to set upper limits.

More details: The GW170817 Neutrino Paper summary

#### 7. The GW170817 Post-merger Paper

Title: Search for post-merger gravitational waves from the remnant of the binary neutron star merger GW170817
arXiv:
1710.09320 [astro-ph.HE]
Journal:
Astrophysical Journal Letters; 851(1):L16(13); 2017
LIGO science summary:
Searching for the neutron star or black hole resulting from GW170817

After the two neutron stars merged, what was left? A larger neutron star or a black hole? Potentially we could detect gravitational waves from a wibbling neutron star, as it sloshes around following the collision. We don’t. It would have to be a lot closer for this to be plausible. However, this paper outlines how to search for such signals; the GW170817 Properties Paper contains a more detailed look at any potential post-merger signal.

More details: The GW170817 Post-merger Paper summary

#### 8. The GW170817 Properties Paper

Title: Properties of the binary neutron star merger GW170817
arXiv:
1805.11579 [gr-qc]

In the GW170817 Discovery Paper we presented initial estimates for the properties of GW170817’s source. These were the best we could do on the tight deadline for the announcement (it was a pretty good job in my opinion). Now we have had a bit more time we can present a new, improved analysis. This uses recalibrated data and a wider selection of waveform models. We also fold in our knowledge of the source location, thanks to the observation of AT 2017gfo by our astronomer partners, for our best results. if you want to know the details of GW170817’s source, this is the paper for you!

If you’re looking for the most up-to-date results regarding GW170817, check out the O2 Catalogue Paper.

More details: The GW170817 Properties Paper summary

#### 9. The GW170817 Equation-of-state Paper

Title: GW170817: Measurements of neutron star radii and equation of state
arXiv:
1805.11581 [gr-qc]

Neutron stars are made of weird stuff: nuclear density material which we cannot replicate here on Earth. Neutron star matter is often described in terms of an equation of state, a relationship that explains how the material changes at different pressures or densities. A stiffer equation of state means that the material is harder to squash, and a softer equation of state is easier to squish. This means that for a given mass, a stiffer equation of state will predict a larger, fluffier neutron star, while a softer equation of state will predict a more compact, denser neutron star. In this paper, we assume that GW170817’s source is a binary neutron star system, where both neutron stars have the same equation of state, and see what we can infer about neutron star stuff™.

More details: The GW170817 Equation-of-state Paper summary

### The GW170817 Discovery Paper

Synopsis: GW170817 Discovery Paper
Read this if: You want all the details of our first gravitational-wave observation of a binary neutron star coalescence
Favourite part: Look how well we measure the chirp mass!

GW170817 was a remarkable gravitational-wave discovery. It is the loudest signal observed to date, and the source with the lowest mass components. I’ve written about some of the highlights of the discovery in my previous GW170817 discovery post.

Binary neutron stars are one of the principal targets for LIGO and Virgo. The first observational evidence for the existence of gravitational waves came from observations of binary pulsars—a binary neutron star system where (at least one) one of the components is a pulsar. Therefore (unlike binary black holes), we knew that these sources existed before we turned on our detectors. What was less certain was how often they merge. In our first advanced-detector observing run (O1), we didn’t find any, allowing us to estimate an upper limit on the merger rate of $12600~\mathrm{Gpc^{-1}\,yr^{-1}}$. Now, we know much more about merging binary neutron stars.

GW170817, as a loud and long signal, is a highly significant detection. You can see it in the data by eye. Therefore, it should have been a easy detection. As is often the case with real experiments, it wasn’t quite that simple. Data transfer from Virgo had stopped over night, and there was a glitch (a non-stationary and non-Gaussian noise feature) in the Livingston detector, which meant that this data weren’t automatically analysed. Nevertheless, GstLAL flagged something interesting in the Hanford data, and there was a mad flurry to get the other data in place so that we could analyse the signal in all three detectors. I remember being sceptical in these first few minutes until I saw the plot of Livingston data which blew me away: the chirp was clearly visible despite the glitch!

Time–frequency plots for GW170104 as measured by Hanford, Livingston and Virgo. The Livinston data have had the glitch removed. The signal is clearly visible in the two LIGO detectors as the upward sweeping chirp; it is not visible in Virgo because of its lower sensitivity and the source’s position in the sky. Figure 1 of the GW170817 Discovery Paper.

Using data from both of our LIGO detectors (as discussed for GW170814, our offline algorithms searching for coalescing binaries only use these two detectors during O2), GW170817 is an absolutely gold-plated detection. GstLAL estimates a false alarm rate (the rate at which you’d expect something at least this signal-like to appear in the detectors due to a random noise fluctuation) of less than one in 1,100,000 years, while PyCBC estimates the false alarm rate to be less than one in 80,000 years.

Parameter estimation (inferring the source properties) used data from all three detectors. We present a (remarkably thorough given the available time) initial analysis in this paper (more detailed results are given in the GW170817 Properties Paper, and the most up-to-date results are in O2 Catalogue Paper). This signal is challenging to analyse because of the glitch and because binary neutron stars are made of stuff™, which can leave an imprint on the waveform. We’ll be looking at the effects of these complications in more detail in the future. Our initial results are

• The source is localized to a region of about $28~\mathrm{deg^2}$ at a distance of $40^{+8}_{-14}~\mathrm{Mpc}$ (we typically quote results at the 90% credible level). This is the closest gravitational-wave source yet.
• The chirp mass is measured to be $1.188_{-0.002}^{+0.004} M_\odot$, much lower than for our binary black hole detections.
• The spins are not well constrained, the uncertainty from this means that we don’t get precise measurements of the individual component masses. We quote results with two choices of spin prior: the astrophysically motivated limit of 0.05, and the more agnostic and conservative upper bound of 0.89. I’ll stick to using the low-spin prior results be default.
• Using the low-spin prior, the component masses are $m_1 = 1.36$$1.60 M_\odot$ and $m_2 = 1.17$$1.36 M_\odot$. We have the convention that $m_1 \geq m_2$, which is why the masses look unequal; there’s a lot of support for them being nearly equal. These masses match what you’d expect for neutron stars.

As mentioned above, neutron stars are made of stuff™, and the properties of this leave an imprint on the waveform. If neutron stars are big and fluffy, they will get tidally distorted. Raising tides sucks energy and angular momentum out of the orbit, making the inspiral quicker. If neutron stars are small and dense, tides are smaller and the inspiral looks like that for tow black holes. For this initial analysis, we used waveforms which includes some tidal effects, so we get some preliminary information on the tides. We cannot exclude zero tidal deformation, meaning we cannot rule out from gravitational waves alone that the source contains at least one black hole (although this would be surprising, given the masses). However, we can place a weak upper limit on the combined dimensionless tidal deformability of $\tilde{\Lambda} \leq 900$. This isn’t too informative, in terms of working out what neutron stars are made from, but we’ll come back to this in the GW170817 Properties Paper and the GW170817 Equation-of-state Paper.

Given the source masses, and all the electromagnetic observations, we’re pretty sure this is a binary neutron star system—there’s nothing to suggest otherwise.

Having observed one (and one one) binary neutron star coalescence in O1 and O2, we can now put better constraints on the merger rate. As a first estimate, we assume that component masses are uniformly distributed between $1 M_\odot$ and $2 M_\odot$, and that spins are below 0.4 (in between the limits used for parameter estimation). Given this, we infer that the merger rate is $1540_{-1220}^{+3200}~\mathrm{Gpc^{-3}\,yr^{-1}}$, safely within our previous upper limit [citation note].

There’s a lot more we can learn from GW170817, especially as we don’t just have gravitational waves as a source of information, and this is explained in the companion papers.

### The Multimessenger Paper

Synopsis: Multimessenger Paper
Read this if: Don’t. Use it too look up which other papers to read.
Favourite part: The figures! It was a truly amazing observational effort to follow-up GW170817

The remarkable thing about this paper is that it exists. Bringing together such a diverse (and competitive) group was a huge effort. Alberto Vecchio was one of the editors, and each evening when leaving the office, he was convinced that the paper would have fallen apart by morning. However, it hung together—the story was too compelling. This paper explains how gravitational waves, short gamma-ray bursts, kilonovae all come from a single source [citation note]. This is the greatest collaborative effort in the history of astronomy.

The paper outlines the discoveries and all of the initial set of observations. If you want to understand the observations themselves, this is not the paper to read. However, using it, you can track down the papers that you do want. A huge amount of care went in to trying to describe how discoveries were made: for example, Fermi observed GRB 170817A independently of the gravitational-wave alert, and we found GW170817 without relying on the GRB alert, however, the communication between teams meant that we took everything much seriously and pushed out alerts as quickly as possible. For more on the history of observations, I’d suggest scrolling through the GCN archive.

The paper starts with an overview of the gravitational-wave observations from the inspiral, then the prompt detection of GRB 170817A, before describing how the gravitational-wave localization enabled discovery of the optical transient AT 2017gfo. This source, in nearby galaxy NGC 4993, was then the subject of follow-up across the electromagnetic spectrum. We have huge amount of photometric and spectroscopy of the source, showing general agreement with models for a kilonova. X-ray and radio afterglows were observed 9 days and 16 days after the merger, respectively [citation note]. No neutrinos were found, which isn’t surprising.

### The GW170817 Gamma-ray Burst Paper

Synopsis: GW170817 Gamma-ray Burst Paper
Read this if: You’re interested in the jets from where short gamma-ray bursts originate or in tests of general relativity
Favourite part: How much science come come from a simple time delay measurement

This joint LIGO–Virgo–FermiINTEGRAL paper combines our observations of GW170817 and GRB 170817A. The result is one of the most contentful of the companion papers.

Detection of GW170817 and GRB 170817A. The top three panels show the gamma-ray lightcurves (first: GBM detectors 1, 2, and 5 for 10–50 keV; second: GBM data for 50–300 keV ; third: the SPI-ACS data starting approximately at 100 keV and with a high energy limit of least 80 MeV), the red line indicates the background.The bottom shows the a time–frequency representation of coherently combined gravitational-wave data from LIGO-Hanford and LIGO-Livingston. Figure 2 of the GW170817 Gamma-ray Burst Paper.

The first item on the to-do list for joint gravitational-wave–gamma-ray science, is to establish that we are really looking at the same source.

From the GW170817 Discovery Paper, we know that its source is consistent with being a binary neutron star system. Hence, there is matter around which can launch create the gamma-rays. The Fermi-GBM and INTEGRAL observations of GRB170817A indicate that it falls into the short class, as hypothesised as the result of a binary neutron star coalescence. Therefore, it looks like we could have the right ingredients.

Now, given that it is possible that the gravitational waves and gamma rays have the same source, we can calculate the probability of the two occurring by chance. The probability of temporal coincidence is $5.0 \times 10^{-6}$, adding in spatial coincidence too, and the probability becomes $5.0 \times 10^{-8}$. It’s safe to conclude that the two are associated: merging binary neutron stars are the source of at least some short gamma-ray bursts!

#### Testing gravity

There is a $\sim1.74\pm0.05~\mathrm{s}$ delay time between the inferred merger time and the gamma-ray burst. Given that signal has travelled for about 85 million years (taking the 5% lower limit on the inferred distance), this is a really small difference: gravity and light must travel at almost exactly the same speed. To derive exact limit you need to make some assumptions about when the gamma-rays were created. We’d expect some delay as it takes time for the jet to be created, and then for the gamma-rays to blast their way out of the surrounding material. We conservatively (and arbitrarily) take a window of the delay being 0 to 10 seconds, this gives

$\displaystyle -3 \times 10^{-15} \leq \frac{v_\mathrm{GW} - v_\mathrm{EM}}{v_\mathrm{EM}} \leq 7 \times 10^{-16}$.

That’s pretty small!

General relativity predicts that gravity and light should travel at the same speed, so I wasn’t too surprised by this result. I was surprised, however, that this result seems to have caused a flurry of activity in effectively ruling out several modified theories of gravity. I guess there’s not much point in explaining what these are now, but they are mostly theories which add in extra fields, which allow you to tweak how gravity works so you can explain some of the effects attributed to dark energy or dark matter. I’d recommend Figure 2 of Ezquiaga & Zumalacárregui (2017) for a summary of which theories pass the test and which are in trouble; Kase & Tsujikawa (2018) give a good review.

Table showing viable (left) and non-viable (right) scalar–tensor theories after discovery of GW170817/GRB 170817A. The theories are grouped as Horndeski theories and (the more general) beyond Horndeski theories. General relativity is a tensor theory, so these models add in an extra scalar component. Figure 2 of Ezquiaga & Zumalacárregui (2017).

We don’t discuss the theoretical implications of the relative speeds of gravity and light in this paper, but we do use the time delay to place bounds for particular on potential deviations from general relativity.

1. We look at a particular type of Lorentz invariance violation. This is similar to what we did for GW170104, where we looked at the dispersion of gravitational waves, but here it is for the case of $\alpha = 2$, which we couldn’t test.
2. We look at the Shapiro delay, which is the time difference travelling in a curved spacetime relative to a flat one. That light and gravity are effected the same way is a test of the weak equivalence principle—that everything falls the same way. The effects of the curvature can be quantified with the parameter $\gamma$, which describes the amount of curvature per unit mass. In general relativity $\gamma_\mathrm{GW} = \gamma_\mathrm{EM} = 1$. Considering the gravitational potential of the Milky Way, we find that $-2.6 \times 10^{-7} \leq \gamma_\mathrm{GW} - \gamma_\mathrm{EM} \leq 1.2 \times 10 ^{-6}$ [citation note].

As you’d expect given the small time delay, these bounds are pretty tight! If you’re working on a modified theory of gravity, you have some extra checks to do now.

#### Gamma-ray bursts and jets

From our gravitational-wave and gamma-ray observations, we can also make some deductions about the engine which created the burst. The complication here, is that we’re not exactly sure what generates the gamma rays, and so deductions are model dependent. Section 5 of the paper uses the time delay between the merger and the burst, together with how quickly the burst rises and fades, to place constraints on the size of the emitting region in different models. The papers goes through the derivation in a step-by-step way, so I’ll not summarise that here: if you’re interested, check it out.

Isotropic energies (left) and luminosities (right) for all gamma-ray bursts with measured distances. These isotropic quantities assume equal emission in all directions, which gives an upper bound on the true value if we are observing on-axis. The short and long gamma-ray bursts are separated by the standard $T_{90} = 2~\mathrm{s}$ duration. The green line shows an approximate detection threshold for Fermi-GBM. Figure 4 from the GW170817 Gamma-ray Burst Paper; you may have noticed that the first version of this paper contained two copies of the energy plot by mistake.

GRB 170817A was unusually dim [citation note]. The plot above compares it to other gamma-ray bursts. It is definitely in the tail. Since it appears so dim, we think that we are not looking at a standard gamma-ray burst. The most obvious explanation is that we are not looking directly down the jet: we don’t expect to see many off-axis bursts, since they are dimmer. We expect that a gamma-ray burst would originate from a jet of material launched along the direction of the total angular momentum. From the gravitational waves alone, we can estimate that the misalignment angle between the orbital angular momentum axis and the line of sight is $\leq 55~\mathrm{deg}$ (adding in the identification of the host galaxy, this becomes $\leq 28~\mathrm{deg}$ using the Planck value for the Hubble constant and $36~\mathrm{deg}$ with the SH0ES value), so this is consistent with viewing the burst off-axis (updated numbers are given in the GW170817 Properties Paper). There are multiple models for such gamma-ray emission, as illustrated below. We could have a uniform top-hat jet (the simplest model) which we are viewing from slightly to the side, we could have a structured jet, which is concentrated on-axis but we are seeing from off-axis, or we could have a cocoon of material pushed out of the way by the main jet, which we are viewing emission from. Other electromagnetic observations will tell us more about the inclination and the structure of the jet [citation note].

Cartoon showing three possible viewing geometries and jet profiles which could explain the observed properties of GRB 170817A. Figure 5 of the GW170817 Gamma-ray Burst Paper.

Now that we know gamma-ray bursts can be this dim, if we observe faint bursts (with unknown distances), we have to consider the possibility that they are dim-and-close in addition to the usual bright-and-far-away.

The paper closes by considering how many more joint gravitational-wave–gamma-ray detections of binary neutron star coalescences we should expect in the future. In our next observing run, we could expect 0.1–1.4 joint detections per year, and when LIGO and Virgo get to design sensitivity, this could be 0.3–1.7 detections per year.

### The GW170817 Hubble Constant Paper

Synopsis: GW170817 Hubble Constant Paper
Read this if: You have an interest in cosmology
Favourite part: In the future, we may be able to settle the argument between the cosmic microwave background and supernova measurements

The Universe is expanding. In the nearby Universe, this can be described using the Hubble relation

$v_H = H_0 D$,

where $v_H$ is the expansion velocity, $H_0$ is the Hubble constant and $D$ is the distance to the source. GW170817 is sufficiently nearby for this relationship to hold. We know the distance from the gravitational-wave measurement, and we can estimate the velocity from the redshift of the host galaxy. Therefore, it should be simple to combine the two to find the Hubble constant. Of course, there are a few complications…

This work is built upon the identification of the optical counterpart AT 2017gfo. This allows us to identify the galaxy NGC 4993 as the host of GW170817’s source: we calculate that there’s a $4 \times 10^{-5}$ probability that AT 2017gfo would be as close to NGC 4993 on the sky by chance. Without a counterpart, it would still be possible to infer the Hubble constant statistically by cross-referencing the inferred gravitational-wave source location with the ensemble of compatible galaxies in a catalogue (you assign a probability to the source being associated with each galaxy, instead of saying it’s definitely in this one). The identification of NGC 4993 makes things much simpler.

As a first ingredient, we need the distance from gravitational waves. For this, a slightly different analysis was done than in the GW170817 Discovery Paper. We fix the sky location of the source to match that of AT 2017gfo, and we use (binary black hole) waveforms which don’t include any tidal effects. The sky position needs to be fixed, because for this analysis we are assuming that we definitely know where the source is. The tidal effects were not included (but precessing spins were) because we needed results quickly: the details of spins and tides shouldn’t make much difference to the distance. From this analysis, we find the distance is $41^{+6}_{-13}~\mathrm{Mpc}$ if we follow our usual convention of quoting the median at symmetric 90% credible interval; however, this paper primarily quotes the most probable value and minimal (not-necessarily symmmetric) 68.3% credible interval, following this convention, we write the distance as $44^{+3}_{-7}~\mathrm{Mpc}$.

While NGC 4993 being close by makes the relationship for calculating the Hubble constant simple, it adds a complication for calculating the velocity. The motion of the galaxy is not only due to the expansion of the Universe, but because of how it is moving within the gravitational potentials of nearby groups and clusters. This is referred to as peculiar motion. Adding this in increases our uncertainty on the velocity. Combining results from the literature, our final estimate for the velocity is $v_H= 3017 \pm 166~\mathrm{km\,s^{-1}}$.

We put together the velocity and the distance in a Bayesian analysis. This is a little more complicated than simply dividing the numbers (although that gives you a similar result). You have to be careful about writing things down, otherwise you might implicitly assume a prior that you didn’t intend (my most useful contribution to this paper is probably a whiteboard conversation with Will Farr where we tracked down a difference in prior assumptions approaching the problem two different ways). This is all explained in the Methods, it’s not easy to read, but makes sense when you work through. The result is $H_0 = 70^{+12}_{-8}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ (quoted as maximum a posteriori value and 68% interval, or $74^{+33}_{-12}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ in the usual median-and-90%-interval convention). An updated set of results is given in the GW170817 Properties Paper: $H_0 = 70^{+19}_{-8}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ (68% interval using the low-spin prior). This is nicely (and diplomatically) consistent with existing results.

The distance has considerable uncertainty because there is a degeneracy between the distance and the orbital inclination (the angle of the normal to the orbital plane relative to the line of sight). If you could figure out the inclination from another observation, then you could tighten constraints on the Hubble constant, or if you’re willing to adopt one of the existing values of the Hubble constant, you can pin down the inclination. Data (updated data) to help you try this yourself are available [citation note].

Two-dimensional posterior probability distribution for the Hubble constant and orbital inclination inferred from GW170817. The contours mark 68% and 95% levels. The coloured bands are measurements from the cosmic microwave background (Planck) and supernovae (SH0ES). Figure 2 of the GW170817 Hubble Constant Paper.

In the future we’ll be able to combine multiple events to produce a more precise gravitational-wave estimate of the Hubble constant. Chen, Fishbach & Holz (2017) is a recent study of how measurements should improve with more events: we should get to 4% precision after around 100 detections.

### The GW170817 Kilonova Paper

Synopsis: GW170817 Kilonova Paper
Read this if: You want to check our predictions for ejecta against observations
Favourite part: We might be able to create all of the heavy r-process elements—including the gold used to make Nobel Prizes—from merging neutron stars

When two neutron stars collide, lots of material gets ejected outwards. This neutron-rich material undergoes nuclear decay—now no longer being squeezed by the strong gravity inside the neutron star, it is unstable, and decays from the strange neutron star stuff™ to become more familiar elements (elements heavier than iron including gold and platinum). As these r-process elements are created, the nuclear reactions power a kilonova, the optical (infrared–ultraviolet) transient accompanying the merger. The properties of the kilonova depends upon how much material is ejected.

In this paper, we try to estimate how much material made up the dynamical ejecta from the GW170817 collision. Dynamical ejecta is material which escapes as the two neutron stars smash into each other (either from tidal tails or material squeezed out from the collision shock). There are other sources of ejected material, such as winds from the accretion disk which forms around the remnant (whether black hole or neutron star) following the collision, so this is only part of the picture; however, we can estimate the mass of the dynamical ejecta from our gravitational-wave measurements using simulations of neutron star mergers. These estimates can then be compared with electromagnetic observations of the kilonova [citation note].

The amount of dynamical ejecta depends upon the masses of the neutron stars, how rapidly they are rotating, and the properties of the neutron star material (described by the equation of state). Here, we use the masses inferred from our gravitational-wave measurements and feed these into fitting formulae calibrated against simulations for different equations of state. These don’t include spin, and they have quite large uncertainties (we include a 72% relative uncertainty when producing our results), so these are not precision estimates. Neutron star physics is a little messy.

We find that the dynamical ejecta is $10^{-3}$$10^{-2} M_\odot$ (assuming the low-spin mass results). These estimates can be feed into models for kilonovae to produce lightcurves, which we do. There is plenty of this type of modelling in the literature as observers try to understand their observations, so this is nothing special in terms of understanding this event. However, it could be useful in the future (once we have hoverboards), as we might be able to use gravitational-wave data to predict how bright a kilonova will be at different times, and so help astronomers decide upon their observing strategy.

Finally, we can consider how much r-process elements we can create from the dynamical ejecta. Again, we don’t consider winds, which may also contribute to the total budget of r-process elements from binary neutron stars. Our estimate for r-process elements needs several ingredients: (i) the mass of the dynamical ejecta, (ii) the fraction of the dynamical ejecta converted to r-process elements, (iii) the merger rate of binary neutron stars, and (iv) the convolution of the star formation rate and the time delay between binary formation and merger (which we take to be $\propto t^{-1}$). Together (i) and (ii) give the mass of r-process elements per binary neutron star (assuming that GW170817 is typical); (iii) and (iv) give total density of mergers throughout the history of the Universe, and combining everything together you get the total mass of r-process elements accumulated over time. Using the estimated binary neutron star merger rate of $1540_{-1220}^{+3200}~\mathrm{Gpc^{-3}\,yr^{-1}}$, we can explain the Galactic abundance of r-process elements if more than about 10% of the dynamical ejecta is converted.

Present day binary neutron star merger rate density versus dynamical ejecta mass. The grey region shows the inferred 90% range for the rate, the blue shows the approximate range of ejecta masses, and the red band shows the band where the Galactic elemental abundance can be reproduced if at least 50% of the dynamical mass gets converted. Part of Figure 5 of the GW170817 Kilonova Paper.

### The GW170817 Stochastic Paper

Synopsis: GW170817 Stochastic Paper
Read this if: You’re impatient for finding a background of gravitational waves
Favourite part: The background symphony

For every loud gravitational-wave signal, there are many more quieter ones. We can’t pick these out of the detector noise individually, but they are still there, in our data. They add together to form a stochastic background, which we might be able to detect by correlating the data across our detector network.

Following the detection of GW150914, we considered the background due to binary black holes. This is quite loud, and might be detectable in a few years. Here, we add in binary neutron stars. This doesn’t change the picture too much, but gives a more accurate picture.

Binary black holes have higher masses than binary neutron stars. This means that their gravitational-wave signals are louder, and shorter (they chirp quicker and chirp up to a lower frequency). Being louder, binary black holes dominate the overall background. Being shorter, they have a different character: binary black holes form a popcorn background of short chirps which rarely overlap, but binary neutron stars are long enough to overlap, forming a more continuous hum.

The dimensionless energy density at a gravitational-wave frequency of 25 Hz from binary black holes is $1.1_{-0.7}^{+1.2} \times 10^{-9}$, and from binary neutron stars it is $0.7_{-0.6}^{+1.5} \times 10^{-9}$. There are on average $0.06_{-0.04}^{+0.06}$ binary black hole signals in detectors at a given time, and $15_{-12}^{+31}$ binary neutron star signals.

Simulated time series illustrating the difference between binary black hole (green) and binary neutron star (red) signals. Each chirp increases in amplitude until the point at which the binary merges. Binary black hole signals are short, loud chirps, while the longer, quieter binary neutron star signals form an overlapping background. Figure 2 from the GW170817 Stochastic Paper.

To calculate the background, we need the rate of merger. We now have an estimate for binary neutron stars, and we take the most recent estimate from the GW170104 Discovery Paper for binary black holes. We use the rates assuming the power law mass distribution for this, but the result isn’t too sensitive to this: we care about the number of signals in the detector, and the rates are derived from this, so they agree when working backwards. We evolve the merger rate density across cosmic history by factoring in the star formation rate and delay time between formation and merger. A similar thing was done in the GW170817 Kilonova Paper, here we used a slightly different star formation rate, but results are basically the same with either. The addition of binary neutron stars increases the stochastic background from compact binaries by about 60%.

Detection in our next observing run, at a moderate significance, is possible, but I think unlikely. It will be a few years until detection is plausible, but the addition of binary neutron stars will bring this closer. When we do detect the background, it will give us another insight into the merger rate of binaries.

### The GW170817 Progenitor Paper

Synopsis: GW170817 Progenitor Paper
Read this if: You want to know about neutron star formation and supernovae
Favourite part: The Spirography figures

The identification of NGC 4993 as the host galaxy of GW170817’s binary neutron star system allows us to make some deductions about how it formed. In this paper, we simulate a large number of binaries, tracing the later stages of their evolution, to see which ones end up similar to GW170817. By doing so, we learn something about the supernova explosion which formed the second of the two neutron stars.

The neutron stars started life as a pair of regular stars [bonus note]. These burned through their hydrogen fuel, and once this is exhausted, they explode as a supernova. The core of the star collapses down to become a neutron star, and the outer layers are blasted off. The more massive star evolves faster, and goes supernova first. We’ll consider the effects of the second supernova, and the kick it gives to the binary: the orbit changes both because of the rocket effect of material being blasted off, and because one of the components loses mass.

From the combination of the gravitational-wave and electromagnetic observations of GW170817, we know the masses of the neutron star, the type of galaxy it is found in, and the position of the binary within the galaxy at the time of merger (we don’t know the exact position, just its projection as viewed from Earth, but that’s something).

Orbital trajectories of simulated binaries which led to GW170817-like merger. The coloured lines show the 2D projection of the orbits in our model galaxy. The white lines mark the initial (projected) circular orbit of the binary pre-supernova, and the red arrows indicate the projected direction of the supernova kick. The background shading indicates the stellar density. Figure 4 of the GW170817 Progenitor Paper; animated equivalents can be found in the Science Summary.

We start be simulating lots of binaries just before the second supernova explodes. These are scattered at different distances from the centre of the galaxy, have different orbital separations, and have different masses of the pre-supernova star. We then add the effects of the supernova, adding in a kick. We fix then neutron star masses to match those we inferred from the gravitational wave measurements. If the supernova kick is too big, the binary flies apart and will never merge (boo). If the binary remains bound, we follow its evolution as it moves through the galaxy. The structure of the galaxy is simulated as a simple spherical model, a Hernquist profile for the stellar component and a Navarro–Frenk–White profile for the dark matter halo [citation note], which are pretty standard. The binary shrinks as gravitational waves are emitted, and eventually merge. If the merger happens at a position which matches our observations (yay), we know that the initial conditions could explain GW170817.

Inferred progenitor properties: (second) supernova kick velocity, pre-supernova progenitor mass, pre-supernova binary separation and galactic radius at time of the supernova. The top row shows how the properties vary for different delay times between supernova and merger. The middle row compares all the binaries which survive the second supernova compared with the GW170817-like ones. The bottom row shows parameters for GW170817-like binaries with different galactic offsets than the $1.8~\mathrm{kpc}$ to $2.2~\mathrm{kpc}$ range used for GW1708017. The middle and bottom rows assume a delay time of at least $1~\mathrm{Gyr}$. Figure 5 of the GW170817 Progenitor Paper; to see correlations between parameters, check out Figure 8 of the GW170817 Progenitor Paper.

The plot above shows the constraints on the progenitor’s properties. The inferred second supernova kick is $V_\mathrm{kick} \simeq 300_{-200}^{+250}~\mathrm{km\,s^{-1}}$, similar to what has been observed for neutron stars in the Milky Way; the per-supernova stellar mass is $M_\mathrm{He} \simeq 3.0_{-1.5}^{+3.5} M_\odot$ (we assume that the star is just a helium core, with the outer hydrogen layers having been stripped off, hence the subscript); the pre-supernova orbital separation was $R_\odot \simeq 3.5_{-1.5}^{+5.0} R_\odot$, and the offset from the centre of the galaxy at the time of the supernova was $2.0_{-1.5}^{+4.0}~\mathrm{kpc}$. The main strongest constraints come from keeping the binary bound after the supernova; results are largely independent of the delay time once this gets above $1~\mathrm{Gyr}$ [citation note].

As we collect more binary neutron star detections, we’ll be able to deduce more about how they form. If you’re interested more in the how to build a binary neutron star system, the introduction to this paper is well referenced; Tauris et al. (2017) is a detailed (pre-GW170817) review.

### The GW170817 Neutrino Paper

Synopsis: GW170817 Neutrino Paper
Read this if: You want a change from gravitational wave–electromagnetic multimessenger astronomy
Favourite part: There’s still something to look forward to with future detections—GW170817 hasn’t stolen all the firsts. Also this paper is not Abbot et al.

This is a joint search by ANTARES, IceCube and the Pierre Auger Observatory for neutrinos coincident with GW170817. Knowing both the location and the time of the binary neutron star merger makes it easy to search for counterparts. No matching neutrinos were detected.

Neutrino candidates at the time of GW170817. The map is is in equatorial coordinates. The gravitational-wave localization is indicated by the red contour, and the galaxy NGC 4993 is indicated by the black cross. Up-going and down-going regions for each detector are indicated, as detectors are more sensitive to up-going neutrinos, as the Cherenkov detectors are subject to a background from cosmic rays hitting the atmosphere. Figure 1 from the GW170817 Neutrino Paper.

Using the non-detections, we can place upper limits on the neutrino flux. These are summarised in the plots below. Optimistic models for prompt emission from an on axis gamma-ray burst would lead to a detectable flux, but otherwise theoretical predictions indicate that a non-detection is expected. From electromagnetic observations, it doesn’t seem like we are on-axis, so the story all fits together.

90% confidence upper limits on neutrino spectral fluence $F$ per flavour (electron, muon and tau) as a function of energy $E$ in $\pm 500~\mathrm{s}$ window (top) about the GW170817 trigger time, and a $14~\mathrm{day}$ window following GW170817 (bottom). IceCube is also sensitive to MeV neutrinos (none were detected). Fluences are the per-flavour sum of neutrino and antineutrino fluence, assuming equal fluence in all flavours. These are compared to theoretical predictions from Kimura et al. (2017) and Fang & Metzger (2017), scaled to a distance of 40 Mpc. The angles labelling the models are viewing angles in excess of the jet opening angle. Figure 2 from the GW170817 Neutrino paper.

Super-Kamiokande have done their own search for neutrinos, form $3.5~\mathrm{MeV}$ to around $100~\mathrm{PeV}$ (Abe et al. 2018). They found nothing in either the $\pm 500~\mathrm{s}$ window around the event or the $14~\mathrm{day}$ window following it. Similarly BUST looked for muon neutrinos and antineutrinos and found nothing in the $\pm 500~\mathrm{s}$ window around the event, and no excess in the $14~\mathrm{day}$ window following it (Petkov et al. 2019). NOvA looked for neutrinos and cosmic rays $1000~\mathrm{s}$ around the event and found nothing (Acero et al. 2020).

The only post-detection neutrino modelling paper I’ve seen is Biehl, Heinze, &Winter (2017). They model prompt emission from the same source as the gamma-ray burst and find that neutrino fluxes would be $10^{-4}$ of current sensitivity.

### The GW170817 Post-merger Paper

Synopsis: GW170817 Post-merger Paper
Read this if: You are an optimist
Favourite part: We really do check everywhere for signals

Following the inspiral of two black holes, we know what happens next: the black holes merge to form a bigger black hole, which quickly settles down to its final stable state. We have a complete model of the gravitational waves from the inspiral–merger–ringdown life of coalescing binary black holes. Binary neutron stars are more complicated.

The inspiral of two binary neutron stars is similar to that for black holes. As they get closer together, we might see some imprint of tidal distortions not present for black holes, but the main details are the same. It is the chirp of the inspiral which we detect. As the neutron stars merge, however, we don’t have a clear picture of what goes on. Material gets shredded and ejected from the neutron stars; the neutron stars smash together; it’s all rather messy. We don’t have a good understanding of what should happen when our neutron stars merge, the details depend upon the properties of the stuff™ neutron stars are made of—if we could measure the gravitational-wave signal from this phase, we would learn a lot.

There are four plausible outcomes of a binary neutron star merger:

1. If the total mass is below the maximum mass for a (non-rotating) neutron star ($M < M^\mathrm{Static}$), we end up with a bigger, but still stable neutron star. Given our inferences from the inspiral (see the plot from the GW170817 Gamma-ray Burst Paper below), this is unlikely.
2. If the total mass is above the limit for a stable, non-rotating neutron star, but can still be supported by uniform rotation ($M^\mathrm{Static} < M < M^\mathrm{Uniform}$), we have a supramassive neutron star. The rotation will slow down due to the emission of electromagnetic and gravitational radiation, and eventually the neutron star will collapse to a black hole. The time until collapse could take something like $10$$5 \times 10^4~\mathrm{s}$; it is unclear if this is long enough for supramassive neutron stars to have a mid-life crisis.
3. If the total mass is above the limit for support from uniform rotation, but can still be supported through differential rotation and thermal gradients($M^\mathrm{Uniform} < M < M^\mathrm{Differential}$), then we have a hypermassive neutron star. The hypermassive neutron star cools quickly through neutrino emission, and its rotation slows through magnetic braking, meaning that it promptly collapses to a black hole in $\lesssim 1~\mathrm{s}$.
4. If the total mass is big enough($M^\mathrm{Differential} < M$), the merging neutron stars collapse down to a black hole.

In the case of the collapse to a black hole, we get a ringdown as in the case of a binary black hole merger. The frequency is around $6~\mathrm{kHz}$, too high for us to currently measure. However, if there is a neutron star, there may be slightly lower frequency gravitational waves from the neutron star matter wibbling about. We’re not exactly sure of the form of these signals, so we perform an unmodelled search for them (knowing the position of GW170817’s source helps for this).

Comparison of inferred component masses with critical mass boundaries for different equations of state. The left panel shows the maximum mass of a non-rotating neutron star compared to the initial baryonic mass (ignoring material ejected during merger and gravitational binding energy); the middle panel shows the maximum mass for a uniformly rotating neutron star; the right panel shows the maximum mass of a non-rotating neutron star compared of the gravitational mass of the heavier component neutron star. Figure 3 of the GW170817 Gamma-ray Burst Paper.

Several different search algorithms were used to hunt for a post-merger signal:

1. coherent WaveBurst (cWB) was used to look for short duration ($< 1~\mathrm{s}$) bursts. This searched a $2~\mathrm{s}$ window including the merger time and covering the $1.7~\mathrm{s}$ delay to the gamma-ray burst detection, and frequencies of $1024$$4096~\mathrm{Hz}$. Only LIGO data were used, as Virgo data suffered from large noise fluctuations above $2.5~\mathrm{kHz}$.
2. cWB was used to look for intermediate duration ($< 500~\mathrm{s}$) bursts. This searched a $1000~\mathrm{s}$ window from the merger time, and frequencies $24$$2048~\mathrm{Hz}$. This used LIGO and Virgo data.
3. The Stochastic Transient Analysis Multi-detector Pipeline (STAMP) was also used to look for intermediate duration signals. This searched the merger time until the end of O2 (in $500~\mathrm{s}$ chunks), and frequencies $24$$4000~\mathrm{Hz}$. This used only LIGO data. There are two variations of STAMP: Zebragard and Lonetrack, and both are used here.

Although GEO is similar to LIGO and Virgo and the searched high-frequencies, its data were not used as we have not yet studied its noise properties in enough detail. Since the LIGO detectors are the most sensitive, their data is most important for the search.

No plausible candidates were found, so we set some upper limits on what could have been detected. From these, it is not surprising that nothing was found, as we would need pretty much all of the mass of the remnant to somehow be converted into gravitational waves to see something. Results are shown in the plot below. An updated analysis which puts upper limits on the post-merger signal is given in the GW170817 Properties Paper.

Noise amplitude spectral density $\sqrt{S_n}$ for the four detectors, and search upper limits $h_\mathrm{rss}$ as a function of frequency. The noise amplitude spectral densities compare the sensitivities of the detectors. The search upper limits are root-sum-squared strain amplitudes at 50% detection efficiency. The colour code of the upper-limit markers indicates the search algorithm and the shape indicates the waveform injected to set the limits (the frequency is the average for this waveform). The bar mode waveform come from the rapid rotation of the supramassive neutron star leading to it becoming distorted (stretched) in a non-axisymmetric way (Lasky, Sarin & Sammut 2017); the magnetar waveform assumes that the (rapidly rotating) supramassive neutron star’s magnetic field generates significant ellipticity (Corsi & Mészáros 2009); the short-duration merger waveforms are from a selection of numerical simulations (Bauswein et al. 2013; Takami et al. 2015; Kawamura et al. 2016; Ciolfi et al. 2017). The open squares are merger waveforms scaled to the distance and orientation inferred from the inspiral of GW170817. The dashed black lines show strain amplitudes for a narrow-band signal with fixed energy content: the top line is the maximum possible value for GW170817. Figure 1 of the GW170817 Post-merger Paper.

We can’t tell the fate of GW170817’s neutron stars from gravitational waves alone [citation note]. As high-frequency sensitivity is improved in the future, we might be able to see something from a really close by binary neutron star merger.

### The GW170817 Properties Paper

Synopsis: GW170817 Properties Paper
Read this if: You want the best results for GW170817’s source, our best measurement of the Hubble constant, or limits on the post-merger signal
Favourite part: Look how tiny the uncertainties are!

As time progresses, we often refine our analyses of gravitational-wave data. This can be because we’ve had time to recalibrate data from our detectors, because better analysis techniques have been developed, or just because we’ve had time to allow more computationally intensive analyses to finish. This paper is our first attempt at improving our inferences about GW170817. The results use an improved calibration of Virgo data, and analyses more of the signal (down to a low frequency of 23 Hz, instead of 30 Hz, which gives use about an extra 1500 cycles), uses improved models of the waveforms, and includes a new analysis looking at the post-merger signal. The results update those given in the GW170817 Discovery Paper, the GW170817 Hubble Constant Paper and the GW170817 Post-merger Paper.

#### Inspiral

Our initial analysis was based upon quick to calculate post-Newtonian waveform known as TaylorF2. We thought this should be a conservative choice: any results with more complicated waveforms should give tighter results. This worked out. We try several different waveform models, each based upon the point particle waveforms we use for analysing binary black hole signals with extra bits to model the tidal deformation of neutron stars. The results are broadly consistent, so I’ll concentrate on discussing our preferred results calculated using IMRPhenomPNRT waveform (which uses IMRPhenomPv2 as a base and adds on numerical-relativity calibrated tides). As in the GW170817 Discovery Paper, we perform the analysis with two priors on the binary spins, one with spins up to 0.89 (which should safely encompass all possibilities for neutron stars), and one with spins of up to 0.05 (which matches observations of binary neutron stars in our Galaxy).

The first analysis we did was to check the location of the source. Reassuringly, we are still perfectly consistent with the location of AT 2017gfo (phew!). The localization is much improved, the 90% sky area is down to just $16~\mathrm{deg^2}$! Go Virgo!

Having established that it still makes sense that AT 2017gfo pin-points the source location, we use this as the position in subsequent analyses. We always use the sky position of the counterpart and the redshift of the host galaxy (Levan et al. 2017), but we don’t typically use the distance. This is because we want to be able to measure the Hubble constant, which relies on using the distance inferred from gravitational waves.

We use the distance from Cantiello et al. (2018) [citation note] for one calculation: an estimation of the inclination angle. The inclination is degenerate with the distance (both affect the amplitude of the signal), so having constraints on one lets us measure the other with improved precision. Without the distance information, we find that the angle between the binary’s total angular momentum and the line of sight is $152^{+21}_{-27}~\mathrm{deg}$ for the high-spin prior and $146^{+25}_{-27}~\mathrm{deg}$ with the low-spin prior. The difference between the two results is because of the spin angular momentum slightly shifts the direction of the total angular momentum. Incorporating the distance information, for the high-spin prior the angle is $153^{+15}_{-11}~\mathrm{deg}$ (so the misalignment angle is $27^{+11}_{-15}~\mathrm{deg}$), and for the low-spin prior it is $151^{+15}_{-11}~\mathrm{deg}$ (misalignment $29^{+11}_{-15}~\mathrm{deg}$) [citation note].

Estimated orientation and magnitude of the two component spins. The left pair is for the high-spin prior and so magnitudes extend to 0.89, and the right pair are for the low-spin prior and extend to 0.05. In each, the distribution for the more massive component is on the left, and for the smaller component on the right. The probability is binned into areas which have uniform prior probabilities. The low-spin prior truncates the posterior distribution, but this is less of an issue for the high-spin prior. Results are shown at a point in the inspiral corresponding to a gravitational-wave frequency of $100~\mathrm{Hz}$. Parts of Figure 8 and 9 of the GW170817 Properties Paper.

Main results include:

• The luminosity distance is $38.7_{-14.3}^{+7.4}~\mathrm{Mpc}$ with the low-spin prior and $40.8_{-12.3}^{+5.6}~\mathrm{Mpc}$ with the high-spin prior. The difference is for the same reason as the difference in inclination measurements. The results are consistent with the distance to NGC 4993 [citation note].
• The chirp mass redshifted to the detector-frame is measured to be $1.1975^{+0.0001}_{-0.0001} M_\odot$ with the low-spin prior and $1.1976^{+0.0001}_{-0.0001} M_\odot$ with the high-spin. This corresponds to a physical chirp mass of $1.186_{-0.001}^{+0.001} M_\odot$.
• The spins are not well constrained. We get the best measurement along the direction of the orbital angular momentum. For the low-spin prior, this is enough to disfavour the spins being antialigned, but that’s about it. For the high-spin prior, we rule out large spins aligned or antialigned, and very large spins in the plane. The aligned components of the spin are best described by the effective inspiral spin parameter $\chi_\mathrm{eff}$, for the low-spin prior it is $0.00^{+0.02}_{-0.01}$ and for the high-spin prior it is $0.02^{+0.08}_{-0.02}$.
• Using the low-spin prior, the component masses are $m_1 = 1.36$$1.60 M_\odot$ and $m_2 = 1.16$$1.36 M_\odot$, and for the high-spin prior they are $m_1 = 1.36$$1.89 M_\odot$ and $m_2 = 1.00$$1.36 M_\odot$.

These are largely consistent with our previous results. There are small shifts, but the biggest change is that the errors are a little smaller.

Estimated masses for the two neutron stars in the binary using the high-spin (left) and low-spin (right) priors. The two-dimensional plot follows a line of constant chirp mass which is too narrow to resolve on this scale. Results are shown for four different waveform models. TaylorF2 (used in the initial analysis), IMRPhenomDNRT and SEOBNRT have aligned spins, while IMRPhenomPNRT includes spin precession. IMRPhenomPNRT is used for the main results.Figure 5 of the GW170817 Properties Paper.

For the Hubble constant, we find $H_0 = 70^{+19}_{-8}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ with the low-spin prior and $H_0 = 70^{+13}_{-7}~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ with the high-spin prior. Here, we quote maximum a posterior value and narrowest 68% intervals as opposed to the usual median and symmetric 90% credible interval. You might think its odd that the uncertainty is smaller when using the wider high-spin prior, but this is just another consequence of the difference in the inclination measurements. The values are largely in agreement with our initial values.

The best measured tidal parameter is the combined dimensionless tidal deformability $\tilde{\Lambda}$. With the high-spin prior, we can only set an upper bound of $\tilde{\Lambda} < 630$ . With the low-spin prior, we find that we are still consistent with zero deformation, but the distribution peaks away from zero. We have $\tilde{\Lambda} = 300^{+500}_{-190}$ using the usual median and symmetric 90% credible interval, and $\tilde{\Lambda} = 300^{+420}_{-230}$ if we take the narrowest 90% interval. This looks like we have detected matter effects, but since we’ve had to use the low-spin prior, which is only appropriate for neutron stars, this would be a circular argument. More details on what we can learn about tidal deformations and what neutron stars are made of, under the assumption that we do have neutron stars, are given in the GW170817 Equation-of-state Paper.

#### Post-merger

Previously, in the GW170817 Post-merger Paper, we searched for a post-merger signal. We didn’t find anything. Now, we try to infer the shape of the signal, assuming it is there (with a peak within $250~\mathrm{ms}$ of the coalescence time). We still don’t find anything, but now we set much tighter upper limits on what signal there could be there.

For this analysis, we use data from the two LIGO detectors, and from GEO 600! We don’t use Virgo data, as it is not well behaved at these high frequencies. We use BayesWave to try to constrain the signal.

Noise amplitude spectral density for the detectors used, prior and posterior strain upper limits, and selected numerical simulations as a function of frequency. The signal upper limits are Bayesian 90% credible bounds for the signal in Hanford, but is derived from a coherent analysis of all three indicated detectors. Figure 13 of the GW170817 Properties Paper.

While the upper limits are much better, they are still about 12–215 times larger than expectations from simulations. Therefore, we’d need to improve our detector sensitivity by about a factor of 3.5–15 to detect a similar signal. Fingers crossed!

### The GW170817 Equation-of-state Paper

Synopsis: GW170817 Equation-of-state Paper
Read this if: You want to know what neutron stars are made of
Favourite part: The beautiful butterfly plots

Usually in our work, we like to remain open minded and not make too many assumptions. In our analysis of GW170817, as presented in the GW170817 Properties Paper, we have remained agnostic about the components of the binary, seeing what the data tell us. However, from the electromagnetic observations, there is solid evidence that the source is a binary neutron star system. In this paper, we take it as granted that the source is made of two neutron stars, and that these neutron stars are made of similar stuff™ [citation note], to see what we can learn about the properties of neutron stars.

When a two neutron stars get close together, they become distorted by each other’s gravity. Tides are raised, kind of like how the Moon creates tides on Earth. Creating tides takes energy out of the orbit, causing the inspiral to proceed faster. This is something we can measure from the gravitational wave signal. Tides are larger when the neutron stars are bigger. The size of neutron stars and how easy they are the stretch and squash depends upon their equation of state. We can use the measurements of the neutron star masses and amount of tidal deformation to infer their size and their equation of state.

The signal is analysed as in the GW170817 Properties Paper (IMRPhenomPNRT waveform, low-spin prior, position set to match AT 2017gfo). However, we also add in some information about the composition of neutron stars.

Calculating the behaviour of this incredibly dense material is difficult, but there are some relations (called universal relations) between the tidal deformability of neutron stars and their radii which are insensitive to the details of the equation of state. One relates symmetric and antisymmetric combinations of the tidal deformations of the two neutron stars as a function of the mass ratio, allows us to calculate consistent tidal deformations. Another relates the tidal deformation to the compactness (mass divided by radius) allows us to convert tidal deformations to radii. The analysis includes the uncertainty in these relations.

In addition to this, we also use a parametric model of the equation of state to model the tidal deformations. By sampling directly in terms of the equation of state, it is easy to impose constraints on the allowed values. For example, we impose that the speed of sound inside the neutron star is less than the speed of light, that the equation of state can support neutron stars of that mass, that it is possible to explain the most massive confirmed neutron star (we use a lower limit for this mass of $1.97 M_\odot$), as well as it being thermodynamically stable. Accommodating the most massive neutron star turns out to be an important piece of information.

The plot below shows the inferred tidal deformation parameters for the two neutron stars. The two techniques, using the equation-of-state insensitive relations and using the parametrised equation-of-state model without included the constraint of matching the $1.97 M_\odot$ neutron star, give similar results. For a $1.4 M_\odot$ neutron star, these results indicate that the tidal deformation parameter would be $\Lambda_{1.4} = 190^{+390}_{-120}$. We favour softer equations of state over stiffer ones [citation note]. I think this means that neutron stars are more huggable.

Probability distributions for the tidal parameters of the two neutron stars. The tidal deformation of the more massive neutron star $\Lambda_1$ must be greater than that for the smaller neutron star $\Lambda_2$. The green shading and (50% and 90%) contours are calculated using the equation-of-state insensitive relations. The blue contours are for the parametrised equation-of-state model. The orange contours are from the GW170817 Properties Paper, where we don’t assume a common equation of state. The black lines are predictions from a selection of different equations of state Figure 1 of the GW170817 Equation-of-state Paper.

We can translate our results into estimates on the size of the neutron stars. The plots below show the inferred radii. The results for the parametrised equation-of-state model now includes the constraint of accommodating a $1.97 M_\odot$ neutron star, which is the main reason for the difference in the plots. Using the equation-of-state insensitive relations we find that the radius of the heavier ($m_1 = 1.36$$1.62M_\odot$) neutron star is $R_1 = 10.8^{+2.0}_{-1.7}~\mathrm{km}$ and the radius of the lighter ($m_2 = 1.15$$1.36M_\odot$) neutron star is $R_2 = 10.7^{+2.1}_{-1.5}~\mathrm{km}$. With the parametrised equation-of-state model, the radii are $R_1 = 11.9^{+1.4}_{-1.4}~\mathrm{km}$ ($m_1 = 1.36$$1.58M_\odot$) and $R_2 = 11.9^{+1.4}_{-1.4}~\mathrm{km}$ ($m_2 = 1.18$$1.36M_\odot$).

Posterior probability distributions for neutron star masses and radii (blue for the more massive neutron star, orange for the lighter). The left plot uses the equation-of-state insensitive relations, and the right uses the parametrised equation-of-state model. In the one-dimensional plots, the dashed lines indicate the priors. The lines in the top left indicate the size of a Schwarzschild Black hole and the Buchadahl limit for the collapse of a neutron star. Figure 3 of the GW170817 Equation-of-state Paper.

When I was an undergraduate, I remember learning that neutron stars were about $15~\mathrm{km}$ in radius. We now know that’s not the case.

If you want to investigate further, you can download the posterior samples from these analyses.

### Bonus notes

#### Standard sirens

In astronomy, we often use standard candles, objects like type IA supernovae of known luminosity, to infer distances. If you know how bright something should be, and how bright you measure it to be, you know how far away it is. By analogy, we can infer how far away a gravitational-wave source is by how loud it is. It is thus not a candle, but a siren. Sean Carrol explains more about this term on his blog.

#### Nature

I know… Nature published the original Schutz paper on measuring the Hubble constant using gravitational waves; therefore, there’s a nice symmetry in publishing the first real result doing this in Nature too.

#### Globular clusters

Instead of a binary neutron star system forming from a binary of two stars born together, it is possible for two neutron stars to come close together in a dense stellar environment like a globular cluster. A significant fraction of binary black holes could be formed this way. Binary neutron stars, being less massive, are not as commonly formed this way. We wouldn’t expect GW170817 to have formed this way. In the GW170817 Progenitor Paper, we argue that the probability of GW170817’s source coming from a globular cluster is small—for predicted rates, see Bae, Kim & Lee (2014).

Levan et al. (2017) check for a stellar cluster at the site of AT 2017gfo, and find nothing. The smallest 30% of the Milky Way’s globular clusters would evade this limit, but these account for just 5% of the stellar mass in globular clusters, and a tiny fraction of dynamical interactions. Fong et al. (2019) perform some detailed observations looking for a globular cluster, and also find nothing. This excludes a cluster down to $1.3\ times 10^4 M_\odot$, which is basically all (99.996%) of them. Therefore, it’s unlikely that a cluster is the source of this binary.

### Citation notes

#### Merger rates

From our gravitational-wave data, we estimate the current binary neutron star merger rate density is $1540_{-1220}^{+3200}~\mathrm{Gpc^{-3}\,yr^{-1}}$. Several electromagnetic observers performed their own rate estimates from the frequency of detection (or lack thereof) of electromagnetic transients.

Kasliwal et al. (2017) consider transients seen by the Palomar Transient Factory, and estimate a rate density of approximately $320~\mathrm{Gpc^{-3}\,yr^{-1}}$ (3-sigma upper limit of $800~\mathrm{Gpc^{-3}\,yr^{-1}}$), towards the bottom end of our range, but their rate increases if not all mergers are as bright as AT 2017gfo.

Siebert et al. (2017) works out the rate of AT 2017gfo-like transients in the Swope Supernova Survey. They obtain an upper limit of $16000~\mathrm{Gpc^{-3}\,yr^{-1}}$. They use to estimate the probability that AT 2017gfo and GW170817 are just a chance coincidence and are actually unrelated. The probability is $9 \times 10^{-6}$ at 90% confidence.

Smartt et al. (2017) estimate the kilonova rate from the ATLAS survey, they calculate a 95% upper limit of $30000~\mathrm{Gpc^{-3}\,yr^{-1}}$, safely above our range.

Yang et al. (2017) calculates upper limits from the DLT40 Supernova survey. Depending upon the reddening assumed, this is between $93000^{+16000}_{-18000}~\mathrm{Gpc^{-3}\,yr^{-1}}$ and $109000^{+28000}_{-18000}~\mathrm{Gpc^{-3}\,yr^{-1}}$. Their figure 3 shows that this is well above expected rates.

Zhang et al. (2017) is interested in the rate of gamma-ray bursts. If you know the rate of short gamma-ray bursts and of binary neutron star mergers, you can learn something about the beaming angle of the jet. The smaller the jet, the less likely we are to observe a gamma-ray burst. In order to do this, they do their own back-of-the-envelope for the gravitational-wave rate. They get $1100_{-910}^{+2500}~\mathrm{Gpc^{-3}\,yr^{-1}}$. That’s not too bad, but do stick with our result.

If you’re interested in the future prospects for kilonova detection, I’d recommend Scolnic et al. (2017). Check out their Table 2 for detection rates (assuming a rate of $1000~\mathrm{Gpc^{-3}\,yr^{-1}}$): LSST and WFIRST will see lots, about 7 and 8 per year respectively.

Using later observational constraints on the jet structure, Gupta & Bartos (2018) use the short gamma-ray burst rate to estimate a binary neutron star merger rate of $500~\mathrm{Gpc^{-3}\,yr^{-1}}$. They project that around 30% of gravitational-wave detections will be accompanied by gamma-ray bursts, once LIGO and Virgo reach design sensitivity.

Della Valle et al. (2018) calculate an observable kilonova rate of $352_{-281}^{+810}~\mathrm{Gpc^{-3}\,yr^{-1}}$. To match up to our binary neutron star merger rate, we either need only a fraction of binary neutron star mergers to produce kilonova or for them to only be observable for viewing angles of less than $40^\circ$. Their table 2 contains a nice compilation of rates for short gamma-ray bursts.

#### The electromagnetic story

Some notes on an incomplete overview of papers describing the electromagnetic discovery. For observational data, I’d recommend looking at the Open Kilonova Project.

Independently of our gravitational-wave detection, a short gamma-ray burst GRB 170817A was observed by Fermi-GBM (Goldstein et al. 2017). Fermi-LAT did not see anything, as it was offline for crossing through the South Atlantic Anomaly. At the time of the merger, INTEGRAL was following up the location of GW170814, fortunately this meant it could still observe the location of GW170817, and following the alert they found GRB 170817A in their data (Savchenko et al. 2017).

Following up on our gravitational-wave localization, an optical transient AT 2017gfo was discovered. The discovery was made by the One-Meter Two-Hemisphere (1M2H) collaboration using the Swope telescope at the Las Campanas Observatory in Chile; they designated the transient as SSS17a (Coulter et al. 2017). That same evening, several other teams also found the transient within an hour of each other:

• The Distance Less Than 40 Mpc (DLT40) search found the transient using the PROMPT 0.4-m telescope at the Cerro Tololo Inter-American Observatory in Chile; they designated the transient DLT17ck (Valenti et al. 2017).
• The VINROUGE collaboration (I think, they don’t actually identify themselves in their own papers) found the transient using VISTA at the European Southern Observatory in Chile (Tanvir et al. 2017). Their paper also describes follow-up observations with the Very Large Telescope, the Hubble Space Telescope, the Nordic Optical Telescope and the Danish 1.54-m Telescope, and has one of my favourite introduction sections of the discovery papers.
• The MASTER collaboration followed up with their network of global telescopes, and it was their telescope at the San Juan National University Observatory in Argentina which found the transient (Lipunov et al. 2017); they, rather catchily denote the transient as OTJ130948.10-232253.3.
• The Dark Energy Survey and the Dark Energy Camera GW–EM (DES and DECam) Collaboration found the transient with the DECam on the Blanco 4-m telescope, which is also at the Cerro Tololo Inter-American Observatory in Chile (Soares-Santos et al. 2017).
• The Las Cumbres Observatory Collaboration used their global network of telescopes, with, unsurprisingly, their 1-m telescope at the Cerro Tololo Inter-American Observatory in Chile first imaging the transient (Arcavi et al. 2017). Their observing strategy is described in a companion paper (Arcavi et al. 2017), which also describes follow-up of GW170814.

From these, you can see that South America was the place to be for this event: it was night at just the right time.

There was a huge amount of follow-up across the infrared–optical–ultraviolet range of AT 2017gfo. Villar et al. (2017) attempts to bring these together in a consistent way. Their Figure 1 is beautiful.

Assembled lightcurves from ultraviolet, optical and infrared observations of AT 2017gfo. The data points are the homogenized data, and the lines are fitted kilonova models. The blue light initially dominates but rapidly fades, while the red light undergoes a slower decay. Figure 1 of Villar et al. (2017).

Hinderer et al. (2018) use numerical relativity simulations to compare theory and observations for gravitational-wave constraints on the tidal deformation and the kilonova lightcurve. They find that observations could be consistent with a neutron star–black hole binary and well as a binary neutron star. Coughline & Dietrich (2019) come to a similar conclusion. I think it’s unlikely that there would be a black hole this low mass, but it’s interesting that there are some simulations which can fit the observations.

AT 2017gfo was also the target of observations across the electromagnetic spectrum. An X-ray afterglow was observed 9 days post merger, and 16 days post merger, just as we thought the excitement was over, a radio afterglow was found:

The afterglow will continue to brighten for a while, so we can expect a series of updates:

• Pooley, Kumar & Wheeler (2017) observed with Chandra 108 and 111 days post merger. Ruan et al. (2017) observed with Chandra 109 days post merger. The large gap in the X-ray observations from the initial observations is because the Sun got in the way.
• Mooley et al. (2017) update the GROWTH radio results up to 107 days post merger (the largest span whilst still pre-empting new X-ray observations), observing with the Very Large Array, Australia Telescope Compact Array and Giant Meterewave Radio Telescope.

Excitingly, the afterglow has also now been spotted in the optical:

• Lyman et al. (2018) observed with Hubble 110 (rest-frame) days post-merger (which is when the Sun was out of the way for Hubble). At this point the kilonova should have faded away, but they found something, and this is quite blue. The conclusion is that it’s the afterglow, and it will peak in about a year.
• Margutti et al. (2018) brings together Chandra X-ray observations, Very Large Array radio observations and Hubble optical observations. The Hubble observations are 137 days post merger, and the Chandra observations are 153 days and 163 days post-merger. They find that they all agree (including the tentative radio signal at 10 days post-merger). They argue that the emission disfavours on-axis jets and spherical fireballs.

Evolution of radio, optical and X-ray spectral energy density of the counterpart to GW170817. The radio and X-ray are always dominated by the afterglow, as indicated by them following the same power law. At early times, the optical is dominated by the kilonova, but as this fades, the afterglow starts to dominate. Figure 1 of Margutti et al. (2018).

• D’Avanzo et al. (2018) observed in X-ray 135 days post-merger with XMM-Newton. They find that the flux is faded compared to the previous trend. They suggest that we’re just at the turn-over, so this is consistent with the most recent Hubble observations.
• Resmi et al. (2018) observed at low radio frequencies with the Giant Meterwave Radio Telescope. They saw the signal at $1390~\mathrm{MHz}$ after 67 days post-merger, but this evolves little over the duration of their observations (to day 152 post-merger), also suggesting a turn-over.
• Dobie et al. (2018) observed in radio 125–200 days post-merger with the Very Large Array and Australia Telescope Compact Array, and they find that the afterglow is starting to fade, with a peak at 149 ± 2 days post-merger.
• Nynka et al. (2018) made X-ray observations at 260 days post-merger. They conclude the afterglow is definitely fading, and that this is not because of passing of the synchrotron cooling frequency.
• Mooley et al. (2018) observed in radio to 298 days. They find the turn-over around 170 days. They argue that results support a narrow, successful jet.
• Troja et al. (2018) observed in radio and X-ray to 359 days. The fading is now obvious, and starting to reveal something about the jet structure. Their best fits seem to favour a structured relativistic jet or a wide-angled cocoon.
• Lamb et al. (2018) observed in optical to 358 days. They infer a peak around 140–160 days. Their observations are well fit either by a Gaussian structured jet or a two-component jet (with the second component being the cocoon), although the two-component model doesn’t fit early X-ray observations well. They conclude there must have been a successful jet of some form.

Radio, optical and X-ray observations to 358 days after merger. The coloured lines show fitted Gaussian jet models. Figure 3 of Lamb et al. (2018).

• Fong et al. (2019) observe in optical to 584 days post-merger, combined with observation in radio to 585 days post-merger and in X-ray 583 days post-merger. These observations favour a structured jet over a quasi-spherical outflow. Hajela et al. (2019) extend the radio and X-ray observations even further, out to 743 days post-merger.

Left: Optical afterglow observed until 584 days post-merger together with predictions for a structured jet and a quasi-spherical outflow (Wu & MacFadyen 2018). Right: Radio, optical and X-ray observations to 535 days, 534 days and 533 days post-merger-respectively. Triangles denote upper limits. Figures 2 and 3 of Fong et al. (2019).

• Troja et al. (2020) observed with Chandra between 935 and 942 days post-merger, and see a nice decline, consistent with a spreading jet. They also looked in radio, but didn’t find anything.
• Makhathini et al. (2020) compile a uniform set of radio, optical and X-ray afterglow observations. Their data set covers 0.5 to 940 days post-merger. It really is a lovely data set!

Optical, radio and X-ray light-curves, scaled by a best-fit spectral index so that the different observations lie on top of each other, for GW170817’s afterglow. The top panel shows the individual observations, labelled by observatory and observing band. The bottom panel shows a moving average. Figure 1 of Makhathini et al. (2020).

• Balasubramanian et al. (2021) continue to obtain radio and X-ray observations until 1270 days  post-merger. The radio is as expected for a structured jet, but there may be some brighting in the X-ray?
• Hajela et al. (2021) do find that there is a brightening in the X-ray after around 900 days. However, there is nothing in the radio. This could suggest some form of kilonova afterglow (which may argue against a prompt collapse to a black hole), or it could be from accretion onto the remnant. Either would be an interesting observation.
• Troja et al. (2021) reanalyse the X-ray data, checking the calibration. They do not find a rise, but do find an excess at late times that is difficult to explain with just the jet afterglow, suggesting that there is some extra emission like a kilonova afterglow.
• Balasubramanian et al. (2022) perform 3 GHz Very Large Array until 29 March 2022. They no longer detect the radio emission, but instead place an upper limit. This suggests no rebrightening.

X-ray (top) and radio (bottom) observations from Chandra and the Very Large Array, respectively. The X-ray observations show an excess after around 900 days, but their is not sign in radio. The red and orange lines show estimated synchrotron emission for different power laws. The grey curve shows synchrotron emission from the dynamical ejecta of a kilonova from a numerical relativity simulation of a neutron star merger. Figure 2 of Hajela at al. (2021).

The story of the most ambitious cross-over of astronomical observations might now be coming to an end?

#### Shapiro delay

Using the time delay between GW170817 and GRB 170817A, a few other teams also did their own estimation of the Shapiro delay before they knew what was in our GW170817 Gamma-ray Burst Paper.

• Wang et al. (2017) consider the Milky Way potential and large scale structure to estimate $-4 \times 10^{-9} \leq \gamma_\mathrm{GW} - \gamma_\mathrm{EM}$.
• Boran et al. (2017) consider all the galaxies in the GLADE catalogue which are within a radius of $400~\mathrm{kpc}$ of the line of sight, and derive $|\gamma_\mathrm{GW} - \gamma_\mathrm{EM}| \leq 3.9 \times 10 ^{-9}$.
• Wei et al. (2017) estimate $|\gamma_\mathrm{GW} - \gamma_\mathrm{EM}| \leq 5.9 \times 10 ^{-8}$ using the Milky Way’s potential and $|\gamma_\mathrm{GW} - \gamma_\mathrm{EM}| \leq 9.2 \times 10 ^{-11}$ using the Virgo cluster’s potential.

Our estimate of $-2.6 \times 10^{-7} \leq \gamma_\mathrm{GW} - \gamma_\mathrm{EM} \leq 1.2 \times 10 ^{-6}$ is the most conservative.

#### Comparison to other gamma-ray bursts

Are the electromagnetic counterparts to GW170817 similar to what has been observed before?

Yue et al. (2017) compare GRB 170817A with other gamma-ray bursts. It is low luminosity, but it may not be alone. There could be other bursts like it (perhaps GRB 070923, GRB 080121 and GRB 090417A), if indeed they are from nearby sources. They suggest that GRB 130603B may be the on-axis equivalent of GRB 170817A [citation note]; however, the non-detection of kilonovae for several bursts indicates that there needs to be some variation in their properties too. This agree with the results of Gompertz et al. (2017), who compares the GW170817 observations with other kilonovae: it is fainter than the other candidate kilonovae (GRB 050709, GRB 060614, GRB 130603B and tentatively GRB 160821B), but equally brighter than upper limits from other bursts. There must be a diversity in kilonovae observations. Fong et al. (2017) look at the diversity of afterglows (across X-ray to radio), and again find GW170817’s counterpart to be faint. This is probably because we are off-axis. The most comprehensive study is von Kienlin et al. (2019) who search ten years of Fermi archives and find 13 GRB 170817A-like short gamma-ray bursts: GRB 081209A, GRB 100328A, GRB 101224A, GRB 110717A; GRB 111024C, GRB 120302B, GRB 120915A, GRB 130502A, GRB 140511A, GRB 150101B, GRB 170111B, GRB 170817A and GRB 180511A. There is a range behaviours in these, with the shorter GRBs showing fast variability. Future observations will help unravel how much variation there is from viewing different angles, and how much intrinsic variation there is from the source—perhaps some short gamma-ray bursts come from neutron star–black hole binaries?

#### Inclination, jets and ejecta

Pretty much every observational paper has a go at estimating the properties of the ejecta, the viewing angle or something about the structure of the jet. I may try to pull these together later, but I’ve not had time yet as it is a very long list! Most of the inclination measurements assumed a uniform top-hat jet, which we now know is not a good model.

In my non-expert opinion, the later results seem more interesting. With very-long baseline interferometry radio observations to 230 days post-merger, Mooley et al. (2018) claim that while the early radio emission was powered by the wide cocoon of a structured jet, the later emission is dominated by a narrow, energetic jet. There was a successful jet, so we would have seen something like a regular short gamma-ray burst on axis. They estimate that the jet opening angle is $< 5~\mathrm{deg}$, and that we are viewing it at an angle of $20 \pm 5~\mathrm{deg}$. With X-ray and radio observations to 359 days, Troja et al. (2018) estimate (folding in gravitational-wave constraints too) that the viewing angle is $22 \pm 6~\mathrm{deg}$, and the width of a Gaussian structured jet would be $3.4 \pm 1.1~\mathrm{deg}$.

#### Hubble constant and misalignment

Guidorzi et al. (2017) try to tighten the measurement of the Hubble constant by using radio and X-ray observations. Their modelling assumes a uniform jet, which doesn’t look like a currently favoured option [citation note], so there is some model-based uncertainty to be included here. Additionally, the jet is unlikely to be perfectly aligned with the orbital angular momentum, which may add a couple of degrees more uncertainty.

Mandel (2018) works the other way and uses the recent Dark Energy Survey Hubble constant estimate to bound the misalignment angle to less than $28~\mathrm{deg}$, which (unsurprisingly) agrees pretty well with the result we obtained using the Planck value. Finstad et al. (2018) uses the luminosity distance from Cantiello et al. (2018) [citation note] as a (Gaussian) prior for an analysis of the gravitational-wave signal, and get a misalignment $32^{+10}_{-13}\pm 2~\mathrm{deg}$ (where the errors are statistical uncertainty and an estimate of systematic error from calibration of the strain).

Hotokezaka et al. (2018) use the inclination results from Mooley et al. (2018) [citation note] (together with the updated posterior samples from the GW170817 Properties Paper) to infer a value of $h = 0.689^{+0.047}_{-0.046}$ (quoting median and 68% symmetric credible interval). Using different jet models changes their value for the Hubble constant a little; the choice of spin prior does not (since we get basically all of the inclination information from their radio observations). The results is still consistent with Planck and SH0ES, but is closer to the Planck value.

Posterior probability distribution for the Hubble constant inferred from GW170817 using only gravitational waves (GWs), and folding in models for the power-law jet (PLJ) model and very-long baseline interferometry (VLBI) radio observations. The lines symmetric mark 68% intervals. The coloured bands are measurements from the cosmic microwave background (Planck) and supernovae (SH0ES). Figure 2 of Hotokezaka et al. (2018)

Dhawan et al. (2019) use broadband photometry of the kilonova to estimate the observation angle as $32.5^{+11.7}_{-9.7}~\mathrm{deg}$. Combining this with results from the Hubble Constant Paper they find $h = 0.724^{+0.079}_{-0.073}$.

#### NGC 4993 properties

In the GW170817 Progenitor Paper we used component properties for NGC 4993 from Lim et al. (2017): a stellar mass of $(10^{10.454}/h^2) M_\odot$ and a dark matter halo mass of $(10^{12.2}/h) M_\odot$, where we use the Planck value of $h = 0.679$ (but conclusions are similar using the SH0ES value for this).

Blanchard et al. (2017) estimate a stellar mass of about $\log(M_\ast/M_\odot) = 10.65^{+0.03}_{-0.03}$. They also look at the star formation history, 90% were formed by $6.8^{+2.2}_{-0.8}~\mathrm{Gyr}$ ago, and the median mass-weighted stellar age is $13.2^{+0.5}_{-0.9}~\mathrm{Gyr}$. From this they infer a merger delay time of $6.8$$13.6~\mathrm{Gyr}$. From this, and assuming that the system was born close to its current location, they estimate that the supernova kick $V_\mathrm{kick} \leq 200~\mathrm{km\,s^{-1}}$, towards the lower end of our estimate. They use $h = 0.677$.

Im et al. (2017) find a mean stellar mass of $0.3$$1.2 \times 10^{11} M_\odot$ and the mean stellar age is greater than about $3~\mathrm{Gyr}$. They also give a luminosity distance estimate of $38.4 \pm 8.9~\mathrm{Mpc}$, which overlaps with our gravitational-wave estimate. I’m not sure what value of $h$ they are using.

Levan et al. (2017) suggest a stellar mass of around $1.4 \times 10^{11} M_\odot$. They find that 60% of stars by mass are older than $5~\mathrm{Gyr}$ and that less than 1% are less than $0.5~\mathrm{Gyr}$ old. Their Figure 5 has some information on likely supernova kicks, they conclude it was probably small, but don’t quantify this. They use $h = 0.696$.

Pan et al. (2017) find $\log(M_\ast/M_\odot) = 10.49^{+0.08}_{-0.20}$. They calculate a mass-weighted mean stellar age of $10.97~\mathrm{Gyr}$ and a likely minimum age for GW170817’s source system of $2.8~\mathrm{Gyr}$. They use $h = 0.7$.

Troja et al. (2017) find a stellar mass of $\log(M_\ast/M_\odot) \sim 10.88$, and suggest an old stellar population of age $> 2~\mathrm{Gyr}$.

Ebrová & Bílek (2018) assume a distance of $41.0~\mathrm{kpc}$ and find a halo mass of $1.939 \times 10^{12} M_\odot$. They suggest that NGC 4993 swallowed a smaller late-type galaxy somewhere between $0.2~\mathrm{Gyr}$ and $1~\mathrm{Gyr}$ ago, most probably around $0.4~\mathrm{Gyr}$ ago.

The consensus seems to be that the stellar population is old (and not much else). Fortunately, the conclusions of the GW170817 Progenitor Paper are pretty robust for delay times longer than $1~\mathrm{Gyr}$ as seems likely.

A couple of other papers look at the distance of the galaxy:

• Hjoth et al. (2017) combine a redshift measurement from MUSE, and a fundamental plane estimate based upon Hubble observations, to obtain an distance of $41.0 \pm 3.1~\mathrm{Mpc}$.
• Cantiello et al. (2018) use Hubble observations to estimate the distance using surface brightness fluctuations. They obtain a distance of $40.7 \pm 1.4 \pm 1.9~\mathrm{Mpc}$. This implies a value for the Hubble constant of $h = 0.719 \pm 0.071$.

The values are consistent with our gravitational-wave estimates.

#### The remnant’s fate

We cannot be certain what happened to the merger remnant from gravitational-wave observations alone. However, electromagnetic observations do give some hints here.

Evans et al. (2017) argue that their non-detection of X-rays when observing with Swift and NuSTAR indicates that there is no neutron star remnant at this point, meaning we must have collapsed to form a black hole by 0.6 days post-merger. This isn’t too restricting in terms of the different ways the remnant could collapse, but does exclude a stable neutron star remnant. MAXI also didn’t detect any X-rays 4.6 hours after the merger (Sugita et al. 2018).

Pooley, Kumar & Wheeler (2017) consider X-ray observations of the afterglow. They calculate that if the remnant was a hypermassive neutron star with a large magnetic field, the early (10 day post-merger) luminosity would be much higher (and we could expect to see magnetar outbursts). Therefore, they think it is more likely that the remnant is a black hole. However, Piro et al. (2018) suggest that if the spin-down of the neutron star remnant is dominated by losses due to gravitational wave emission, rather than electromagnetic emission, then the scenario is still viable. They argue that a tentatively identified X-ray flare seen 155 days post-merger, could be evidence of dissipation of the neutron star’s toroidal magnetic field.

Kasen et al. (2017) use the observed red component of the kilonova to argue that the remnant must have collapsed to a black hole in $< 10~\mathrm{ms}$. A neutron star would irradiate the ejecta with neutrinos, lower the neutron fraction and making the ejecta bluer. Since it is red, the neutrino flux must have been shut off, and the neutron star must have collapsed. We are in case b in their figure below.

Cartoon of the different components of matter ejected from neutron star mergers. Red colours show heavy r-process elements and blue colours light r-process elements. There is a tidal tail of material forming a torus in the orbital plane, roughly spherical winds from the accretion disk, and material squeezed into the polar reasons during the collision. In case a, we have a long-lived neutron star, and its neutrino irradiation leads to blue ejecta. In case b the neutron star collapses, cutting off the neutrino flux. In case c, there is a neutron star–black hole merger, and we don’t have the polar material from the collision. Figure 1 of Kasen et al. (2017); also see Figure 1 of Margalit & Metzger (2017).

Ai et al. (2018) find that there are some corners of parameter space for certain equations of state where a long-lived neutron star is possible, even given the observations. Therefore, we should remain open minded.

Margalit & Metzger (2017) and Bauswein et al. (2017) note that the relatively large amount of ejecta inferred from observations [citation note] is easier to explain when there is delayed (on timescales of $> 10~\mathrm{ms}$). This is difficult to resolve unless neutron star radii are small ($\lesssim 11~\mathrm{km}$). Metzger, Thompson & Quataert (2018) derive how this tension could be resolved if the remnant was a rapidly spinning magnetar with a life time of $0.1$$1~\mathrm{s}$Matsumoto et al. (2018), suggest that the optical emission is powered by the jet and material accreting onto the central object, rather than r-process decay, and this permits much smaller amounts of ejecta, which could also solve the issue. Yu & Dai (2017) suggest that accretion onto a long-lived neutron star could power the emission, and would only require a single opacity for the ejecta. Li et al. (2018) put forward a similar theory, arguing that both the high ejecta mass and low opacity are problems for the standard r-process explanation, but fallback onto a neutron star could work. However, Margutti et al. (2018) say that X-ray emission powered by a central engine is disfavoured at all times.

In conclusion, it seems probable that we ended up with a black hole, and we had an a unstable neutron star for a short time after merger, but I don’t think it’s yet settled how long this was around.

Gill, Nathanail & Rezzolla (2019) considered how long it would take to produce the observed amount of ejecta, and the relative amounts of red and blue eject, as well as the delay time between the gravitational-wave measurement of the merger and the observation of the gamma-ray burst, to estimate how long it took the remnant to collapse to a black hole. They find a lifetime of $= 0.98^{+0.31}_{-0.26}~\mathrm{s}$.

#### Twin stars

We might not have two neutron stars with the same equation of state if they can undergo a phase transition. This would be kind of of like if one one made up of fluffer marshmallow, and the other was made up of gooey toasted marshmallow: they have the same ingredient, but in one the type of stuff has changed, giving it different physical properties. Standard neutron stars could be made of hadronic matter, kind of like a giant nucleus, but we could have another type where the hadrons break down into their component quarks. We could therefore have two neutron stars with similar masses but with very different equations of state. This is referred to as the twin star scenario. Hybrid stars which have quark cores surrounded by hadronic outer layers are often discussed in this context.

#### Neutron star equation of state

Several papers have explored what we can deduce about the nature of neutron star stuff™ from gravitational wave or electromagnetic observations the neutron star coalescence. It is quite a tricky problem. Below are some investigations into the radii of neutron stars and their tidal deformations; these seem compatible with the radii inferred in the GW170817 Equation-of-state Paper.

Bauswein et al. (2017) argue that the amount of ejecta inferred from the kilonova is too large for there to have been a prompt collapse to a black hole [citation note]. Using this, they estimate that the radius of a non-rotating neutron star of mass $1.6~\mathrm{M_\odot}$ has a radius of at least $10.68_{-0.04}^{+0.15}~\mathrm{km}$. They also estimate that the radius for the maximum mass nonrotating neutron star must be greater than $9.60_{-0.03}^{+0.14}~\mathrm{km}$. Köppel, Bovard & Rezzolla (2019) calculate a similar, updated analysis, using a new approach to fit for the maximum mass of a neutron star, and they find a radius for $1.6~\mathrm{M_\odot}$ is greater than  $10.90~\mathrm{km}$, and for $1.4~\mathrm{M_\odot}$  is greater than $10.92~\mathrm{km}$.

Annala et al. (2018) combine our initial measurement of the tidal deformation, with the requirement hat the equation of state supports a $2 M_\odot$ neutron star (which they argue requires that the tidal deformation of a $1.4 M_\odot$ neutron star is at least $120$). They argue that the latter condition implies that the radius of a $1.4 M_\odot$ neutron star is at least $9.9~\mathrm{km}$ and the former that it is less than $13.6~\mathrm{km}$.

Radice et al. (2018) combine together observations of the kilonova (the amount of ejecta inferred) with gravitational-wave measurements of the masses to place constraints on the tidal deformation. From their simulations, they argue that to explain the ejecta, the combined dimensionless tidal deformability must be $\tilde{\Lambda} > 400$. This is consistent with results in the GW170817 Properties Paper, but would eliminate the main peak of the distribution we inferred from gravitational waves alone. However, Kuichi et al. (2019) show that it is possible to get the required ejecta for smaller tidal deformations, depending upon assumptions about the maximum neutron star mass (higher masses allow smaller tidal deformations)mand asymmetry of the binary components.

Lim & Holt (2018) perform some equation-of-state calculations. They find that their particular method (chiral effective theory) is already in good agreement with estimates of the maximum neutron star mass and tidal deformations. Which is nice. Using their models, they predict that for GW170817’s chirp mass $\tilde{\Lambda} = 532^{+106}_{-119}$.

Raithel, Özel & Psaltis (2018) argue that for a given chirp mass, $\tilde{\Lambda}$ is only a weak function of component masses, and depends mostly on the radii. Therefore, from our initial inferred value, they put a 90% upper limit on the radii of $13~\mathrm{km}$.

Most et al. (2018) consider a wide range of parametrised equations of state. They consider both hadronic (made up of particles like neutrons and protons) equation of states, and ones where they undergo phase transitions (with hadrons breaking into quarks), which could potentially mean that the two neutron stars have quite different properties [citation note]. A number of different constraints are imposed, to give a selection of potential radius ranges. Combining the requirement that neutron stars can be up to $2.01 M_\odot$ (Antoniadis et al. 2013), the maximum neutron star mass of $2.17 M_\odot$ inferred by Margalit & Metzger (2017), our initial gravitational-wave upper limit on the tidal deformation and the lower limit from Radice et al. (2018), they estimate that the radius of a $1.4 M_\odot$ neutron star is $12.00$$13.45~\mathrm{km}$ for the hadronic equation of state. For the equation of state with the phase transition, they do the same, but without the tidal deformation from Radice et al. (2018), and find the radius of a $1.4 M_\odot$ neutron star is $8.53$$13.74~\mathrm{km}$.

Paschalidis et al. (2018) consider in more detail the idea equations of state with hadron–quark phase transitions, and the possibility that one of the components of GW170817’s source was a hadron–quark hybrid star. They find that the initial tidal measurements are consistent with this.

Burgio et al. (2018) further explore the possibility that the two binary components have different properties. They consider both there being a hadron–quark phase transition, and also that one star is hadronic and the other is a quark star (made up of deconfined quarks, rather than ones packaged up inside hadrons). X-ray observations indicate that neutron stars have radii in the range $9.9$$11.2~\mathrm{km}$, whereas most of the radii inferred for GW170817’s components are larger. This paper argues that this can be resolved if one of the components of GW170817’s source was a hadron–quark hybrid star or a quark star.

De et al. (2018) perform their own analysis of the gravitational signal, with a variety of different priors on the component masses. They assume that the two neutron stars have the same radii. In the GW170817 Equation-of-state Paper we find that the difference can be up to about $2~\mathrm{km}$, which I think makes this an OK approximation; Zhao & Lattimer (2018) look at this in more detail. Within their approximation, they estimate the neutron stars to have a common radius of $8.9$$13.2~\mathrm{km}$.

Malik et al. (2018) use the initial gravitational-wave upper bound on tidal deformation and the lower bound from Radice et al. (2018) in combination with several equations of state (calculated using relativistic mean field and of Skyrme Hartree–Fock recipes, which sound delicious). For a $1.4 M_\odot$ neutron star, they obtain a tidal deformation in the range $344$$859$ and the radius in the range $11.82$$13.72~\mathrm{km}$.

Radice & Dai (2018) do their own analysis of our gravitational-wave data (using relative binning) and combine this with an analysis of the electromagnetic observations using models for the accretion disc. They find that the areal radius of a $1.4 M_\odot$ is $12.2^{+1.0}_{-0.8} \pm 0.2~\mathrm{km}$. These results are in good agreement with ours, their inclusion of electromagnetic data pushes their combined results towards larger values for the tidal deformation.

Montaña et al. (2018) consider twin star scenarios [citation note] where we have a regular hadronic neutron star and a hybrid hadron–quark star. They find the data are consistent with neutron star–neutron star, neutron star–hybrid star or hybrid star–hybrid star binaries. Their Table II is a useful collection of results for the radius of a  $1.4 M_\odot$ neutron star, including the possibility of phase transitions.

Coughlin et al. (2018) use our LIGO–Virgo results and combine them with constraints from the observation of the kilonova (combined with fits to numerical simulations) and the gamma-ray burst. The electromagnetic observations give some extra information of the tidal deformability, mass ratio and inclination. They use the approximation that the neutron stars have equal radii. They find that the tidal deformability $\tilde{\Lambda}$ has a 90% interval $279$$822$ and the neutron star radius is $11.1$$13.4~\mathrm{km}$.

Zhou, Chen & Zhang (2019) use data from heavy ion collider experiments, which constrains the properties of nuclear density stuff™ at one end of the spectrum, the existence of $2 M_\odot$ neutron stars, and our GW170817 Equation-of-state Paper constraints on the tidal deformation to determine that the radius of a $1.4 M_\odot$ neutron star is $11.1$$13.3~\mathrm{km}$.

Kumar & Landry (2019) use the GW170817 Equation-of-state Paper constraints, and combine these of electromagnetic constraints to get an overall tidal deformability measurement. They use of observations of X-ray bursters from Özel et al. (2016) which give mass and radius measurements, and translate these using universal relations. Their overall result is the tidal deformability of a $1.4 M_\odot$ neutron star is $112^{+46}_{-33}$.

Gamba, Read & Wade (2019) estimate the systematic error in the GW170817 Equation-of-state Paper results for the neutron star radius which may have been introduced from assumptions about the crust’s equation of state. They find that the error could be $0.3~\mathrm{km}$ (about 3%).

# GW170608—The underdog

Detected in June, GW170608 has had a difficult time. It was challenging to analyse, and neglected in favour of its louder and shinier siblings. However, we can now introduce you to our smallest chirp-mass binary black hole system!

The growing family of black holes. From Dawn Finney.

Our family of binary black holes is now growing large. During our first observing run (O1) we found three: GW150914, LVT151012 and GW151226. The advanced detector observing run (O2) ran from 30 November 2016 to 25 August 2017 (with a couple of short breaks). From our O1 detections, we were expecting roughly one binary black hole per month. The first same in January, GW170104, and we have announced the first detection which involved Virgo from August, GW170814, so you might be wondering what happened in-between? Pretty much everything was dropped following the detection of our first binary neutron star system, GW170817, as a sizeable fraction of the astronomical community managed to observe its electromagnetic counterparts. Now, we are starting to dig our way out of the O2 back-log.

On 8 June 2017, a chirp was found in data from LIGO Livingston. At the time, LIGO Hanford was undergoing planned engineering work [bonus explanation]. We would not normally analyse this data, as the detector is disturbed; however, we had to follow up on the potential signal in Livingston. Only low frequency data in Hanford should have been affected, so we limited our analysis to above 30 Hz (this sounds easier than it is—I was glad I was not on rota to analyse this event [bonus note]). A coincident signal was found [bonus note]. Hello GW170608, the June event!

Time–frequency plots for GW170608 as measured by LIGO Hanford and Livingston. The chirp is clearer in Hanford, despite it being less sensitive, because of the sources position. Figure 1 of the GW170608 Paper.

Analysing data from both Hanford and Livingston (limiting Hanford to above 30 Hz) [bonus note], GW170608 was found by both of our offline searches for binary signals. PyCBC detected it with a false alarm rate of less than 1 in 3000 years, and GstLAL estimated a false alarm rate of 1 in 160000 years. The signal was also picked up by coherent WaveBurst, which doesn’t use waveform templates, and so is more flexible in what it can detect at the cost off sensitivity: this analysis estimates a false alarm rate of about 1 in 30 years. GW170608 probably isn’t a bit of random noise.

GW170608 comes from a low mass binary. Well, relatively low mass for a binary black hole. For low mass systems, we can measure the chirp mass $\mathcal{M}$, the particular combination of the two black hole masses which governs the inspiral, well. For GW170608, the chirp mass is $7.9_{-0.2}^{+0.2} M_\odot$. This is the smallest chirp mass we’ve ever measured, the next smallest is GW151226 with $8.9_{-0.3}^{+0.3} M_\odot$. GW170608 is probably the lowest mass binary we’ve found—the total mass and individual component masses aren’t as well measured as the chirp mass, so there is small probability (~11%) that GW151226 is actually lower mass. The plot below compares the two.

Estimated masses $m_1 \geq m_2$ for the two black holes in the binary. The two-dimensional shows the probability distribution for GW170608 as well as 50% and 90% contours for GW151226, the other contender for the lightest black hole binary. The one-dimensional plots on the sides show results using different waveform models. The dotted lines mark the edge of our 90% probability intervals. The one-dimensional plots at the top show the probability distributions for the total mass $M$ and chirp mass $\mathcal{M}$. Figure 2 of the GW170608 Paper. I think this plot is neat.

One caveat with regards to the masses is that the current results only consider spin magnitudes up to 0.89, as opposed to the usual 0.99. There is a correlation between the mass ratio and the spins: you can have a more unequal mass binary with larger spins. There’s not a lot of support for large spins, so it shouldn’t make too much difference. We use the full range in updated analysis in the O2 Catalogue Paper.

Speaking of spins, GW170608 seems to prefer small spins aligned with the angular momentum; spins are difficult to measure, so there’s a lot of uncertainty here. The best measured combination is the effective inspiral spin parameter $\chi_\mathrm{eff}$. This is a combination of the spins aligned with the orbital angular momentum. For GW170608 it is $0.07_{-0.09}^{+0.23}$, so consistent with zero and leaning towards being small and positive. For GW151226 it was $0.21_{-0.10}^{+0.20}$, and we could exclude zero spin (at least one of the black holes must have some spin). The plot below shows the probability distribution for the two component spins (you can see the cut at a maximum magnitude of 0.89). We prefer small spins, and generally prefer spins in the upper half of the plots, but we can’t make any definite statements other than both spins aren’t large and antialigned with the orbital angular momentum.

Estimated orientation and magnitude of the two component spins. The distribution for the more massive black hole is on the left, and for the smaller black hole on the right. The probability is binned into areas which have uniform prior probabilities, so if we had learnt nothing, the plot would be uniform. This analysis assumed spin magnitudes less than 0.89, which is why there is an apparent cut-off. Part of Figure 3 of the GW170608 Paper. For the record, I voted against this colour scheme.

The properties of GW170608’s source are consistent with those inferred from observations of low-mass X-ray binaries (here the low-mass refers to the companion star, not the black hole). These are systems where mass overflows from a star onto a black hole, swirling around in an accretion disc before plunging in. We measure the X-rays emitted from the hot gas from the disc, and these measurements can be used to estimate the mass and spin of the black hole. The similarity suggests that all these black holes—observed with X-rays or with gravitational waves—may be part of the same family.

Estimated black hole masses inferred from low-mass X-ray binary observations. Figure 1 of Farr et al. (2011). The masses overlap those of the lower mass binary black holes found by LIGO and Virgo.

We’ll present update merger rates and results for testing general relativity in our end-of-O2 paper. The low mass of GW170608’s source will make it a useful addition to our catalogue here. Small doesn’t mean unimportant.

Title: GW170608: Observation of a 19 solar-mass binary black hole coalescence
Journal: Astrophysical Journal Letters; 851(2):L35(11); 2017
arXiv: 1711.05578 [gr-qc] [bonus note]
Science summary: GW170608: LIGO’s lightest black hole binary?
Data release: LIGO Open Science Center

If you’re looking for the most up-to-date results regarding GW170608, check out the O2 Catalogue Paper.

### Bonus notes

#### Detector engineering

A lot of time and effort goes into monitoring, maintaining and tweaking the detectors so that they achieve the best possible performance. The majority of work on the detectors happens during engineering breaks between observing runs, as we progress towards design sensitivity. However, some work is also needed during observing runs, to keep the detectors healthy.

On 8 June, Hanford was undergoing angle-to-length (A2L) decoupling, a regular maintenance procedure which minimises the coupling between the angular position of the test-mass mirrors and the measurement of strain. Our gravitational-wave detectors carefully measure the time taken for laser light to bounce between the test-mass mirrors in their arms. If one of these mirrors gets slightly tilted, then the laser could bounce of part of the mirror which is slightly closer or further away than usual: we measure a change in travel time even though the length of the arm is the same. To avoid this, the detectors have control systems designed to minimise angular disturbances. Every so often, it is necessary to check that these are calibrated properly. To do this, the mirrors are given little pushes to rotate them in various directions, and we measure the output to see the impact.

Examples of how angular fluctuations can couple to length measurements. Here are examples of how pitch $p$ rotations in the suspension level above the test mass (L3 is the test mass, L2 is the level above) can couple to length measurement $l$. Yaw fluctuations (rotations about the vertical axis) can also have an impact. Figure 1 of Kasprzack & Yu (2016).

The angular pushes are done at specific frequencies, so we we can tease apart the different effects of rotations in different directions. The frequencies are in the range 19–23 Hz. 30 Hz is a safe cut-off for effects of the procedure (we see no disturbances above this frequency).

Imprint of angular coupling testing in Hanford. The left panel shows a spectrogram of strain data, you can clearly see the excitations between ~19 Hz and ~23 Hz. The right panel shows the amplitude spectral density for Hanford before and during the procedure, as well as for Livingston. The procedure adds extra noise in the broad peak about 20 Hz. There are no disturbances above ~30 Hz. Figure 4 of GW170608 Paper.

While we normally wouldn’t analyse data from during maintenance, we think it is safe to do so, after discarding the low-frequency data. If you are worried about the impact of including addition data in our rate estimates (there may be a bias only using time when you know there are signals), you can be reassured that it’s only a small percent of the total time, and so should introduce an error less significant than uncertainty from the calibration accuracy of the detectors.

#### Parameter estimation rota

Unusually for an O2 event, Aaron Zimmerman was not on shift for the Parameter Estimation rota at the time of GW170608. Instead, it was Patricia Schmidt and Eve Chase who led this analysis. Due to the engineering work in Hanford, and the low mass of the system (which means a long inspiral signal), this was one of the trickiest signals to analyse: I’d say only GW170817 was more challenging (if you ignore all the extra work we did for GW150914 as it was the first time).

Since this wasn’t a standard detection, it took a while to send out an alert (about thirteen and a half hours). Since this is a binary black hole merger, we wouldn’t expect that there is anything to see with telescopes, so the delay isn’t as important as it would be for a binary neutron star. Several observing teams did follow up the laert. Details can be found in the GCN Circular archive. So far, papers on follow-up have appeared from:

• CALET—a gamma-ray search. This paper includes upper limits for GW151226, GW170104, GW170608, GW170814 and GW170817.
• DLT40—an optical search designed for supernovae. This paper covers the whole of O2 including GW170104GW170814, GW170817 plus GW170809 and GW170823.
• Mini-GWAC—a optical survey (the precursor to GWAC). This paper covers the whole of their O2 follow-up (including GW170104).
• NOvA—a search for neutrinos and cosmic rays over a wide range of energies. This paper covers all the events from O1 and O2, plus triggers from O3.
• The VLA and VLITE—radio follow-up, particularly targeting a potentially interesting gamma-ray transient spotted by Fermi.

#### Virgo?

If you are wondering about the status of Virgo: on June 8 it was still in commissioning ahead of officially joining the run on 1 August. We have data at the time of the event. The sensitivity is of the detector is not great. We often quantify detector sensitivity by quoting the binary neutron star range (the average distance a binary neutron star could be detected). Around the time of the event, this was something like 7–8 Mpc for Virgo. During O2, the LIGO detectors have been typically in the 60–100 Mpc region; when Virgo joined O2, it had a range of around 25–30 Mpc. Unsurprisingly, Virgo didn’t detect the signal. We could have folded the data in for parameter estimation, but it was decided that it was probably not well enough understood at the time to be worthwhile.

#### Journal

The GW170608 Paper is the first discovery paper to be made public before journal acceptance (although the GW170814 Paper was close, and we would have probably gone ahead with the announcement anyway). I have mixed feelings about this. On one hand, I like that the Collaboration is seen to take their detections seriously and follow the etiquette of peer review. On the other hand, I think it is good that we can get some feedback from the broader community on papers before they’re finalised. I think it is good that the first few were peer reviewed, it gives us credibility, and it’s OK to relax now. Binary black holes are becoming routine.

This is also the first discovery paper not to go to Physical Review Letters. I don’t think there’s any deep meaning to this, the Collaboration just wanted some variety. Perhaps GW170817 sold everyone that we were astrophysicists now? Perhaps people thought that we’ve abused Physical Review Letters‘ page limits too many times, and we really do need that appendix. I was still in favour of Physical Review Letters for this paper, if they would have had us, but I approve of sharing the love. There’ll be plenty more events.

# GW170814—Enter Virgo

On 14 August 2017 a gravitational wave signal (GW170814), originating from the coalescence of a binary black hole system, was observed by the global gravitational-wave observatory network of the two Advanced LIGO detectors and Advanced Virgo.  That’s right, Virgo is in the game!

Very few things excite me like unlocking a new character in Smash Bros. A new gravitational wave observatory might come close.

Advanced Virgo joined O2, the second observing run of the advanced detector era, on 1 August. This was a huge achievement. It has not been an easy route commissioning the new detector—it never ceases to amaze me how sensitive these machines are. Together, Advanced Virgo (near Pisa) and the two Advanced LIGO detectors (in Livingston and Hanford in the US) would take data until the end of O2 on 25 August.

On 14 August, we found a signal. A signal that was observable in all three detectors [bonus note]. Virgo is less sensitive than the LIGO instruments, so there is no impressive plot that shows something clearly popping out, but the Virgo data do complement the LIGO observations, indicating a consistent signal in all three detectors [bonus note].

A cartoon of three different ways to visualise GW170814 in the three detectors. These take a bit of explaining. The top panel shows the signal-to-noise ratio the search template that matched GW170814. They peak at the time corresponding to the merger. The peaks are clear in Hanford and Livingston. The peak in Virgo is less exceptional, but it matches the expected time delay and amplitude for the signal. The middle panels show time–frequency plots. The upward sweeping chirp is visible in Hanford and Livingston, but less so in Virgo as it is less sensitive. The plot is zoomed in so that its possible to pick out the detail in Virgo, but the chirp is visible for a longer stretch of time than plotted in Livingston. The bottom panel shows whitened and band-passed strain data, together with the 90% region of the binary black hole templates used to infer the parameters of the source (the narrow dark band), and an unmodelled, coherent reconstruction of the signal (the wider light band) . The agreement between the templates and the reconstruction is a check that the gravitational waves match our expectations for binary black holes. The whitening of the data mirrors how we do the analysis, by weighting noise at different frequency by an estimate of their typical fluctuations. The signal does certainly look like the inspiral, merger and ringdown of a binary black hole. Figure 1 of the GW170814 Paper.

The signal originated from the coalescence of two black holes. GW170814 is thus added to the growing family of GW150914, LVT151012, GW151226 and GW170104.

GW170814 most closely resembles GW150914 and GW170104 (perhaps there’s something about ending with a 4). If we compare the masses of the two component black holes of the binary ($m_1$ and $m_2$), and the black hole they merge to form ($M_\mathrm{f}$), they are all quite similar

• GW150914: $m_1 = 36.2^{+5.2}_{-3.8} M_\odot$, $m_2 = 29.1^{+3.7}_{-4.4} M_\odot$, $M_\mathrm{f} = 62.3^{+3.7}_{-3.1} M_\odot$;
• GW170104: $m_1 = 31.2^{+5.4}_{-6.0} M_\odot$, $m_2 = 19.4^{+5.3}_{-5.9} M_\odot$, $M_\mathrm{f} = 48.7^{+5.7}_{-4.6} M_\odot$;
• GW170814: $m_1 = 30.5^{+5.7}_{-3.0} M_\odot$, $m_2 = 25.3^{+2.8}_{-4.2} M_\odot$, $M_\mathrm{f} = 53.2^{+3.2}_{-2.5} M_\odot$.

GW170814’s source is another high-mass black hole system. It’s not too surprising (now we know that these systems exist) that we observe lots of these, as more massive black holes produce louder gravitational wave signals.

GW170814 is also comparable in terms of black holes spins. Spins are more difficult to measure than masses, so we’ll just look at the effective inspiral spin $\chi_\mathrm{eff}$, a particular combination of the two component spins that influences how they inspiral together, and the spin of the final black hole $a_\mathrm{f}$

• GW150914: $\chi_\mathrm{eff} = -0.06^{+0.14}_{-0.14}$, $a_\mathrm{f} = 0.70^{+0.07}_{-0.05}$;
• GW170104:$\chi_\mathrm{eff} = -0.12^{+0.21}_{-0.30}$, $a_\mathrm{f} = 0.64^{+0.09}_{-0.20}$;
• GW170814:$\chi_\mathrm{eff} = 0.06^{+0.12}_{-0.12}$, $a_\mathrm{f} = 0.70^{+0.07}_{-0.05}$.

There’s some spread, but the effective inspiral spins are all consistent with being close to zero. Small values occur when the individual spins are small, if the spins are misaligned with each other, or some combination of the two. I’m starting to ponder if high-mass black holes might have small spins. We don’t have enough information to tease these apart yet, but this new system is consistent with the story so far.

One of the things Virgo helps a lot with is localizing the source on the sky. Most of the information about the source location comes from the difference in arrival times at the detectors (since we know that gravitational waves should travel at the speed of light). With two detectors, the time delay constrains the source to a ring on the sky; with three detectors, time delays can narrow the possible locations down to a couple of blobs. Folding in the amplitude of the signal as measured by the different detectors adds extra information, since detectors are not equally sensitive to all points on the sky (they are most sensitive to sources over head or underneath). This can even help when you don’t observe the signal in all detectors, as you know the source must be in a direction that detector isn’t too sensitive too. GW170814 arrived at LIGO Livingston first (although it’s not a competition), then ~8 ms later at LIGO Hanford, and finally ~14 ms later at Virgo.  If we only had the two LIGO detectors, we’d have an uncertainty on the source’s sky position of over 1000 square degrees, but adding in Virgo, we get this down to 60 square degrees. That’s still pretty large by astronomical standards (the full Moon is about a quarter of a square degree), but a fantastic improvement [bonus note]!

90% probability localizations for GW170814. The large banana shaped (and banana coloured, but not banana flavoured) curve uses just the two LIGO detectors, the area is 1160 square degrees. The green shows the improvement adding Virgo, the area is just 100 square degrees. Both of these are calculated using BAYESTAR, a rapid localization algorithm. The purple map is the final localization from our full parameter estimation analysis (LALInference), its area is just 60 square degrees! Whereas BAYESTAR only uses the best matching template from the search, the full parameter estimation analysis is free to explore a range of different templates. Part of Figure 3 of the GW170814 Paper.

Having additional detectors can help improve gravitational wave measurements in other ways too. One of the predictions of general relativity is that gravitational waves come in two polarizations. These polarizations describe the pattern of stretching and squashing as the wave passes, and are illustrated below.

The two polarizations of gravitational waves: plus (left) and cross (right). Here, the wave is travelling into or out of the screen. Animations adapted from those by MOBle on Wikipedia.

These two polarizations are the two tensor polarizations, but other patterns of squeezing could be present in modified theories of gravity. If we could detect any of these we would immediately know that general relativity is wrong. The two LIGO detectors are almost exactly aligned, so its difficult to get any information on other polarizations. (We tried with GW150914 and couldn’t say anything either way). With Virgo, we get a little more information. As a first illustration of what we may be able to do, we compared how well the observed pattern of radiation at the detectors matched different polarizations, to see how general relativity’s tensor polarizations compared to a signal of entirely vector or scalar radiation. The tensor polarizations are clearly preferred, so general relativity lives another day. This isn’t too surprising, as most modified theories of gravity with other polarizations predict mixtures of the different polarizations (rather than all of one). To be able to constrain all the  mixtures with these short signals we really need a network of five detectors, so we’ll have to wait for KAGRA and LIGO-India to come on-line.

The six polarizations of a metric theory of gravity. The wave is travelling in the $z$ direction. (a) and (b) are the plus and cross tensor polarizations of general relativity. (c) and (d) are the scalar breathing and longitudinal modes, and (e) and (f) are the vector $x$ and $y$ polarizations. The tensor polarizations (in red) are transverse, the vector and longitudinal scalar mode (in green) are longitudinal. The scalar breathing mode (in blue) is an isotropic expansion and contraction, so its a bit of a mix of transverse and longitudinal. Figure 10 from (the excellent) Will (2014).

We’ll be presenting a more detailed analysis of GW170814 later, in papers summarising our O2 results, so stay tuned for more.

Title: GW170814: A three-detector observation of gravitational waves from a binary black hole coalescence
arXiv: 1709.09660 [gr-qc]
Journal: Physical Review Letters; 119(14):141101(16) [bonus note]
Data release: LIGO Open Science Center
Science summary: GW170814: A three-detector observation of gravitational waves from a binary black hole coalescence

If you’re looking for the most up-to-date results regarding GW170814, check out the O2 Catalogue Paper.

### Bonus notes

#### Signs of paranoia

Those of you who have been following the story of gravitational waves for a while may remember the case of the Big Dog. This was a blind injection of a signal during the initial detector era. One of the things that made it an interesting signal to analyse, was that it had been injected with an inconsistent sign in Virgo compared to the two LIGO instruments (basically it was upside down). Making this type of sign error is easy, and we were a little worried that we might make this sort of mistake when analysing the real data. The Virgo calibration team were extremely careful about this, and confident in their results. Of course, we’re quite paranoid, so during the preliminary analysis of GW170814, we tried some parameter estimation runs with the data from Virgo flipped. This was clearly disfavoured compared to the right sign, so we all breathed easily.

I am starting to believe that God may be a detector commissioner. At the start of O1, we didn’t have the hardware injection systems operational, but GW150914 showed that things were working properly. Now, with a third detector on-line, GW170814 shows that the network is functioning properly. Astrophysical injections are definitely the best way to confirm things are working!

#### Signal hunting

Our usual way to search for binary black hole signals is compare the data to a bank of waveform templates. Since Virgo is less sensitive the the two LIGO detectors, and would only be running for a short amount of time, these main searches weren’t extended to use data from all three detectors. This seemed like a sensible plan, we were confident that this wouldn’t cause us to miss anything, and we can detect GW170814 with high significance using just data from Livingston and Hanford—the false alarm rate is estimated to be less than 1 in 27000 years (meaning that if the detectors were left running in the same state, we’d expect random noise to make something this signal-like less than once every 27000 years). However, we realised that we wanted to be able to show that Virgo had indeed seen something, and the search wasn’t set up for this.

Therefore, for the paper, we list three different checks to show that Virgo did indeed see the signal.

1. In a similar spirit to the main searches, we took the best fitting template (it doesn’t matter in terms of results if this is the best matching template found by the search algorithms, or the maximum likelihood waveform from parameter estimation), and compared this to a stretch of data. We then calculated the probability of seeing a peak in the signal-to-noise ratio (as shown in the top row of Figure 1) at least as large as identified for GW170814, within the time window expected for a real signal. Little blips of noise can cause peaks in the signal-to-noise ratio, for example, there’s a glitch about 50 ms after GW170814 which shows up. We find that there’s a 0.3% probability of getting a signal-to-ratio peak as large as GW170814. That’s pretty solid evidence for Virgo having seen the signal, but perhaps not overwhelming.
2. Binary black hole coalescences can also be detected (if the signals are short) by our searches for unmodelled signals. This was the case for GW170814. These searches were using data from all three detectors, so we can compare results with and without Virgo. Using just the two LIGO detectors, we calculate a false alarm rate of 1 per 300 years. This is good enough to claim a detection. Adding in Virgo, the false alarm rate drops to 1 per 5900 years! We see adding in Virgo improves the significance by almost a factor of 20.
3. Using our parameter estimation analysis, we calculate the evidence (marginal likelihood) for (i) there being a coherent signal in Livingston and Hanford, and Gaussian noise in Virgo, and (ii) there being a coherent signal in all three detectors. We then take the ratio to calculate the Bayes factor. We find that a coherent signal in all three detectors is preferred by a factor of over 1600. This is a variant of a test proposed in Veitch & Vecchio (2010); it could be fooled if the noise in Virgo is non-Gaussian (if there is a glitch), but together with the above we think that the simplest explanation for Virgo’s data is that there is a signal.

In conclusion: Virgo works. Probably.

#### Follow-up observations

Adding Virgo to the network greatly improves localization of the source, which is a huge advantage when searching for counterparts. For a binary black hole, as we have here, we don’t expect a counterpart (which would make finding one even more exciting). So far, no counterpart has been reported.

i

#### Announcement

This is the first observation we’ve announced before being published. The draft made public at time at announcement was accepted, pending fixing up some minor points raised by the referees (who were fantastically quick in reporting back). I guess that binary black holes are now familiar enough that we are on solid ground claiming them. I’d be interested to know if people think that it would be good if we didn’t always wait for the rubber stamp of peer review, or whether they would prefer to for detections to be externally vetted? Sharing papers before publication would mean that we get more chance for feedback from the community, which is would be good, but perhaps the Collaboration should be seen to do things properly?

One reason that the draft paper is being shared early is because of an opportunity to present to the G7 Science Ministers Meeting in Italy. I think any excuse to remind politicians that international collaboration is a good thing™ is worth taking. Although I would have liked the paper to be a little more polished [bonus advice]. The opportunity to present here only popped up recently, which is one reason why things aren’t as perfect as usual.

I also suspect that Virgo were keen to demonstrate that they had detected something prior to any Nobel Prize announcement. There’s a big difference between stories being written about LIGO and Virgo’s discoveries, and having as an afterthought that Virgo also ran in August.

The main reason, however, was to get this paper out before the announcement of GW170817. The identification of GW170817’s counterpart relied on us being able to localize the source. In that case, there wasn’t a clear signal in Virgo (the lack of a signal tells us the source wan’t in a direction wasn’t particularly sensitive to). People agreed that we really need to demonstrate that Virgo can detect gravitational waves in order to be convincing that not seeing a signal is useful information. We needed to demonstrate that Virgo does work so that our case for GW170817 was watertight and bulletproof (it’s important to be prepared).

Some useful advice I was given when a PhD student was that done is better than perfect. Having something finished is often more valuable than having lots of really polished bits that don’t fit together to make a cohesive whole, and having everything absolutely perfect takes forever. This is useful to remember when writing up a thesis. I think it might apply here too: the Paper Writing Team have done a truly heroic job in getting something this advanced in little over a month. There’s always one more thing to do… [one more bonus note]

#### One more thing

One point I was hoping that the Paper Writing Team would clarify is our choice of prior probability distribution for the black hole spins. We don’t get a lot of information about the spins from the signal, so our choice of prior has an impact on the results.

The paper says that we assume “no restrictions on the spin orientations”, which doesn’t make much sense, as one of the two waveforms we use to analyse the signal only includes spins aligned with the orbital angular momentum! What the paper meant was that we assume a prior distribution which has an isotopic distribution of spins, and for the aligned spin (no precession) waveform, we assume a prior probability distribution on the aligned components of the spins which matches what you would have for an isotropic distribution of spins (in effect, assuming that we can only measure the aligned components of the spins, which is a good approximation).

# Observing run 1—The papers

The second observing run (O2) of the advanced gravitational wave detectors is now over, which has reminded me how dreadfully behind I am in writing about papers. In this post I’ll summarise results from our first observing run (O1), which ran from September 2015 to January 2016.

I’ll add to this post as I get time, and as papers are published. I’ve started off with papers searching for compact binary coalescences (as these are closest to my own research). There are separate posts on our detections GW150914 (and its follow-up papers: set I, set II) and GW151226 (this post includes our end-of-run summary of the search for binary black holes, including details of LVT151012).

### Transient searches

#### The O1 Binary Neutron Star/Neutron Star–Black Hole Paper

Title: Upper limits on the rates of binary neutron star and neutron-star–black-hole mergers from Advanced LIGO’s first observing run
arXiv: 1607.07456 [astro-ph.HE]
Journal: Astrophysical Journal Letters; 832(2):L21(15); 2016

Our main search for compact binary coalescences targets binary black holes (binaries of two black holes), binary neutron stars (two neutron stars) and neutron-star–black-hole binaries (one of each). Having announced the results of our search for binary black holes, this paper gives the detail of the rest. Since we didn’t make any detections, we set some new, stricter upper limits on their merger rates. For binary neutron stars, this is $12,600~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ .

#### The O1 Gamma-Ray Burst Paper

Title: Search for gravitational waves associated with gamma-ray bursts during the first Advanced LIGO observing run and implications for the origin of GRB 150906B
arXiv: 1611.07947 [astro-ph.HE]
Journal: Astrophysical Journal; 841(2):89(18); 2016
LIGO science summary: What’s behind the mysterious gamma-ray bursts? LIGO’s search for clues to their origins

Some binary neutron star or neutron-star–black-hole mergers may be accompanied by a gamma-ray burst. This paper describes our search for signals coinciding with observations of gamma-ray bursts (including GRB 150906B, which was potentially especially close by). Knowing when to look makes it easy to distinguish a signal from noise. We don’t find anything, so we we can exclude any close binary mergers as sources of these gamma-ray bursts.

More details: O1 Gamma-Ray Burst Paper summary

#### The O1 Intermediate Mass Black Hole Binary Paper

Title: Search for intermediate mass black hole binaries in the first observing run of Advanced LIGO
arXiv: 1704.04628 [gr-qc]
Journal: Physical Review D; 96(2):022001(14); 2017
LIGO science summary: Search for mergers of intermediate-mass black holes

Our main search for binary black holes in O1 targeted systems with masses less than about 100 solar masses. There could be more massive black holes out there. Our detectors are sensitive to signals from binaries up to a few hundred solar masses, but these are difficult to detect because they are so short. This paper describes our specially designed such systems. This combines techniques which use waveform templates and those which look for unmodelled transients (bursts). Since we don’t find anything, we set some new upper limits on merger rates.

More details: O1 Intermediate Mass Black Hole Binary Paper summary

#### The O1 Burst Paper

Title: All-sky search for short gravitational-wave bursts in the first Advanced LIGO run
arXiv: 1611.02972 [gr-qc]
Journal: Physical Review D; 95(4):042003(14); 2017

If we only search for signals for which we have models, we’ll never discover something new. Unmodelled (burst) searches are more flexible and don’t assume a particular form for the signal. This paper describes our search for short bursts. We successfully find GW150914, as it is short and loud, and burst searches are good for these type of signals, but don’t find anything else. (It’s not too surprising GW151226 and LVT151012 are below the threshold for detection because they are longer and quieter than GW150914).

More details: O1 Burst Paper summary

### The O1 Binary Neutron Star/Neutron Star–Black Hole Paper

Synopsis: O1 Binary Neutron Star/Neutron Star–Black Hole Paper
Read this if: You want a change from black holes
Favourite part: We’re getting closer to detection (and it’ll still be interesting if we don’t find anything)

The Compact Binary Coalescence (CBC) group target gravitational waves from three different flavours of binary in our main search: binary neutron stars, neutron star–black hole binaries and binary black holes. Before O1, I would have put my money on us detecting a binary neutron star first, around-about O3. Reality had other ideas, and we discovered binary black holes. Those results were reported in the O1 Binary Black Hole Paper; this paper goes into our results for the others (which we didn’t detect).

To search for signals from compact binaries, we use a bank of gravitational wave signals  to match against the data. This bank goes up to total masses of 100 solar masses. We split the bank up, so that objects below 2 solar masses are considered neutron stars. This doesn’t make too much difference to the waveforms we use to search (neutrons stars, being made of stuff, can be tidally deformed by their companion, which adds some extra features to the waveform, but we don’t include these in the search). However, we do limit the spins for neutron stars to less the 0.05, as this encloses the range of spins estimated for neutron star binaries from binary pulsars. This choice shouldn’t impact our ability to detect neutron stars with moderate spins too much.

We didn’t find any interesting events: the results were consistent with there just being background noise. If you read really carefully, you might have deduced this already from the O1 Binary Black Hole Paper, as the results from the different types of binaries are completely decoupled. Since we didn’t find anything, we can set some upper limits on the merger rates for binary neutron stars and neutron star–black hole binaries.

The expected number of events found in the search is given by

$\Lambda = R \langle VT \rangle$

where $R$ is the merger rate, and $\langle VT \rangle$ is the surveyed time–volume (you expect more detections if your detectors are more sensitive, so that they can find signals from further away, or if you leave them on for longer). We can estimate $\langle VT \rangle$ by performing a set of injections and seeing how many are found/missed at a given threshold. Here, we use a false alarm rate of one per century. Given our estimate for $\langle VT \rangle$ and our observation of zero detections we can, calculate a probability distribution for $R$ using Bayes’ theorem. This requires a choice for a prior distribution of $\Lambda$. We use a uniform prior, for consistency with what we’ve done in the past.

With a uniform prior, the $c$ confidence level limit on the rate is

$\displaystyle R_c = \frac{-\ln(1-c)}{\langle VT \rangle}$,

so the 90% confidence upper limit is $R_{90\%} = 2.30/\langle VT \rangle$. This is quite commonly used, for example we make use of it in the O1 Intermediate Mass Black Hole Binary Search. For comparison, if we had used a Jeffrey’s prior of $1/\sqrt{\Lambda}$, the equivalent results is

$\displaystyle R_c = \frac{\left[\mathrm{erf}^{-1}(c)\right]^2}{\langle VT \rangle}$,

and hence $R_{90\%} = 1.35/\langle VT \rangle$, so results would be the same to within a factor of 2, but the results with the uniform prior are more conservative.

The plot below shows upper limits for different neutron star masses, assuming that neutron spins are (uniformly distributed) between 0 and 0.05 and isotropically orientated. From our observations of binary pulsars, we have seen that most of these neutron stars have masses of ~1.35 solar masses, so we can also put a limit of the binary neutron star merger rate assuming that their masses are normally distributed with mean of 1.35 solar masses and standard deviation of 0.13 solar masses. This gives an upper limit of $R_{90\%} = 12,100~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ for isotropic spins up to 0.05, and $R_{90\%} = 12,600~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ if you allow the spins up to 0.4.

90% confidence upper limits on the binary neutron star merger rate. These rates assume randomly orientated spins up to 0.05. Results are calculated using PyCBC, one of our search algorithms; GstLAL gives similar results. Figure 4 of the O1 Binary Neutron Star/Neutron Star–Black Hole Paper.

For neutron star–black hole binaries there’s a greater variation in possible merger rates because the black holes can have a greater of masses and spins. The upper limits range from about $R_{90\%} = 1,200~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ to $3,600~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ for a 1.4 solar mass neutron star and a black hole between 30 and 5 solar masses and a range of different spins (Table II of the paper).

It’s not surprising that we didn’t see anything in O1, but what about in future runs. The plots below compare projections for our future sensitivity with various predictions for the merger rates of binary neutron stars and neutron star–black hole binaries. A few things have changed since we made these projections, for example O2 ended up being 9 months instead of 6 months, but I think we’re still somewhere in the O2 band. We’ll have to see for O3. From these, it’s clear that a detection on O1 was overly optimistic. In O2 and O3 it becomes more plausible. This means even if we don’t see anything, we’ll be still be doing some interesting astrophysics as we can start ruling out some models.

Comparison of upper limits for binary neutron star (BNS; top) and neutron star–black hole binaries (NSBH; bottom) merger rates with theoretical and observational limits. The blue bars show O1 limits, the green and orange bars show projections for future observing runs. Figures 6 and 7 from the O1 Binary Neutron Star/Neutron Star–Black Hole Paper.

Binary neutron star or neutron star–black hole mergers may be the sources of gamma-ray bursts. These are some of the most energetic explosions in the Universe, but we’re not sure where they come from (I actually find that kind of worrying). We look at this connection a bit more in the O1 Gamma-Ray Burst Paper. The theory is that during the merger, neutron star matter gets ripped apart, squeezed and heated, and as part of this we get jets blasted outwards from the swirling material. There are always jets in these type of things. We see the gamma-ray burst if we are looking down the jet: the wider the jet, the larger the fraction of gamma-ray bursts we see. By comparing our estimated merger rates, with the estimated rate of gamma-ray bursts, we can place some lower limits on the opening angle of the jet. If all gamma-ray bursts come from binary neutron stars, the opening angle needs to be bigger than $2.3_{-1.7}^{+1.7}~\mathrm{deg}$ and if they all come from neutron star–black hole mergers the angle needs to be bigger than $4.3_{-1.9}^{+3.1}~\mathrm{deg}$.

### The O1 Gamma-Ray Burst Paper

Synopsis: O1 Gamma-Ray Burst Paper
Read this if: You like explosions. But from a safe distance
Favourite part: We exclude GRB 150906B from being associated with galaxy NGC 3313

Gamma-ray bursts are extremely violent explosions. They come in two (overlapping) classes: short and long. Short gamma-ray bursts are typically shorter than ~2 seconds and have a harder spectrum (more high energy emission). We think that these may come from the coalescence of neutron star binaries. Long gamma-ray bursts are (shockingly) typically longer than ~2 seconds, and have a softer spectrum (less high energy emission). We think that these could originate from the collapse of massive stars (like a supernova explosion). The introduction of the paper contains a neat review of the physics of both these types of sources. Both types of progenitors would emit gravitational waves that could be detected if the source was close enough.

The binary mergers could be picked up by our templated search (as reported in the O1 Binary Neutron Star/Neutron Star–Black Hole Paper): we have a good models for what these signals look like, which allows us to efficiently search for them. We don’t have good models for the collapse of stars, but our unmodelled searches could pick these up. These look for the same signal in multiple detectors, but since they don’t know what they are looking for, it is harder to distinguish a signal from noise than for the templated search. Cross-referencing our usual searches with the times of gamma-ray bursts could help us boost the significance of a trigger: it might not be noteworthy as just a weak gravitational-wave (or gamma-ray) candidate, but considering them together makes it much more unlikely that a coincidence would happen by chance. The on-line RAVEN pipeline monitors for alerts to minimise the chance that miss a coincidence. As well as relying on our standard searches, we also do targeted searches following up on gamma-ray bursts, using the information from these external triggers.

We used two search algorithms:

• X-Pipeline is an unmodelled search (similar to cWB) which looks for a coherent signal, consistent with the sky position of the gamma-ray burst. This was run for all the gamma-ray bursts (long and short) for which we have good data from both LIGO detectors and a good sky location.
• PyGRB is a modelled search which looks for binary signals using templates. Our main binary search algorithms check for coincident signals: a signal matching the same template in both detectors with compatible times. This search looks for coherent signals, factoring the source direction. This gives extra sensitivity (~20%–25% in terms of distance). Since we know what the signal looks like, we can also use this algorithm to look for signals when only one detector is taking data. We used this algorithm on all short (or ambiguously classified) gamma-ray bursts for which we data from at least one detector.

In total we analysed times corresponding to 42 gamma-ray bursts: 41 which occurred during O1 plus GRB 150906B. This happening in the engineering run before the start of O1, and luckily Handord was in a stable observing state at the time. GRB 150906B was localised to come from part of the sky close to the galaxy NGC 3313, which is only 54 megaparsec away. This is within the regime where we could have detected a binary merger. This caused much excitement at the time—people thought that this could be the most interesting result of O1—but this dampened down a week later with the detection of GW150914.

Interplanetary Network (IPN) localization for GRB 150906B and nearby galaxies. Figure 1 from the O1 Gamma-Ray Burst Paper.

We didn’t find any gravitational-wave counterparts. These means that we could place some lower limits on how far away their sources could be. We performed injections of signals—using waveforms from binaries, collapsing stars (approximated with circular sine–Gaussian waveforms), and unstable discs (using an accretion disc instability model)—to see how far away we could have detected a signal, and set 90% probability limits on the distances (see Table 3 of the paper). The best of these are ~100–200 megaparsec (the worst is just 4 megaparsec, which is basically next door). These results aren’t too interesting yet, they will become more so in the future, and around the time we hit design sensitivity we will start overlapping with electromagnetic measurements of distances for short gamma-ray bursts. However, we can rule out GRB 150906B coming from NGC 3133 at high probability!

### The O1 Intermediate Mass Black Hole Binary Paper

Synopsis: O1 Intermediate Mass Black Hole Binary Paper
Read this if: You like intermediate mass black holes (black holes of ~100 solar masses)
Favourite part: The teamwork between different searches

Black holes could come in many sizes. We know of stellar-mass black holes, the collapsed remains of dead stars, which are a few to a few tens of times the mas of our Sun, and we know of (super)massive black holes, lurking in the centres of galaxies, which are tens of thousands to billions of times the mass of our Sun. Between the two, lie the elusive intermediate mass black holes. There have been repeated claims of observational evidence for their existence, but these are notoriously difficult to confirm. Gravitational waves provide a means of confirming the reality of intermediate mass black holes, if they do exist.

The gravitational wave signal emitted by a binary depends upon the mass of its components. More massive objects produce louder signals, but these signals also end at lower frequencies. The merger frequency of a binary is inversely proportional to the total mass. Ground-based detectors can’t detect massive black hole binaries as they are too low frequency, but they can detect binaries of a few hundred solar masses. We look for these in this search.

Our flagship search for binary black holes looks for signals using matched filtering: we compare the data to a bank of template waveforms. The bank extends up to a total mass of 100 solar masses. This search continues above this (there’s actually some overlap as we didn’t want to miss anything, but we shouldn’t have worried). Higher mass binaries are hard to detect as they as shorter, and so more difficult to distinguish from a little blip of noise, which is why this search was treated differently.

As well as using templates, we can do an unmodelled (burst) search for signals by looking for coherent signals in both detectors. This type of search isn’t as sensitive, as you don’t know what you are looking for, but can pick up short signals (like GW150914).

Our search for intermediate mass black holes uses both a modelled search (with templates spanning total masses of 50 to 600 solar masses) and a specially tuned burst search. Both make sure to include low frequency data in their analysis. This work is one of the few cross-working group (CBC for the templated search, and Burst for the unmodelled) projects, and I was pleased with the results.

This is probably where you expect me to say that we didn’t detect anything so we set upper limits. That is actually not the case here: we did detect something! Unfortunately, it wasn’t what we were looking for. We detected GW150914, which was a relief as it did lie within the range we where searching, as well as LVT151012 and GW151226. These were more of a surprise. GW151226 has a total mass of just ~24 solar masses (as measured with cosmological redshift), and so is well outside our bank. It was actually picked up just on the edge, but still, it’s impressive that the searches can find things beyond what they are aiming to pick up. Having found no intermediate mass black holes, we went and set some upper limits. (Yay!)

To set our upper limits, we injected some signals from binaries with specific masses and spins, and then saw how many would have be found with greater significance than our most significant trigger (after excluding GW150914, LVT151012 and GW151226). This is effectively asking the question of when would we see something as significant as this trigger which we think is just noise. This gives us a sensitive time–volume $\langle VT \rangle$ which we have surveyed and found no mergers. We use this number of events to set 90% upper limits on the merge rates $R_{90\%} = 2.3/\langle VT \rangle$, and define an effective distance $D_{\langle VT \rangle}$ defined so that $\langle VT \rangle = T_a (4\pi D_{\langle VT \rangle}^3/3)$ where $T_a$ is the analysed amount of time. The plot below show our limits on rate and effective distance for our different injections.

Results from the O1 search for intermediate mass black hole binaries. The left panel shows the 90% confidence upper limit on the merger rate. The right panel shows the effective search distance. Each circle is a different injection. All have zero spin, except two 100+100 solar mass sets, where $\chi$ indicates the spin aligned with the orbital angular momentum. Figure 2 of the O1 Intermediate Mass Black Hole Binary Paper.

There are a couple of caveats associated with our limits. The waveforms we use don’t include all the relevant physics (like orbital eccentricity and spin precession). Including everything is hard: we may use some numerical relativity waveforms in the future. However, they should give a good impression on our sensitivity. There’s quite a big improvement compared to previous searches (S6 Burst Search; S6 Templated Search). This comes form the improvement of Advanced LIGO’s sensitivity at low frequencies compared to initial LIGO. Future improvements to the low frequency sensitivity should increase our probability of making a detection.

I spent a lot of time working on this search as I was the review chair. As a reviewer, I had to make sure everything was done properly, and then reported accurately. I think our review team did a thorough job. I was glad when we were done, as I dislike being the bad cop.

### The O1 Burst Paper

Synopsis: O1 Burst Paper
Read this if: You like to keep an open mind about what sources could be out there
Favourite part: GW150914 (of course)

The best way to find a signal is to know what you are looking for. This makes it much easier to distinguish a signal from random noise. However, what about the sources for which we don’t have good models? Burst searches aim to find signals regardless of their shape. To do this, they look for coherent signals in multiple detectors. Their flexibility means that they are less sensitive than searches targeting a specific signal—the signal needs to be louder before we can be confident in distinguishing it from noise—but they could potentially detect a wider number of sources, and crucially catch signals missed by other searches.

This paper presents our main results looking for short burst signals (up to a few seconds in length). Complementary burst searches were done as part of the search for intermediate mass black hole binaries (whose signals can be so short that it doesn’t matter too much if you have  a model or not) and for counterparts to gamma-ray bursts.

There are two-and-a-half burst search pipelines. There is coherent WaveBurst (cWB), Omicron–LALInferenceBurst (oLIB), and BayesWave follow-up to cWB. More details of each are found in the GW150914 Burst Companion Paper.

cWB looks for coherent power in the detectors—it looks for clusters of excess power in time and frequency. The search in O1 was split into a low-frequency component (signals below 1024 Hz) and a high-frequency component (1024 Hz). The low-frequency search was further divided into three classes:

• C1 for signals which have a small range of frequencies (80% of the power in just a 5 Hz range). This is designed to catch blip glitches, short bursts of transient noise in our detectors. We’re not sure what causes blip glitches yet, but we know they are not real signals as they are seen independently in both detectors.
• C3 looks for signals which increase in frequency with time—chirps. I suspect that this was (cheekily) designed to find binary black hole coalescences.
• C2 (no, I don’t understand the ordering either) is everything else.

The false alarm rate is calculated independently for each division using time-slides. We analyse data from the two detectors which has been shifted in time, so that there can be no real coincident signals between the two, and compare this background of noise-only triggers to the no-slid data.

oLIB works in two stages. First (the Omicron bit), data from the individual detectors are searches for excess power. If there is anything interesting, the data from both detectors are analysed coherently. We use a sine–Gaussian template, and compare the probability that the same signal is in both detectors, to there being independent noise (potentially a glitch) in the two. This analysis is split too: there is a high-quality factor vs  low quality-factor split, which is similar to cWB’s splitting off C1 to catch narrow band features (the low quality-factor group catches the blip glitches). The false alarm rate is computed with time slides.

BayesWave is run as follow-up to triggers produced by cWB: it is too computationally expensive to run on all the data. BayesWave’s approach is similar to oLIB’s. It compares three hypotheses: just Gaussian noise, Gaussian noise and a glitch, and Gaussian noise and a signal. It constructs its signal using a variable number of sine–Gaussian wavelets. There are no cuts on its data. Again, time slides are used to estimate the false alarm rate.

The search does find a signal: GW150914. It is clearly found by all three algorithms. It is cWB’s C3, with a false alarm rate of less than 1 per 350 years; it is is oLIB’s high quality-factor bin with a false alarm rate of less than 1 per 230 years, and is found by BayesWave with a false alarm rate of less than 1 per 1000 years. You might notice that these results are less stringent than in the initial search results presented at the time of the detection. This is because only a limited number of time slides were done: we could get higher significance if we did more, but it was decided that it wasn’t worth the extra computing time, as we’re already convinced that GW150914 is a real signal. I’m a little sad they took GW150914 out of their plots (I guess it distorted the scale since it’s such an outlier from the background). Aside from GW150914, there are no detections.

Given the lack of detections, we can set some upper limits. I’ll skip over the limits for binary black holes, since our templated search is more sensitive here. The plot below shows limits on the amount of gravitational-wave energy emitted by a burst source at 10 kpc, which could be detected with a false alarm rate of 1 per century 50% of the time. We use some simple waveforms for this calculation. The energy scales with the inverse distance squared, so at a distance of 20 kpc, you need to increase the energy by a factor of 4.

Gravitational-wave energy at 50% detection efficiency for standard sources at a distance of 10 kpc. Results are shown for the three different algorithms. Figure 2 of the O1 Burst Paper.

Maybe next time we’ll find something unexpected, but it will either need to be really energetic (like a binary black hole merger) or really close by (like a supernova in our own Galaxy)

# GW170104 and me

On 4 January 2017, Advanced LIGO made a new detection of gravitational waves. The signal, which we call GW170104 [bonus note], came from the coalescence of two black holes, which inspiralled together (making that characteristic chirp) and then merged to form a single black hole.

On 4 January 2017, I was just getting up off the sofa when my phone buzzed. My new year’s resolution was to go for a walk every day, and I wanted to make use of the little available sunlight. However, my phone informed me that PyCBC (one or our search algorithms for signals from coalescing binaries) had identified an interesting event. I sat back down. I was on the rota to analyse interesting signals to infer their properties, and I was pretty sure that people would be eager to see results. They were. I didn’t leave the sofa for the rest of the day, bringing my new year’s resolution to a premature end.

Since 4 January, my time has been dominated by working on GW170104 (you might have noticed a lack of blog posts). Below I’ll share some of my war stories from life on the front line of gravitational-wave astronomy, and then go through some of the science we’ve learnt. (Feel free to skip straight to the science, recounting the story was more therapy for me).

Time–frequency plots for GW170104 as measured by Hanford (top) and Livingston (bottom). The signal is clearly visible as the upward sweeping chirp. The loudest frequency is something between E3 and G♯3 on a piano, and it tails off somewhere between D♯4/E♭4 and F♯4/G♭4. Part of Fig. 1 of the GW170104 Discovery Paper.

### The story

In the second observing run, the Parameter Estimation group have divided up responsibility for analysing signals into two week shifts. For each rota shift, there is an expert and a rookie. I had assumed that the first slot of 2017 would be a quiet time. The detectors were offline over the holidays, due back online on 4 January, but the instrumentalists would probably find some extra tinkering they’d want to do, so it’d probably slip a day, and then the weather would be bad, so we’d probably not collect much data anyway… I was wrong. Very wrong. The detectors came back online on time, and there was a beautifully clean detection on day one.

My partner for the rota was Aaron Zimmerman. 4 January was his first day running parameter estimation on live signals. I think I would’ve run and hidden underneath my duvet in his case (I almost did anyway, and I lived through the madness of our first detection GW150914), but he rose to the occasion. We had first results after just a few hours, and managed to send out a preliminary sky localization to our astronomer partners on 6 January. I think this was especially impressive as there were some difficulties with the initial calibration of the data. This isn’t a problem for the detection pipelines, but does impact the parameters which we infer, particularly the sky location. The Calibration group worked quickly, and produced two updates to the calibration. We therefore had three different sets of results (one per calibration) by 6 January [bonus note]!

Producing the final results for the paper was slightly more relaxed. Aaron and I conscripted volunteers to help run all the various permutations of the analysis we wanted to double-check our results [bonus note].

Recovered gravitational waveforms from analysis of GW170104. The broader orange band shows our estimate for the waveform without assuming a particular source (wavelet). The narrow blue bands show results if we assume it is a binary black hole (BBH) as predicted by general relativity. The two match nicely, showing no evidence for any extra features not included in the binary black hole models. Figure 4 of the GW170104 Discovery Paper.

I started working on GW170104 through my parameter estimation duties, and continued with paper writing.

Ahead of the second observing run, we decided to assemble a team to rapidly write up any interesting binary detections, and I was recruited for this (I think partially because I’m not too bad at writing and partially because I was in the office next to John Veitch, one of the chairs of the Compact Binary Coalescence group,so he can come and check that I wasn’t just goofing off eating doughnuts). We soon decided that we should write a paper about GW170104, and you can decide whether or not we succeeded in doing this rapidly…

Being on the paper writing team has given me huge respect for the teams who led the GW150914 and GW151226 papers. It is undoubtedly one of the most difficult things I’ve ever done. It is extremely hard to absorb negative remarks about your work continuously for months [bonus note]—of course people don’t normally send comments about things that they like, but that doesn’t cheer you up when you’re staring at an inbox full of problems that need fixing. Getting a collaboration of 1000 people to agree on a paper is like herding cats while being a small duckling.

On of the first challenges for the paper writing team was deciding what was interesting about GW170104. It was another binary black hole coalescence—aren’t people getting bored of them by now? The signal was quieter than GW150914, so it wasn’t as remarkable. However, its properties were broadly similar. It was suggested that perhaps we should title the paper “GW170104: The most boring gravitational-wave detection”.

One potentially interesting aspect was that GW170104 probably comes from greater distance than GW150914 or GW151226 (but perhaps not LVT151012) [bonus note]. This might make it a good candidate for testing for dispersion of gravitational waves.

Dispersion occurs when different frequencies of gravitational waves travel at different speeds. A similar thing happens for light when travelling through some materials, which leads to prisms splitting light into a spectrum (and hence the creation of Pink Floyd album covers). Gravitational waves don’t suffered dispersion in general relativity, but do in some modified theories of gravity.

It should be easier to spot dispersion in signals which have travelled a greater distance, as the different frequencies have had more time to separate out. Hence, GW170104 looks pretty exciting. However, being further away also makes the signal quieter, and so there is more uncertainty in measurements and it is more difficult to tell if there is any dispersion. Dispersion is also easier to spot if you have a larger spread of frequencies, as then there can be more spreading between the highest and lowest frequencies. When you throw distance, loudness and frequency range into the mix, GW170104 doesn’t always come out on top, depending upon the particular model for dispersion: sometimes GW150914’s loudness wins, other times GW151226’s broader frequency range wins. GW170104 isn’t too special here either.

Even though GW170104 didn’t look too exciting, we started work on a paper, thinking that we would just have a short letter describing our observations. The Compact Binary Coalescence group decided that we only wanted a single paper, and we wouldn’t bother with companion papers as we did for GW150914. As we started work, and dug further into our results, we realised that actually there was rather a lot that we could say.

I guess the moral of the story is that even though you might be overshadowed by the achievements of your siblings, it doesn’t mean that you’re not awesome. There might not be one outstanding feature of GW170104, but there are lots of little things that make it interesting. We are still at the beginning of understanding the properties of binary black holes, and each new detection adds a little more to our picture.

I think GW170104 is rather neat, and I hope you do too.

As we delved into the details of our results, we realised there was actually a lot of things that we could say about GW170104, especially when considered with our previous observations. We ended up having to move some of the technical details and results to Supplemental Material. With hindsight, perhaps it would have been better to have a companion paper or two. However, I rather like how packed with science this paper is.

The paper, which Physical Review Letters have kindly accommodated, despite its length, might not be as polished a classic as the GW150914 Discovery Paper, but I think they are trying to do different things. I rarely ever refer to the GW150914 Discovery Paper for results (more commonly I use it for references), whereas I think I’ll open up the GW170104 Discovery Paper frequently to look up numbers.

Although perhaps not right away, I’d quite like some time off first. The weather’s much better now, perfect for walking…

Success! The view across Lac d’Annecy. Taken on a stroll after the Gravitational Wave Physics and Astronomy Workshop, the weekend following the publication of the paper.

### The science

Advanced LIGO’s first observing run was hugely successful. Running from 12 September 2015 until 19 January 2016, there were two clear gravitational-wave detections, GW1501914 and GW151226, as well as a less certain candidate signal LVT151012. All three (assuming that they are astrophysical signals) correspond to the coalescence of binary black holes.

The second observing run started 30 November 2016. Following the first observing run’s detections, we expected more binary black hole detections. On 4 January, after we had collected almost 6 days’ worth of coincident data from the two LIGO instruments [bonus note], there was a detection.

#### The searches

The signal was first spotted by an online analysis. Our offline analysis of the data (using refined calibration and extra information about data quality) showed that the signal, GW170104, is highly significant. For both GstLAL and PyCBC, search algorithms which use templates to search for binary signals, the false alarm rate is estimated to be about 1 per 70,000 years.

The signal is also found in unmodelled (burst) searches, which look for generic, short gravitational wave signals. Since these are looking for more general signals than just binary coalescences, the significance associated with GW170104 isn’t as great, and coherent WaveBurst estimates a false alarm rate of 1 per 20,000 years. This is still pretty good! Reconstructions of the waveform from unmodelled analyses also match the form expected for binary black hole signals.

The search false alarm rates are the rate at which you’d expect something this signal-like (or more signal-like) due to random chance, if you data only contained noise and no signals. Using our knowledge of the search pipelines, and folding in some assumptions about the properties of binary black holes, we can calculate a probability that GW170104 is a real astrophysical signal. This comes out to be greater than $1 - (3\times10^5) = 0.99997$.

#### The source

As for the previous gravitational wave detections, GW170104 comes from a binary black hole coalescence. The initial black holes were $31.2^{+8.4}_{-6.0} M_\odot$ and $19.4^{+5.3}_{-5.9} M_\odot$ (where $1 M_\odot$ is the mass of our Sun), and the final black hole was $48.7^{+5.7}_{-4.6} M_\odot$. The quoted values are the median values and the error bars denote the central 90% probable range. The plot below shows the probability distribution for the masses; GW170104 neatly nestles in amongst the other events.

Estimated masses for the two black holes in the binary $m_1 \geq m_2$. The two-dimensional shows the probability distribution for GW170104 as well as 50% and 90% contours for all events. The one-dimensional plot shows results using different waveform models. The dotted lines mark the edge of our 90% probability intervals. Figure 2 of the GW170104 Discovery Paper.

GW150914 was the first time that we had observed stellar-mass black holes with masses greater than around $25 M_\odot$. GW170104 has similar masses, showing that our first detection was not a fluke, but there really is a population of black holes with masses stretching up into this range.

Black holes have two important properties: mass and spin. We have good measurements on the masses of the two initial black holes, but not the spins. The sensitivity of the form of the gravitational wave to spins can be described by two effective spin parameters, which are mass-weighted combinations of the individual spins.

• The effective inspiral spin parameter $\chi_\mathrm{eff}$ qualifies the impact of the spins on the rate of inspiral, and where the binary plunges together to merge. It ranges from +1, meaning both black holes are spinning as fast as possible and rotate in the same direction as the orbital motion, to −1, both black holes spinning as fast as possible but in the opposite direction to the way that the binary is orbiting. A value of 0 for $\chi_\mathrm{eff}$ could mean that the black holes are not spinning, that their rotation axes are in the orbital plane (instead of aligned with the orbital angular momentum), or that one black hole is aligned with the orbital motion and the other is antialigned, so that their effects cancel out.
• The effective precession spin parameter $\chi_\mathrm{p}$ qualifies the amount of precession, the way that the orbital plane and black hole spins wobble when they are not aligned. It is 0 for no precession, and 1 for maximal precession.

We can place some constraints on $\chi_\mathrm{eff}$, but can say nothing about $\chi_\mathrm{p}$. The inferred value of the effective inspiral spin parameter is $-0.12^{+0.21}_{-0.30}$. Therefore, we disfavour large spins aligned with the orbital angular momentum, but are consistent with small aligned spins, misaligned spins, or spins antialigned with the angular momentum. The value is similar to that for GW150914, which also had a near-zero, but slightly negative $\chi_\mathrm{eff}$ of $-0.06^{+0.14}_{-0.14}$.

Estimated effective inspiral spin parameter $\chi_\mathrm{eff}$ and effective precession spin $\chi_\mathrm{p}$ parameter. The two-dimensional shows the probability distribution for GW170104 as well as 50% and 90% contours. The one-dimensional plot shows results using different waveform models, as well as the prior probability distribution. The dotted lines mark the edge of our 90% probability intervals. We learn basically nothing about precession. Part of Figure 3 of the GW170104 Discovery Paper.

Converting the information about $\chi_\mathrm{eff}$, the lack of information about $\chi_\mathrm{p}$, and our measurement of the ratio of the two black hole masses, into probability distributions for the component spins gives the plots below [bonus note]. We disfavour (but don’t exclude) spins aligned with the orbital angular momentum, but can’t say much else.

Estimated orientation and magnitude of the two component spins. The distribution for the more massive black hole is on the left, and for the smaller black hole on the right. The probability is binned into areas which have uniform prior probabilities, so if we had learnt nothing, the plot would be uniform. Part of Figure 3 of the GW170104 Discovery Paper.

One of the comments we had on a draft of the paper was that we weren’t making any definite statements about the spins—we would have if we could, but we can’t for GW170104, at least for the spins of the two inspiralling black holes. We can be more definite about the spin of the final black hole. If two similar mass black holes spiral together, the angular momentum from the orbit is enough to give a spin of around $0.7$. The spins of the component black holes are less significant, and can make it a bit higher of lower. We infer a final spin of $0.64^{+0.09}_{-0.20}$; there is a tail of lower spin values on account of the possibility that the two component black holes could be roughly antialigned with the orbital angular momentum.

Estimated mass $M_\mathrm{f}$ and spin$a_\mathrm{f}$ for the final black hole. The two-dimensional shows the probability distribution for GW170104 as well as 50% and 90% contours. The one-dimensional plot shows results using different waveform models. The dotted lines mark the edge of our 90% probability intervals. Figure 6 of the GW170104 Supplemental Material (Figure 11 of the arXiv version).

If you’re interested in parameter describing GW170104, make sure to check out the big table in the Supplemental Material. I am a fan of tables [bonus note].

#### Merger rates

Adding the first 11 days of coincident data from the second observing run (including the detection of GW170104) to the results from the first observing run, we find merger rates consistent with those from the first observing run.

To calculate the merger rates, we need to assume a distribution of black hole masses, and we use two simple models. One uses a power law distribution for the primary (larger) black hole and a uniform distribution for the mass ratio; the other uses a distribution uniform in the logarithm of the masses (both primary and secondary). The true distribution should lie somewhere between the two. The power law rate density has been updated from $31^{+42}_{-21}~\mathrm{Gpc^{-3}\,yr^{-1}}$ to $32^{+33}_{-20}~\mathrm{Gpc^{-3}\,yr^{-1}}$, and the uniform in log rate density goes from $97^{+135}_{-67}~\mathrm{Gpc^{-3}\,yr^{-1}}$ to $103^{+110}_{-63}~\mathrm{Gpc^{-3}\,yr^{-1}}$. The median values stay about the same, but the additional data have shrunk the uncertainties a little.

#### Astrophysics

The discoveries from the first observing run showed that binary black holes exist and merge. The question is now how exactly they form? There are several suggested channels, and it could be there is actually a mixture of different formation mechanisms in action. It will probably require a large number of detections before we can make confident statements about the the probable formation mechanisms; GW170104 is another step towards that goal.

There are two main predicted channels of binary formation:

• Isolated binary evolution, where a binary star system lives its life together with both stars collapsing to black holes at the end. To get the black holes close enough to merge, it is usually assumed that the stars go through a common envelope phase, where one star puffs up so that the gravity of its companion can steal enough material that they lie in a shared envelope. The drag from orbiting inside this then shrinks the orbit.
• Dynamical evolution where black holes form in dense clusters and a binary is created by dynamical interactions between black holes (or stars) which get close enough to each other.

It’s a little artificial to separate the two, as there’s not really such a thing as an isolated binary: most stars form in clusters, even if they’re not particularly large. There are a variety of different modifications to the two main channels, such as having a third companion which drives the inner binary to merge, embedding the binary is a dense disc (as found in galactic centres), or dynamically assembling primordial black holes (formed by density perturbations in the early universe) instead of black holes formed through stellar collapse.

All the channels can predict black holes around the masses of GW170104 (which is not surprising given that they are similar to the masses of GW150914).

The updated rates are broadly consistent with most channels too. The tightening of the uncertainty of the rates means that the lower bound is now a little higher. This means some of the channels are now in tension with the inferred rates. Some of the more exotic channels—requiring a third companion (Silsbee & Tremain 2017; Antonini, Toonen & Hamers 2017) or embedded in a dense disc (Bartos et al. 2016; Stone, Metzger & Haiman 2016; Antonini & Rasio 2016)—can’t explain the full rate, but I don’t think it was ever expected that they could, they are bonus formation mechanisms. However, some of the dynamical models are also now looking like they could predict a rate that is a bit low (Rodriguez et al. 2016; Mapelli 2016; Askar et al. 2017; Park et al. 2017). Assuming that this result holds, I think this may mean that some of the model parameters need tweaking (there are more optimistic predictions for the merger rates from clusters which are still perfectly consistent), that this channel doesn’t contribute all the merging binaries, or both.

The spins might help us understand formation mechanisms. Traditionally, it has been assumed that isolated binary evolution gives spins aligned with the orbital angular momentum. The progenitor stars were probably more or less aligned with the orbital angular momentum, and tides, mass transfer and drag from the common envelope would serve to realign spins if they became misaligned. Rodriguez et al. (2016) gives a great discussion of this. Dynamically formed binaries have no correlation between spin directions, and so we would expect an isotropic distribution of spins. Hence it sounds quite simple: misaligned spins indicates dynamical formation (although we can’t tell if the black holes are primordial or stellar), and aligned spins indicates isolated binary evolution. The difficulty is the traditional assumption for isolated binary evolution potentially ignores a number of effects which could be important. When a star collapses down to a black hole, there may be a supernova explosion. There is an explosion of matter and neutrinos and these can give the black hole a kick. The kick could change the orbital plane, and so misalign the spin. Even if the kick is not that big, if it is off-centre, it could torque the black hole, causing it to rotate and so misalign the spin that way. There is some evidence that this can happen with neutron stars, as one of the pulsars in the double pulsar system shows signs of this. There could also be some instability that changes the angular momentum during the collapse of the star, possibly with different layers rotating in different ways [bonus note]. The spin of the black hole would then depend on how many layers get swallowed. This is an area of research that needs to be investigated further, and I hope the prospect of gravitational wave measurements spurs this on.

For GW170104, we know the spins are not large and aligned with the orbital angular momentum. This might argue against one variation of isolated binary evolution, chemically homogeneous evolution, where the progenitor stars are tidally locked (and so rotate aligned with the orbital angular momentum and each other). Since the stars are rapidly spinning and aligned, you would expect the final black holes to be too, if the stars completely collapse down as is usually assumed. If the stars don’t completely collapse down though, it might still be possible that GW170104 fits with this model. Aside from this, GW170104 is consistent with all the other channels.

Estimated effective inspiral spin parameter $\chi_\mathrm{eff}$ for all events. To indicate how much (or little) we’ve learnt, the prior probability distribution for GW170104 is shown (the other priors are similar).All of the events have $|\chi_\mathrm{eff}| < 0.35$ at 90% probability. Figure 5 of the GW170104 Supplemental Material (Figure 10 of the arXiv version). This is one of my favourite plots [bonus note].

If we start looking at the population of events, we do start to notice something about the spins. All of the inferred values of $\chi_\mathrm{eff}$ are close to zero. Only GW151226 is inconsistent with zero. These values could be explained if spins are typically misaligned (with the orbital angular momentum or each other) or if the spins are typically small (or both). We know that black holes spins can be large from observations of X-ray binaries, so it would be odd if they are small for binary black holes. Therefore, we have a tentative hint that spins are misaligned. We can’t say why the spins are misaligned, but it is intriguing. With more observations, we’ll be able to confirm if it is the case that spins are typically misaligned, and be able to start pinning down the distribution of spin magnitudes and orientations (as well as the mass distribution). It will probably take a while to be able to say anything definite though, as we’ll probably need about 100 detections.

#### Tests of general relativity

As well as giving us an insight into the properties of black holes, gravitational waves are the perfect tools for testing general relativity. If there are any corrections to general relativity, you’d expect them to be most noticeable under the most extreme conditions, where gravity is strong and spacetime is rapidly changing, exactly as in a binary black hole coalescence.

For GW170104 we repeated tests previously performed. Again, we found no evidence of deviations.

We added extra terms to to the waveform and constrained their potential magnitudes. The results are pretty much identical to at the end of the first observing run (consistent with zero and hence general relativity). GW170104 doesn’t add much extra information, as GW150914 typically gives the best constraints on terms that modify the post-inspiral part of the waveform (as it is louder), while GW151226 gives the best constraint on the terms which modify the inspiral (as it has the longest inspiral).

We also chopped the waveform at a frequency around that of the innermost stable orbit of the remnant black hole, which is about where the transition from inspiral to merger and ringdown occurs, to check if the low frequency and high frequency portions of the waveform give consistent estimates for the final mass and spin. They do.

We have also done something slightly new, and tested for dispersion of gravitational waves. We did something similar for GW150914 by putting a limit on the mass of the graviton. Giving the graviton mass is one way of adding dispersion, but we consider other possible forms too. In all cases, results are consistent with there being no dispersion. While we haven’t discovered anything new, we can update our gravitational wave constraint on the graviton mass of less than $7.7 \times 10^{-23}~\mathrm{eV}/c^2$.

#### The search for counterparts

We don’t discuss observations made by our astronomer partners in the paper (they are not our results). A number (28 at the time of submission) of observations were made, and I expect that there will be a series of papers detailing these coming soon. So far papers have appeared from:

• AGILE—hard X-ray and gamma-ray follow-up. They didn’t find any gamma-ray signals, but did identify a weak potential X-ray signal occurring about 0.46 s before GW170104. It’s a little odd to have a signal this long before the merger. The team calculate a probability for such a coincident to happen by chance, and find quite a small probability, so it might be interesting to follow this up more (see the INTEGRAL results below), but it’s probably just a coincidence (especially considering how many people did follow-up the event).
• ANTARES—a search for high-energy muon neutrinos. No counterparts are identified in a ±500 s window around GW170104, or over a ±3 month period.
• AstroSat-CZTI and GROWTH—a collaboration of observations across a range of wavelengths. They don’t find any hard X-ray counterparts. They do follow up on a bright optical transient ATLASaeu, suggested as a counterpart to GW170104, and conclude that this is a likely counterpart of long, soft gamma-ray burst GRB 170105A.
• ATLAS and Pan-STARRS—optical follow-up. They identified a bright optical transient 23 hours after GW170104, ATLAS17aeu. This could be a counterpart to GRB 170105A. It seems unlikely that there is any mechanism that could allow for a day’s delay between the gravitational wave emission and an electromagnetic signal. However, the team calculate a small probability (few percent) of finding such a coincidence in sky position and time, so perhaps it is worth pondering. I wouldn’t put any money on it without a distance estimate for the source: assuming it’s a normal afterglow to a gamma-ray burst, you’d expect it to be further away than GW170104’s source.
• Borexino—a search for low-energy neutrinos. This paper also discusses GW150914 and GW151226. In all cases, the observed rate of neutrinos is consistent with the expected background.
• CALET—a gamma-ray search. This paper includes upper limits for GW151226, GW170104, GW170608, GW170814 and GW170817.
• DLT40—an optical search designed for supernovae. This paper covers the whole of O2 including GW170608, GW170814, GW170817 plus GW170809 and GW170823.
• Fermi (GBM and LAT)—gamma-ray follow-up. They covered an impressive fraction of the sky localization, but didn’t find anything.
• INTEGRAL—gamma-ray and hard X-ray observations. No significant emission is found, which makes the event reported by AGILE unlikely to be a counterpart to GW170104, although they cannot completely rule it out.
• The intermediate Palomar Transient Factory—an optical survey. While searching, they discovered iPTF17cw, a broad-line type Ic supernova which is unrelated to GW170104 but interesting as it an unusual find.
• Mini-GWAC—a optical survey (the precursor to GWAC). This paper covers the whole of their O2 follow-up including GW170608.
• NOvA—a search for neutrinos and cosmic rays over a wide range of energies. This paper covers all the events from O1 and O2, plus triggers from O3.
• The Owens Valley Radio Observatory Long Wavelength Array—a search for prompt radio emission.
• TOROS—optical follow-up. They identified no counterparts to GW170104 (although they did for GW170817).

If you are interested in what has been reported so far (no compelling counterpart candidates yet to my knowledge), there is an archive of GCN Circulars sent about GW170104.

### Summary

Advanced LIGO has made its first detection of the second observing run. This is a further binary black hole coalescence. GW170104 has taught us that:

• The discoveries of the first observing run were not a fluke. There really is a population of stellar mass black holes with masses above $25 M_\odot$ out there, and we can study them with gravitational waves.
• Binary black hole spins may be typically misaligned or small. This is not certain yet, but it is certainly worth investigating potential mechanisms that could cause misalignment.
• General relativity still works, even after considering our new tests.
• If someone asks you to write a discovery paper, run. Run and do not look back.

Title: GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2
Journal:
Physical Review Letters; 118(22):221101(17); 2017 (Supplemental Material)
arXiv: 1706.01812 [gr-qc]
Data release: GRavitational Wave Open Science Center
Science summary:
GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2

If you’re looking for the most up-to-date results regarding GW170104, check out the O2 Catalogue Paper.

### Bonus notes

#### Naming

Gravitational wave signals (at least the short ones, which are all that we have so far), are named by their detection date. GW170104 was discovered 2017 January 4. This isn’t too catchy, but is at least better than the ID number in our database of triggers (G268556) which is used in corresponding with our astronomer partners before we work out if the “GW” title is justified.

Previous detections have attracted nicknames, but none has stuck for GW170104. Archisman Ghosh suggested the Perihelion Event, as it was detected a few hours before the Earth reached its annual point closest to the Sun. I like this name, its rather poetic.

More recently, Alex Nitz realised that we should have called GW170104 the Enterprise-D Event, as the USS Enterprise’s registry number was NCC-1701. For those who like Star Trek: the Next Generation, I hope you have fun discussing whether GW170104 is the third or fourth (counting LVT151012) detection: “There are four detections!

#### The 6 January sky map

I would like to thank the wi-fi of Chiltern Railways for their role in producing the preliminary sky map. I had arranged to visit London for the weekend (because my rota slot was likely to be quiet… ), and was frantically working on the way down to check results so they could be sent out. I’d also like to thank John Veitch for putting together the final map while I was stuck on the Underground.

#### Binary black hole waveforms

The parameter estimation analysis works by matching a template waveform to the data to see how well it matches. The results are therefore sensitive to your waveform model, and whether they include all the relevant bits of physics.

In the first observing run, we always used two different families of waveforms, to see what impact potential errors in the waveforms could have. The results we presented in discovery papers used two quick-to-calculate waveforms. These include the effects of the black holes’ spins in different ways

• SEOBNRv2 has spins either aligned or antialigned with the orbital angular momentum. Therefore, there is no precession (wobbling of orientation, like that of a spinning top) of the system.
• IMRPhenomPv2 includes an approximate description of precession, packaging up the most important information about precession into a single parameter $\chi_\mathrm{p}$.

For GW150914, we also performed a follow-up analysis using a much more expensive waveform SEOBNRv3 which more fully includes the effect of both spins on precession. These results weren’t ready at the time of the announcement, because the waveform is laborious to run.

For GW170104, there were discussions that using a spin-aligned waveform was old hat, and that we should really only use the two precessing models. Hence, we started on the endeavour of producing SEOBNRv3 results. Fortunately, the code has been sped up a little, although it is still not quick to run. I am extremely grateful to Scott Coughlin (one of the folks behind Gravity Spy), Andrea Taracchini and Stas Babak for taking charge of producing results in time for the paper, in what was a Herculean effort.

I spent a few sleepless nights, trying to calculate if the analysis was converging quickly enough to make our target submission deadline, but it did work out in the end. Still, don’t necessarily expect we’ll do this for a all future detections.

Since the waveforms have rather scary technical names, in the paper we refer to IMRPhenomPv2 as the effective precession model and SEOBNRv3 as the full precession model.

#### On distance

Distance measurements for gravitational wave sources have significant uncertainties. The distance is difficult to measure as it determined from the signal amplitude, but this is also influences by the binary’s inclination. A signal could either be close and edge on or far and face on-face off.

Estimated luminosity distance $D_\mathrm{L}$ and binary inclination angle $\theta_{JN}$. The two-dimensional shows the probability distribution for GW170104 as well as 50% and 90% contours. The one-dimensional plot shows results using different waveform models. The dotted lines mark the edge of our 90% probability intervals. Figure 4 of the GW170104 Supplemental Material (Figure 9 of the arXiv version).

The uncertainty on the distance rather awkwardly means that we can’t definitely say that GW170104 came from a further source than GW150914 or GW151226, but it’s a reasonable bet. The 90% credible intervals on the distances are 250–570 Mpc for GW150194, 250–660 Mpc for GW151226, 490–1330 Mpc for GW170104 and 500–1500 Mpc for LVT151012.

Translating from a luminosity distance to a travel time (gravitational waves do travel at the speed of light, our tests of dispersion are consistent wit that!), the GW170104 black holes merged somewhere between 1.3 and 3.0 billion years ago. This is around the time that multicellular life first evolved on Earth, and means that black holes have been colliding longer than life on Earth has been reproducing sexually.

#### Time line

A first draft of the paper (version 2; version 1 was a copy-and-paste of the Boxing Day Discovery Paper) was circulated to the Compact Binary Coalescence and Burst groups for comments on 4 March. This was still a rough version, and we wanted to check that we had a good outline of the paper. The main feedback was that we should include more about the astrophysical side of things. I think the final paper has a better balance, possibly erring on the side of going into too much detail on some of the more subtle points (but I think that’s better than glossing over them).

A first proper draft (version 3) was released to the entire Collaboration on 12 March in the middle of our Collaboration meeting in Pasadena. We gave an oral presentation the next day (I doubt many people had read the paper by then). Collaboration papers are usually allowed two weeks for people to comment, and we followed the same procedure here. That was not a fun time, as there was a constant trickle of comments. I remember waking up each morning and trying to guess how many emails would be in my inbox–I normally low-balled this.

I wasn’t too happy with version 3, it was still rather rough. The members of the Paper Writing Team had been furiously working on our individual tasks, but hadn’t had time to look at the whole. I was much happier with the next draft (version 4). It took some work to get this together, following up on all the comments and trying to address concerns was a challenge. It was especially difficult as we got a series of private comments, and trying to find a consensus probably made us look like the bad guys on all sides. We released version 4 on 14 April for a week of comments.

The next step was approval by the LIGO and Virgo executive bodies on 24 April. We prepared version 5 for this. By this point, I had lost track of which sentences I had written, which I had merely typed, and which were from other people completely. There were a few minor changes, mostly adding technical caveats to keep everyone happy (although they do rather complicate the flow of the text).

The paper was circulated to the Collaboration for a final week of comments on 26 April. Most comments now were about typos and presentation. However, some people will continue to make the same comment every time, regardless of how many times you explain why you are doing something different. The end was in sight!

The paper was submitted to Physical Review Letters on 9 May. I was hoping that the referees would take a while, but the reports were waiting in my inbox on Monday morning.

The referee reports weren’t too bad. Referee A had some general comments, Referee B had some good and detailed comments on the astrophysics, and Referee C gave the paper a thorough reading and had some good suggestions for clarifying the text. By this point, I have been staring at the paper so long that some outside perspective was welcome. I was hoping that we’d have a more thorough review of the testing general relativity results, but we had Bob Wald as one of our Collaboration Paper reviewers (the analysis, results and paper are all reviewed internally), so I think we had already been held to a high standard, and there wasn’t much left to say.

We put together responses to the reports. There were surprisingly few comments from the Collaboration at this point. I guess that everyone was getting tired. The paper was resubmitted and accepted on 20 May.

One of the suggestions of Referee A was to include some plots showing the results of the searches. People weren’t too keen on showing these initially, but after much badgering they were convinced, and it was decided to put these plots in the Supplemental Material which wouldn’t delay the paper as long as we got the material submitted by 26 May. This seemed like plenty of time, but it turned out to be rather frantic at the end (although not due to the new plots). The video below is an accurate representation of us trying to submit the final version.

I have an email which contains the line “Many Bothans died to bring us this information” from 1 hour and 18 minutes before the final deadline.

After this, things were looking pretty good. We had returned the proofs of the main paper (I had a fun evening double checking the author list. Yes, all of them). We were now on version 11 of the paper.

Of course, there’s always one last thing. On 31 May, the evening before publication, Salvo Vitale spotted a typo. Nothing serious, but annoying. The team at Physical Review Letters were fantastic, and took care of it immediately!

There’ll still be one more typo, there always is…

Looking back, it is clear that the principal bottle-neck in publishing the results is getting the Collaboration to converge on the paper. I’m not sure how we can overcome this… Actually, I have some ideas, but none that wouldn’t involve some form of doomsday device.

#### Detector status

The sensitivities of the LIGO Hanford and Livinston detectors are around the same as they were in the first observing run. After the success of the first observing run, the second observing run is the difficult follow up album. Livingston has got a little better, while Hanford is a little worse. This is because the Livingston team concentrate on improving low frequency sensitivity whereas the Hanford team focused on improving high frequency sensitivity. The Hanford team increased the laser power, but this introduces some new complications. The instruments are extremely complicated machines, and improving sensitivity is hard work.

The current plan is to have a long commissioning break after the end of this run. The low frequency tweaks from Livingston will be transferred to Hanford, and both sites will work on bringing down other sources of noise.

While the sensitivity hasn’t improved as much as we might have hoped, the calibration of the detectors has! In the first observing run, the calibration uncertainty for the first set of published results was about 10% in amplitude and 10 degrees in phase. Now, uncertainty is better than 5% in amplitude and 3 degrees in phase, and people are discussing getting this down further.

#### Spin evolution

As the binary inspirals, the orientation of the spins will evolve as they precess about. We always quote measurements of the spins at a point in the inspiral corresponding to a gravitational wave frequency of 20 Hz. This is most convenient for our analysis, but you can calculate the spins at other points. However, the resulting probability distributions are pretty similar at other frequencies. This is because the probability distributions are primarily determined by the combination of three things: (i) our prior assumption of a uniform distribution of spin orientations, (ii) our measurement of the effective inspiral spin, and (iii) our measurement of the mass ratio. A uniform distribution stays uniform as spins evolve, so this is unaffected, the effective inspiral spin is approximately conserved during inspiral, so this doesn’t change much, and the mass ratio is constant. The overall picture is therefore qualitatively similar at different moments during the inspiral.

#### Footnotes

I love footnotes. It was challenging for me to resist having any in the paper.

#### Gravity waves

It is possible that internal gravity waves (that is oscillations of the material making up the star, where the restoring force is gravity, not gravitational waves, which are ripples in spacetime), can transport angular momentum from the core of a star to its outer envelope, meaning that the two could rotate in different directions (Rogers, Lin & Lau 2012). I don’t think anyone has studied this yet for the progenitors of binary black holes, but it would be really cool if gravity waves set the properties of gravitational wave sources.

I really don’t want to proof read the paper which explains this though.

#### Colour scheme

For our plots, we use a consistent colour coding for our events. GW150914 is blue; LVT151012 is green; GW151226 is red–orange, and GW170104 is purple. The colour scheme is designed to be colour blind friendly (although adopting different line styles would perhaps be more distinguishable), and is implemented in Python in the Seaborn package as colorblind. Katerina Chatziioannou, who made most of the plots showing parameter estimation results is not a fan of the colour combinations, but put a lot of patient effort into polishing up the plots anyway.

# The Boxing Day Event

Advanced LIGO’s first observing run (O1) got off to an auspicious start with the detection of GW150914 (The Event to its friends). O1 was originally planned to be three months long (September to December), but after the first discovery, there were discussions about extending the run. No major upgrades to the detectors were going to be done over the holidays anyway, so it was decided that we might as well leave them running until January.

By the time the Christmas holidays came around, I was looking forward to some time off. And, of course, lots of good food and the Doctor Who Christmas Special. The work on the first detection had been exhausting, and the Collaboration reached the collective decision that we should all take some time off [bonus note]. Not a creature was stirring, not even a mouse.

On Boxing Day, there was a sudden flurry of emails. This could only mean one thing. We had another detection! Merry GW151226 [bonus note]!

I assume someone left out milk and cookies at the observatories. A not too subtle hint from Nutsinee Kijbunchoo’s comic in the LIGO Magazine.

I will always be amazed how lucky we were detecting GW150914. This could have been easily missed if we were just a little later starting observing. If that had happened, we might not have considered extended O1, and would have missed GW151226 too!

GW151226 is another signal from a binary black hole coalescence. This wasn’t too surprising at the time, as we had estimated such signals should be pretty common. It did, however, cause a slight wrinkle in discussions of what to do in the papers about the discovery of GW150914. Should we mention that we had another potential candidate? Should we wait until we had analysed the whole of O1 fully? Should we pack it all in and have another slice of cake? In the end we decided that we shouldn’t delay the first announcement, and we definitely shouldn’t rush the analysis of the full data set. Therefore, we went ahead with the original plan of just writing about the first month of observations and giving slightly awkward answers, mumbling about still having data to analyse, when asked if we had seen anything else [bonus note]. I’m not sure how many people outside the Collaboration suspected.

### The science

What have we learnt from analysing GW151226, and what have we learnt from the whole of O1? We’ve split our results into two papers.

#### 0. The Boxing Day Discovery Paper

Title: GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole
arXiv: 1606.04855 [gr-qc]
Journal: Physical Review Letters116(24):241103(14)
LIGO science summary: GW151226: Observation of gravitational waves from a 22 solar-mass binary black hole (by Hannah Middleton and Carl-Johan Haster)

This paper presents the discovery of GW151226 and some of the key information about it. GW151226 is not as loud as GW150914, you can’t spot it by eye in the data, but it still stands out in our search. This is a clear detection! It is another binary black hole system, but it is a lower mass system than GW150914 (hence the paper’s title—it’s a shame they couldn’t put in the error bars though).

This paper summarises the highlights of the discovery, so below, I’ll explain these without going into too much technical detail.

More details: The Boxing Day Discovery Paper summary

#### 1. The O1 Binary Black Hole Paper

Title: Binary black hole mergers in the first Advanced LIGO observing run
arXiv: 1606.04856 [gr-qc]
Journal: Physical Review X6(4):041015(36)
Posterior samples: Release v1.0

This paper brings together (almost) everything we’ve learnt about binary black holes from O1. It discusses GW150915, LVT151012 and GW151226, and what we are starting to piece together about stellar-mass binary black holes from this small family of gravitational-wave events.

For the announcement of GW150914, we put together 12 companion papers to go out with the detection announcement. This paper takes on that role. It is Robin, Dr Watson, Hermione and Samwise Gamgee combined. There’s a lot of delicious science packed into this paper (searches, parameter estimation, tests of general relativity, merger rate estimation, and astrophysical implications). In my summary below, I’ll delve into what we have done and what our results mean.

The results of this paper have now largely been updated in the O2 Catalogue Paper.

More details: The O1 Binary Black Hole Paper summary

If you are interested in our science results, you can find data releases accompanying the events at the LIGO Open Science Center. These pages also include some wonderful tutorials to play with.

### The Boxing Day Discovery Paper

Synopsis: Boxing Day Discovery Paper
Favourite part: We’ve done it again!

#### The signal

GW151226 is not as loud as GW150914, you can’t spot it by eye in the data. Therefore, this paper spends a little more time than GW150914’s Discovery Paper talking about the ingredients for our searches.

GW151226 was found by two pipelines which specifically look for compact binary coalescences: the inspiral and merger of neutron stars or black holes. We have templates for what we think these signals should look like, and we filter the data against a large bank of these to see what matches [bonus note].

For the search to work, we do need accurate templates. Figuring out what the waveforms for binary black coalescence should look like is a difficult job, and has taken almost as long as figuring out how to build the detectors!

The signal arrived at Earth 03:38:53 GMT on 26 December 2015 and was first identified by a search pipeline within 70 seconds. We didn’t have a rapid templated search online at the time of GW150914, but decided it would be a good idea afterwards. This allowed us to send out an alert to our astronomer partners so they could look for any counterparts (I don’t think any have been found [bonus note]).

The unmodelled searches (those which don’t use templates, but just coherent signals in both detectors) which first found GW150914 didn’t find GW151226. This isn’t too surprising, as they are less sensitive. You can think of the templated searches as looking for Wally (or Waldo if you’re North American), using the knowledge that he’s wearing glasses, and a red and white stripped bobble hat, but the unmodelled searches are looking for him just knowing that he’s the person that’s on on every page.

GW151226 is the second most significant event in the search for binary black holes after The Event. Its significance is not quite off the charts, but is great enough that we have a hard time calculating exactly how significant it is. Our two search pipelines give estimates of the p-value (the probability you’d see something at least this signal-like if you only had noise in your detectors) of $< 10^{-7}$ and $3.5 \times 10^{-6}$, which are pretty good!

#### The source

To figure out the properties of the source, we ran our parameter-estimation analysis.

GW151226 comes from a black hole binary with masses of $14.2^{+8.3}_{-3.7} M_\odot$ and $7.5^{+2.3}_{-2.3} M_\odot$ [bonus note], where $M_\odot$ is the mass of our Sun (about 330,000 times the mass of the Earth). The error bars indicate our 90% probability ranges on the parameters. These black holes are less massive than the source of GW150914 (the more massive black hole is similar to the less massive black hole of LVT151012). However, the masses are still above what we believe is the maximum possible mass of a neutron star (around $3 M_\odot$). The masses are similar to those observed for black holes in X-ray binaries, so perhaps these black holes are all part of the same extended family.

A plot showing the probability distributions for the masses is shown below. It makes me happy. Since GW151226 is lower mass than GW150914, we see more of the inspiral, the portion of the signal where the two black holes are spiralling towards each other. This means that we measure the chirp mass, a particular combination of the two masses really well. It is this which gives the lovely banana shape to the distribution. Even though I don’t really like bananas, it’s satisfying to see this behaviour as this is what we have been expecting too see!

Estimated masses for the two black holes in the binary of the Boxing Day Event. The dotted lines mark the edge of our 90% probability intervals. The different coloured curves show different models: they agree which again made me happy! The two-dimensional distribution follows a curve of constant chirp mass. The sharp cut-off at the top-left is because $m_1^\mathrm{source}$ is defined to be bigger than $m_2^\mathrm{source}$. Figure 3 of The Boxing Day Discovery Paper.

The two black holes merge to form a final black hole of $20.8^{+6.1}_{-1.7} M_\odot$ [bonus note].

If you add up the initial binary masses and compare this to the final mass, you’ll notice that something is missing. Across the entire coalescence, gravitational waves carry away $1.0^{+0.1}_{-0.2} M_\odot c^2 \simeq 1.8^{+0.2}_{-0.4} \times 10^{47}~\mathrm{J}$ of energy (where $c$ is the speed of light, which is used to convert masses to energies). This isn’t quite as impressive as the energy of GW150914, but it would take the Sun 1000 times the age of the Universe to output that much energy.

The mass measurements from GW151226 are cool, but what’re really exciting are the spin measurements. Spin, as you might guess, is a measure of how much angular momentum a black hole has. We define it to go from zero (not spinning) to one (spinning as much as is possible). A black hole is fully described by its mass and spin. The black hole masses are most important in defining what a gravitational wave looks like, but the imprint of spin is more subtle. Therefore its more difficult to get a good measurement of the spins than the masses.

For GW150915 and LVT151012, we get a little bit of information on the spins. We can conclude that the spins are probably not large, or at least they are not large and aligned with the orbit of the binary. However, we can’t say for certain that we’ve seen any evidence that the black holes are spinning. For GW151226, al least one of the black holes (although we can’t say which) has to be spinning [bonus note].

The plot below shows the probability distribution for the two spins of the binary black holes. This shows the both the magnitude of the spin and the direction that of the spin (if the tilt is zero the black hole and the binary’s orbit both go around in the same way). You can see we can’t say much about the spin of the lower mass black hole, but we have a good idea about the spin of the more massive black hole (the more extreme the mass ratio, the less important the spin of lower mass black is, making it more difficult to measure). Hopefully we’ll learn more about spins in future detections as these could tell us something about how these black holes formed.

Estimated orientation and magnitude of the two component spins. Calculated with our precessing waveform model. The distribution for the more massive black hole is on the left, and for the smaller black hole on the right. Part of Figure 4 of The Boxing Day Discovery Paper.

There’s still a lot to learn about binary black holes, and future detections will help with this. More information about what we can squeeze out of our current results are given in the O1 Binary Black Hole Paper.

### The O1 Binary Black Hole Paper

Synopsis: O1 Binary Black Hole Paper
Read this if: You want to know everything we’ve learnt about binary black holes
Favourite part: The awesome table of parameters at the end

This paper contains too much science to tackle all at once, so I’ve split it up into more bite-sized pieces, roughly following the flow of the paper. First we discuss how we find signals. Then we discuss the parameters inferred from the signals. This is done assuming that general relativity is correct, so we check for any deviations from predictions in the next section. After that, we consider the rate of mergers and what we expect for the population of binary black holes from our detections. Finally, we discuss our results in the context of wider astrophysics.

#### Searches

Looking for signals hidden amongst the data is the first thing to do. This paper only talks about the template search for binary black holes: other search results (including the results for binaries including neutron stars) we will reported elsewhere.

The binary black hole search was previously described in the Compact Binary Coalescence Paper. We have two pipelines which look for binary black holes using templates: PyCBC and GstLAL. These look for signals which are found in both detectors (within 15 ms of each other) which match waveforms in the template bank. A few specifics of these have been tweaked since the start of O1, but these don’t really change any of the results. An overview of the details for both pipelines are given in Appendix A of the paper.

The big difference from Compact Binary Coalescence Paper is the data. We are now analysing the whole of O1, and we are using an improved version of the calibration (although this really doesn’t affect the search). Search results are given in Section II. We have one new detection: GW151226.

Search results for PyCBC (left) and GstLAL (right). The histograms show the number of candidate events (orange squares) compare to the background. The further an orange square is to the right of the lines, the more significant it is. Different backgrounds are shown including and excluding GW150914 (top row) and GW151226 (bottom row). Figure 3 from the O1 Binary Black Hole Paper.

The plots above show the search results. Candidates are ranked by a detection statistic (a signal-to-noise ratio modified by a self-consistency check $\hat{\rho}_c$ for PyCBC, and a ratio of likelihood for the signal and noise hypotheses $\ln \mathcal{L}$ for GstLAL). A larger detection statistic means something is more signal-like and we assess the significance by comparing with the background of noise events. The further above the background curve an event is, the more significant it is. We have three events that stand out.

Number 1 is GW150914. Its significance has increased a little from the first analysis, as we can now compare it against more background data. If we accept that GW150914 is real, we should remove it from the estimation of the background: this gives us the purple background in the top row, and the black curve in the bottom row.

GW151226 is the second event. It clearly stands out when zooming in for the second row of plots. Identifying GW150914 as a signal greatly improves GW151226’s significance.

The final event is LVT151012. Its significance hasn’t changed much since the initial analysis, and is still below our threshold for detection. I’m rather fond of it, as I do love an underdog.

#### Parameter estimation

To figure out the properties of all three events, we do parameter estimation. This was previously described in the Parameter Estimation Paper. Our results for GW150914 and LVT151012 have been updated as we have reran with the newer calibration of the data. The new calibration has less uncertainty, which improves the precision of our results, although this is really only significant for the sky localization. Technical details of the analysis are given in Appendix B and results are discussed in Section IV. You may recognise the writing style of these sections.

The probability distributions for the masses are shown below. There is quite a spectrum, from the low mass GW151226, which is consistent with measurements of black holes in X-ray binaries, up to GW150914, which contains the biggest stellar-mass black holes ever observed.

Estimated masses for the two binary black holes for each of the events in O1. The contours mark the 50% and 90% credible regions. The grey area is excluded from our convention that $m_1^\mathrm{source} \geq m_2^\mathrm{source}$. Part of Figure 4 of the O1 Binary Black Hole Paper.

The distributions for the lower mass GW151226 and LVT151012 follow the curves of constant chirp mass. The uncertainty is greater for LVT151012 as it is a quieter (lower SNR) signal. GW150914 looks a little different, as the merger and ringdown portions of the waveform are more important. These place tighter constraints on the total mass, explaining the shape of the distribution.

Another difference between the lower mass inspiral-dominated signals and the higher mass GW150915 can be seen in the plot below. The shows the probability distributions for the mass ratio $q = m_2^\mathrm{source}/m_1^\mathrm{source}$ and the effective spin parameter $\chi_\mathrm{eff}$, which is a mass-weighted combination of the spins aligned with the orbital angular momentum. Both play similar parts in determining the evolution of the inspiral, so there are stretching degeneracies for GW151226 and LVT151012, but this isn’t the case for GW150914.

Estimated mass ratios $q$ and effective spins $\chi_\mathrm{eff}$ for each of the events in O1. The contours mark the 50% and 90% credible regions. Part of Figure 4 of the O1 Binary Black Hole Paper.

If you look carefully at the distribution of $\chi_\mathrm{eff}$ for GW151226, you can see that it doesn’t extend down to zero. You cannot have a non-zero $\chi_\mathrm{eff}$ unless at least one of the black holes is spinning, so this clearly shows the evidence for spin.

The final masses of the remnant black holes are shown below. Each is around 5% less than the total mass of the binary which merged to form it, with the rest radiated away as gravitational waves.