neutron star–black hole binaries

GW200115 and GW200105—Completing the set

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GW200115 and GW200105 are the first gravitational-wave candidates announced from the second half of LIGO and Virgo’s third observing run (O3b). They may be our first ever observations of neutron star–black hole binaries [bonus note]. These mixed binaries of one neutron star and one black hole have long proved elusive, but we are now on our way to revealing their secrets.

Masses of neutron stars and stellar-mass black holes

The population of compact objects (black holes and neutron stars) observed with gravitational waves and with electromagnetic astronomy, including a few that are uncertain. The sources for GW200115 (left) and GW200105 (right) are highlighted. Source: Northwestern

The first gravitational-wave signal ever detected, GW150914, came from a binary black hole system: two black holes that inspiralled together to form a bigger black hole. (I hope you are all imagining a bloopy chirp to accompany this). We had never before observed a binary black hole system. However, binary black holes have proved to be the most common source of gravitational waves, and we are now starting to understand their properties. We found our next type of gravitational-wave source with GW170817, which came from a binary neutron star system (two neutron stars that orbited each other). Before we had gravitational-wave astronomy, we knew this type of binary existed as we had observed pulsars in binaries thanks to radio astronomy. Yet, our second binary neutron star observation, GW190425, still showed that we didn’t know everything about their properties. After finding binary black holes and binary neutron stars, what about a mixed neutron star–black hole binary? These should exist, but finding evidence for them has proved difficult.

The LIGO checklist

Time to tick neutron star–black hole binaries off the checklist. Part of a comic by Nutsinee Kijbunchoo drawn following the discovery of GW170817 showing Rai Weiss rather happy with his work. [Update]

Previous candidates

The first hints of neutron star–black hole binaries came in the first half of LIGO and Virgo’s third observing run (O3a, yes we are the best at thinking up names). The gravitational-wave candidate GW190426_152155 (the best at names) looks like it could have come from a neutron star–black hole binary. However, this is a quiet signal, so we are not sure whether it is real or a false alarm.

Our detection pipelines search the data from the detectors looking for signals. Our searches designed to specifically look for signals from binaries match the data against templates of what the signals should look like. From this comparison, they consider two pieces of information: how loud a signal is (its signal-to-noise ratio), and how consistent the signal is with the template. These are combined into a ranking statistic, and by comparing the ranking statistic with values produced by a background of noise, we can compute a false alarm rate of how often something at least this signal-like would happen in random noise. For GW190426_152155, this is 1.4~\mathrm{yr^{-1}}, which isn’t too great.

The false alarm rate is not the end of the story though: we need to consider the true alarm rate: how often we expect to detect such a signal. If something is an everyday occurrence, you don’t need much evidence to convince yourself it’s real.  Consider the quality of a photo you would need to convince yourself there was a horse walking around outside, and the quality needed to convince yourself there is a unicorn. For gravitational waves, a false alarm rate of 1.4~\mathrm{yr^{-1}} would be enough to give you a fair (but not necessarily conclusive) probability of the signal being real if the source were a binary black hole, as we know they are pretty common. We don’t yet know how common gravitational waves from neutron star–black hole binaries are, but the fact that we are lacking good examples indicates that they are at least somewhat rare. Therefore, with the balance of probability, it seems plausible that GW190426_152155 is noise, and the hunt needs to continue.

All O3a masses

Estimated total mass M = m_1 + m_2 and mass ratio $q = m_2/m_1 \leq 1$ of the binary sources for the candidates in O3a. The contours mark the 90% credible regions. The dashed lines mark a robust upper limit on the maximum neutron star mass. Figure 6 of the GWTC-2 Paper.

The next potential candidate was GW190814. This is a super clear detection. However, the nature of the source is more mysterious. The primary (the more massive object in the binary) is definitely a black hole, but the secondary, at around 2.6 M_\odot (where 1 M_\odot is a solar mass) is either potentially too large to be a neutron star. We’re not entirely sure of the maximum mass a neutron star can be before collapsing. Hence, we’re not quite sure if we have a massive neutron star, or a really small black hole. I think the black hole is more likely. The curious nature of GW190814’s source means we are still missing an unambiguous neutron star–black hole.

Discovery

Observations in O3b changed everything. Within the space of ten days in January 2020 [bonus note], we collected two neutron star–black hole candidates: GW200105_162426 (GW200105 for short) and GW200115_042309 (GW200115).

GW200115 is a clear detection. All three detectors were observing at the time, and we get a good signal in both LIGO Livingston and LIGO Hanford (Virgo, being less sensitive currently, has less informative data). From these observations, our search algorithm GstLAL estimates a false alarm rate of <1/(1 \times 10^5)~\mathrm{yr^{-1}}, PyCBC estimates <1/(5.6\times 10^4)~\mathrm{yr^{-1}}, and MBTA (being used for the first time for final search results) estimates 1/182~\mathrm{yr^{-1}}. All of the search algorithms agree that this is a significant detection.

GW200105 is more difficult. LIGO Hanford was offline at the time, so we only have LIGO Livingston and Virgo. In Livingston data we can see a beautiful chirp, but in Virgo the signal is too quiet for the detection algorithms to use. This is like the case for GW190425, we must try to establish the significance using a single detector.

Normalised spectrograms for GW200105 and GW200115

Time–frequency plots for GW200105 (left) and GW200115 (right) as measured by LIGO Hanford, LIGO Livingston and Virgo. LIGO Hanford was not observing at the time of GW200105. The chirp of a binary coalescence is clearest in Livingston for GW200105; these are usually hard to see for these types of signals. The Livingston data for GW200105 is shown after glitch subtraction, and the Livingston data for GW200115 shows light-scattering glitches at low frequencies. Figure 1 of the NSBH Discovery Paper.

When we have multiple detectors, we can ask how often we would expect to see the same signal at compatible times in multiple detectors. It is much less likely that multiple detectors would have the same random bit of noise in one detector and at the same time in another. We can estimate how often this would happen, for example, by comparing data from the detectors at different times. Considering many different time offsets, we can build up statistics for tens of thousands of years, even though we have only been observing for a few months (the upper limit on the false alarm rate quoted for GW200115 is because it stands out after we have exhausted all these times slides). When we have a single detector, we can’t do this.

GW200105 stands out from anything we have seen in the data we’ve analysed. We could therefore assign a false alarm rate of one per observing time. However, that doesn’t quite encode everything we know. We expect louder noise artifacts to be rarer than quieter ones. An outlier with signal-to-noise ratio of 12 should be rarer than one with signal-to-noise ratio of 11 (and GW200105 is over 13), and hence we can use this knowledge to try to extrapolate a false alarm rate.

Comparison of GW200105, GW200115 and GW190426_152155 to O3 data

Detection statistics for GW200105, GW200115 and GW190426_152155, showing they compare to background data. The plot shows the signal-to-noise \rho ratio and signal-consistency statistic \xi from the GstLAL algorithm. The coloured density plot shows the distribution of background triggers. LHO indicates a trigger from LIGO Hanford, and LLO indicates a trigger from LIGO Livingston. GW200105 is distinct from anything else seen in O3. However, GW200105 is calculated less significant than GW200115 as it only has a trigger from a single detector. Figure 3 of the NSBH Discovery Paper.

Currently, only GstLAL can calculate single-detector false alarm rates. PyCBC and MBTA both identify the same feature in the data, but cannot assign a significance to this. Using GstLAL’s extrapolation, which is chosen to be conservative (not as conservative as one per observing time, but a better representation of the data), we calculate a false alarm rate of 1/2.8~\mathrm{yr^{-1}}. This is good enough to be interesting, and better than for GW190426_152155, but not enough to be absolutely conclusive. I think we may see some active development of estimating single-detector false alarm rates (or lowering the threshold for Virgo data to be used) in the future to try to address these difficulties.

It is very tempting to look at GW200105‘s clear chirp and convince yourself it must be real. However, our detection algorithms are more sensitive than our eyes and more reliable. They are carefully tested, and build up their statistics analysing large chunks of data. Hence, we should acknowledge that the difficulty in assigning a false alarm rate is an intrinsic difficulty when you only have so much data. Even the best signal can only end up with a modest false alarm rate. It’s kind of like winning the lottery on your third go if you don’t know how the lottery works: you can estimate that the probability of winning is about 1/3, even if you suspect it should be much smaller. The results computed for this paper only use a fraction of O3b, so we could be able to do a little better in the future.

Sources

Let us assume both signals are real, where do they come from? Do we at last have our undisputable neutron star–black hole binaries?

We infer [bonus note] that GW200115 comes from a binary with component masses 5.7^{+1.8}_{-2.1} M_\odot and 1.5^{+0.7}_{-0.3} M_\odot (or 5.9^{+1.4}_{-2.1} M_\odot and 1.4^{+0.2}_{-0.2} M_\odot if we restrict the secondary’s spin to < 0.05). The primary here looks to be a black hole. It is one of the smallest we have seen. The uncertainties on the measurement potentially take it into the hypothesised lower mass gap between neutron stars and black holes suggested from X-ray observations (and somewhat questioned by GW190814); however, there is a 70% chance that the mass is > 5 M_\odot, so it is pretty consistent with the population of black holes we’ve seen in X-ray binaries. The secondary is perfectly in the neutron star range. Hence, this looks like a great neutron star–black hole binary candidate.

For GW200105, we infer that the primary has mass 8.9^{+1.2}_{-1.5} M_\odot and secondary has mass 1.9^{+0.3}_{-0.2} M_\odot (or 8.9^{+1.1}_{-1.3} M_\odot and 1.9^{+0.2}_{-0.2} M_\odot with low secondary spin). The primary is a nice black hole, the secondary is a nice plump neutron star. It is towards the more massive end of the distribution we have seen with radio observations, but it is consistent with past observations. Unlike for GW190814, we do not have any trouble explaining such as mass given what we know about the stiffness of neutron star stuff™. This is another good neutron star–black hole binary candidate.

Binary component masses for neutron star–black hole binary candidates

Estimated masses for the binary primary and secondary masses m_1 and m_2 for neutron star–black hole binary candidates. The two-dimensional plot shows the 90% probability contour. For GW200105 and GW200115 we show results for two different spin priors for the secondary. The one-dimensional plot shows individual masses; the vertical lines mark 90% bounds away from equal mass. Estimates for the maximum neutron star mass (based upon Galactic neutron stars and studies of the equation of state) are shown for comparison with the mass of the secondary. Figure 4 of the NSBH Discovery Paper.

The masses for GW200115 overlap nicely with those inferred for GW190426_152155 5.7^{+3.9}_{-2.3} M_\odot and 1.5^{+0.8}_{-0.5} [bonus note]. The uncertainties for GW190426_152155 are larger, on account of it being quieter. Perhaps this could indicate this is fairly typical for neutron star–black hole binaries (and we might need to revise that true alarm rate)? It’s still too early to say, but I very much look forward to finding out!

The masses align nicely with expectations for neutron star–black hole binaries, so there are no surprises there. Ideally, we would confirm that we have seen neutron stars by measuring the tidal distortion of the neutron star [bonus note]. Unfortunately, these effects get harder to measure when the asymmetry in masses gets more significant, and we can’t pick anything out of the data. However, we did compare the secondary masses to various expectations for the maximum neutron star mass, and find that there’s over a 93% probability that the secondaries are safely below this. In conclusion, I think we have a good case for having completed our set of binaries and found neutron star–black hole binaries.

Orientation and magnitudes of the two spins for GW200105 and GW200115

Estimated orientation and magnitude of the two component spins for GW200105 (left) and GW200115 (right). The distribution for the more massive primary component is on the left, and for the lighter secondary component on the right. The probability is binned into areas which have uniform prior probabilities, so if we had learnt nothing, the plot would be uniform. The maximum spin magnitude of 1 is appropriate for black holes. The solid line shows the 90% credible region using the high spin prior (which is used for the rest of the plot) and the dashed line shows the 90% contour for the low-spin prior. Figure 6 of the NSBH Discovery Paper.

The spins are more interesting. Spins range from zero for non-spinning, to one for a maximally spinning black hole. As a consequence of the large mass asymmetry, we measure the spin of the black holes better than for the neutron stars. For GW200105, we can constrain the spin magnitude to be < 0.23 at 90% probability (or < 0.22 with the low neutron star spin prior). This matches what we have seen for a lot of our black holes (as for GW190814‘s primary, but probably not for GW190412‘s primary), that their spins are small and nicely consistent with being zero.

For GW200115, the primary spin is also consistent with zero. However, there is also support for larger spins, and intriguingly, spin misaligned (or even antialigned as there’s little evidence of spin components in the orbital plane) with the orbital angular momentum. It is often convenient to work with the effective inspiral spin, which is a mass-weighted combination of the two spins projected along the direction of the orbital momentum. A positive value indicates the spins are overall aligned with the orbital angular momentum, while a negative value indicates the spins are overall misaligned. For GW200105, we find -0.01^{+0.11}_{-0.15} (or -0.01^{+0.08}_{-0.12} with low neutron star spin). This is consistent with zero, and what you would expect if spins were small, or if there were no preferred alignment. For GW200115 however, we find -0.19^{+0.23}_{-0.35} (-0.14^{+0.17}_{-0.34} with low neutron star spin). This is still consistent with positive or zero values, but prefers negative values.

Generally aligned spins are expected for binaries formed from two binary stars that lived their lives together. The stars would have formed from the same cloud of gas, so you would expect the stars to start out rotating the same way. Tides and mass transfer between the stars should also help to align spins. Supernova explosions could tilt the spins, but it’s hard to get a complete reversal without disrupting the binary. This did happen for the double pulsar, so it’s not impossible, but overall you would expect it to be rare. However, for binaries formed dynamically, the spins would be randomly aligned.

Does the spin for GW200115 thus point to a dynamical origin? That would be unexpected, as isolated evolution generally predicts higher rates of forming neutron star–black hole binaries than dynamical channels. Dynamical channels tend to prefer making more massive binaries. The spin is perfectly consistent with being small and aligned, so perhaps that is the correct answer, and there’s nothing unexpected to see.

Primary mass, spin aligned with orbital angular momentum and spin incomponent in the the orbital plane for GW200115

Estimated primary mass m_1, spin component in the orbital plane \chi_{1\perp}, and spin component aligned with the orbital angular momentum \chi_{1,z} and  for GW200115. The (off-diagonal) two-dimensional plots show the correlations between parameters. The solid lines indicate 50% and 90% credible regions with the high-spin prior for the secondary, and the dashed lines show the same for the low-spin prior. The (on-diagonal) one-dimensional plots show probability densities. The vertical lines indicate 90% credible intervals. The black lines show the priors. Figure 7 of the NSBH Discovery Paper.

Since the spin is correlated with the mass, if we impose that GW200115‘s primary spin is small and aligned, we also find that the primary mass is towards the upper end of its range. This would keep it safely out of the proposed range of the lower mass gap. I’m not sure if that is of any physical relevance (as I’m not sure if I believe there is a gap), but it is potentially worth keeping in mind if you want to model the progenitor (you need to fit mass and spin together).

I look forward to lots of studies looking at how to form these systems.

Rates

Now we have confirmation that neutron star–black hole binaries exist, how many do we think there are out there? To go from our detections to a merger rate density, we need to assume something about the population of neutron star–black hole binaries (we need to know about the systems that we could have observed but didn’t). This is rather tricky, as neutron star–black hole binaries could potentially have a diverse range of properties, and we can’t be sure of this distribution with only a couple of observations. Therefore, we’ve tried a few different things.

First, we considered what are the rates of binaries that match the inferred properties of the two sources. We infer that the rate of GW200115-like binaries is 36^{+82}_{-20}~\mathrm{Gpc^{-3}\,yr^{-1}} using the results of GstLAL (and 40^{+92}_{-34}~\mathrm{Gpc^{-3}\,yr^{-1}} using PyCBC). The rate of GW200105-like binaries is 16^{+38}_{-14}~\mathrm{Gpc^{-3}\,yr^{-1}} (since PyCBC couldn’t detect this event, we could only set an upper limit, which is less interesting). GW200115 is less massive than GW200105, and so could not be detected to as great a distance. Therefore, since we’ve detected one of both, it means that the rate of GW200115-like binaries should be a bit higher. If we assume all neutron star–black hole binaries are like one of the two, we find an overall event-based rate of 45^{+75}_{-33}~\mathrm{Gpc^{-3}\,yr^{-1}}.

Neutron star–black hole binary merger rate density

Probability distribution for the neutron star–black hole binary merger rate density. The green curve shows the event-based rate assuming all neutron star–black hole binaries are like GW200105 or GW200115. The black line assumes a broader population that also includes GW190814 and higher mass black holes. The vertical lines mark the 90% credible interval. Figure 9 of the NSBH Discovery Paper.

The second approach is to take a much more agnostic approach, and consider all output from our detection pipelines over a plausible mass range. The population here is defined more for convenience than anything else. We picked search triggers (down to a signal-to-noise ratio) corresponding to binaries with a primary mass between 2.5 M_\odot and 40 M_\odot and a secondary mass between 1 M_\odot and 3 M_\odot. The upper limit on the primary mass is set by the limits of our waveforms. Potentially, this mass could catch some binary neutron stars or binary black holes too. Therefore, we consider a mixture model and probabilistically assign candidates to being either noise, binary neutron star (if both components are below 2.5 M_\odot), binary black hole (if both components are above 5 M_\odot), and neutron star–black hole binaries (for things in between). I think we’ve been very inclusive in defining the neutron star–black hole space here, both excluding the possibility of binary neutron star components above 2.5 M_\odot (which I think unlikely, but possible), and binary black hole components below 5 M_\odot (which I think probable). Therefore, we should absolutely not be missing any neutron star–black holes (GW190814’s source is counted as a neutron star–black hole in this calculation). This rate comes out as 130^{+112}_{-69}~\mathrm{Gpc^{-3}\,yr^{-1}}.

I don’t think these will rule out any models, but they give the ballpark to aim for. As we find more neutron star–black hole candidates, these rates should evolve as our uncertainties will shrink, and we get a better understanding of the source population.

Predictions for neutron star–black hole binary rates in different COMPAS models

Predictions for the neutron star–black hole binary merger rate density as modelled by the COMPAS population synthesis code. The different models illustrate variations in the input physics, highlighting the range of predictions for isolated binary evolution. Other channels could potentially form neutron star–black hole binaries too. Figure 9 of Broekgaarden et al. (2021).

Summary

We have finally found our neutron star–black hole binaries. They’re pretty neat. These are the first discoveries from O3b. They will not be the last.

Title: Observation of gravitational waves from two neutron star–black hole coalescences
Journal: Astrophysical Journal Letters; 915(1):L5(25)
arXiv: 2106.15163 [astro-ph.HE]
Science summary: A new source of gravitational waves: Neutron star–black hole binaries
Data release: GW200105; GW200115
GW200105 Rating: 🐦🍨🥇😮
GW200115 Rating: 🐭🍨😮🙃🏆

Bonus notes

Cookies

I like to think of neutron star–black hole binaries as the mirror counterparts of fluffernutter cookies. Black holes are black and super dense, completely unlike marshmallows. Neutron stars are made of something mysterious that we don’t know the properties of, but we think all neutron stars are made of the same type of stuff™, whereas peanut butter is made of well known ingredients, but has both smooth and crunchy equations of state. Despite the difference in ingredients, for both, when we mix the two types we get something delicious.

Even years

Previously, all our LIGO–Virgo discoveries came during odd-numbered years, so I was kind of hoping for a quiet 2020. This didn’t work out.

Waveform models

One of the most difficult things with inferring the properties of neutron star–black hole binaries is the waveform models that we use. We need accurate models to compare with the data to get good estimates of the parameters. Unfortunately, we don’t have models that include all the physics we want (spin precession, higher-order multipole moments, and the effects of the neutron star stuff™). From our tests, it seems like spin precession and higher-order multipole moments are more important. The latter is certainly important for asymmetric binaries. Therefore, for our main results, we use binary black hole waveforms that include spin precession and higher-order multipole moments (but no neutron star stuff™ effects). These models should be a pretty good representation of the overall physics (especially if the neutron tar gets swallowed whole). However, they may not give the best estimate of the final black hole mass. In the paper, we used the neutron star–black hole waveforms that include neutron star stuff™ effects but not spin precession and higher-order multipole moments, but I think it’s a bit confusing to mix the two results here, so I’ll skip over final masses and spins.

GW190426_152155’s properties

While GW190426_152155 agrees nicely with GW200115‘s masses, its other properties are somewhat different. Its effective inspiral spin is -0.03^{+0.32}_{-0.30} (compared with -0.19^{+0.23}_{-0.35}), and its distance is 0.37^{+0.18}_{-0.16}~\mathrm{Gpc}. (compared with 0.30^{+0.15}_{-0.10}~\mathrm{Gpc}). The sky positions are also not significantly overlapping.

Electromagnetic observations

An electromagnetic counterpart, as was found for GW170817, would confirm the presence of stuff™, and that we didn’t just have two black holes. However, with these mass black holes, we would expect the neutron stars to be pretty much swallowed whole (like me consuming a fluffernutter cookie) with nothing to see [bonus bonus note]. So far nothing has been reported, which is about as surprising as failing to find a needle in a haystack, when there is no needle.

Ejecta

We estimate that the amount of neutron star stuff ejected during the merger is less than 10^{-6} M_\odot. This is very small by astronomical standards, but is still pretty large. It’s around a third of the mass of the Earth, and would correspond to around 1,000,000,000,000,000,000,000 elephants. Sadly, it is not expected that material ejected from neutron stars would directly turn into elephants, and elephants do remain endangered.

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GW190814—The mystery of a 2.6 solar mass compact object

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GW190814 is an exception discovery from the third observing run (O3) of the LIGO and Virgo gravitational wave detectors. The signal came from the coalescence of a binary made up of a component about 23 times the mass of our Sun (solar masses) and one about 2.6 solar masses. The more massive component would be a black hole, similar to past discoveries. The less massive component, however, we’re not sure about. This is a mass range where observations have been lacking. It could be a neutron star. In this case, GW190814 would be the first time we have seen a neutron star–black hole binary. This could also be the most massive neutron star ever found, certainly the most massive in a compact-object (black hole or neutron star) binary. Alternatively, it could be a black hole, in which case it would be the smallest black hole ever found. We have discovered something special, we’re just not sure exactly what…

Black hole and neutron star masses highlighting GW190814

The population of compact objects (black holes and neutron stars) observed with gravitational waves and with electromagnetic astronomy, including a few which are uncertain. GW190814 is highlighted. It is not clear if its lighter component is a black hole or neutron star. Source: Northwestern

Detection

14 August 2019 marked the second birthday of GW170814—the first gravitational wave we clearly detected using all three of our detectors. As a present, we got an even more exciting detection.

I was at the MESA Summer School at the time [bonus advertisement], learning how to model stars. My student Chase come over excitedly as soon as he saw the alert. We snuck a look at the data in a private corner of the class. GW190814 (then simply known as candidate S190814bv) was a beautifully clear chirp. You shouldn’t assess how plausible a candidate signal is by eye (that’s why we spent years building detection algorithms [bonus note]), but GW190814 was a clear slam dunk that hit it out of the park straight into the bullseye. Check mate!

Normalised spectrograms for GW190814

Time–frequency plots for GW190814 as measured by LIGO Hanford, LIGO Livingston and Virgo. The chirp of a binary coalescence is clearest in Livingston. For long signals, like GW190814, it is usually hard to pick out the chirp by eye. Figure 1 of the GW190814 Discovery Paper.

Unlike GW170814, however, it seemed that we only had two detectors observing. LIGO Hanford was undergoing maintenance (the same procedure as when GW170608 occurred). However, after some quick checks, it was established that the Hanford data was actually good to use—the detectors had been left alone in the 5 minutes around the signal (phew), so the data were clean (wooh)! We had another three-detector detection.

The big difference that having three detectors make is a much better localization of the source. For GW190814 we get a beautifully tight localization. This was exciting, as GW190814 could be a neutron star–black hole. The initial source classification (which is always pretty uncertain as it’s done before we have detailed analysis) went back and forth between being a binary black hole with one component in the the 3–5 solar mass range, and a neutron star–black hole (which means the less massive component is below 3 solar masses, not necessarily a neutron star). Neutron star–black hole mergers may potentially have an electromagnetic counterparts which can be found by telescopes. Not all neutron star–black hole binaries will have counterparts as sometimes, when the black hole is much bigger than the neutron star, it will be swallowed whole. Even if there is a counterpart, it may be too faint to see (we expect this to be increasingly common as our detectors detect gravitational waves from more distance sources). GW190814’s source is about 240 Mpc away (six times the distance of GW170817, meaning any light emitted would be about 36 times fainter) [bonus note]. Many teams searched for counterparts, but none have been reported. Despite the excellent localization, we have no multimessenger counterpart this time.

Sky map for GW190814

Sky localizations for GW190814’s source. The blue dashed contour shows the preliminary localization using only LIGO Livingston and Virgo data, and the solid orange shows the preliminary localization adding in Hanford data. The dashed green contour shows and updated localization used by many for their follow-up studies. The solid purple contour shows our final result, which has an area of just 18.5~\mathrm{deg^2}. All contours are for 90% probabilities. Figure 2 of the GW190814 Discovery Paper.

The sky localisation for GW190814 demonstrates nicely how localization works for gravitational-wave sources. We get most of our information from the delay time between the signal reaching the different detectors. With a two-detector network, a single time delay corresponds to a ring on the sky. We kind of see this with the blue dashed localization above, which was the initial result using just LIGO Livingston and Virgo data. There are actual arcs corresponding to two different time delays. This is because the signal is quiet in Virgo, and so we don’t get an absolute lock on the arrival time: if you shift the signal so it’s one cycle different, it still matches pretty well, so we get two possibilities. The arcs aren’t full circles because information on the phase of the signals, and the relative amplitudes (since detectors are not uniformal sensitive in all directions) add extra information. Adding in LIGO Hanford data gives us more information on the timing. The Hanford–Livingston circle of constant time delay slices through the Livingston–Virgo one, leaving us with just the two overlapping islands as possibilities. The sky localizations shifted a little bit as we refined the analysis, but remained pretty consistent.

Whodunnit?

From the gravitational wave signal we inferred that GW190814 came from a binary with masses m_1 = 23.2^{+1.1}_{-1.0} solar masses (quoting the 90% range for parameters), and the other m_2 = 2.59^{+0.08}_{-0.09} solar masses. This is remarkable for two reasons: first, the lower mass object is right in the range where we might hit the maximum mass of a neutron star, and second, this is the most asymmetric masses from any of our gravitational wave sources.

Binary component masses for GW190814

Estimated masses for the two components in the binary m_i \geq m_2. We show results several different waveform models (which include spin precession and higher order multiple moments). The two-dimensional shows the 90% probability contour. The one-dimensional plot shows individual masses; the dotted lines mark 90% bounds away from equal mass. Estimates for the maximum neutron star mass are shown for comparison with the mass of the lighter component m_2. Figure 3 of the GW190814 Discovery Paper.

Neutron star or black hole?

Neutron stars are massive balls of stuff™. They are made of matter in its most squished form. A neutron star about 1.4 solar masses would have a radius of only about 12 kilometres. For comparison, that’s roughly the same as trying to fit the mass of 3\times 10^{33} M&Ms (plain; for peanut butter it would be different, and of course, more delicious) into the volume of just 1.2 \times 10^{19} M&Ms (ignoring the fact that you can’t perfectly pack them)! Neutron stars are about 3 \times 10^{14} times more dense than M&Ms. As you make neutron stars heavier, their gravity gets stronger until at some point the strange stuff™ they are made of can’t take the pressure. At this point the neutron star will collapse down to a black hole. Since we don’t know the properties of neutron star stuff™ we don’t know the maximum mass of a neutron star.

We have observed neutron stars of a range of masses. The recently discovered pulsar J0740+6620 may be around 2.1 solar masses, and potentially pulsar J1748−2021B may be around 2.7 solar masses (although that measurement is more uncertain as it requires some strong assumptions about the pulsar’s orbit and its companion star). Using observations of GW170817, estimates have been made that the maximum neutron star mass should be below 2.2 or 2.3 solar masses; using late-time observations of short gamma-ray bursts (assuming that they all come from binary neutron star mergers) indicates an upper limit of 2.4 solar masses, and looking at the observed population of neutron stars, it could be anywhere between 2 and 3 solar masses. About 3 solar masses is a safe upper limit,  as it’s not possible to make stuff™ stiff enough to withstand more pressure than that.

At about 2.6 solar masses, it’s not too much of a stretch to believe that the less massive component is a neutron star. In this case, we have learnt something valuable about the properties of neutron star stuff™. Assuming that we have a neutron star, we can infer the properties of neutron star stuff™. We find that a typical neutron star 1.4 solar masses, the radius would be R_{1.4} = 12.9^{+0.8}_{-0.7}~\mathrm{km} and the tidal deformability \Lambda_{1.4} = 616^{+273}_{-158}.

The plot below shows our results fitting the neutron star equation of state, which describes how the density pf neutron star stuff™ changes with pressure. The dashed lines show the 90% range of our prior (what the analysis would return with no input information). The blue curve shows results adding in GW170817 (what we would have if GW190814 was a binary black hole), we prefer neutron stars made of softer stuff™ (which is squisher to hug, and would generally result in more compact neutron stars). Adding in GW190814 (assuming a neutron star–black hole) pushes us back up to stiffer stuff™ as we now need to support a massive maximum mass.

Neutron star pressure and density

Constraints on the neutron star equation of state, showing how density \rho changes with pressure $p$. The blue curve just uses GW170817, implicitly assuming that GW190814 is from a binary black hole, while the orange shows what happens if we include GW190814, assuming it is from a neutron star–black hole binary. The 90% and 50% credible contours are shown as the dark and lighter bands, and the dashed lines indicate the 90% region of the prior. Figure 8 of the GW190814 Discovery Paper.

What if it’s not a neutron star?

In this case we must have a black hole. In theory black holes can be any mass: you just need to squish enough mass into a small enough space. However, from our observations of X-ray binaries, there seem to be no black holes below about 5 solar masses. This is referred to as the lower mass gap, or the core collapse mass gap. The theory was that when the cores of massive stars collapse, there are different types of explosions and implosions depending upon the core’s mass. When you have a black hole, more material from outside the core falls back than when you have a neutron star. All the extra material would always mean that black holes are born above 5 solar masses. If we’ve found a black hole below this, either this theory is wrong and we need a new explanation for the lack of X-ray observations, or we have a black hole formed via a different means.

Potentially, we could if we measured the effects of the tidal distortion of the neutron star in the gravitational wave signal. Unfortunately, tidal effects are weaker for more unequal mass binaries. GW190814 is extremely unequal, so we can’t measure anything and say either way. Equally, seeing an electromagnetic counterpart would be evidence for a neutron star, but with such unequal masses the neutron star would likely be eaten whole, like me eating an M&M. The mass ratio means that we can’t be certain what we have.

The calculation we can do, is use past observations of neutron stars and measurements of the stiffness of neutron star stuff™ to estimate the probability the the mass of the less massive component is below the maximum neutron star mass. Using measurements from GW170817 for the stuff™ stiffness, we estimate that there’s only a 3% probability of the mass being below the maximum neutron star mass, and using the observed population of neutron stars the probability is 29%. It seems that it is improbable, but not impossible, that the component is a neutron star.

I’m yet to be convinced one way or the other on black hole vs neutron star [bonus note], but I do like the idea of extra small black holes. They would be especially cute, although you must never try to hug them.

The unequal masses

Most of the binaries we’ve seen with gravitational waves so far are consistent with having equal masses. The exception is GW190412, which has a mass ratio of q = m_2/m_1 = 0.28^{+0.13}_{-0.07}. The mass ratio changes a few things about the gravitational wave signal. When you have unequal masses, it is possible to observe higher harmonics in the gravitational wave signal: chirps at multiples of the orbital frequency (the dominant two form a perfect fifth). We observed higher harmonics for the first time with GW190412. GW190814 has a more extreme mass ratio q = 0.112^{+0.008}_{-0.009}. We again spot the next harmonic in GW190814, this time it is even more clear. Modelling gravitational waves from systems with mass ratios of q \sim 0.1 is tricky, it is important to include the higher order multipole moments in order to get good estimates of the source parameters.

Having unequal masses makes some of the properties of the lighter component, like its tidal deformability of its spin, harder to measure. Potentially, it can be easier to pick out the spin of the more massive component. In the case of GW190814, we find that the spin is small, \chi_1 < 0.07. This is our best ever measurement of black hole spin!

Orientation and magnitudes of the two spins

Estimated orientation and magnitude of the two component spins. The distribution for the more massive component is on the left, and for the lighter component on the right. The probability is binned into areas which have uniform prior probabilities, so if we had learnt nothing, the plot would be uniform. The maximum spin magnitude of 1 is appropriate for black holes. On account of the mass ratio, we get a good measurement of the spin of the more massive component, but not the lighter one. Figure 6 of the GW190814 Discovery Paper.

Typically, it is easier to measure the amount of spin aligned with the orbital angular momentum. We often characterise this as the effective inspiral spin parameter. In this case, we measure \chi_\mathrm{eff} = -0.002^{+0.060}_{-0.061}. Harder to measure is the spin in the orbital plane. This controls the amount of spin precession (wobbling in the spin orientation as the orbital angular momentum is not aligned with the total angular momentum), and is characterised by the effective precession spin parameter. For GW190814, we find \chi_\mathrm{p} < 0.07, which is our tightest measurement. It might seem odd that we get our best measurement of in-plane spin in the case when there is no precession. However, this is because if there were precession, we would clearly measure it. Since there is no support for precession in the data, we know that it isn’t there, and hence that the amount of in-plane spin is small.

Implications

While we haven’t solved the mystery of neutron star vs black hole, what can we deduce?

  1. Einstein is still not wrong yet. Our tests of general relativity didn’t give us any evidence that something was wrong. We even tried a new test looking for deviations in the spin-induced quadrupole moment. GW190814 was initially thought to be a good case to try this, on account of its mass ratio, unfortunately, since there’s little hint of spin, we don’t get particularly informative results. Next time.
  2. The Universe is expanded about as fast as we’d expect. We have a wonderfully tight localization: GW190814 has the best localization of all our gravitational waves except for GW170817. This means we can cross-reference with galaxy catalogues to estimate the Hubble constant, a measure of the expansion rate of the Universe. We get the distance from our gravitational wave measurement, and the redshift from the catalogue, and putting them together give the Hubble constant H_0. From GW190814 alone, we get H_0 = 83^{+55}_{-53}~\mathrm{km\,s^{-1}\,Mpc^{-1}} (quoting numbers with our usual median and symmetric 90% interval convention; if you like mode and narrowest 68% region, it’s H_0 = 75^{+59}_{-13}~\mathrm{km\,s^{-1}\,Mpc^{-1}}). If we combine with results for GW170817, we get H_0 = 77^{+33}_{-23}~\mathrm{km\,s^{-1}\,Mpc^{-1}} (or H_0 = 70^{+17}_{-8}~\mathrm{km\,s^{-1}\,Mpc^{-1}}) [bonus note].
  3. The merger rate density for a population of GW190814-like systems is 7^{+16}_{-6}~\mathrm{Gpc^{-3}\,yr^{-1}}. If you think you know how GW190814 formed, you’ll need to make sure to get a compatible rate estimate.

What can we say about potential formation channels for the source? This is rather tricky as many predictions assume supernova models which lead to a mass group, so there’s nothing with a compatible mass for the lighter component. I expect there will be lots of checking what happens without this assumption.

Given the mass of the black hole, we would expect that it formed from a low metallicity star. That is a star which doesn’t have too many of the elements heavier than hydrogen and helium. Heavier elements lead to stronger stellar winds, meaning that stars are smaller at the end of their lives and it is harder to get a black hole that’s 23 solar masses. The same is true for many of the black holes we’ve seen in gravitational waves.

Massive stars have short lives. The bigger they are, the more quickly they burn up all their nuclear fuel. This has an important implication for the mass of the lighter component: it probably has not grown much since it formed. We could either have the bigger component forming from the initially bigger star (which is the simpler scenario to imagine). In this case, the black hole forms first, and there is no chance for the lighter component to grow after it forms as it’s sitting next to a black hole. It is possible that the lighter component formed first if when its parent star started expanding in middle age (as many of us do) it transferred lots of mass to its companion star. The mass transfer would reverse which of the stars was more massive, and we could then have some accretion back onto the lighter compact object to grow it a bit. However, the massive partner star would only have a short lifetime, and compact objects can only swallow a relatively small rate of material, so you wouldn’t be able the lighter component by much more than 0.1 solar masses, not nearly enough to bridge the gap from what we would consider a typical neutron star. We do need to figure out a way to form compact objects about 2.6 solar masses.

How to form GW190814-like systems through isolated binary evolution.

Two possible ways of forming GW190814-like systems through isolated binary evolution. In Channel A the heavier black hole forms first from the initially more massive star. In Channel B, the initially more massive star transfers so much mass to its companion that we get a mass inversion, and the lighter component forms first. In the plot, a is the orbital separation, e is the orbital inclination, t is the time since the stars started their life on the main sequence. The letters on the right indicate the evolution phase: ZAMS is zero-age main sequence, MS is main sequence (burning hydrogen), CHeB is core helium burning (once the hydrogen has been used up), and BH and NS mean black hole and neutron star. At low metallicities Z (when stars have few elements heavier than hydrogen and helium), the two channels are about as common, as metallicity increases Channel A becomes more common. Figure 6 of Zevin et al. (2020).

The mass ratio is difficult to produce. It’s not what you would expect for dynamically formed binaries in globular clusters (as you’d expect heavier objects to pair up). It could maybe happen in the discs around active galactic nuclei, although there are lots of uncertainties about this, and since this is only a small part of space, I wouldn’t expect a large numbers of events. Isolated binaries (or higher multiples) can form these mass ratios, but they are rare for binaries that go on to merge. Again, it might be difficult to produce enough systems to explain our observation of GW190814. We need to do some more sleuthing to figure out how binaries form.

Epilogue

The LIGO and Virgo gravitational wave detectors embody decades of work by thousand of scientists across the globe. It took many hard years of research to create the technology capable of observing gravitational waves. Many doubted it would ever be possible. Finally, in 2015, we succeeded. The first detection of gravitational waves opened a new field of astronomy—our goal was not to just detect gravitational waves once, but to use them to explore our Universe. Since then we have continued to work improving our detectors and our analyses. More discoveries have come. LIGO and Virgo are revolutionising our understanding of astrophysics, and GW190814 is the latest advancement in our knowledge. It will not be the last. Gravitational wave astronomy thrives thanks to, and as a consequence of, many people working together towards a common goal.

If a few thousand people can work together to imagine, create and operate gravitational wave detectors, think what we could achieve if millions, or billions, or if we all worked together. Let’s get to work.

Title: GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object
Journal: Astrophysical Journal Letters; 896(2):L44(20); 2020
arXiv: 2006.12611 [astro.ph-HE]
Science summary: The curious case of GW190814: The coalescence of a stellar-mass black hole and a mystery compact object
Data release: Gravitational Wave Open Science Center; Parameter estimation results
Rating: 🍩🐦🦚🦆❔

Bonus notes

MESA Summer School

Modules for Experiments in Stellar Astrophysics (MESA) is a code for simulating the evolution of stars. It’s pretty neat, and can do all sorts of cool things. The summer school is a chance to be taught how to use it as well as some theory behind the lives of stars. The school is aimed at students (advanced undergrads and postgrads) and postdocs starting out using or developing the code, but there’ll let faculty attend if there’s space. I was lucky enough to get a spot together with my fantastic students Chase, Monica and Kyle. I was extremely impressed by everything. The ratio of demonstrators to students was high, all the sessions were well thought out, and ice cream was plentiful. I would definitely recommend attending if you are interested in stellar evolution, and if you want to build the user base for your scientific code, this is certainly a wonderful model to follow.

Detection significance

For our final (for now) detection significance we only used data from LIGO Livingston and Virgo. Although the Hanford data are good, we wouldn’t have looked at this time without the prompt from the other detectors. We therefore need to be careful not to bias ourselves. For simplicity we’ve stuck with using just the two detectors. Since Hanford would boost the significance, these results should be conservative. GstLAL and PyCBC identified the event with false alarm rates of better than 1 in 100,000 years and 1 in 42,000 years, respectively.

Distance

The luminosity distance of GW190814’s source is estimated as 241^{+41}_{-45}~\mathrm{Mpc}. The luminosity distance is a measure which incorporates the effects of the signal travelling through an expanding Universe, so it’s not quite the same as the actual distance between us and the source. Given the uncertainties on the luminosity distance, it would have taken the signal somewhere between 600 million and 850 million years to reach us. It therefore set out during the Neoproterozoic era here on Earth, which is pretty cool.

In this travel time, the signal would have covered about 6 sextillion kilometres, or to put it in easier to understand units, about 400,000,000,000,000,000,000,000,000 M&Ms laid end-to-end. Eating that many M&Ms would give you about 2 \times 10^{27} calories. That seems like a lot of energy, but it’s less than 2 \times 10^{-16} of the energy emitted as gravitational waves for GW190814.

Betting

Given current uncertainties on what the maximum mass of a neutron star should be, it is hard to offer odds for whether of not the smaller component of GW190814’s binary is a black hole or neutron star. Since it does seem higher mass than expected for neutron stars from other observations, a black hole origin does seem more favoured, but as GW190425 showed, we might be missing the full picture about the neutron star population. I wouldn’t be too surprised if our understanding shifted over the next few years. Consequently, I’d stretch to offering odds of one peanut butter M&M to one plain chocolate M&M in favour of black holes over neutron stars.

Hubble constant

Using the Dark Energy Survey galaxy catalogue, Palmese et al. (2020) calculate a Hubble constant of H_0 = 66^{+55}_{-18}~\mathrm{km\,s^{-1}\,Mpc^{-1}} (mode and narrowest 68% region) using GW190814. Adding in GW170814 they get H_0 = 68^{+43}_{-21}~\mathrm{km\,s^{-1}\,Mpc^{-1}} as a gravitational-wave-only measurement, and including GW170817 and its electromagnetic counterpart gives H_0 = 69.0^{+14.0}_{-7.5}~\mathrm{km\,s^{-1}\,Mpc^{-1}}.

 

Observing run 1—The papers

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

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

Transient searches

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

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

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

More details: O1 Binary Neutron Star/Neutron Star–Black Hole Paper Paper summary

The O1 Gamma-Ray Burst Paper

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

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

More details: O1 Gamma-Ray Burst Paper summary

The O1 Intermediate Mass Black Hole Binary Paper

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

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

More details: O1 Intermediate Mass Black Hole Binary Paper summary

The O1 Burst Paper

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

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

More details: O1 Burst Paper summary

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

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

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

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

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

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

\Lambda = R \langle VT \rangle

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

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

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

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

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

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

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

Upper merger rate limits for binary neutron stars

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

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

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

Comparison of merger rates

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

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

The O1 Gamma-Ray Burst Paper

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

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

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

We used two search algorithms:

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

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

GRB 150906B sky location

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

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

The O1 Intermediate Mass Black Hole Binary Paper

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

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

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

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

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

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

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

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

Intermediate mass black hole binary search results

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

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

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

The O1 Burst Paper

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

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

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

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

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

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

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

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

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

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

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

Upper limits on energy at different frequencies

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

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