# 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 pot of gold at the end of the rainbow

Advanced LIGO and Advanced Virgo have detected their first binary neutron star inspiral. Remarkably, this event was observed not just with gravitational waves, but also across the electromagnetic spectrum, from gamma-rays to radio. This discovery confirms the theory that binary neutron star mergers are the progenitors of short gamma-ray bursts and kilonovae, and may be the primary source of heavy elements like gold.

In this post, I’ll go through some of the story of GW170817. As for GW150914, I’ll write another post on the more technical details of our papers, once I’ve had time to catch up on sleep.

### Discovery

The second observing run (O2) of the advanced gravitational-wave detectors started on 30 November 2016. The first detection came in January—GW170104. I was heavily involved in the analysis and paper writing for this. We finally finished up in June, at which point I was thoroughly exhausted. I took some time off in July [bonus note], and was back at work for August. With just one month left in the observing run, it would all be downhill from here, right?

August turned out to be the lava-filled, super-difficult final level of O2. As we have now announced, on August 14, we detected a binary black hole coalescence—GW170814. This was the first clear detection including Virgo, giving us superb sky localization. This is fantastic for astronomers searching for electromagnetic counterparts to our gravitational-wave signals. There was a flurry of excitement, and we thought that this was a fantastic conclusion to O2. We were wrong, this was just the save point before the final opponent. On August 17, we met the final, fire-ball throwing boss.

Text messages from our gravitational-wave candidate event database GraceDB. The final message is for GW170817, or as it was known at the time, G298048. It certainly caught my attention. The messages above are for GW170814, that was picked up multiple times by our search algorithms. It was a busy week.

At 1:58 pm BST my phone buzzed with a text message, an automated alert of a gravitational-wave trigger. I was obviously excited—I recall that my exact thoughts were “What fresh hell is this?” I checked our online event database and saw that it was a single-detector trigger, it was only seen by our Hanford instrument. I started to relax, this was probably going to turn out to be a glitch. The template masses, were low, in the neutron star range, not like the black holes we’ve been finding. Then I saw the false alarm rate was better than one in 9000 years. Perhaps it wasn’t just some noise after all—even though it’s difficult to estimate false alarm rates accurately online, as especially for single-detector triggers, this was significant! I kept reading. Scrolling down the page there was an external coincident trigger, a gamma-ray burst (GRB 170817A) within a couple of seconds…

We’re gonna need a bigger author list. Credit: Zanuck/Brown Productions

Short gamma-ray bursts are some of the most powerful explosions in the Universe. I’ve always found it mildly disturbing that we didn’t know what causes them. The leading theory has been that they are the result of two neutron stars smashing together. Here seemed to be the proof.

The rapid response call was under way by the time I joined. There was a clear chirp in Hanford, you could be see it by eye! We also had data from Livingston and Virgo too. It was bad luck that they weren’t folded into the online alert. There had been a drop out in the data transfer from Italy to the US, breaking the flow for Virgo. In Livingston, there was a glitch at the time of the signal which meant the data wasn’t automatically included in the search. My heart sank. Glitches are common—check out Gravity Spy for some examples—so it was only a matter of time until one overlapped with a signal [bonus note], and with GW170817 being such a long signal, it wasn’t that surprising. However, this would complicate the analysis. Fortunately, the glitch is short and the signal is long (if this had been a high-mass binary black hole, things might not have been so smooth). We were able to exorcise the glitch. A preliminary sky map using all three detectors was sent out at 12:54 am BST. Not only did we defeat the final boss, we did a speed run on the hard difficulty setting first time [bonus note].

Spectrogram of Livingston data showing part of GW170817’s chirp (which sweeps upward in frequncy) as well as the glitch (the big blip at about $-0.6~\mathrm{s}$). The lower panel shows how we removed the glitch: the grey line shows gating window that was applied for preliminary results, to zero the affected times, the blue shows a fitted model of the glitch that was subtracted for final results. You can clearly see the chirp well before the glitch, so there’s no danger of it being an artefect of the glitch. Figure 2 of the GW170817 Discovery Paper

The three-detector sky map provided a great localization for the source—this preliminary map had a 90% area of ~30 square degrees. It was just in time for that night’s observations. The plot below shows our gravitational-wave localizations in green—the long band is without Virgo, and the smaller is with all three detectors—as with GW170814, Virgo makes a big difference. The blue areas are the localizations from Fermi and INTEGRAL, the gamma-ray observatories which measured the gamma-ray burst. The inset is something new…

Localization of the gravitational-wave, gamma-ray, and optical signals. The main panel shows initial gravitational-wave 90% areas in green (with and without Virgo) and gamma-rays in blue (the IPN triangulation from the time delay between Fermi and INTEGRAL, and the Fermi GBM localization). The inset shows the location of the optical counterpart (the top panel was taken 10.9 hours after merger, the lower panel is a pre-merger reference without the transient). Figure 1 of the Multimessenger Astronomy Paper.

That night, the discoveries continued. Following up on our sky location, an optical counterpart (AT 2017gfo) was found. The source is just on the outskirts of galaxy NGC 4993, which is right in the middle of the distance range we inferred from the gravitational wave signal. At around 40 Mpc, this is the closest gravitational wave source.

After this source was reported, I think about every single telescope possible was pointed at this source. I think it may well be the most studied transient in the history of astronomy. I think there are ~250 circulars about follow-up. Not only did we find an optical counterpart, but there was emission in X-ray and radio. There was a delay in these appearing, I remember there being excitement at our Collaboration meeting as the X-ray emission was reported (there was a lack of cake though).

The figure below tries to summarise all the observations. As you can see, it’s a mess because there is too much going on!

The timeline of observations of GW170817’s source. Shaded dashes indicate times when information was reported in a Circular. Solid lines show when the source was observable in a band: the circles show a comparison of brightnesses for representative observations. Figure 2 of the Multimessenger Astronomy Paper.

The observations paint a compelling story. Two neutron stars insprialled together and merged. Colliding two balls of nuclear density material at around a third of the speed of light causes a big explosion. We get a jet blasted outwards and a gamma-ray burst. The ejected, neutron-rich material decays to heavy elements, and we see this hot material as a kilonova [bonus material]. The X-ray and radio may then be the afterglow formed by the bubble of ejected material pushing into the surrounding interstellar material.

### Science

What have we learnt from our results? Here are some gravitational wave highlights.

We measure several thousand cycles from the inspiral. It is the most beautiful chirp! This is the loudest gravitational wave signal yet found, beating even GW150914. GW170817 has a signal-to-noise ratio of 32, while for GW150914 it is just 24.

Time–frequency plots for GW170104 as measured by Hanford, Livingston and Virgo. 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. The Livingston data have the glitch removed. Figure 1 of the GW170817 Discovery Paper.

The signal-to-noise ratios in the Hanford, Livingston and Virgo were 19, 26 and 2 respectively. The signal is quiet in Virgo, which is why you can’t spot it by eye in the plots above. The lack of a clear signal is really useful information, as it restricts where on the sky the source could be, as beautifully illustrated in the video below.

While we measure the inspiral nicely, we don’t detect the merger: we can’t tell if a hypermassive neutron star is formed or if there is immediate collapse to a black hole. This isn’t too surprising at current sensitivity, the system would basically need to convert all of its energy into gravitational waves for us to see it.

From measuring all those gravitational wave cycles, we can measure the chirp mass stupidly well. Unfortunately, converting the chirp mass into the component masses is not easy. The ratio of the two masses is degenerate with the spins of the neutron stars, and we don’t measure these well. In the plot below, you can see the probability distributions for the two masses trace out bananas of roughly constant chirp mass. How far along the banana you go depends on what spins you allow. We show results for two ranges: one with spins (aligned with the orbital angular momentum) up to 0.89, the other with spins up to 0.05. There’s nothing physical about 0.89 (it was just convenient for our analysis), but it is designed to be agnostic, and above the limit you’d plausibly expect for neutron stars (they should rip themselves apart at spins of ~0.7); the lower limit of 0.05 should safely encompass the spins of the binary neutron stars (which are close enough to merge in the age of the Universe) we have estimated from pulsar observations. The masses roughly match what we have measured for the neutron stars in our Galaxy. (The combinations at the tip of the banana for the high spins would be a bit odd).

Estimated masses for the two neutron stars in the binary. We show results for two different spin limits, $\chi_z$ is the component of the spin aligned with the orbital angular momentum. The two-dimensional shows the 90% probability contour, which follows a line of constant chirp mass. The one-dimensional plot shows individual masses; the dotted lines mark 90% bounds away from equal mass. Figure 4 of the GW170817 Discovery Paper.

If we were dealing with black holes, we’d be done: they are only described by mass and spin. Neutron stars are more complicated. Black holes are just made of warped spacetime, neutron stars are made of delicious nuclear material. This can get distorted during the inspiral—tides are raised on one by the gravity of the other. These extract energy from the orbit and accelerate the inspiral. The tidal deformability depends on the properties of the neutron star matter (described by its equation of state). The fluffier a neutron star is, the bigger the impact of tides; the more compact, the smaller the impact. We don’t know enough about neutron star material to predict this with certainty—by measuring the tidal deformation we can learn about the allowed range. Unfortunately, we also didn’t yet have good model waveforms including tides, so for to start we’ve just done a preliminary analysis (an improved analysis was done for the GW170817 Properties Paper). We find that some of the stiffer equations of state (the ones which predict larger neutron stars and bigger tides) are disfavoured; however, we cannot rule out zero tides. This means we can’t rule out the possibility that we have found two low-mass black holes from the gravitational waves alone. This would be an interesting discovery; however, the electromagnetic observations mean that the more obvious explanation of neutron stars is more likely.

From the gravitational wave signal, we can infer the source distance. Combining this with the electromagnetic observations we can do some cool things.

First, the gamma ray burst arrived at Earth 1.7 seconds after the merger. 1.7 seconds is not a lot of difference after travelling something like 85–160 million years (that’s roughly the time since the Cretaceous or Late Jurassic periods). Of course, we don’t expect the gamma-rays to be emitted at exactly the moment of merger, but allowing for a sensible range of emission times, we can bound the difference between the speed of gravity and the speed of light. In general relativity they should be the same, and we find that the difference should be no more than three parts in $10^{15}$.

Second, we can combine the gravitational wave distance with the redshift of the galaxy to measure the Hubble constant, the rate of expansion of the Universe. Our best estimates for the Hubble constant, from the cosmic microwave background and from supernova observations, are inconsistent with each other (the most recent supernova analysis only increase the tension). Which is awkward. Gravitational wave observations should have different sources of error and help to resolve the difference. Unfortunately, with only one event our uncertainties are rather large, which leads to a diplomatic outcome.

Posterior probability distribution for the Hubble constant $H_0$ inferred from GW170817. The lines mark 68% and 95% intervals. The coloured bands are measurements from the cosmic microwave background (Planck) and supernovae (SHoES). Figure 1 of the Hubble Constant Paper.

Finally, we can now change from estimating upper limits on binary neutron star merger rates to estimating the rates! We estimate the merger rate density is in the range $1540^{+3200}_{-1220}~\mathrm{Gpc^{-3}\,yr^{-1}}$ (assuming a uniform of neutron star masses between one and two solar masses). This is surprisingly close to what the Collaboration expected back in 2010: a rate of between $10~\mathrm{Gpc^{-3}\,yr^{-1}}$ and $10000~\mathrm{Gpc^{-3}\,yr^{-1}}$, with a realistic rate of $1000~\mathrm{Gpc^{-3}\,yr^{-1}}$. This means that we are on track to see many more binary neutron stars—perhaps one a week at design sensitivity!

### Summary

Advanced LIGO and Advanced Virgo observed a binary neutron star insprial. The rest of the astronomical community has observed what happened next (sadly there are no neutrinos). This is the first time we have such complementary observations—hopefully there will be many more to come. There’ll be a huge number of results coming out over the following days and weeks. From these, we’ll start to piece together more information on what neutron stars are made of, and what happens when you smash them together (take that particle physicists).

Also: I’m exhausted, my inbox is overflowing, and I will have far too many papers to read tomorrow.

GW170817 Discovery Paper: GW170817: Observation of gravitational waves from a binary neutron star inspiral
Multimessenger Astronomy Paper: Multi-messenger observations of a binary neutron star merger
Data release:
LIGO Open Science Center

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

### Bonus notes

#### Inbox zero

Over my vacation I cleaned up my email. I had a backlog starting around September 2015.  I think there were over 6000 which I sorted or deleted. I had about 20 left to deal with when I got back to work. GW170817 undid that. Despite doing my best to keep up, there are over a 1000 emails in my inbox…

#### Worst case scenario

Around the start of O2, I was asked when I expected our results to be public. I said it would depend upon what we found. If it was only high-mass black holes, those are quick to analyse and we know what to do with them, so results shouldn’t take long, now we have the first few out of the way. In this case, perhaps a couple months as we would have been generating results as we went along. However, the worst case scenario would be a binary neutron star overlapping with non-Gaussian noise. Binary neutron stars are more difficult to analyse (they are longer signals, and there are matter effects to worry about), and it would be complicated to get everyone to be happy with our results because we were doing lots of things for the first time. Obviously, if one of these happened at the end of the run, there’d be quite a delay…

I think I got that half-right. We’re done amazingly well analysing GW170817 to get results out in just two months, but I think it will be a while before we get the full O2 set of results out, as we’ve been neglecting otherthings (you’ll notice we’ve not updated our binary black hole merger rate estimate since GW170104, nor given detailed results for testing general relativity with the more recent detections).

At the time of the GW170817 alert, I was working on writing a research proposal. As part of this, I was explaining why it was important to continue working on gravitational-wave parameter estimation, in particular how to deal with non-Gaussian or non-stationary noise. I think I may be a bit of a jinx. For GW170817, the glitch wasn’t a big problem, these type of blips can be removed. I’m more concerned about the longer duration ones, which are less easy to separate out from background noise. Don’t say I didn’t warn you in O3.

#### Parameter estimation rota

The duty of analysing signals to infer their source properties was divided up into shifts for O2. On January 4, the time of GW170104, I was on shift with my partner Aaron Zimmerman. It was his first day. Having survived that madness, Aaron signed back up for the rota. Can you guess who was on shift for the week which contained GW170814 and GW170817? Yep, Aaron (this time partnered with the excellent Carl-Johan Haster). Obviously, we’ll need to have Aaron on rota for the entirety of O3. In preparation, he has already started on paper drafting

Methods Section: Chained ROTA member to a terminal, ignored his cries for help. Detections followed swiftly.

The lightest elements (hydrogen, helium and lithium) we made during the Big Bang. Stars burn these to make heavier elements. Energy can be released up to around iron. Therefore, heavier elements need to be made elsewhere, for example in the material ejected from supernova or (as we have now seen) neutron star mergers, where there are lots of neutrons flying around to be absorbed. Elements (like gold and platinum) formed by this rapid neutron capture are known as r-process elements, I think because they are beloved by pirates.

A couple of weeks ago, the Nobel Prize in Physics was announced for the observation of gravitational waves. In December, the laureates will be presented with a gold (not chocolate) medal. I love the idea that this gold may have come from merging neutron stars.

Here’s one we made earlier. Credit: Associated Press/F. Vergara

# 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).

# 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
Read this if: You are excited about the discovery of GW151226
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.

Estimated masses $M_\mathrm{f}^\mathrm{source}$ and spins $a_\mathrm{f}$ of the remnant black holes 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.

The plot also shows the final spins. These are much better constrained than the component spins as they are largely determined by the angular momentum of the binary as it merged. This is why the spins are all quite similar. To calculate the final spin, we use an updated formula compared to the one in the Parameter Estimation Paper. This now includes the effect of the components’ spin which isn’t aligned with the angular momentum. This doesn’t make much difference for GW150914 or LVT151012, but the change is slightly more for GW151226, as it seems to have more significant component spins.

The luminosity distance for the sources is shown below. We have large uncertainties because the luminosity distance is degenerate with the inclination. For GW151226 and LVT151012 this does result in some beautiful butterfly-like distance–inclination plots. For GW150914, the butterfly only has the face-off inclination wing (probably as consequence of the signal being louder and the location of the source on the sky). The luminosity distances for GW150914 and GW151226 are similar. This may seem odd, because GW151226 is a quieter signal, but that is because it is also lower mass (and so intrinsically quieter).

Probability distributions for the luminosity distance of the source of each of the three events in O1. Part of Figure 4 of the O1 Binary Black Hole Paper.

Sky localization is largely determined by the time delay between the two observatories. This is one of the reasons that having a third detector, like Virgo, is an awesome idea. The plot below shows the localization relative to the Earth. You can see that each event has a localization that is part of a ring which is set by the time delay. GW150914 and GW151226 were seen by Livingston first (apparently there is some gloating about this), and LVT151012 was seen by Hanford first.

Estimated sky localization relative to the Earth for each of the events in O1. The contours mark the 50% and 90% credible regions. H+ and L+ mark the locations of the two observatories. Part of Figure 5 of the O1 Binary Black Hole Paper.

Both GW151226 and LVT151012 are nearly overhead. This isn’t too surprising, as this is where the detectors are most sensitive, and so where we expect to make the most detections.

The improvement in the calibration of the data is most evident in the sky localization. For GW150914, the reduction in calibration uncertainty improves the localization by a factor of ~2–3! For LVT151012 it doesn’t make much difference because of its location and because it is a much quieter signal.

The map below shows the localization on the sky (actually where in Universe the signal came from). The maps have rearranged themselves because of the Earth’s rotation (each event was observed at a different sidereal time).

Estimated sky localization (in right ascension and declination) for each of the events in O1. The contours mark the 50% and 90% credible regions. Part of Figure 5 of the O1 Binary Black Hole Paper.

We’re nowhere near localising sources to single galaxies, so we may never know exactly where these signals originated from.

#### Tests of general relativity

The Testing General Relativity Paper reported several results which compared GW150914 with the predictions of general relativity. Either happily or sadly, depending upon your point of view, it passed them all. In Section V of the paper, we now add GW151226 into the mix. (We don’t add LVT151012 as it’s too quiet to be much use).

A couple of the tests for GW150914 looked at the post-inspiral part of the waveform, looking at the consistency of mass and spin estimates, and trying to match the ringdown frequency. Since GW151226 is lower mass, we can’t extract any meaningful information from the post-inspiral portion of the waveform, and so it’s not worth repeating these tests.

However, the fact that GW151226 has such a lovely inspiral means that we can place some constraints on post-Newtonian parameters. We have lots and lots of cycles, so we are sensitive to any small deviations that arise during inspiral.

The plot below shows constraints on deviations for a set of different waveform parameters. A deviation of zero indicates the value in general relativity. The first four boxes (for parameters referred to as $\varphi_i$ in the Testing General Relativity Paper) are parameters that affect the inspiral. The final box on the right is for parameters which impact the merger and ringdown. The top row shows results for GW150914, these are updated results using the improved calibrated data. The second row shows results for GW151226, and the bottom row shows what happens when you combine the two.

Probability distributions for waveform parameters. The top row shows bounds from just GW150914, the second from just GW151226, and the third from combining the two. A deviation of zero is consistent with general relativity. Figure 6 from the O1 Binary Black hole Paper.

All the results are happily about zero. There were a few outliers for GW150914, but these are pulled back in by GW151226. We see that GW151226 dominates the constraints on the inspiral parameters, but GW150914 is more important for the merger–ringdown $\alpha_i$ parameters.

Again, Einstein’s theory passes the test. There is no sign of inconsistency (yet). It’s clear that adding more results greatly improves our sensitivity to these parameters, so these tests will continue put general relativity through tougher and tougher tests.

#### Rates

We have a small number of events, around 2.9 in total, so any estimates of how often binary black holes merge will be uncertain. Of course, just because something is tricky, it doesn’t mean we won’t give it a go! The Rates Paper discussed estimates after the first 16 days of coincident data, when we had just 1.9 events. Appendix C gives technical details and Section VI discusses results.

The whole of O1 is about 52 days’ worth of coincident data. It’s therefore about 3 times as long as the initial stretch. in that time we’ve observed about 3/2 times as many events. Therefore, you might expect that the event rate is about 1/2 of our original estimates. If you did, get yourself a cookie, as you are indeed about right!

To calculate the rates we need to assume something about the population of binary black holes. We use three fiducial distributions:

1. We assume that binary black holes are either like GW150914, LVT151012 or GW151226. This event-based rate is different from the previous one as it now includes an extra class for GW151226.
2. A flat-in-the-logarithm-of-masses distribution, which we expect gives a sensible lower bound on the rate.
3. A power law slope for the larger black hole of $-2.35$, which we expect gives a sensible upper bound on the rate.

We find that the rates are 1. $54^{+111}_{-40}~\mathrm{Gpc^{-3}\,yr^{-1}}$, 2. $30^{+46}_{-21}~\mathrm{Gpc^{-3}\,yr^{-1}}$, and 3. $97^{+149}_{-68}~\mathrm{Gpc^{-3}\,yr^{-1}}$. As expected, the first rate is nestled between the other two.

Despite the rates being lower, there’s still a good chance we could see 10 events by the end of O2 (although that will depend on the sensitivity of the detectors).

A new results that is included in with the rates, is a simple fit for the distribution of black hole masses [bonus note]. The method is described in Appendix D. It’s just a repeated application of Bayes’ theorem to go from the masses we measured from the detected sources, to the distribution of masses of the entire population.

We assume that the mass of the larger black hole is distributed according to a power law with index $\alpha$, and that the less massive black hole has a mass uniformly distributed in mass ratio, down to a minimum black hole mass of $5 M_\odot$. The cut-off, is the edge of a speculated mass gap between neutron stars and black holes.

We find that $\alpha = 2.5^{+1.5}_{-1.6}$. This has significant uncertainty, so we can’t say too much yet. This is a slightly steeper slope than used for the power-law rate (although entirely consistent with it), which would nudge the rates a little lower. The slope does fit in with fits to the distribution of masses in X-ray binaries. I’m excited to see how O2 will change our understanding of the distribution.

#### Astrophysical implications

With the announcement of GW150914, the Astrophysics Paper reviewed predictions for binary black holes in light of the discovery. The high masses of GW150914 indicated a low metallicity environment, perhaps no more than half of solar metallicity. However, we couldn’t tell if GW150914 came from isolated binary evolution (two stars which have lived and died together) or a dynamical interaction (probably in a globular cluster).

Since then, various studies have been performed looking at both binary evolution (Eldridge & Stanway 2016; Belczynski et al. 2016de Mink & Mandel 2016Hartwig et al. 2016; Inayoshi et al. 2016; Lipunov et al. 2016) and dynamical interactions (O’Leary, Meiron & Kocsis 2016; Mapelli 2016; Rodriguez et al. 2016), even considering binaries around supermassive black holes (Bartos et al. 2016; Stone, Metzger & Haiman 2016). We don’t have enough information to tell the two pathways apart. GW151226 gives some new information. Everything is reviewed briefly in Section VII.

GW151226 and LVT151012 are lower mass systems, and so don’t need to come from as low a metallicity environment as GW150914 (although they still could). Both are also consistent with either binary evolution or dynamical interactions. However, the low masses of GW151226 mean that it probably does not come from one particular binary formation scenario, chemically homogeneous evolution, and it is less likely to come from dynamical interactions.

Building up a population of sources, and getting better measurements of spins and mass ratios will help tease formation mechanisms apart. That will take a while, but perhaps it will be helped if we can do multi-band gravitational-wave astronomy with eLISA.

This section also updates predictions from the Stochastic Paper for the gravitational-wave background from binary black holes. There’s a small change from an energy density of $\Omega_\mathrm{GW} = 1.1^{+2.7}_{-0.9} \times 10^{-9}$ at a frequency of 25 Hz to $\Omega_\mathrm{GW} = 1.2^{+1.9}_{-0.9} \times 10^{-9}$. This might be measurable after a few years at design sensitivity.

#### Conclusion

We are living in the future. We may not have hoverboards, but the era of gravitational-wave astronomy is here. Not in 20 years, not in the next decade, not in five more years, now. LIGO has not just opened a new window, it’s smashed the window and jumped through it just before the explosion blasts the side off the building. It’s so exciting that I can’t even get my metaphors straight. The introductory paragraphs of papers on gravitational-wave astronomy will never be the same again.

Although we were lucky to discover GW150914, it wasn’t just a fluke. Binary black coalescences aren’t that rare and we should be detecting more. Lots more. You know that scene in a movie where the heroes have defeated a wave of enemies and then the camera pans back to show the approaching hoard that stretches to the horizon? That’s where we are now. O2 is coming. The second observing run, will start later this year, and we expect we’ll be adding many entries to our list of binary black holes.

We’re just getting started with LIGO and Virgo. There’ll be lots more science to come.

If you made it this far, you deserve a biscuit. A fancy one too, not just a digestive.

Or, if you’re hungry for more, here are some blogs from my LIGO colleagues

• Daniel Williams (a PhD student at University of Glasgow)
• Matt Pitkin (who is hunting for continuous gravitational waves)
• Shane Larson (who is also investigating mutli-band gravitational-wave astronomy)
• Amber Sturver (who works at the Livingston Observatory)

My group at Birmingham also made some short reaction videos (I’m too embarrassed to watch mine).

### Bonus notes

#### Christmas cease-fire

In the run-up to the holidays, there were lots of emails that contained phrases like “will have to wait until people get back from holidays” or “can’t reply as the group are travelling and have family commitments”. No-one ever said that they were taking a holiday, but just that it was happening in general, so we’d all have to wait for a couple of weeks. No-one ever argued with this, because, of course, while you were waiting for other people to do things, there was nothing you could do, and so you might as well take some time off. And you had been working really hard, so perhaps an evening off and an extra slice of cake was deserved…

Rather guiltily, I must confess to ignoring the first few emails on Boxing Day. (Although I saw them, I didn’t read them for reasons of plausible deniability). I thought it was important that my laptop could have Boxing Day off. Thankfully, others in the Collaboration were more energetic and got things going straight-away.

#### Naming

Gravitational-wave candidates (or at least the short ones from merging binary black holes which we have detected so far), start off life named by a number in our database. This event started life out as G211117. After checks and further analysis, to make sure we can’t identify any environmental effects which could have caused the detector to misbehave, candidates are renamed. Those which are significant enough to be claimed as a detection get the Gravitational Wave (GW) prefix. Those we are less certain of get the LIGO–Virgo Trigger (LVT) prefix. The rest of the name is the date in Coordinated Universal Time (UTC). The new detection is GW151226.

Informally though, it is the Boxing Day Event. I’m rather impressed that this stuck as the Collaboration is largely US based: it was still Christmas Day in the US when the detection was made, and Americans don’t celebrate Boxing Day anyway.

#### Other searches

We are now publishing the results of the O1 search for binary black holes with a template bank which goes up to total observed binary masses of $100 M_\odot$. Therefore we still have to do the same about searches for anything else. The results from searches for other compact binaries should appear soon (binary neutron star and neutron star–black hole upper limits; intermediate mass black hole binary upper limits). It may be a while before we have all the results looking for continuous waves.

#### Matched filtering

The compact binary coalescence search uses matched filtering to hunt for gravitational waves. This is a well established technique in signal processing. You have a template signal, and you see how this correlates with the data. We use the detectors’ sensitivity to filter the data, so that we give more weight to bits which match where we are sensitive, and little weight to matches where we have little sensitivity.

I imagine matched filtering as similar to how I identify a piece of music: I hear a pattern of notes and try to compare to things I know. Dum-dum-dum-daah? Beethoven’s Fifth.

Filtering against a large number of templates takes a lot of computational power, so we need to be cunning as to which templates we include. We don’t want to miss anything, so we need enough templates to cover all possibilities, but signals from similar systems can look almost identical, so we just need one representative template included in the bank. Think of trying to pick out Under Pressure, you could easily do this with a template for Ice Ice Baby, and you don’t need both Mr Brightside and Ode to Joy.

It doesn’t matter if the search doesn’t pick out a template that perfectly fits the properties of the source, as this is what parameter estimation is for.

The figure below shows how effective matched filtering can be.

• The top row shows the data from the two interferometers. It’s been cleaned up a little bit for the plot (to keep the experimentalists happy), but you can see that the noise in the detectors is seemingly much bigger than the best match template (shown in black, the same for both detectors).
• The second row shows the accumulation of signal-to-noise ratio (SNR). If you correlate the data with the template, you see that it matches the template, and keeps matching the template. This is the important part, although, at any moment it looks like there’s just random wibbles in the detector, when you compare with a template you find that there is actually a signal which evolves in a particular way. The SNR increases until the signal stops (because the black holes have merged). It is a little lower in the Livinston detector as this was slightly less sensitive around the time of the Boxing Day Event.
• The third row shows how much total SNR you would get if you moved the best match template around in time. There’s a clear peak. This is trying to show that the way the signal changes is important, and you wouldn’t get a high SNR when the signal isn’t there (you would normally expect it to be about 1).
• The final row shows the amount of energy at a particular frequency at a particular time. Compact binary coalescences have a characteristic chirp, so you would expect a sweep from lower frequencies up to higher frequencies. You can just about make it out in these plots, but it’s not obvious as for GW150914. This again shows the value of matched filtering, but it also shows that there’s no other weird glitchy stuff going on in the detectors at the time.

Observation of The Boxing Day Event in LIGO Hanford and LIGO Livingston. The top row shows filtered data and best match template. The second row shows how this template accumulates signal-to-noise ratio. The third row shows signal-to-noise ratio of this template at different end times. The fourth row shows a spectrogram of the data. Figure 1 of the Boxing Day Discovery Paper.

#### Electromagnetic and neutrino follow-up

Reports by electromagnetic astronomers on their searches for counterparts so far are:

Reports by neutrino astronomers are:

• ANTARES and IceCube—a search for high-energy neutrinos (above 100 GeV) coincident with LVT151012 or GW151226.
• KamLAND—a search for neutrinos (1.8 MeV to 111 MeV) coincident with GW150914, LVT151012 or GW151226.
• Pierre Auger Observatory—a search for ultra high-energy (above 100 PeV) neutrinos coincident with GW150914, LVT151012 or GW151226.
• Super-Kamiokande—a search for neutrinos (of a wide range of energies, from 3.5 MeV to 100 PeV) coincident with GW150914 or GW151226.
• Borexino—a search for low-energy (250 keV to 15 MeV) neutrinos coincident with GW150914, GW151226 and GW170104.
• NOvA—a search for neutrinos and cosmic rays (or a wide range of energies, from 10 MeV to over a GeV) coincident with all events from O1 and O2, plus triggers from O3.

No counterparts have been claimed, which isn’t surprising for a binary black hole coalescence.

#### Rounding

In various places, the mass of the smaller black hole is given as $8 M_\odot$. The median should really round to $7 M_\odot$ as to three significant figures it is $7.48 M_\odot$. This really confused everyone though, as with rounding you’d have a binary with components of masses $14 M_\odot$ and $7 M_\odot$ and total mass $22 M_\odot$. Rounding is a pain! Fortunately, $8 M_\odot$ lies well within the uncertainty: the 90% range is $5.2\text{--}9.8 M_\odot$.

#### Black holes are massive

I tried to find a way to convert the mass of the final black hole into every day scales. Unfortunately, the thing is so unbelievably massive, it just doesn’t work: it’s no use relating it to elephants or bowling balls. However, I did have some fun looking up numbers. Currently, it costs about £2 to buy a 180 gram bar of Cadbury’s Bourneville. Therefore, to buy an equivalent amount of dark chocolate would require everyone on Earth to save up for about 600 millions times the age of the Universe (assuming GDP stays constant). By this point, I’m sure the chocolate will be past its best, so it’s almost certainly a big waste of time.

#### Maximum minimum spin

One of the statistics people really seemed to latch on to for the Boxing Day Event was that at least one of the binary black holes had to have a spin of greater than 0.2 with 99% probability. It’s a nice number for showing that we have a preference for some spin, but it can be a bit tricky to interpret. If we knew absolutely nothing about the spins, then we would have a uniform distribution on both spins. There’d be a 10% chance that the spin of the more massive black hole is less than 0.1, and a 10% chance that the spin of the other black hole is less than 0.1. Hence, there’s a 99% probability that there is at least one black hole with spin greater than 0.1, even though we have no evidence that the black holes are spinning (or not). Really, you need to look at the full probability distributions for the spins, and not just the summary statistics, to get an idea of what’s going on.

#### Just one more thing…

The fit for the black hole mass distribution was the last thing to go in the paper. It was a bit frantic to get everything reviewed in time. In the last week, there were a couple of loud exclamations from the office next to mine, occupied by John Veitch, who as one of the CBC chairs has to keep everything and everyone organised. (I’m not quite sure how John still has so much of his hair). It seems that we just can’t stop doing science. There is a more sophisticated calculation in the works, but the foot was put down that we’re not trying to cram any more into the current papers.

# Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes

I love collecting things, there’s something extremely satisfying about completing a set. I suspect that this is one of the alluring features of Pokémon—you’ve gotta catch ’em all. The same is true of black hole hunting. Currently, we know of stellar-mass black holes which are a few times the mass of our Sun, up to a few tens of the mass of our Sun (the black holes of GW150914 are the biggest yet to be observed), and we know of supermassive black holes, which are ten thousand to ten billion times the mass our Sun. However, we are missing intermediate-mass black holes which lie in the middle. We have Charmander and Charizard, but where is Charmeleon? The elusive ones are always the most satisfying to capture.

Adorable black hole (available for adoption). I’m sure this could be a Pokémon. It would be a Dark type. Not that I’ve given it that much thought…

Intermediate-mass black holes have evaded us so far. We’re not even sure that they exist, although that would raise questions about how you end up with the supermassive ones (you can’t just feed the stellar-mass ones lots of rare candy). Astronomers have suggested that you could spot intermediate-mass black holes in globular clusters by the impact of their gravity on the motion of other stars. However, this effect would be small, and near impossible to conclusively spot. Another way (which I’ve discussed before), would to be to look at ultra luminous X-ray sources, which could be from a disc of material spiralling into the black hole.  However, it’s difficult to be certain that we understand the source properly and that we’re not misclassifying it. There could be one sure-fire way of identifying intermediate-mass black holes: gravitational waves.

The frequency of gravitational waves depend upon the mass of the binary. More massive systems produce lower frequencies. LIGO is sensitive to the right range of frequencies for stellar-mass black holes. GW150914 chirped up to the pitch of a guitar’s open B string (just below middle C). Supermassive black holes produce gravitational waves at too low frequency for LIGO (a space-based detector would be perfect for these). We might just be able to detect signals from intermediate-mass black holes with LIGO.

In a recent paper, a group of us from Birmingham looked at what we could learn from gravitational waves from the coalescence of an intermediate-mass black hole and a stellar-mass black hole [bonus note].  We considered how well you would be able to measure the masses of the black holes. After all, to confirm that you’ve found an intermediate-mass black hole, you need to be sure of its mass.

The signals are extremely short: we only can detect the last bit of the two black holes merging together and settling down as a final black hole. Therefore, you might think there’s not much information in the signal, and we won’t be able to measure the properties of the source. We found that this isn’t the case!

We considered a set of simulated signals, and analysed these with our parameter-estimation code [bonus note]. Below are a couple of plots showing the accuracy to which we can infer a couple of different mass parameters for binaries of different masses. We show the accuracy of measuring the chirp mass $\mathcal{M}$ (a much beloved combination of the two component masses which we are usually able to pin down precisely) and the total mass $M_\mathrm{total}$.

Measured chirp mass for systems of different total masses. The shaded regions show the 90% credible interval and the dashed lines show the true values. The mass ratio $q$ is the mass of the stellar-mass black hole divided by the mass of the intermediate-mass black hole. Figure 1 of Haster et al. (2016).

Measured total mass for systems of different total masses. The shaded regions show the 90% credible interval and the dashed lines show the true values. Figure 2 of Haster et al. (2016).

For the lower mass systems, we can measure the chirp mass quite well. This is because we get a little information from the part of the gravitational wave from when the two components are inspiralling together. However, we see less and less of this as the mass increases, and we become more and more uncertain of the chirp mass.

The total mass isn’t as accurately measured as the chirp mass at low masses, but we see that the accuracy doesn’t degrade at higher masses. This is because we get some constraints on its value from the post-inspiral part of the waveform.

We found that the transition from having better fractional accuracy on the chirp mass to having better fractional accuracy on the total mass happened when the total mass was around 200–250 solar masses. This was assuming final design sensitivity for Advanced LIGO. We currently don’t have as good sensitivity at low frequencies, so the transition will happen at lower masses: GW150914 is actually in this transition regime (the chirp mass is measured a little better).

Given our uncertainty on the masses, when can we conclude that there is an intermediate-mass black hole? If we classify black holes with masses more than 100 solar masses as intermediate mass, then we’ll be able to say to claim a discovery with 95% probability if the source has a black hole of at least 130 solar masses. The plot below shows our inferred probability of there being an intermediate-mass black hole as we increase the black hole’s mass (there’s little chance of falsely identifying a lower mass black hole).

Probability that the larger black hole is over 100 solar masses (our cut-off mass for intermediate-mass black holes $M_\mathrm{IMBH}$). Figure 7 of Haster et al. (2016).

Gravitational-wave observations could lead to a concrete detection of intermediate mass black holes if they exist and merge with another black hole. However, LIGO’s low frequency sensitivity is important for detecting these signals. If detector commissioning goes to plan and we are lucky enough to detect such a signal, we’ll finally be able to complete our set of black holes.

arXiv: 1511.01431 [astro-ph.HE]
Journal: Monthly Notices of the Royal Astronomical Society457(4):4499–4506; 2016
Birmingham science summary: Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes (by Carl)
Other collectables: Breakthrough, Gruber, Shaw, Kavli

### Bonus notes

#### Jargon

The coalescence of an intermediate-mass black hole and a stellar-mass object (black hole or neutron star) has typically been known as an intermediate mass-ratio inspiral (an IMRI). This is similar to the name for the coalescence of a a supermassive black hole and a stellar-mass object: an extreme mass-ratio inspiral (an EMRI). However, my colleague Ilya has pointed out that with LIGO we don’t really see much of the intermediate-mass black hole and the stellar-mass black hole inspiralling together, instead we see the merger and ringdown of the final black hole. Therefore, he prefers the name intermediate mass-ratio coalescence (or IMRAC). It’s a better description of the signal we measure, but the acronym isn’t as good.

#### Parameter-estimation runs

The main parameter-estimation analysis for this paper was done by Zhilu, a summer student. This is notable for two reasons. First, it shows that useful research can come out of a summer project. Second, our parameter-estimation code installed and ran so smoothly that even an undergrad with no previous experience could get some useful results. This made us optimistic that everything would work perfectly in the upcoming observing run (O1). Unfortunately, a few improvements were made to the code before then, and we were back to the usual level of fun in time for The Event.