The O2 Catalogue—It goes up to 11

December 7, 2018January 26, 2020 / CPLB / Leave a comment

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 $\chi_\mathrm{eff}$ .

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.

All effective precession spin parameters

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.

Parametric and binned spin magnitude distributions

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…

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA

June 16, 2018August 20, 2019 / CPLB / Leave a comment

This paper, known as the Observing Scenarios Document with the Collaboration, outlines the observing plans of the ground-based detectors over the coming decade. If you want to search for electromagnetic or neutrino signals from our gravitational-wave sources, this is the paper for you. It is a living review—a document that is continuously updated.

This is the second published version, the big changes since the last version are

We have now detected gravitational waves
We have observed our first gravitational wave with a mulitmessenger counterpart [bonus note]
We now include KAGRA, along with LIGO and Virgo

As you might imagine, these are quite significant updates! The first showed that we can do gravitational-wave astronomy. The second showed that we can do exactly the science this paper is about. The third makes this the first joint publication of the LIGO Scientific, Virgo and KAGRA Collaborations—hopefully the first of many to come.

I lead both this and the previous version. In my blog on the previous version, I explained how I got involved, and the long road that a collaboration must follow to get published. In this post, I’ll give an overview of the key details from the new version together with some behind-the-scenes background (working as part of a large scientific collaboration allows you to do amazing science, but it can also be exhausting). If you’d like a digest of this paper’s science, check out the LIGO science summary.

Commissioning and observing phases

The first section of the paper outlines the progression of detector sensitivities. The instruments are incredibly sensitive—we’ve never made machines to make these types of measurements before, so it takes a lot of work to get them to run smoothly. We can’t just switch them on and have them work at design sensitivity [bonus note].

Target evolution of the Advanced LIGO and Advanced Virgo detectors with time. The lower the sensitivity curve, the further away we can detect sources. The distances quoted are binary neutron star (BNS) ranges, the average distance we could detect a binary neutron star system. The BNS-optimized curve is a proposal to tweak the detectors for finding BNSs. Figure 1 of the Observing Scenarios Document.

The plots above show the planned progression of the different detectors. We had to get these agreed before we could write the later parts of the paper because the sensitivity of the detectors determines how many sources we will see and how well we will be able to localize them. I had anticipated that KAGRA would be the most challenging here, as we had not previously put together this sequence of curves. However, this was not the case, instead it was Virgo which was tricky. They had a problem with the silica fibres which suspended their mirrors (they snapped, which is definitely not what you want). The silica fibres were replaced with steel ones, but it wasn’t immediately clear what sensitivity they’d achieve and when. The final word was they’d observe in August 2017 and that their projections were unchanged. I was sceptical, but they did pull it out of the bag! We had our first clear three-detector observation of a gravitational wave 14 August 2017. Bravo Virgo!

Plausible time line of observing runs with Advanced LIGO (Hanford and Livingston), advanced Virgo and KAGRA. It is too early to give a timeline for LIGO India. The numbers above the bars give binary neutron star ranges (italic for achieved, roman for target); the colours match those in the plot above. Currently our third observing run (O3) looks like it will start in early 2019; KAGRA might join with an early sensitivity run at the end of it. Figure 2 of the Observing Scenarios Document.

Searches for gravitational-wave transients

The second section explain our data analysis techniques: how we find signals in the data, how we work out probable source locations, and how we communicate these results with the broader astronomical community—from the start of our third observing run (O3), information will be shared publicly!

The information in this section hasn’t changed much [bonus note]. There is a nice collection of references on the follow-up of different events, including GW170817 (I’d recommend my blog for more on the electromagnetic story). The main update I wanted to include was information on the detection of our first gravitational waves. It turned out to be more difficult than I imagined to come up with a plot which showed results from the five different search algorithms (two which used templates, and three which did not) which found GW150914, and harder still to make a plot which everyone liked. This plot become somewhat infamous for the amount of discussion it generated. I think we ended up with something which was a good compromise and clearly shows our detections sticking out above the background of noise.

Offline transient search results from our first observing run (O1). The plot shows the number of events found verses false alarm rate: if there were no gravitational waves we would expect the points to follow the dashed line. The left panel shows the results of the templated search for compact binary coalescences (binary black holes, binary neutron stars and neutron star–black hole binaries), the right panel shows the unmodelled burst search. GW150914, GW151226 and LVT151012 are found by the templated search; GW150914 is also seen in the burst search. Arrows indicate bounds on the significance. Figure 3 of the Observing Scenarios Document.

Observing scenarios

The third section brings everything together and looks at what the prospects are for (gravitational-wave) multimessenger astronomy during each observing run. It’s really all about the big table.

Ranges, binary neutron star detections, and localization precesion

Summary of different observing scenarios with the advanced detectors. We assume a 70–75% duty factor for each instrument (including Virgo for the second scenario’s sky localization, even though it only joined our second observing run for the final month). Table 3 from the Observing Scenarios Document.

I think there are three really awesome take-aways from this

Actual binary neutron stars detected = 1. We did it!
Using the rates inferred using our observations so far (including GW170817), once we have the full five detector network of LIGO-Hanford, LIGO-Livingston, Virgo, KAGRA and LIGO-India, we could be detected 11–180 binary neutron stars a year. That something like between one a month to one every other day! I’m kind of scared…
With the five detector network the sky localization is really good. The median localization is about 9–12 square degrees, about the area the LSST could cover in a single pointing! This really shows the benefit of adding more detector to the network. The improvement comes not because a source is much better localized with five detectors than four, but because when you have five detectors you almost always have at least three detectors(the number needed to get a good triangulation) online at any moment, so you get a nice localization for pretty much everything.

In summary, the prospects for observing and localizing gravitational-wave transients are pretty great. If you are an astronomer, make the most of the quiet before O3 begins next year.

arXiv: 1304.0670 [gr-qc]
Journal: Living Reviews In Relativity; 21:3(57); 2018
Science summary: A Bright today and brighter tomorrow: Prospects for gravitational-wave astronomy With Advanced LIGO, Advanced Virgo, and KAGRA
Prospects for the next update: After two updates, I’ve stepped down from preparing the next one. Wooh!

Bonus notes

GW170817 announcement

The announcement of our first multimessenger detection came between us submitting this update and us getting referee reports. We wanted an updated version of this paper, with the current details of our observing plans, to be available for our astronomer partners to be able to cite when writing their papers on GW170817.

Predictably, when the referee reports came back, we were told we really should include reference to GW170817. This type of discovery is exactly what this paper is about! There was avalanche of results surrounding GW170817, so I had to read through a lot of papers. The reference list swelled from 8 to 13 pages, but this effort was handy for my blog writing. After including all these new results, it really felt like this was version 2.5 of the Observing Scenarios, rather than version 2.

Design sensitivity

We use the term design sensitivity to indicate the performance the current detectors were designed to achieve. They are the targets we aim to achieve with Advanced LIGO, Advance Virgo and KAGRA. One thing I’ve had to try to train myself not to say is that design sensitivity is the final sensitivity of our detectors. Teams are currently working on plans for how we can upgrade our detectors beyond design sensitivity. Reaching design sensitivity will not be the end of our journey.

Binary black holes vs binary neutron stars

Our first gravitational-wave detections were from binary black holes. Therefore, when we were starting on this update there was a push to switch from focusing on binary neutron stars to binary black holes. I resisted on this, partially because I’m lazy, but mostly because I still thought that binary neutron stars were our best bet for multimessenger astronomy. This worked out nicely.

GW170608—The underdog

November 16, 2017January 22, 2020 / CPLB / 2 Comments

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

The growing family of black holes. From Dawn Finney.

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

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

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

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

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

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

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

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

Orientation and magnitudes of the two spins

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

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

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

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

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

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

Bonus notes

Detector engineering

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

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

Coupling of angular disturbances to length

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

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

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

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

Parameter estimation rota

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

Alerts and follow-up

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

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

Virgo?

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

Journal

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

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

GW170817—The pot of gold at the end of the rainbow

October 16, 2017January 18, 2020 / CPLB / 4 Comments

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 message alert from Thursday 17 August 2017 13:58 BST

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…

Overlapping localizations for GW170817's source

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!

Gravitational-wave, gamma-ray, ultraviolet, optical, infrared and radio observations

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.

Especially made

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

Observing run 1—The papers

September 24, 2017October 13, 2017 / CPLB / Leave a comment

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

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

The O1 Gamma-Ray Burst Paper

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

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

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

We used two search algorithms:

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

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

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

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

The O1 Intermediate Mass Black Hole Binary Paper

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

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

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

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

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

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

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

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

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)

GW170104 and me

June 1, 2017February 8, 2020 / CPLB / 6 Comments

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

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

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

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

The story

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

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

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

Estimated waveforms from different models for GW170104

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The science

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

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

The searches

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

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

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

The source

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

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

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

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

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

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

Effective inspiral and precession spin parameters

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

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

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

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

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

Merger rates

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

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

Astrophysics

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

There are two main predicted channels of binary formation:

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

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

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

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

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

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

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

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

Tests of general relativity

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

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

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

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

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

The search for counterparts

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

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

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

Summary

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

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

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

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

Bonus notes

Naming

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

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

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

The 6 January sky map

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

Binary black hole waveforms

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

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

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

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

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

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

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

On distance

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

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

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

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

Time line

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Detector status

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

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

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

Spin evolution

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

Footnotes

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

Gravity waves

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

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

Colour scheme

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

GW150914—The papers II

December 10, 2016February 9, 2020 / CPLB / Leave a comment

GW150914, The Event to its friends, was our first direct observation of gravitational waves. To accompany the detection announcement, the LIGO Scientific & Virgo Collaboration put together a suite of companion papers, each looking at a different aspect of the detection and its implications. Some of the work we wanted to do was not finished at the time of the announcement; in this post I’ll go through the papers we have produced since the announcement.

The papers

I’ve listed the papers below in an order that makes sense to me when considering them together. Each started off as an investigation to check that we really understood the signal and were confident that the inferences made about the source were correct. We had preliminary results for each at the time of the announcement. Since then, the papers have evolved to fill different niches [bonus points note].

13. The Basic Physics Paper

Title: The basic physics of the binary black hole merger GW150914
arXiv: 1608.01940 [gr-qc]
Journal: Annalen der Physik; 529(1–2):1600209(17); 2017

The Event was loud enough to spot by eye after some simple filtering (provided that you knew where to look). You can therefore figure out some things about the source with back-of-the-envelope calculations. In particular, you can convince yourself that the source must be two black holes. This paper explains these calculations at a level suitable for a keen high-school or undergraduate physics student.

More details: The Basic Physics Paper summary

14. The Precession Paper

Title: Improved analysis of GW150914 using a fully spin-precessing waveform model
arXiv: 1606.01210 [gr-qc]
Journal: Physical Review X; 6(4):041014(19); 2016

To properly measure the properties of GW150914’s source, you need to compare the data to predicted gravitational-wave signals. In the Parameter Estimation Paper, we did this using two different waveform models. These models include lots of features binary black hole mergers, but not quite everything. In particular, they don’t include all the effects of precession (the wibbling of the orbit because of the black holes spins). In this paper, we analyse the signal using a model that includes all the precession effects. We find results which are consistent with our initial ones.

More details: The Precession Paper summary

15. The Systematics Paper

Title: Effects of waveform model systematics on the interpretation of GW150914
arXiv: 1611.07531 [gr-qc]
Journal: Classical & Quantum Gravity; 34(10):104002(48); 2017
LIGO science summary: Checking the accuracy of models of gravitational waves for the first measurement of a black hole merger

To check how well our waveform models can measure the properties of the source, we repeat the parameter-estimation analysis on some synthetic signals. These fake signals are calculated using numerical relativity, and so should include all the relevant pieces of physics (even those missing from our models). This paper checks to see if there are any systematic errors in results for a signal like GW150914. It looks like we’re OK, but this won’t always be the case.

More details: The Systematics Paper summary

16. The Numerical Relativity Comparison Paper

Title: Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence
arXiv: 1606.01262 [gr-qc]
Journal: Physical Review D; 94(6):064035(30); 2016
LIGO science summary: Directly comparing the first observed gravitational waves to supercomputer solutions of Einstein’s theory

Since GW150914 was so short, we can actually compare the data directly to waveforms calculated using numerical relativity. We only have a handful of numerical relativity simulations, but these are enough to give an estimate of the properties of the source. This paper reports the results of this investigation. Unsurprisingly, given all the other checks we’ve done, we find that the results are consistent with our earlier analysis.

If you’re interested in numerical relativity, this paper also gives a nice brief introduction to the field.

More details: The Numerical Relativity Comparison Paper summary

The Basic Physics Paper

Synopsis: Basic Physics Paper
Read this if: You are teaching a class on gravitational waves
Favourite part: This is published in Annalen der Physik, the same journal that Einstein published some of his monumental work on both special and general relativity

It’s fun to play with LIGO data. The Gravitational Wave Open Science Center (GWOSC), has put together a selection of tutorials to show you some of the basics of analysing signals; we also have papers which introduce gravitational wave data analysis. I wouldn’t blame you if you went of to try them now, instead of reading the rest of this post. Even though it would mean that no-one read this sentence. Purple monkey dishwasher.

The GWOSC tutorials show you how to make your own version of some of the famous plots from the detection announcement. This paper explains how to go from these, using the minimum of theory, to some inferences about the signal’s source: most significantly that it must be the merger of two black holes.

GW150914 is a chirp. It sweeps up from low frequency to high. This is what you would expect of a binary system emitting gravitational waves. The gravitational waves carry away energy and angular momentum, causing the binary’s orbit to shrink. This means that the orbital period gets shorter, and the orbital frequency higher. The gravitational wave frequency is twice the orbital frequency (for circular orbits), so this goes up too.

The rate of change of the frequency depends upon the system’s mass. To first approximation, it is determined by the chirp mass,

$\displaystyle \mathcal{M} = \frac{(m_1 m_2)^{3/5}}{(m_1 + m_2)^{1/5}}$ ,

where $m_1$ and $m_2$ are the masses of the two components of the binary. By looking at the signal (go on, try the GWOSC tutorials), we can estimate the gravitational wave frequency $f_\mathrm{GW}$ at different times, and so track how it changes. You can rewrite the equation for the rate of change of the gravitational wave frequency $\dot{f}_\mathrm{GW}$ , to give an expression for the chirp mass

$\displaystyle \mathcal{M} = \frac{c^3}{G}\left(\frac{5}{96} \pi^{-8/3} f_\mathrm{GW}^{-11/3} \dot{f}_\mathrm{GW}\right)^{3/5}$ .

Here $c$ and $G$ are the speed of light and the gravitational constant, which usually pop up in general relativity equations. If you use this formula (perhaps fitting for the trend $f_\mathrm{GW}$ ) you can get an estimate for the chirp mass. By fiddling with your fit, you’ll see there is some uncertainty, but you should end up with a value around $30 M_\odot$ [bonus note].

Next, let’s look at the peak gravitational wave frequency (where the signal is loudest). This should be when the binary finally merges. The peak is at about $150~\mathrm{Hz}$ . The orbital frequency is half this, so $f_\mathrm{orb} \approx 75~\mathrm{Hz}$ . The orbital separation $R$ is related to the frequency by

$\displaystyle R = \left[\frac{GM}{(2\pi f_\mathrm{orb})^2}\right]^{1/3}$ ,

where $M = m_1 + m_2$ is the binary’s total mass. This formula is only strictly true in Newtonian gravity, and not in full general relativity, but it’s still a reasonable approximation. We can estimate a value for the total mass from our chirp mass; if we assume the two components are about the same mass, then $M = 2^{6/5} \mathcal{M} \approx 70 M_\odot$ . We now want to compare the binary’s separation to the size of black hole with the same mass. A typical size for a black hole is given by the Schwarzschild radius

$\displaystyle R_\mathrm{S} = \frac{2GM}{c^2}$ .

If we divide the binary separation by the Schwarzschild radius we get the compactness $\mathcal{R} = R/R_\mathrm{S} \approx 1.7$ . A compactness of $\sim 1$ could only happen for black holes. We could maybe get a binary made of two neutron stars to have a compactness of $\sim2$ , but the system is too heavy to contain two neutron stars (which have a maximum mass of about $3 M_\odot$ ). The system is so compact, it must contain black holes!

What I especially like about the compactness is that it is unaffected by cosmological redshifting. The expansion of the Universe will stretch the gravitational wave, such that the frequency gets lower. This impacts our estimates for the true orbital frequency and the masses, but these cancel out in the compactness. There’s no arguing that we have a highly relativistic system.

You might now be wondering what if we don’t assume the binary is equal mass (you’ll find it becomes even more compact), or if we factor in black hole spin, or orbital eccentricity, or that the binary will lose mass as the gravitational waves carry away energy? The paper looks at these and shows that there is some wiggle room, but the signal really constrains you to have black holes. This conclusion is almost as inescapable as a black hole itself.

There are a few things which annoy me about this paper—I think it could have been more polished; “Virgo” is improperly capitalised on the author line, and some of the figures are needlessly shabby. However, I think it is a fantastic idea to put together an introductory paper like this which can be used to show students how you can deduce some properties of GW150914’s source with some simple data analysis. I’m happy to be part of a Collaboration that values communicating our science to all levels of expertise, not just writing papers for specialists!

During my undergraduate degree, there was only a single lecture on gravitational waves [bonus note]. I expect the topic will become more popular now. If you’re putting together such a course and are looking for some simple exercises, this paper might come in handy! Or if you’re a student looking for some project work this might be a good starting reference—bonus points if you put together some better looking graphs for your write-up.

If this paper has whetted your appetite for understanding how different properties of the source system leave an imprint in the gravitational wave signal, I’d recommend looking at the Parameter Estimation Paper for more.

The Precession Paper

Synopsis: Precession Paper
Read this if: You want our most detailed analysis of the spins of GW150914’s black holes
Favourite part: We might have previously over-estimated our systematic error

The Basic Physics Paper explained how you could work out some properties of GW150914’s source with simple calculations. These calculations are rather rough, and lead to estimates with large uncertainties. To do things properly, you need templates for the gravitational wave signal. This is what we did in the Parameter Estimation Paper.

In our original analysis, we used two different waveforms:

The first we referred to as EOBNR, short for the lengthy technical name SEOBNRv2_ROM_DoubleSpin. In short: This includes the spins of the two black holes, but assumes they are aligned such that there’s no precession. In detail: The waveform is calculated by using effective-one-body dynamics (EOB), an approximation for the binary’s motion calculated by transforming the relevant equations into those for a single object. The S at the start stands for spin: the waveform includes the effects of both black holes having spins which are aligned (or antialigned) with the orbital angular momentum. Since the spins are aligned, there’s no precession. The EOB waveforms are tweaked (or calibrated, if you prefer) by comparing them to numerical relativity (NR) waveforms, in particular to get the merger and ringdown portions of the waveform right. While it is easier to solve the EOB equations than full NR simulations, they still take a while. To speed things up, we use a reduced-order model (ROM), a surrogate model constructed to match the waveforms, so we can go straight from system parameters to the waveform, skipping calculating the dynamics of the binary.
The second we refer to as IMRPhenom, short for the technical IMRPhenomPv2. In short: This waveform includes the effects of precession using a simple approximation that captures the most important effects. In detail: The IMR stands for inspiral–merger–ringdown, the three phases of the waveform (which are included in in the EOBNR model too). Phenom is short for phenomenological: the waveform model is constructed by tuning some (arbitrary, but cunningly chosen) functions to match waveforms calculated using a mix of EOB, NR and post-Newtonian theory. This is done for black holes with (anti)aligned spins to first produce the IMRPhenomD model. This is then twisted up, to include the dominant effects of precession to make IMRPhenomPv2. This bit is done by combining the two spins together to create a single parameter, which we call $\chi_\mathrm{p}$ , which determines the amount of precession. Since we are combining the two spins into one number, we lose a bit of the richness of the full dynamics, but we get the main part.

The EOBNR and IMRPhenom models are created by different groups using different methods, so they are useful checks of each other. If there is an error in our waveforms, it would lead to systematic errors in our estimated paramters

In this paper, we use another waveform model, a precessing EOBNR waveform, technically known as SEOBNRv3. This model includes all the effects of precession, not just the simple model of the IMRPhenom model. However, it is also computationally expensive, meaning that the analysis takes a long time (we don’t have a ROM to speed things up, as we do for the other EOBNR waveform)—each waveform takes over 20 times as long to calculate as the IMRPhenom model [bonus note].

Our results show that all three waveforms give similar results. The precessing EOBNR results are generally more like the IMRPhenom results than the non-precessing EOBNR results are. The plot below compares results from the different waveforms [bonus note].

Comparison of results from non-precessing EOBNR, precessing IMRPhenom and precessing EOBNR waveforms

Comparison of parameter estimates for GW150914 using different waveform models. The bars show the 90% credible intervals, the dark bars show the uncertainty on the 5%, 50% and 95% quantiles from the finite number of posterior samples. The top bar is for the non-precessing EOBNR model, the middle is for the precessing IMRPhenom model, and the bottom is for the fully precessing EOBNR model. Figure 1 of the Precession Paper; see Figure 9 for a comparison of averaged EOBNR and IMRPhenom results, which we have used for our overall results.

We had used the difference between the EOBNR and IMRPhenom results to estimate potential systematic error from waveform modelling. Since the two precessing models are generally in better agreement, we have may have been too pessimistic here.

The main difference in results is that our new refined analysis gives tighter constraints on the spins. From the plot above you can see that the uncertainty for the spin magnitudes of the heavier black hole $a_1$ , the lighter black hole $a_2$ and the final black hole (resulting from the coalescence) $a_\mathrm{f}$ , are slightly narrower. This makes sense, as including the extra imprint from the full effects of precession gives us a bit more information about the spins. The plots below show the constraints on the spins from the two precessing waveforms: the distributions are more condensed with the new results.

Black hole spins estimated using precessing IMRPhenom and EOBNR waveforms

Comparison of orientations and magnitudes of the two component spins. The spin is perfectly aligned with the orbital angular momentum if the angle is 0. The left disk shows results using the precessing IMRPhenom model, the right using the precessing EOBNR model. In each, the distribution for the more massive black hole is on the left, and for the smaller black hole on the right. Adapted from Figure 5 of the Parameter Estimation Paper and Figure 4 of the Precession Paper.

In conclusion, this analysis had shown that included the full effects of precession do give slightly better estimates of the black hole spins. However, it is safe to trust the IMRPhenom results.

If you are looking for the best parameter estimates for GW150914, these results are better than the original results in the Parameter Estimation Paper. However, the O2 Catalogue Paper includes results using improved calibration and noise power spectral density estimation, as well as using precessing waveforms!

The Systematics Paper

Synopsis: Systematics Paper
Read this if: You want to know how parameter estimation could fare for future detections
Favourite part: There’s no need to panic yet

The Precession Paper highlighted how important it is to have good waveform templates. If there is an error in our templates, either because of modelling or because we are missing some physics, then our estimated parameters could be wrong—we would have a source of systematic error.

We know our waveform models aren’t perfect, so there must be some systematic error, the question is how much? From our analysis so far (such as the good agreement between different waveforms in the Precession Paper), we think that systematic error is less significant than the statistical uncertainty which is a consequence of noise in the detectors. In this paper, we try to quantify systematic error for GW150914-like systems.

To asses systematic errors, we analyse waveforms calculated by numerical relativity simulations into data around the time of GW150914. Numerical relativity exactly solves Einstein’s field equations (which govern general relativity), so results of these simulations give the most accurate predictions for the form of gravitational waves. As we know the true parameters for the injected waveforms, we can compare these to the results of our parameter estimation analysis to check for biases.

We use waveforms computed by two different codes: the Spectral Einstein Code (SpEC) and the Bifunctional Adaptive Mesh (BAM) code. (Don’t the names make them sound like such fun?) Most waveforms are injected into noise-free data, so that we know that any offset in estimated parameters is dues to the waveforms and not detector noise; however, we also tried a few injections into real data from around the time of GW150914. The signals are analysed using our standard set-up as used in the Parameter Estimation Paper (a couple of injections are also included in the Precession Paper, where they are analysed with the fully precessing EOBNR waveform to illustrate its accuracy).

The results show that in most cases, systematic errors from our waveform models are small. However, systematic errors can be significant for some orientations of precessing binaries. If we are looking at the orbital plane edge on, then there can be errors in the distance, the mass ratio and the spins, as illustrated below [bonus note]. Thankfully, edge-on binaries are quieter than face-on binaries, and so should make up only a small fraction of detected sources (GW150914 is most probably face off). Furthermore, biases are only significant for some polarization angles (an angle which describes the orientation of the detectors relative to the stretch/squash of the gravitational wave polarizations). Factoring this in, a rough estimate is that about 0.3% of detected signals would fall into the unlucky region where waveform biases are important.

Inclination dependence of parameter recovery

Parameter estimation results for two different GW150914-like numerical relativity waveforms for different inclinations and polarization angles. An inclination of $0^\circ$ means the binary is face on, $180^\circ$ means it face off, and an inclination around $90^\circ$ is edge on. The bands show the recovered 90% credible interval; the dark lines the median values, and the dotted lines show the true values. The (grey) polarization angle $\psi = 82^\circ$ was chosen so that the detectors are approximately insensitive to the $h_+$ polarization. Figure 4 of the Systematics Paper.

While it seems that we don’t have to worry about waveform error for GW150914, this doesn’t mean we can relax. Other systems may show up different aspects of waveform models. For example, our approximants only include the dominant modes (spherical harmonic decompositions of the gravitational waves). Higher-order modes have more of an impact in systems where the two black holes are unequal masses, or where the binary has a higher total mass, so that the merger and ringdown parts of the waveform are more important. We need to continue work on developing improved waveform models (or at least, including our uncertainty about them in our analysis), and remember to check for biases in our results!

The Numerical Relativity Comparison Paper

Synopsis: Numerical Relativity Comparison Paper
Read this if: You are really suspicious of our waveform models, or really like long tables or numerical data
Favourite part: We might one day have enough numerical relativity waveforms to do full parameter estimation with them

In the Precession Paper we discussed how important it was to have accurate waveforms; in the Systematics Paper we analysed numerical relativity waveforms to check the accuracy of our results. Since we do have numerical relativity waveforms, you might be wondering why we don’t just use these in our analysis? In this paper, we give it a go.

Our standard parameter-estimation code (LALInference) randomly hops around parameter space, for each set of parameters we generate a new waveform and see how this matches the data. This is an efficient way of exploring the parameter space. Numerical relativity waveforms are too computationally expensive to generate one each time we hop. We need a different approach.

The alternative, is to use existing waveforms, and see how each of them match. Each simulation gives the gravitational waves for a particular mass ratio and combination of spins, we can scale the waves to examine different total masses, and it is easy to consider what the waves would look like if measured at a different position (distance, inclination or sky location). Therefore, we can actually cover a fair range of possible parameters with a given set of simulations.

To keep things quick, the code averages over positions, this means we don’t currently get an estimate on the redshift, and so all the masses are given as measured in the detector frame and not as the intrinsic masses of the source.

The number of numerical relativity simulations is still quite sparse, so to get nice credible regions, a simple Gaussian fit is used for the likelihood. I’m not convinced that this capture all the detail of the true likelihood, but it should suffice for a broad estimate of the width of the distributions.

The results of this analysis generally agree with those from our standard analysis. This is a relief, but not surprising given all the other checks that we have done! It hints that we might be able to get slightly better measurements of the spins and mass ratios if we used more accurate waveforms in our standard analysis, but the overall conclusions are sound.

I’ve been asked if since these results use numerical relativity waveforms, they are the best to use? My answer is no. As well as potential error from the sparse sampling of simulations, there are several small things to be wary of.

We only have short numerical relativity waveforms. This means that the analysis only goes down to a frequency of $30~\mathrm{Hz}$ and ignores earlier cycles. The standard analysis includes data down to $20~\mathrm{Hz}$ , and this extra data does give you a little information about precession. (The limit of the simulation length also means you shouldn’t expect this type of analysis for the longer LVT151012 or GW151226 any time soon).
This analysis doesn’t include the effects of calibration uncertainty. There is some uncertainty in how to convert from the measured signal at the detectors’ output to the physical strain of the gravitational wave. Our standard analysis fold this in, but that isn’t done here. The estimates of the spin can be affected by miscalibration. (This paper also uses the earlier calibration, rather than the improved calibration of the O1 Binary Black Hole Paper).
Despite numerical relativity simulations producing waveforms which include all higher modes, not all of them are actually used in the analysis. More are included than in the standard analysis, so this will probably make negligible difference.

Finally, I wanted to mention one more detail, as I think it is not widely appreciated. The gravitational wave likelihood is given by an inner product

$\displaystyle L \propto \exp \left[- \int_{-\infty}^{\infty} \mathrm{d}f \frac{|s(f) - h(f)|^2}{S_n(f)} \right]$ ,

where $s(f)$ is the signal, $h(f)$ is our waveform template and $S_n(f)$ is the noise spectral density (PSD). These are the three things we need to know to get the right answer. This paper, together with the Precession Paper and the Systematics Paper, has been looking at error from our waveform models $h(f)$ . Uncertainty from the calibration of $s(f)$ is included in the standard analysis, so we know how to factor this in (and people are currently working on more sophisticated models for calibration error). This leaves the noise PSD $S_n(f)$ …

The noise PSD varies all the time, so it needs to be estimated from the data. If you use a different stretch of data, you’ll get a different estimate, and this will impact your results. Ideally, you would want to estimate from the time span that includes the signal itself, but that’s tricky as there’s a signal in the way. The analysis in this paper calculates the noise power spectral density using a different time span and a different method than our standard analysis; therefore, we expect some small difference in the estimated parameters. This might be comparable to (or even bigger than) the difference from switching waveforms! We see from the similarity of results that this cannot be a big effect, but it means that you shouldn’t obsess over small differences, thinking that they could be due to waveform differences, when they could just come from estimation of the noise PSD.

Lots of work is currently going into making sure that the numerator term $|s(f) - h(f)|^2$ is accurate. I think that the denominator $S_n(f)$ needs attention too. Since we have been kept rather busy, including uncertainty in PSD estimation will have to wait for a future set papers.

Bonus notes

Finches

100 bonus points to anyone who folds up the papers to make beaks suitable for eating different foods.

The right answer

Our current best estimate for the chirp mass (from the O2 Catalogue Paper) would be $31.2_{-1.5}^{+1.7} M_\odot$ . You need proper templates for the gravitational wave signal to calculate this. If you factor in the the gravitational wave gets redshifted (shifted to lower frequency by the expansion of the Universe), then the true chirp mass of the source system is $28.6_{-1.5}^{+1.6} M_\odot$ .

Formative experiences

My one undergraduate lecture on gravitational waves was the penultimate lecture of the fourth-year general relativity course. I missed this lecture, as I had a PhD interview (at the University of Birmingham). Perhaps if I had sat through it, my research career would have been different?

Good things come…

The computational expense of a waveform is important, as when we are doing parameter estimation, we calculate lots (tens of millions) of waveforms for different parameters to see how they match the data. Before O1, the task of using SEOBNRv3 for parameter estimation seemed quixotic. The first detection, however, was enticing enough to give it a try. It was a truly heroic effort by Vivien Raymond and team that produced these results—I am slightly suspicious the Vivien might actually be a wizard.

GW150914 is a short signal, meaning it is relatively quick to analyse. Still, it required us using all the tricks at our disposal to get results in a reasonable time. When it came time to submit final results for the Discovery Paper, we had just about 1,000 samples from the posterior probability distribution for the precessing EOBNR waveform. For comparison, we had over 45,000 sample for the non-precessing EOBNR waveform. 1,000 samples isn’t enough to accurately map out the probability distributions, so we decided to wait and collect more samples. The preliminary results showed that things looked similar, so there wouldn’t be a big difference in the science we could do. For the Precession Paper, we finally collected 2,700 samples. This is still a relatively small number, so we carefully checked the uncertainty in our results due to the finite number of samples.

The Precession Paper has shown that it is possible to use the precessing EOBNR for parameter estimation, but don’t expect it to become the norm, at least until we have a faster implementation of it. Vivien is only human, and I’m sure his family would like to see him occasionally.

Parameter key

In case you are wondering what all the symbols in the results plots stand for, here are their usual definitions. First up, the various masses

$m_1$ —the mass of the heavier black hole, sometimes called the primary black hole;
$m_2$ —the mass of the lighter black hole, sometimes called the secondary black hole;
$M$ —the total mass of the binary, $M = m_1 + m_2$ ;
$M_\mathrm{f}$ —the mass of the final black hole (after merger);
$\mathcal{M}$ —the chirp mass, the combination of the two component masses which sets how the binary inspirals together;
$q$ —the mass ratio, $q = m_1/m_2 \leq 1$ . Confusingly, numerical relativists often use the opposite convention $q = m_2/m_1 \geq 1$ (which is why the Numerical Relativity Comparison Paper discusses results in terms of $1/q$ : we can keep the standard definition, but all the numbers are numerical relativist friendly).

A superscript “source” is sometimes used to distinguish the actual physical masses of the source from those measured by the detector which have been affected by cosmological redshift. The measured detector-frame mass is $m = (1 + z) m^\mathrm{source}$ , where $m^\mathrm{source}$ is the true, redshift-corrected source-frame mass and $z$ is the redshift. The mass ratio $q$ is independent of the redshift. On the topic of redshift, we have

$z$ —the cosmological redshift ( $z = 0$ would be now);
$D_\mathrm{L}$ —the luminosity distance.

The luminosity distance sets the amplitude of the signal, as does the orientation which we often describe using

$\iota$ —the inclination, the angle between the line of sight and the orbital angular momentum ( $\boldsymbol{L}$ ). This is zero for a face-on binary.
$\theta_{JN}$ —the angle between the line of sight ( $\boldsymbol{N}$ ) and the total angular momentum of the binary ( $\boldsymbol{J}$ ); this is approximately equal to the inclination, but is easier to use for precessing binaries.

As well as masses, black holes have spins

$a_1$ —the (dimensionless) spin magnitude of the heavier black hole, which is between $0$ (no spin) and $1$ (maximum spin);
$a_2$ —the (dimensionless) spin magnitude of the lighter black hole;
$a_\mathrm{f}$ —the (dimensionless) spin magnitude of the final black hole;
$\chi_\mathrm{eff}$ —the effective inspiral spin parameter, a combinations of the two component spins which has the largest impact on the rate of inspiral (think of it as the spin equivalent of the chirp mass);
$\chi_\mathrm{p}$ —the effective precession spin parameter, a combination of spins which indicate the dominant effects of precession, it’s $0$ for no precession and $1$ for maximal precession;
$\theta_{LS_1}$ —the primary tilt angle, the angle between the orbital angular momentum and the heavier black holes spin ( $\boldsymbol{S_1}$ ). This is zero for aligned spin.
$\theta_{LS_2}$ —the secondary tilt angle, the angle between the orbital angular momentum and the lighter black holes spin ( $\boldsymbol{S_2}$ ).
$\phi_{12}$ —the angle between the projections of the two spins on the orbital plane.

The orientation angles change in precessing binaries (when the spins are not perfectly aligned or antialigned with the orbital angular momentum), so we quote values at a reference time corresponding to when the gravitational wave frequency is $20~\mathrm{Hz}$ . Finally (for the plots shown here)

$\psi$ —the polarization angle, this is zero when the detector arms are parallel to the $h_+$ polarization’s stretch/squash axis.

For more detailed definitions, check out the Parameter Estimation Paper or the LALInference Paper.

The Boxing Day Event

June 15, 2016February 8, 2020 / CPLB / 2 Comments

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 Letters; 116(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 X; 6(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 and GW150914, GW151226 and LVT151012

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).

Sky localization in equatorial coordinates

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:

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.
A flat-in-the-logarithm-of-masses distribution, which we expect gives a sensible lower bound on the rate.
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. 2016; de Mink & Mandel 2016; Hartwig 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.

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.

The effectiveness of matched filtering for GW151226

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:

CALET—an X-ray and gamma-ray search. This team also have a paper on their analysis and upper limits for GW151226, GW170104, GW170608, GW170814 and GW170817.
Dark Energy Camera—an optical search.
Fermi GBM & LAT—an X-ray and gamma-ray search for counterparts to GW151226 and LVT151012.
Jansky Very Large Array—a radio search for counterparts to GW150914 and GW151226. A separate effort later followed up the most probable 100 square degrees later, as a test of a new on-the-fly mosaicing technique.
J-GEM—an optical and near-infrared survey.
Liverpool Telescope—an optical and near-infrared search for counterparts to GW150914 and GW151226.
MAXI—an X-ray monitor on the International Space Station.
Pan-STARRS & PESSTO—an optical search which didn’t find a counterpart, but did find an unusual Type Ibn supernova.
Swift—an X-ray search.
GRAWITA—an optical search.

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.

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO and Advanced Virgo

March 5, 2016June 16, 2018 / CPLB / Leave a comment

The week beginning February 8th was a big one for the LIGO and Virgo Collaborations. You might remember something about a few papers on the merger of a couple of black holes; however, those weren’t the only papers we published that week. In fact, they are not even (currently) the most cited…

Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo is known within the Collaboration as the Observing Scenarios Document. It has a couple of interesting aspects

Its content is a mix of a schedule for detector commissioning and an explanation of data analysis. It is a rare paper that spans both the instrumental and data-analysis sides of the Collaboration.
It is a living review: it is intended to be periodically updated as we get new information.

There is also one further point of interest for me: I was heavily involved in producing this latest version.

In this post I’m going to give an outline of the paper’s content, but delve a little deeper into the story of how this paper made it to print.

The Observing Scenarios

The paper is divided up into four sections.

It opens, as is traditional, with the introduction. This has no mentions of windows, which is a good start.
Section 2 is the instrumental bit. Here we give a possible timeline for the commissioning of the LIGO and Virgo detectors and a plausible schedule for our observing runs.
Next we talk about data analysis for transient (short) gravitational waves. We discuss detection and then sky localization.
Finally, we bring everything together to give an estimate of how well we expect to be able to locate the sources of gravitational-wave signals as time goes on.

Packaged up, the paper is useful if you want to know when LIGO and Virgo might be observing or if you want to know how we locate the source of a signal on the sky. The aim was to provide a guide for those interested in multimessenger astronomy—astronomy where you rely on multiple types of signals like electromagnetic radiation (light, radio, X-rays, etc.), gravitational waves, neutrinos or cosmic rays.

The development of the detectors’ sensitivity is shown below. It takes many years of tweaking and optimising to reach design sensitivity, but we don’t wait until then to do some science. It’s just as important to practise running the instruments and analysing the data as it is to improve the sensitivity. Therefore, we have a series of observing runs at progressively higher sensitivity. Our first observing run (O1), featured just the two LIGO detectors, which were towards the better end of the expected sensitivity.

Plausible evolution of the Advanced LIGO and Advanced Virgo detectors with time. The lower the sensitivity curve, the further away we can detect sources. The distances quoted are ranges we could observe binary neutrons stars (BNSs) to. The BNS-optimized curve is a proposal to tweak the detectors for finding BNSs. Fig. 1 of the Observing Scenarios Document.

It’s difficult to predict exactly how the detectors will progress (we’re doing many things for the first time ever), but the plot above shows our current best plan.

I’ll not go into any more details about the science in the paper as I’ve already used up my best ideas writing the LIGO science summary.

If you’re particularly interested in sky localization, you might like to check out the data releases for studies using (simulated) binary neutron star and burst signals. The binary neutron star analysis is similar to that we do for any compact binary coalescence (the merger of a binary containing neutron stars or black holes), and the burst analysis works more generally as it doesn’t require a template for the expected signal.

The path to publication

Now, this is the story of how a Collaboration paper got published. I’d like to take a minute to tell you how I became responsible for updating the Observing Scenarios…

In the beginning

The Observing Scenarios has its origins long before I joined the Collaboration. The first version of the document I can find is from July 2012. Amongst the labyrinth of internal wiki pages we have, the earliest reference I’ve uncovered was from August 2012 (the plan was to have a mature draft by September). The aim was to give a road map for the advanced-detector era, so the wider astronomical community would know what to expect.

I imagine it took a huge effort to bring together all the necessary experts from across the Collaboration to sit down and write the document.

Any document detailing our plans would need to be updated regularly as we get a better understanding of our progress on commissioning the detectors (and perhaps understanding what signals we will see). Fortunately, there is a journal that can cope with just that: Living Reviews in Relativity. Living Reviews is designed so that authors can update their articles so that they never become (too) out-of-date.

A version was submitted to Living Reviews early in 2013, around the same time as a version was posted to the arXiv. We had referee reports (from two referees), and were preparing to resubmit. Unfortunately, Living Reviews suspended operations before we could. However, work continued.

Updating sky localization

I joined the LIGO Scientific Collaboration when I started at the University of Birmingham in October 2013. I soon became involved in a variety of activities of the Parameter Estimation group (my boss, Alberto Vecchio, is the chair of the group).

Sky localization was a particularly active area as we prepared for the first runs of Advanced LIGO. The original version of the Observing Scenarios Document used a simple approximate means of estimating sky localization, using just timing triangulation (it didn’t even give numbers for when we only had two detectors running). We knew we could do better.

We had all the code developed, but we needed numbers for a realistic population of signals. I was one of the people who helped running the analyses to get these. We had the results by the summer of 2014; we now needed someone to write up the results. I have a distinct recollection of there being silence on our weekly teleconference. Then Alberto asked me if I would do it? I said yes: it would probably only take me a week or two to write a short technical note.

Saying yes is a slippery slope.

That note became Parameter estimation for binary neutron-star coalescences with realistic noise during the Advanced LIGO era, a 24-page paper (it considers more than just sky localization).

Numbers in hand, it was time to update the Observing Scenarios. Even if things were currently on hold with Living Reviews, we could still update the arXiv version. I thought it would be easiest if I put them in, with a little explanation, myself. I compiled a draft and circulated in the Parameter Estimation group. Then it was time to present to the Data Analysis Council.

The Data Analysis Council either sounds like a shadowy organisation orchestrating things from behind the scene, or a place where people bicker over trivial technical issues. In reality it is a little of both. This is the body that should coordinate all the various bits of analysis done by the Collaboration, and they have responsibility for the Observing Scenarios Document. I presented my update on the last call before Christmas 2014. They were generally happy, but said that the sky localization on the burst side needed updating too! There was once again a silence on the call when it came to the question of who would finish off the document. The Observing Scenarios became my responsibility.

(I had though that if I helped out with this Collaboration paper, I could take the next 900 off. This hasn’t worked out.)

The review

With some help from the Burst group (in particular Reed Essick, who had lead their sky localization study), I soon had a new version with fully up-to-date sky localization. This was ready for our March Collaboration meeting. I didn’t go (I was saving my travel budget for the summer), so Alberto presented on my behalf. It was now agreed that the document should go through internal review.

It’s this which I really want to write about. Peer review is central to modern science. New results are always discussed by experts in the community, to try to understand the value of the work; however, peer review is formalised in the refereeing of journal articles, when one or more (usually anonymous) experts examine work before it can be published. There are many ups and down with this… For Collaboration papers, we want to be sure that things are right before we share them publicly. We go through internal peer review. In my opinion this is much more thorough than journal review, and this shows how seriously the Collaboration take their science.

Unfortunately, setting up the review was also where we hit a hurdle—it took until July. I’m not entirely sure why there was a delay: I suspect it was partly because everyone was busy assembling things ahead of O1 and partly because there were various discussions amongst the high-level management about what exactly we should be aiming for. Working as part of a large collaboration can mean that you get to be involved in wonderful science, but it can means lots of bureaucracy and politics. However, in the intervening time, Living Reviews was back in operation.

The review team consisted of five senior people, each of whom had easily five times as much experience as I do, with expertise in each of the areas covered in the document. The chair of the review was Alan Weinstein, head of the Caltech LIGO Laboratory Astrophysics Group, who has an excellent eye for detail. Our aim was to produce the update for the start of O1 in September. (Spolier: We didn’t make it)

The review team discussed things amongst themselves and I got the first comments at the end of August. The consensus was that we should not just update the sky localization, but update everything too (including the structure of the document). This precipitated a flurry of conversations with the people who organise the schedules for the detectors, those who liaise with our partner astronomers on electromagnetic follow-up, and everyone who does sky localization. I was initially depressed that we wouldn’t make our start of O1 deadline; however, then something happened that altered my perspective.

On September 14, four days before the official start of O1, we made a detection. GW150914 would change everything.

First, we could no longer claim that binary neutron stars were expected to be our most common source—instead they became the source we expect would most commonly have an electromagnetic counterpart.

Second, we needed to be careful how we described engineering runs. GW150914 occurred in our final engineering run (ER8). Practically, there was difference between the state of the detector then and in O1. The point of the final engineering run was to get everything running smoothly so all we needed to do at the official start of O1 was open the champagne. However, we couldn’t make any claims about being able to make detections during engineering runs without being krass and letting the cat out of the bag. I’m rather pleased with the sentence

Engineering runs in the commissioning phase allow us to understand our detectors and analyses in an observational mode; these are not intended to produce astrophysical results, but that does not preclude the possibility of this happening.

I don’t know if anyone noticed the implication. (Checking my notes, this was in the September 18 draft, which shows how quickly we realised the possible significance of The Event).

Finally, since the start of observations proved to be interesting, and because the detectors were running so smoothly, it was decided to extend O1 from three months to four so that it would finish in January. No commissioning was going to be done over the holidays, so it wouldn’t affect the schedule. I’m not sure how happy the people who run the detectors were about working over this period, but they agreed to the plan. (No-one asked if we would be happy to run parameter estimation over the holidays).

After half-a-dozen drafts, the review team were finally happy with the document. It was now October 20, and time to proceed to the next step of review: circulation to the Collaboration.

Collaboration papers go through a sequence of stages. First they are circulated to the everyone for comments. This can be pointing out typos, suggesting references or asking questions about the analysis. This lasts two weeks. During this time, the results must also be presented on a Collaboration-wide teleconference. After comments are addressed, the paper is sent for examination Executive Committees of the LIGO and Virgo Collaborations. After approval from them (and the review team check any changes), the paper is circulated to the Collaboration again for any last comments and checking of the author list. At the same time it is sent to the Gravitational Wave International Committee, a group of all the collaborations interested in gravitational waves. This final stage is a week. Then you can you can submit the paper.

Peer review for the journal doesn’t seem to arduous in comparison does it?

Since things were rather busy with all the analysis of GW150914, the Observing Scenario took a little longer than usual to clear all these hoops. I presented to the Collaboration on Friday 13 November. (This was rather unlucky as I was at a workshop in Italy and I had to miss the tour of the underground Laboratori Nazionali del Gran Sasso). After addressing comments from everyone (the Executive Committees do read things carefully), I got the final sign-off to submit December 21. At least we made it before the end of O1.

Good things come…

This may sound like a tale of frustration and delay. However, I hope that it is more than that, and it shows how careful the Collaboration is. The Observing Scenarios is really a review: it doesn’t contain new science. The updated sky localization results are from studies which have appeared in peer-reviewed journals, and are based upon codes that have been separately reviewed. Despite this, every statement was examined and every number checked and rechecked, and every member of the Collaboration had opportunity to examine the results and comment on the document.

I guess this attention to detail isn’t surprising given that our work is based on measuring a change in length of one part in 1,000,000,000,000,000,000,000.

Since this is how we treat review articles, can you imagine how much scrutiny the Discovery Paper had? Everything had at least one extra layer of review, every number had to be signed-off individually by the appropriate review team, and there were so many comments on the paper that the editors had to switch to using a ticketing system we normally use for tracking bugs in our software. This level of oversight helped me to sleep a little more easily: there are six numbers in the abstract alone I could have potentially messed up.

Had a nightmare that all my numbers changed when I reran my analysis. Went back to sleep after remembering dreams aren't reviewed yet.

— Christopher Berry (@cplberry) January 14, 2016

Of course, all this doesn’t mean we can’t make mistakes…

Looking forward

The Living Reviews version was accepted January 22, just after the end of O1. We made had to make a couple of tweaks to correct tenses. The final version appeared February 8, in time to be the last paper of the pre-discovery era.

It is now time to be thinking about the next update! There are certainly a few things on the to-do list (perhaps even some news on LIGO-India). We are having a Collaboration meeting in a couple of weeks’ time, so hopefully I can start talking to people about it then. Perhaps it’ll be done by the start of O2? [update]

arXiv: 1304.0670 [gr-qc]
Journal: Living Reviews In Relativity; 19:1(39); 2016
Science summary: Planning for a Bright Tomorrow: Prospects for Gravitational-wave Astronomy with Advanced LIGO and Advanced Virgo
Bonus fact: This is the only paper whose arXiv ID I know by heart [update].

arXiv IDs

Papers whose arXiv numbers I know by heart are: 1304.0670, 1602.03840 (I count to other GW150914 companion papers from here), 1606.04856 and 1706.01812. These might tell you something about my reading habits.

The next version

Despite aiming for the start of O2, the next version wasn’t ready for submission until just after the end of O2, in September 2017. It was finally published (after an excpetionally long time in type-setting) in April 2018.

GW150914—The papers

February 23, 2016March 3, 2021 / CPLB / 3 Comments

In 2015 I made a resolution to write a blog post for each paper I had published. In 2016 I’ll have to break this because there are too many to keep up with. A suite of papers were prepared to accompany the announcement of the detection of GW150914 [bonus note], and in this post I’ll give an overview of these.

The papers

As well as the Discovery Paper published in Physical Review Letters [bonus note], there are 12 companion papers. All the papers are listed below in order of arXiv posting. My favourite is the Parameter Estimation Paper.

Subsequently, we have produced additional papers on GW150914, describing work that wasn’t finished in time for the announcement. The most up-to-date results are currently given in the O2 Catalogue Paper.

0. The Discovery Paper

Title: Observation of gravitational waves from a binary black hole merger
arXiv: 1602.03837 [gr-qc]
Journal: Physical Review Letters; 116(6):061102(16); 2016
LIGO science summary: Observation of gravitational waves from a binary black hole merger

This is the central paper that announces the observation of gravitational waves. There are three discoveries which are describe here: (i) the direct detection of gravitational waves, (ii) the existence of stellar-mass binary black holes, and (iii) that the black holes and gravitational waves are consistent with Einstein’s theory of general relativity. That’s not too shabby in under 11 pages (if you exclude the author list). Coming 100 years after Einstein first published his prediction of gravitational waves and Schwarzschild published his black hole solution, this is the perfect birthday present.

More details: The Discovery Paper summary

1. The Detector Paper

Title: GW150914: The Advanced LIGO detectors in the era of first discoveries
arXiv: 1602.03838 [gr-qc]
Journal: Physical Review Letters; 116(13):131103(12); 2016
LIGO science summary: GW150914: The Advanced LIGO detectors in the era of the first discoveries

This paper gives a short summary of how the LIGO detectors work and their configuration in O1 (see the Advanced LIGO paper for the full design). Giant lasers and tiny measurements, the experimentalists do some cool things (even if their paper titles are a little cheesy and they seem to be allergic to error bars).

More details: The Detector Paper summary

2. The Compact Binary Coalescence Paper

Title: GW150914: First results from the search for binary black hole coalescence with Advanced LIGO
arXiv: 1602.03839 [gr-qc]
Journal: Physical Review D; 93(12):122003(21); 2016
LIGO science summary: How we searched for merging black holes and found GW150914

Here we explain how we search for binary black holes and calculate the significance of potential candidates. This is the evidence to back up (i) in the Discovery Paper. We can potentially detect binary black holes in two ways: with searches that use templates, or with searches that look for coherent signals in both detectors without assuming a particular shape. The first type is also used for neutron star–black hole or binary neutron star coalescences, collectively known as compact binary coalescences. This type of search is described here, while the other type is described in the Burst Paper.

This paper describes the compact binary coalescence search pipelines and their results. As well as GW150914 there is also another interesting event, LVT151012. This isn’t significant enough to be claimed as a detection, but it is worth considering in more detail.

More details: The Compact Binary Coalescence Paper summary

3. The Parameter Estimation Paper

Title: Properties of the binary black hole merger GW150914
arXiv: 1602.03840 [gr-qc]
Journal: Physical Review Letters; 116(24):241102(19); 2016
LIGO science summary: The first measurement of a black hole merger and what it means

If you’re interested in the properties of the binary black hole system, then this is the paper for you! Here we explain how we do parameter estimation and how it is possible to extract masses, spins, location, etc. from the signal. These are the results I’ve been most heavily involved with, so I hope lots of people will find them useful! This is the paper to cite if you’re using our best masses, spins, distance or sky maps. The masses we infer are so large we conclude that the system must contain black holes, which is discovery (ii) reported in the Discovery Paper.

More details: The Parameter Estimation Paper summary

4. The Testing General Relativity Paper

Title: Tests of general relativity with GW150914
arXiv: 1602.03841 [gr-qc]
Journal: Physical Review Letters; 116(22):221101(19); 2016
LIGO science summary: Was Einstein right about strong gravity?

The observation of GW150914 provides a new insight into the behaviour of gravity. We have never before probed such strong gravitational fields or such highly dynamical spacetime. These are the sorts of places you might imagine that we could start to see deviations from the predictions of general relativity. Aside from checking that we understand gravity, we also need to check to see if there is any evidence that our estimated parameters for the system could be off. We find that everything is consistent with general relativity, which is good for Einstein and is also discovery (iii) in the Discovery Paper.

More details: The Testing General Relativity Paper summary

5. The Rates Paper

Title: The rate of binary black hole mergers inferred from Advanced LIGO observations surrounding GW150914
arXiv: 1602.03842 [astro-ph.HE]; 1606.03939 [astro-ph.HE]
Journal: Astrophysical Journal Letters; 833(1):L1(8); 2016; Astrophysical Journal Supplement Series; 227(2):14(11); 2016
LIGO science summary: The first measurement of a black hole merger and what it means

Given that we’ve spotted one binary black hole (plus maybe another with LVT151012), how many more are out there and how many more should we expect to find? We answer this here, although there’s a large uncertainty on the estimates since we don’t know (yet) the distribution of masses for binary black holes.

More details: The Rates Paper summary

6. The Burst Paper

Title: Observing gravitational-wave transient GW150914 with minimal assumptions
arXiv: 1602.03843 [gr-qc]
Journal: Physical Review D; 93(12):122004(20); 2016

What can you learn about GW150914 without having to make the assumptions that it corresponds to gravitational waves from a binary black hole merger (as predicted by general relativity)? This paper describes and presents the results of the burst searches. Since the pipeline which first found GW150914 was a burst pipeline, it seems a little unfair that this paper comes after the Compact Binary Coalescence Paper, but I guess the idea is to first present results assuming it is a binary (since these are tightest) and then see how things change if you relax the assumptions. The waveforms reconstructed by the burst models do match the templates for a binary black hole coalescence.

More details: The Burst Paper summary

7. The Detector Characterisation Paper

Title: Characterization of transient noise in Advanced LIGO relevant to gravitational wave signal GW150914
arXiv: 1602.03844 [gr-qc]
Journal: Classical & Quantum Gravity; 33(13):134001(34); 2016
LIGO science summary: How do we know GW150914 was real? Vetting a Gravitational Wave Signal of Astrophysical Origin
CQG+ post: How do we know LIGO detected gravitational waves? [featuring awesome cartoons]

Could GW150914 be caused by something other than a gravitational wave: are there sources of noise that could mimic a signal, or ways that the detector could be disturbed to produce something that would be mistaken for a detection? This paper looks at these problems and details all the ways we monitor the detectors and the external environment. We can find nothing that can explain GW150914 (and LVT151012) other than either a gravitational wave or a really lucky random noise fluctuation. I think this paper is extremely important to our ability to claim a detection and I’m surprised it’s not number 2 in the list of companion papers. If you want to know how thorough the Collaboration is in monitoring the detectors, this is the paper for you.

More details: The Detector Characterisation Paper summary

8. The Calibration Paper

Title: Calibration of the Advanced LIGO detectors for the discovery of the binary black-hole merger GW150914
arXiv: 1602.03845 [gr-qc]
Journal: Physical Review D; 95(6):062003(16); 2017
LIGO science summary: Calibration of the Advanced LIGO detectors for the discovery of the binary black-hole merger GW150914

Completing the triumvirate of instrumental papers with the Detector Paper and the Detector Characterisation Paper, this paper describes how the LIGO detectors are calibrated. There are some cunning control mechanisms involved in operating the interferometers, and we need to understand these to quantify how they effect what we measure. Building a better model for calibration uncertainties is high on the to-do list for improving parameter estimation, so this is an interesting area to watch for me.

More details: The Calibration Paper summary

9. The Astrophysics Paper

Title: Astrophysical implications of the binary black-hole merger GW150914
arXiv: 1602.03846 [astro-ph.HE]
Journal: Astrophysical Journal Letters; 818(2):L22(15); 2016
LIGO science summary: The first measurement of a black hole merger and what it means

Having estimated source parameters and rate of mergers, what can we say about astrophysics? This paper reviews results related to binary black holes to put our findings in context and also makes statements about what we could hope to learn in the future.

More details: The Astrophysics Paper summary

10. The Stochastic Paper

Title: GW150914: Implications for the stochastic gravitational wave background from binary black holes
arXiv: 1602.03847 [gr-qc]
Journal: Physical Review Letters; 116(13):131102(12); 2016
LIGO science summary: Background of gravitational waves expected from binary black hole events like GW150914

For every loud signal we detect, we expect that there will be many more quiet ones. This paper considers how many quiet binary black hole signals could add up to form a stochastic background. We may be able to see this background as the detectors are upgraded, so we should start thinking about what to do to identify it and learn from it.

More details: The Stochastic Paper summary

11. The Neutrino Paper

Title: High-energy neutrino follow-up search of gravitational wave event GW150914 with ANTARES and IceCube
arXiv: 1602.05411 [astro-ph.HE]
Journal: Physical Review D; 93(12):122010(15); 2016
LIGO science summary: Search for neutrinos from merging black holes

We are interested so see if there’s any other signal that coincides with a gravitational wave signal. We wouldn’t expect something to accompany a black hole merger, but it’s good to check. This paper describes the search for high-energy neutrinos. We didn’t find anything, but perhaps we will in the future (perhaps for a binary neutron star merger).

More details: The Neutrino Paper summary

12. The Electromagnetic Follow-up Paper

Title: Localization and broadband follow-up of the gravitational-wave transient GW150914
arXiv: 1602.08492 [astro-ph.HE]; 1604.07864 [astro-ph.HE]
Journal: Astrophysical Journal Letters; 826(1):L13(8); 2016; Astrophysical Journal Supplement Series; 225(1):8(15); 2016

As well as looking for coincident neutrinos, we are also interested in electromagnetic observations (gamma-ray, X-ray, optical, infra-red or radio). We had a large group of observers interesting in following up on gravitational wave triggers, and 25 teams have reported observations. This companion describes the procedure for follow-up observations and discusses sky localisation.

This work split into a main article and a supplement which goes into more technical details.

More details: The Electromagnetic Follow-up Paper summary

BEST. ARXIV. EVER!

We have 1602.03837 to 1602.03847 on #GravitationalWaves. A couple more to come. pic.twitter.com/HRdwcm60Mr

— Christopher Berry (@cplberry) February 12, 2016

The Discovery Paper

Synopsis: Discovery Paper
Read this if: You want an overview of The Event
Favourite part: The entire conclusion:

The LIGO detectors have observed gravitational waves from the merger of two stellar-mass black holes. The detected waveform matches the predictions of general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

The Discovery Paper gives the key science results and is remarkably well written. It seems a shame to summarise it: you should read it for yourself! (It’s free).

The Detector Paper

Synopsis: Detector Paper
Read this if: You want a brief description of the detector configuration for O1
Favourite part: It’s short!

The LIGO detectors contain lots of cool pieces of physics. This paper briefly outlines them all: the mirror suspensions, the vacuum (the LIGO arms are the largest vacuum envelopes in the world and some of the cleanest), the mirror coatings, the laser optics and the control systems. A full description is given in the Advanced LIGO paper, but the specs there are for design sensitivity (it is also heavy reading). The main difference between the current configuration and that for design sensitivity is the laser power. Currently the circulating power in the arms is $100~\mathrm{kW}$ , the plan is to go up to $750~\mathrm{kW}$ . This will reduce shot noise, but raises all sorts of control issues, such as how to avoid parametric instabilities.

The noise amplitude spectral density. The curves for the current observations are shown in red (dark for Hanford, light for Livingston). This is around a factor 3 better than in the final run of initial LIGO (green), but still a factor of 3 off design sensitivity (dark blue). The light blue curve shows the impact of potential future upgrades. The improvement at low frequencies is especially useful for high-mass systems like GW150914. Part of Fig. 1 of the Detector Paper.

The Compact Binary Coalescence Paper

Synopsis: Compact Binary Coalescence Paper
Read this if: You are interested in detection significance or in LVT151012
Favourite part: We might have found a second binary black hole merger

There are two compact binary coalescence searches that look for binary black holes: PyCBC and GstLAL. Both match templates to the data from the detectors to look for anything binary like, they then calculate the probability that such a match would happen by chance due to a random noise fluctuation (the false alarm probability or p-value [unhappy bonus note]). The false alarm probability isn’t the probability that there is a gravitational wave, but gives a good indication of how surprised we should be to find this signal if there wasn’t one. Here we report the results of both pipelines on the first 38.6 days of data (about 17 days where both detectors were working at the same time).

Both searches use the same set of templates to look for binary black holes [bonus note]. They look for where the same template matches the data from both detectors within a time interval consistent with the travel time between the two. However, the two searches rank candidate events and calculate false alarm probabilities using different methods. Basically, both searches use a detection statistic (the quantity used to rank candidates: higher means less likely to be noise), that is based on the signal-to-noise ratio (how loud the signal is) and a goodness-of-fit statistic. They assess the significance of a particular value of this detection statistic by calculating how frequently this would be obtained if there was just random noise (this is done by comparing data from the two detectors when there is not a coincident trigger in both). Consistency between the two searches gives us greater confidence in the results.

PyCBC’s detection statistic is a reweighted signal-to-noise ratio $\hat{\rho}_c$ which takes into account the consistency of the signal in different frequency bands. You can get a large signal-to-noise ratio from a loud glitch, but this doesn’t match the template across a range of frequencies, which is why this test is useful. The consistency is quantified by a reduced chi-squared statistic. This is used, depending on its value, to weight the signal-to-noise ratio. When it is large (indicating inconsistency across frequency bins), the reweighted signal-to-noise ratio becomes smaller.

To calculate the background, PyCBC uses time slides. Data from the two detectors are shifted in time so that any coincidences can’t be due to a real gravitational wave. Seeing how often you get something signal-like then tells you how often you’d expect this to happen due to random noise.

GstLAL calculates the signal-to-noise ratio and a residual after subtracting the template. As a detection statistic, it uses a likelihood ratio $\mathcal{L}$ : the probability of finding the particular values of the signal-to-noise ratio and residual in both detectors for signals (assuming signal sources are uniformly distributed isotropically in space), divided by the probability of finding them for noise.

The background from GstLAL is worked out by looking at the likelihood ratio fro triggers that only appear in one detector. Since there’s no coincident signal in the other, these triggers can’t correspond to a real gravitational wave. Looking at their distribution tells you how frequently such things happen due to noise, and hence how probable it is for both detectors to see something signal-like at the same time.

The results of the searches are shown in the figure below.

Search results for PyCBC (left) and GstLAL (right). The histograms show the number of candidate events (orange squares) compare to the background. The black line includes GW150914 in the background estimate, the purple removes it (assuming that it is a signal). The further an orange square is above the lines, the more significant it is. Particle physicists like to quote significance in terms of $\sigma$ and for some reason we’ve copied them. The second most significant event (around $2\sigma$ ) is LVT151012. Fig. 7 from the Compact Binary Coalescence Paper.

GW150914 is the most significant event in both searches (it is the most significant PyCBC event even considering just single-detector triggers). They both find GW150914 with the same template values. The significance is literally off the charts. PyCBC can only calculate an upper bound on the false alarm probability of $< 2 \times 10^{-7}$ . GstLAL calculates a false alarm probability of $1.4 \times 10^{-11}$ , but this is reaching the level that we have to worry about the accuracy of assumptions that go into this (that the distribution of noise triggers in uniform across templates—if this is not the case, the false alarm probability could be about $10^3$ times larger). Therefore, for our overall result, we stick to the upper bound, which is consistent with both searches. The false alarm probability is so tiny, I don’t think anyone doubts this signal is real.

There is a second event that pops up above the background. This is LVT151012. It is found by both searches. Its signal-to-noise ratio is $9.6$ , compared with GW150914’s $24$ , so it is quiet. The false alarm probability from PyCBC is $0.02$ , and from GstLAL is $0.05$ , consistent with what we would expect for such a signal. LVT151012 does not reach the standards we would like to claim a detection, but it is still interesting.

Running parameter estimation on LVT151012, as we did for GW150914, gives beautiful results. If it is astrophysical in origin, it is another binary black hole merger. The component masses are lower, $m_1^\mathrm{source} = 23^{+18}_{-5} M_\odot$ and $m_2^\mathrm{source} 13^{+4}_{-5} M_\odot$ (the asymmetric uncertainties come from imposing $m_1^\mathrm{source} \geq m_2^\mathrm{source}$ ); the chirp mass is $\mathcal{M} = 15^{+1}_{-1} M_\odot$ . The effective spin, as for GW150914, is close to zero $\chi_\mathrm{eff} = 0.0^{+0.3}_{-0.2}$ . The luminosity distance is $D_\mathrm{L} = 1100^{+500}_{-500}~\mathrm{Mpc}$ , meaning it is about twice as far away as GW150914’s source. I hope we’ll write more about this event in the future; there are some more details in the Rates Paper.

Is it random noise or is it a gravitational wave? LVT151012 remains a mystery. This candidate event is discussed in the Compact Binary Coalescence Paper (where it is found), the Rates Paper (which calculates the probability that it is extraterrestrial in origin), and the Detector Characterisation Paper (where known environmental sources fail to explain it). SPOILERS

The Parameter Estimation Paper

Synopsis: Parameter Estimation Paper
Read this if: You want to know the properties of GW150914’s source
Favourite part: We inferred the properties of black holes using measurements of spacetime itself!

The gravitational wave signal encodes all sorts of information about its source. Here, we explain how we extract this information to produce probability distributions for the source parameters. I wrote about the properties of GW150914 in my previous post, so here I’ll go into a few more technical details.

To measure parameters we match a template waveform to the data from the two instruments. The better the fit, the more likely it is that the source had the particular parameters which were used to generate that particular template. Changing different parameters has different effects on the waveform (for example, changing the distance changes the amplitude, while changing the relative arrival times changes the sky position), so we often talk about different pieces of the waveform containing different pieces of information, even though we fit the whole lot at once.

The shape of the gravitational wave encodes the properties of the source. This information is what lets us infer parameters. The example signal is GW150914. I made this explainer with Ban Farr and Nutsinee Kijbunchoo for the LIGO Magazine.

The waveform for a binary black hole merger has three fuzzily defined parts: the inspiral (where the two black holes orbit each other), the merger (where the black holes plunge together and form a single black hole) and ringdown (where the final black hole relaxes to its final state). Having waveforms which include all of these stages is a fairly recent development, and we’re still working on efficient ways of including all the effects of the spin of the initial black holes.

We currently have two favourite binary black hole waveforms for parameter estimation:

The first we refer to as EOBNR, short for its proper name of SEOBNRv2_ROM_DoubleSpin. This is constructed by using some cunning analytic techniques to calculate the dynamics (known as effective-one-body or EOB) and tuning the results to match numerical relativity (NR) simulations. This waveform only includes the effects of spins aligned with the orbital angular momentum of the binary, so it doesn’t allow us to measure the effects of precession (wobbling around caused by the spins).
The second we refer to as IMRPhenom, short for IMRPhenomPv2. This is constructed by fitting to the frequency dependence of EOB and NR waveforms. The dominant effects of precession of included by twisting up the waveform.

We’re currently working on results using a waveform that includes the full effects of spin, but that is extremely slow (it’s about half done now), so those results won’t be out for a while.

The results from the two waveforms agree really well, even though they’ve been created by different teams using different pieces of physics. This was a huge relief when I was first making a comparison of results! (We had been worried about systematic errors from waveform modelling). The consistency of results is partly because our models have improved and partly because the properties of the source are such that the remaining differences aren’t important. We’re quite confident that we’ve most of the parameters are reliably measured!

The component masses are the most important factor for controlling the evolution of the waveform, but we don’t measure the two masses independently. The evolution of the inspiral is dominated by a combination called the chirp mass, and the merger and ringdown are dominated by the total mass. For lighter mass systems, where we gets lots of inspiral, we measure the chirp mass really well, and for high mass systems, where the merger and ringdown are the loudest parts, we measure the total mass. GW150914 is somewhere in the middle. The probability distribution for the masses are shown below: we can compensate for one of the component masses being smaller if we make the other larger, as this keeps chirp mass and total mass about the same.

Estimated masses for the two black holes in the binary. Results are shown for the EOBNR waveform and the IMRPhenom: both agree well. The Overall results come from averaging the two. The dotted lines mark the edge of our 90% probability intervals. The sharp diagonal line cut-off in the two-dimensional plot is a consequence of requiring $m_1^\mathrm{source} \geq m_2^\mathrm{source}$ . Fig. 1 from the Parameter Estimation Paper.

To work out these masses, we need to take into account the expansion of the Universe. As the Universe expands, it stretches the wavelength of the gravitational waves. The same happens to light: visible light becomes redder, so the phenomenon is known as redshifting (even for gravitational waves). If you don’t take this into account, the masses you measure are too large. To work out how much redshift there is you need to know the distance to the source. The probability distribution for the distance is shown below, we plot the distance together with the inclination, since both of these affect the amplitude of the waves (the source is quietest when we look at it edge-on from the side, and loudest when seen face-on/off from above/below).

Estimated luminosity distance and binary inclination angle. An inclination of $\theta_{JN} = 90^\circ$ means we are looking at the binary (approximately) edge-on. Results are shown for the EOBNR waveform and the IMRPhenom: both agree well. The Overall results come from averaging the two. The dotted lines mark the edge of our 90% probability intervals. Fig. 2 from the Parameter Estimation Paper.

After the masses, the most important properties for the evolution of the binary are the spins. We don’t measure these too well, but the probability distribution for their magnitudes and orientations from the precessing IMRPhenom model are shown below. Both waveform models agree that the effective spin $\chi_\mathrm{eff}$ , which is a combination of both spins in the direction of the orbital angular momentum) is small. Therefore, either the spins are small or are larger but not aligned (or antialigned) with the orbital angular momentum. The spin of the more massive black hole is the better measured of the two.

Estimated orientation and magnitude of the two component spins from the precessing IMRPhenom model. The magnitude is between 0 and 1 and is perfectly aligned with the orbital angular momentum if the angle is 0. The distribution for the more massive black hole is on the left, and for the smaller black hole on the right. Part of Fig. 5 from the Parameter Estimation Paper.

The Testing General Relativity Paper

Synopsis: Testing General Relativity Paper
Read this if: You want to know more about the nature of gravity.
Favourite part: Einstein was right! (Or more correctly, we can’t prove he was wrong… yet)

The Testing General Relativity Paper is one of my favourites as it packs a lot of science in. Our first direct detection of gravitational waves and of the merger of two black holes provides a new laboratory to test gravity, and this paper runs through the results of the first few experiments.

Before we start making any claims about general relativity being wrong, we first have to check if there’s any weird noise present. You don’t want to have to rewrite the textbooks just because of an instrumental artifact. After taking out a good guess for the waveform (as predicted by general relativity), we find that the residuals do match what we expect for instrumental noise, so we’re good to continue.

I’ve written about a couple of tests of general relativity in my previous post: the consistency of the inspiral and merger–ringdown parts of the waveform, and the bounds on the mass of the graviton (from evolution of the signal). I’ll cover the others now.

The final part of the signal, where the black hole settles down to its final state (the ringdown), is the place to look to check that the object is a black hole and not some other type of mysterious dark and dense object. It is tricky to measure this part of the signal, but we don’t see anything odd. We can’t yet confirm that the object has all the properties you’d want to pin down that it is exactly a black hole as predicted by general relativity; we’re going to have to wait for a louder signal for this. This test is especially poignant, as Steven Detweiler, who pioneered a lot of the work calculating the ringdown of black holes, died a week before the announcement.

We can allow terms in our waveform (here based on the IMRPhenom model) to vary and see which values best fit the signal. If there is evidence for differences compared with the predictions from general relativity, we would have evidence for needing an alternative. Results for this analysis are shown below for a set of different waveform parameters $\hat{p}_i$ : the $\varphi_i$ parameters determine the inspiral, the $\alpha_i$ parameters determine the merger–ringdown and the $\beta_i$ parameters cover the intermediate regime. If the deviation $\delta \hat{p}_i$ is zero, the value coincides with the value from general relativity. The plot shows what would happen if you allow all the variable to vary at once (the multiple results) and if you tried just that parameter on its own (the single results).

Probability distributions for waveform parameters. The single analysis only varies one parameter, the multiple analysis varies all of them, and the J0737-3039 result is the existing bound from the double pulsar. A deviation of zero is consistent with general relativity. Fig. 7 from the Testing General Relativity Paper.

Overall the results look good. Some of the single results are centred away from zero, but we think that this is just a random fluctuate caused by noise (we’ve seen similar behaviour in tests, so don’t panic yet). It’s not surprising the $\varphi_3$ , $\varphi_4$ and $\varphi_{5l}$ all show this behaviour, as they are sensitive to similar noise features. These measurements are much tighter than from any test we’ve done before, except for the measurement of $\varphi_0$ which is better measured from the double pulsar (since we have lots and lots of orbits of that measured).

The final test is to look for additional polarizations of gravitational waves. These are predicted in several alternative theories of gravity. Unfortunately, because we only have two detectors which are pretty much aligned we can’t say much, at least without knowing for certain the location of the source. Extra detectors will be useful here!

In conclusion, we have found no evidence to suggest we need to throw away general relativity, but future events will help us to perform new and stronger tests.

The Rates Paper

Synopsis: Rates Paper
Read this if: You want to know how often binary black holes merge (and how many we’ll detect)
Favourite part: There’s a good chance we’ll have ten detections by the end of our second observing run (O2)

Before September 14, we had never seen a binary stellar-mass black hole system. We were therefore rather uncertain about how many we would see. We had predictions based on simulations of the evolution of stars and their dynamical interactions. These said we shouldn’t be too surprised if we saw something in O1, but that we shouldn’t be surprised if we didn’t see anything for many years either. We weren’t really expecting to see a black hole system so soon (the smart money was on a binary neutron star). However, we did find a binary black hole, and this happened right at the start of our observations! What do we now believe about the rate of mergers?

To work out the rate, you first need to count the number of events you have detected and then work out how sensitive you are to the population of signals (how many could you see out of the total).

Counting detections sounds simple: we have GW150914 without a doubt. However, what about all the quieter signals? If you have 100 events each with a 1% probability of being real, then even though you can’t say with certainty that anyone is an actual signal, you would expect one to be so. We want to work out how many events are real and how many are due to noise. Handily, trying to tell apart different populations of things when you’re not certain about individual members is a common problem is astrophysics (where it’s often difficult to go and check what something actually is), so there exists a probabilistic framework for doing this.

Using the expected number of real and noise events for a given detection statistic (as described in the Compact Binary Coalescence Paper), we count the number of detections and as a bonus, get a probability that each event is of astrophysical origin. There are two events with more than a 50% chance of being real: GW150914, where the probability is close to 100%, and LVT151012, where to probability is 84% based on GstLAL and 91% based on PyCBC.

By injecting lots of fake signals into some data and running our detection pipelines, we can work out how sensitive they are (in effect, how far away can they find particular types of sources). For a given number of detections, the more sensitive we are, the lower the actual rate of mergers should be (for lower sensitivity we would miss more, while there’s no hiding for higher sensitivity).

There is one final difficulty in working out the total number of binary black hole mergers: we need to know the distribution of masses, because our sensitivity depends on this. However, we don’t yet know this as we’ve only seen GW150914 and (maybe) LVT151012. Therefore, we try three possibilities to get an idea of what the merger rate could be.

We assume that binary black holes are either like GW150914 or like LVT151012. Given that these are our only possible detections at the moment, this should give a reasonable estimate. A similar approach has been used for estimating the population of binary neutron stars from pulsar observations [bonus note].
We assume that the distribution of masses is flat in the logarithm of the masses. This probably gives more heavy black holes than in reality (and so a lower merger rate)
We assume that black holes follow a power law like the initial masses of stars. This probably gives too many low mass black holes (and so a higher merger rate)

The estimated merger rates (number of binary black hole mergers per volume per time) are then: 1. $83^{+168}_{-63}~\mathrm{Gpc^{-3}\,yr^{-1}}$ ; 2. $61^{+124}_{-48}~\mathrm{Gpc^{-3}\,yr^{-1}}$ , and 3. $200^{+400}_{-160}~\mathrm{Gpc^{-3}\,yr^{-1}}$ . There is a huge scatter, but the flat and power-law rates hopefully bound the true value.

We’ll pin down the rate better after a few more detections. How many more should we expect to see? Using the projected sensitivity of the detectors over our coming observing runs, we can work out the probability of making $N$ more detections. This is shown in the plot below. It looks like there’s about about a 10% chance of not seeing anything else in O1, but we’re confident that we’ll have 10 more by the end of O2, and 35 more by the end of O3! I may need to lie down…

The percentage chance of making 0, 10, 35 and 70 more detections of binary black holes as time goes on and detector sensitivity improves (based upon our data so far). This is a simplified version of part of Fig. 3 of the Rates Paper taken from the science summary.

The Burst Paper

Synopsis: Burst Paper
Read this if: You want to check what we can do without a waveform template
Favourite part: You don’t need a template to make a detection

When discussing what we can learn from gravitational wave astronomy, you can almost guarantee that someone will say something about discovering the unexpected. Whenever we’ve looked at the sky in a new band of the electromagnetic spectrum, we found something we weren’t looking for: pulsars for radio, gamma-ray burst for gamma-rays, etc. Can we do the same in gravitational wave astronomy? There may well be signals we weren’t anticipating out there, but will we be able to detect them? The burst pipelines have our back here, at least for short signals.

The burst search pipelines, like their compact binary coalescence partners, assign candidate events a detection statistic and then work out a probability associated with being a false alarm caused by noise. The difference is that the burst pipelines try to find a wider range of signals.

There are three burst pipelines described: coherent WaveBurst (cWB), which famously first found GW150914; omicron–LALInferenceBurst (oLIB), and BayesWave, which follows up on cWB triggers.

As you might guess from the name, cWB looks for a coherent signal in both detectors. It looks for excess power (indicating a signal) in a time–frequency plot, and then classifies candidates based upon their structure. There’s one class for blip glitches and resonance lines (see the Detector Characterisation Paper), these are all thrown away as noise; one class for chirp-like signals that increase in frequency with time, this is where GW150914 was found, and one class for everything else. cWB’s detection statistic $\eta_c$ is something like a signal-to-noise ratio constructed based upon the correlated power in the detectors. The value for GW150914 was $\eta_c = 20$ , which is higher than for any other candidate. The false alarm probability (or p-value), folding in all three search classes, is $2\times 10^{-6}$ , which is pretty tiny, even if not as significant as for the tailored compact binary searches.

The oLIB search has two stages. First it makes a time–frequency plot and looks for power coincident between the two detectors. Likely candidates are then followed up by matching a sine–Gaussian wavelet to the data, using a similar algorithm to the one used for parameter estimation. It’s detection statistic is something like a likelihood ratio for the signal verses noise. It calculates a false alarm probability of about $2\times 10^{-6}$ too.

BayesWave fits a variable number of sine–Gaussian wavelets to the data. This can model both a signal (when the wavelets are the same for both detectors) and glitches (when the wavelets are independent). This is really clever, but is too computationally expensive to be left running on all the data. Therefore, it follows up on things highlighted by cWB, potentially increasing their significance. It’s detection statistic is the Bayes factor comparing the signal and glitch models. It estimates the false alarm probability to be about $7 \times 10^{-7}$ (which agrees with the cWB estimate if you only consider chirp-like triggers).

None of the searches find LVT151012. However, as this is a quiet, lower mass binary black hole, I think that this is not necessarily surprising.

cWB and BayesWave also output a reconstruction of the waveform. Reassuringly, this does look like binary black hole coalescence!

Estimated waveforms from different models

Gravitational waveforms from our analyses of GW150914. The wiggly grey line are the data from Hanford (top) and Livinston (bottom); these are analysed coherently. The plots show waveforms whitened by the noise power spectral density. The dark band shows the waveform reconstructed by BayesWave without assuming that the signal is from a binary black hole (BBH). The light bands show the distribution of BBH template waveforms that were found to be most probable from our parameter-estimation analysis. The two techniques give consistent results: the match between the two models is $94^{+2}_{-3}\%$ . Fig. 6 of the Parameter Estimation Paper.

The paper concludes by performing some simple fits to the reconstructed waveforms. For this, you do have to assume that the signal cane from a binary black hole. They find parameters roughly consistent with those from the full parameter-estimation analysis, which is a nice sanity check of our results.

The Detector Characterisation Paper

Synopsis: Detector Characteristation Paper
Read this if: You’re curious if something other than a gravitational wave could be responsible for GW150914 or LVT151012
Favourite part: Mega lightning bolts can cause correlated noise

The output from the detectors that we analyses for signals is simple. It is a single channel that records the strain. To monitor instrumental behaviour and environmental conditions the detector characterisation team record over 200,000 other channels. These measure everything from the alignment of the optics through ground motion to incidence of cosmic rays. Most of the data taken by LIGO is to monitor things which are not gravitational waves.

This paper examines all the potential sources of noise in the LIGO detectors, how we monitor them to ensure they are not confused for a signal, and the impact they could have on estimating the significance of events in our searches. It is amazingly thorough work.

There are lots of potential noise sources for LIGO. Uncorrelated noise sources happen independently at both sites, therefore they can only be mistaken for a gravitational wave if by chance two occur at the right time. Correlated noise sources effect both detectors, and so could be more confusing for our searches, although there’s no guarantee that they would cause a disturbance that looks anything like a binary black hole merger.

Sources of uncorrelated noise include:

Ground motion caused by earthquakes or ocean waves. These create wibbling which can affect the instruments, even though they are well isolated. This is usually at low frequencies (below $0.1~\mathrm{Hz}$ for earthquakes, although it can be higher if the epicentre is near), unless there is motion in the optics around (which can couple to cause higher frequency noise). There is a network of seismometers to measure earthquakes at both sites. There where two magnitude 2.1 earthquakes within 20 minutes of GW150914 (one off the coast of Alaska, the other south-west of Seattle), but both produced ground motion that is ten times too small to impact the detectors. There was some low frequency noise in Livingston at the time of LVT151012 which is associated with a period of bad ocean waves. however, there is no evidence that these could be converted to the frequency range associated with the signal.
People moving around near the detectors can also cause vibrational or acoustic disturbances. People are kept away from the detectors while they are running and accelerometers, microphones and seismometers monitor the environment.
Modulation of the lasers at $9~\mathrm{MHz}$ and $45~\mathrm{MHz}$ is done to monitor and control several parts of the optics. There is a fault somewhere in the system which means that there is a coupling to the output channel and we get noise across $10~\mathrm{Hz}$ to $2~\mathrm{kHz}$ , which is where we look for compact binary coalescences. Rai Weiss suggested shutting down the instruments to fix the source of this and delaying the start of observations—it’s a good job we didn’t. Periods of data where this fault occurs are flagged and not included in the analysis.
Blip transients are a short glitch that occurs for unknown reasons. They’re quite mysterious. They are at the right frequency range ( $30~\mathrm{Hz}$ to $250~\mathrm{Hz}$ ) to be confused with binary black holes, but don’t have the right frequency evolution. They contribute to the background of noise triggers in the compact binary coalescence searches, but are unlikely to be the cause of GW150914 or LVT151012 since they don’t have the characteristic chirp shape.
A time–frequency plot of a blip glitch in LIGO-Livingston. Blip glitches are the right frequency range to be confused with binary coalescences, but don’t have the chirp-like structure. Blips are symmetric in time, whereas binary coalescences sweep up in frequency. Fig. 3 of the Detector Characterisation Paper.

Correlated noise can be caused by:

Electromagnetic signals which can come from lightning, solar weather or radio communications. This is measured by radio receivers and magnetometers, and its extremely difficult to produce a signal that is strong enough to have any impact of the detectors’ output. There was one strong (peak current of about $500~\mathrm{kA}$ ) lightning strike in the same second as GW150914 over Burkino Faso. However, the magnetic disturbances were at least a thousand times too small to explain the amplitude of GW150914.
Cosmic ray showers can cause electromagnetic radiation and particle showers. The particle flux become negligible after a few kilometres, so it’s unlikely that both Livingston and Hanford would be affected, but just in case there is a cosmic ray detector at Hanford. It has seen nothing suspicious.

All the monitoring channels give us a lot of insight into the behaviour of the instruments. Times which can be identified as having especially bad noise properties (where the noise could influence the measured output), or where the detectors are not working properly, are flagged and not included in the search analyses. Applying these vetoes mean that we can’t claim a detection when we know something else could mimic a gravitational wave signal, but it also helps us clean up our background of noise triggers. This has the impact of increasing the significance of the triggers which remain (since there are fewer false alarms they could be confused with). For example, if we leave the bad period in, the PyCBC false alarm probability for LVT151012 goes up from $0.02$ to $0.14$ . The significance of GW150914 is so great that we don’t really need to worry about the effects of vetoes.

At the time of GW150914 the detectors were running well, the data around the event are clean, and there is nothing in any of the auxiliary channels that record anything which could have caused the event. The only source of a correlated signal which has not been rules out is a gravitational wave from a binary black hole merger. The time–frequency plots of the measured strains are shown below, and its easy to pick out the chirps.

Time–frequency plots for GW150914 as measured by Hanford (left) and Livingston (right). These show the characteristic increase in frequency with time of the chirp of a binary merger. The signal is clearly visible above the noise. Fig. 10 of the Detector Characterisation Paper.

The data around LVT151012 are significantly less stationary than around GW150914. There was an elevated noise transient rate around this time. This is probably due to extra ground motion caused by ocean waves. This low frequency noise is clearly visible in the Livingston time–frequency plot below. There is no evidence that this gets converted to higher frequencies though. None of the detector characterisation results suggest that LVT151012 has was caused by a noise artifact.

Time–frequency plots for LVT151012 as measured by Hanford (left) and Livingston (right). You can see the characteristic increase in frequency with time of the chirp of a binary merger, but this is mixed in with noise. The scale is reduced compared with for GW150914, which is why noise features appear more prominent. The band at low frequency in Livingston is due to ground motion; this is not present in Hanford. Fig. 13 of the Detector Characterisation Paper.

If you’re curious about the state of the LIGO sites and their array of sensors, you can see more about the physical environment monitors at pem.ligo.org.

The Calibration Paper

Synopsis: Calibration Paper
Read this if: You like control engineering or precision measurement
Favourite part: Not only are the LIGO detectors sensitive enough to feel the push from a beam of light, they are so sensitive that you have to worry about where on the mirrors you push

We want to measure the gravitational wave strain—the change in length across our detectors caused by a passing gravitational wave. What we actually record is the intensity of laser light out the output of our interferometer. (The output should be dark when the strain is zero, and the intensity increases when the interferometer is stretched or squashed). We need a way to convert intensity to strain, and this requires careful calibration of the instruments.

The calibration is complicated by the control systems. The LIGO instruments are incredibly sensitive, and maintaining them in a stable condition requires lots of feedback systems. These can impact how the strain is transduced into the signal readout by the interferometer. A schematic of how what would be the change in the length of the arms without control systems $\Delta L_\mathrm{free}$ is changed into the measured strain $h$ is shown below. The calibration pipeline build models to correct for the effects of the control system to provide an accurate model of the true gravitational wave strain.

Model for how a differential arm length caused by a gravitational wave $\Delta L_\mathrm{free}$ or a photon calibration signal $x_\mathrm{T}^\mathrm{(PC)}$ is converted into the measured signal $h$ . Fig. 2 from the Calibration Paper.

To measure the different responses of the system, the calibration team make several careful measurements. The primary means is using photon calibration: an auxiliary laser is used to push the mirrors and the response is measured. The spots where the lasers are pointed are carefully chosen to minimise distortion to the mirrors caused by pushing on them. A secondary means is to use actuators which are parts of the suspension system to excite the system.

As a cross-check, we can also use two auxiliary green lasers to measure changes in length using either a frequency modulation or their wavelength. These are similar approaches to those used in initial LIGO. These go give consistent results with the other methods, but they are not as accurate.

Overall, the uncertainty in the calibration of the amplitude of the strain is less than $10\%$ between $20~\mathrm{Hz}$ and $1~\mathrm{kHz}$ , and the uncertainty in phase calibration is less than $10^\circ$ . These are the values that we use in our parameter-estimation runs. However, the calibration uncertainty actually varies as a function of frequency, with some ranges having much less uncertainty. We’re currently working on implementing a better model for the uncertainty, which may improve our measurements. Fortunately the masses, aren’t too affected by the calibration uncertainty, but sky localization is, so we might get some gain here. We’ll hopefully produce results with updated calibration in the near future.

The Astrophysics Paper

Synopsis: Astrophysics Paper
Read this if: You are interested in how binary black holes form
Favourite part: We might be able to see similar mass binary black holes with eLISA before they merge in the LIGO band [bonus note]

This paper puts our observations of GW150914 in context with regards to existing observations of stellar-mass black holes and theoretical models for binary black hole mergers. Although it doesn’t explicitly mention LVT151012, most of the conclusions would be just as applicable to it’s source, if it is real. I expect there will be rapid development of the field now, but if you want to catch up on some background reading, this paper is the place to start.

The paper contains lots of references to good papers to delve into. It also highlights the main conclusion we can draw in italics, so its easy to skim through if you want a summary. I discussed the main astrophysical conclusions in my previous post. We will know more about binary black holes and their formation when we get more observations, so I think it is a good time to get interested in this area.

The Stochastic Paper

Synopsis: Stochastic Paper
Read this if: You like stochastic backgrounds
Favourite part: We might detect a background in the next decade

A stochastic gravitational wave background could be created by an incoherent superposition of many signals. In pulsar timing, they are looking for a background from many merging supermassive black holes. Could we have a similar thing from stellar-mass black holes? The loudest signals, like GW150914, are resolvable, they stand out from the background. However, for every loud signal, there will be many quiet signals, and the ones below our detection threshold could form a background. Since we’ve found that binary black hole mergers are probably plentiful, the background may be at the high end of previous predictions.

The background from stellar-mass black holes is different than the one from supermassive black holes because the signals are short. While the supermassive black holes produce an almost constant hum throughout your observations, stellar-mass black hole mergers produce short chirps. Instead of having lots of signals that overlap in time, we have a popcorn background, with one arriving on average every 15 minutes. This might allow us to do some different things when it comes to detection, but for now, we just use the standard approach.

This paper calculates the energy density of gravitational waves from binary black holes, excluding the contribution from signals loud enough to be detected. This is done for several different models. The standard (fiducial) model assumes parameters broadly consistent with those of GW150914’s source, plus a particular model for the formation of merging binaries. There are then variations on the the model for formation, considering different time delays between formation and merger, and adding in lower mass systems consistent with LVT151012. All these models are rather crude, but give an idea of potential variations in the background. Hopefully more realistic distributions will be considered in the future. There is some change between models, but this is within the (considerable) statistical uncertainty, so predictions seems robust.

Models for a binary black hole stochastic background

Different models for the stochastic background of binary black holes. This is plotted in terms of energy density. The red band indicates the uncertainty on the fiducial model. The dashed line indicates the sensitivity of the LIGO and Virgo detectors after several years at design sensitivity. Fig. 2 of the Stochastic Paper.

After a couple of years at design sensitivity we may be able to make a confident detection of the stochastic background. The background from binary black holes is more significant than we expected.

If you’re wondering about if we could see other types of backgrounds, such as one of cosmological origin, then the background due to binary black holes could make detection more difficult. In effect, it acts as another source of noise, masking the other background. However, we may be able to distinguish the different backgrounds by measuring their frequency dependencies (we expect them to have different slopes), if they are loud enough.

The Neutrino Paper

Synopsis: Neutrino Paper
Read this if: You really like high energy neutrinos
Favourite part: We’re doing astronomy with neutrinos and gravitational waves—this is multimessenger astronomy without any form of electromagnetic radiation

There are multiple detectors that can look for high energy neutrinos. Currently, LIGO–Virgo Observations are being followed up by searches from ANTARES and IceCube. Both of these are Cherenkov detectors: they look for flashes of light created by fast moving particles, not the neutrinos themselves, but things they’ve interacted with. ANTARES searches the waters of the Mediterranean while IceCube uses the ice of Antarctica.

Within 500 seconds either side of the time of GW150914, ANTARES found no neutrinos and IceCube found three. These results are consistent with background levels (you would expect on average less than one and 4.4 neutrinos over that time from the two respectively). Additionally, none of the IceCube neutrinos are consistent with the sky localization of GW150914 (even though the sky area is pretty big). There is no sign of a neutrino counterpart, which is what we were expecting.

Subsequent non-detections have been reported by KamLAND, the Pierre Auger Observatory, Super-Kamiokande, Borexino and NOvA.

The Electromagnetic Follow-up Paper

Synopsis: Electromagnetic Follow-up Paper
Read this if: You are interested in the search for electromagnetic counterparts
Favourite part: So many people were involved in this work that not only do we have to abbreviate the list of authors (Abbott, B.P. et al.), but we should probably abbreviate the list of collaborations too (LIGO Scientific & Virgo Collaboration et al.)

This is the last of the set of companion papers to be released—it took a huge amount of coordinating because of all the teams involved. The paper describes how we released information about GW150914. This should not be typical of how we will do things going forward (i) because we didn’t have all the infrastructure in place on September 14 and (ii) because it was the first time we had something we thought was real.

The first announcement was sent out on September 16, and this contained sky maps from the Burst codes cWB and LIB. In the future, we should be able to send out automated alerts with a few minutes latency.

For the first alert, we didn’t have any results which assumed the the source was a binary, as the searches which issue triggers at low latency were only looking for lower mass systems which would contain a neutron star. I suspect we’ll be reprioritising things going forward. The first information we shared about the potential masses for the source was shared on October 3. Since this was the first detection, everyone was cautious about triple-checking results, which caused the delay. Revised false alarm rates including results from GstLAL and PyCBC were sent out October 20.

The final sky maps were shared January 13. This is when we’d about finished our own reviews and knew that we would be submitting the papers soon [bonus note]. Our best sky map is the one from the Parameter Estimation Paper. You might it expect to be more con straining than the results from the burst pipelines since it uses a proper model for the gravitational waves from a binary black hole. This is the case if we ignore calibration uncertainty (which is not yet included in the burst codes), then the 50% area is $48~\mathrm{deg}^2$ and the 90% area is $150~\mathrm{deg^2}$ . However, including calibration uncertainty, the sky areas are $150~\mathrm{deg^2}$ and $590~\mathrm{deg^2}$ at 50% and 90% probability respectively. Calibration uncertainty has the largest effect on sky area. All the sky maps agree that the source is in in some region of the annulus set by the time delay between the two detectors.

The different sky maps for GW150914 in an orthographic projection. The contours show the 90% region for each algorithm. The faint circles show lines of constant time delay $\Delta t_\mathrm{HL}$ between the two detectors. BAYESTAR rapidly computes sky maps for binary coalescences, but it needs the output of one of the detection pipelines to run, and so was not available at low latency. The LALInference map is our best result. All the sky maps are available as part of the data release. Fig. 2 of the Electromagnetic Follow-up Paper.

A timeline of events is shown below. There were follow-up observations across the electromagnetic spectrum from gamma-rays and X-rays through the optical and near infra-red to radio.

Timeline for observations of GW15014. The top (grey) band shows information about gravitational waves. The second (blue) band shows high-energy (gamma- and X-ray) observations. The third and fourth (green) bands show optical and near infra-red observations respectively. The bottom (red) band shows radio observations. Fig. 1 from the Electromagnetic Follow-up Paper.

Observations have been reported (via GCN notices) by

the Australian Square Kilometre Array Pathfinder (ASKAP) Collaboration
the BOOTES Collaboration
the Dark Energy Camera GW–EM Collaboration (Paper I, Paper II)
the Fermi GBM Collaboration
the Fermi LAT Collaboration
the Gravitational Wave Inaf Team (GRAWITA)
the INTEGRAL Collaboration
the Intermediate Palomar Transient Factory (iPTF) Collaboration (radio follow-up from the Jansky Very Large Array)
the Interplanetary Network (IPN)
the J-GEM Collaboration
the La Silla–Quest Survey
the Liverpool Telescope Collaboration
the Low Frequency Array (LOFAR) Collaboration
the MASTER Collaboration
the Monitor of All-sky X-ray Image (MAXI) Collaboration
the Murchison Wide-field Array (MWA) Collaboration
the Pan-STARRS Collaboration and the PESSTO Collaboration
the Pi of the Sky Collaboration
the SkyMapper Collaboration
the Swift Collaboration
the TAROT, Zadko, Algerian National Observatory and C2PU Collaboration
the TOROS Collaboration
the VISTA Collaboration

Together they cover an impressive amount of the sky as shown below. Many targeted the Large Magellanic Cloud before the knew the source was a binary black hole.

Footprints of observations compared with the 50% and 90% areas of the initially distributed (cWB: thick lines; LIB: thin lines) sky maps, also in orthographic projection. The all-sky observations are not shown. The grey background is the Galactic plane. Fig. 3 of the Electromagnetic Follow-up Paper.

Additional observations have been done using archival data by XMM-Newton and AGILE.

We don’t expect any electromagnetic counterpart to a binary black hole. No-one found anything with the exception of Fermi GBM. This has found a weak signal which may be coincident. More work is required to figure out if this is genuine (the statistical analysis looks OK, but some times you do have a false alarm). It would be a surprise if it is, so most people are sceptical. However, I think this will make people more interested in following up on our next binary black hole signal!

Bonus notes

Naming The Event

GW150914 is the name we have given to the signal detected by the two LIGO instruments. The “GW” is short for gravitational wave (not galactic worm), and the numbers give the date the wave reached the detectors (2015 September 14). It was originally known as G184098, its ID in our database of candidate events (most circulars sent to and from our observer partners use this ID). That was universally agreed to be terrible to remember. We tried to think of a good nickname for the event, but failed to, so rather by default, it has informally become known as The Event within the Collaboration. I think this is fitting given its significance.

LVT151012 is the name of the most significant candidate after GW150914, it doesn’t reach our criteria to claim detection (a false alarm rate of less than once per century), which is why it’s not GW151012. The “LVT” is short for LIGO–Virgo trigger. It took a long time to settle on this and up until the final week before the announcement it was still going by G197392. Informally, it was known as The Second Monday Event, as it too was found on a Monday. You’ll have to wait for us to finish looking at the rest of the O1 data to see if the Monday trend continues. If it does, it could have serious repercussions for our understanding of Garfield.

Following the publication of the O2 Catalogue Paper, LVT151012 was upgraded to GW151012, AND we decided to get rid of the LVT class as it was rather confusing.

Publishing in Physical Review Letters

Several people have asked me if the Discovery Paper was submitted to Science or Nature. It was not. The decision that any detection would be submitted to Physical Review was made ahead of the run. As far as I am aware, there was never much debate about this. Physical Review had been good about publishing all our non-detections and upper limits, so it only seemed fair that they got the discovery too. You don’t abandon your friends when you strike it rich. I am glad that we submitted to them.

Gaby González, the LIGO Spokesperson, contacted the editors of Physical Review Letters ahead of submission to let them know of the anticipated results. They then started to line up some referees to give confidential and prompt reviews.

The initial plan was to submit on January 19, and we held a Collaboration-wide tele-conference to discuss the science. There were a few more things still to do, so the paper was submitted on January 21, following another presentation (and a long discussion of whether a number should be a six or a two) and a vote. The vote was overwhelmingly in favour of submission.

We got the referee reports back on January 27, although they were circulated to the Collaboration the following day. This was a rapid turnaround! From their comments, I suspect that Referee A may be a particle physicist who has dealt with similar claims of first detection—they were most concerned about statistical significance; Referee B seemed like a relativist—they made comments about the effect of spin on measurements, knew about waveforms and even historical papers on gravitational waves, and I would guess that Referee C was an astronomer involved with pulsars—they mentioned observations of binary pulsars potentially claiming the title of first detection and were also curious about sky localization. While I can’t be certain who the referees were, I am certain that I have never had such positive reviews before! Referee A wrote

The paper is extremely well written and clear. These results are obviously going to make history.

Referee B wrote

This paper is a major breakthrough and a milestone in gravitational science. The results are overall very well presented and its suitability for publication in Physical Review Letters is beyond question.

and Referee C wrote

It is an honor to have the opportunity to review this paper. It would not be an exaggeration to say that it is the most enjoyable paper I’ve ever read. […] I unreservedly recommend the paper for publication in Physical Review Letters. I expect that it will be among the most cited PRL papers ever.

I suspect I will never have such emphatic reviews again [happy bonus note][unhappy bonus note].

Publishing in Physical Review Letters seems to have been a huge success. So much so that their servers collapsed under the demand, despite them adding two more in anticipation. In the end they had to quintuple their number of servers to keep up with demand. There were 229,000 downloads from their website in the first 24 hours. Many people remarked that it was good that the paper was freely available. However, we always make our papers public on the arXiv or via LIGO’s Document Control Center [bonus bonus note], so there should never be a case where you miss out on reading a LIGO paper!

Publishing the Parameter Estimation Paper

The reviews for the Parameter Estimation Paper were also extremely positive. Referee A, who had some careful comments on clarifying notation, wrote

This is a beautiful paper on a spectacular result.

Referee B, who commendably did some back-of-the-envelope checks, wrote

The paper is also very well written, and includes enough background that I think a decent fraction of it will be accessible to non-experts. This, together with the profound nature of the results (first direct detection of gravitational waves, first direct evidence that Kerr black holes exist, first direct evidence that binary black holes can form and merge in a Hubble time, first data on the dynamical strong-field regime of general relativity, observation of stellar mass black holes more massive than any observed to date in our galaxy), makes me recommend this paper for publication in PRL without hesitation.

Referee C, who made some suggestions to help a non-specialist reader, wrote

This is a generally excellent paper describing the properties of LIGO’s first detection.

Physical Review Letters were also kind enough to publish this paper open access without charge!

Publishing the Rates Paper

It wasn’t all clear sailing getting the companion papers published. Referees did give papers the thorough checking that they deserved. The most difficult review was of the Rates Paper. There were two referees, one astrophysics, one statistics. The astrophysics referee was happy with the results and made a few suggestions to clarify or further justify the text. The statistics referee has more serious complaints…

There are five main things which I think made the statistics referee angry. First, the referee objected to our terminology

While overall I’ve been impressed with the statistics in LIGO papers, in one respect there is truly egregious malpractice, but fortunately easy to remedy. It concerns incorrectly using the term “false alarm probability” (FAP) to refer to what statisticians call a p-value, a deliberately vague term (“false alarm rate” is similarly misused). […] There is nothing subtle or controversial about the LIGO usage being erroneous, and the practice has to stop, not just within this paper, but throughout the LIGO collaboration (and as a matter of ApJ policy).

I agree with this. What we call the false alarm probability is not the probability that the detection is a false alarm. It is not the probability that the given signal is noise rather that astrophysical, but instead it is the probability that if we only had noise that we would get a detection statistic as significant or more so. It might take a minute to realise why those are different. The former (the one we should call p-value) is what the search pipelines give us, but is less useful than the latter for actually working out if the signal is real. The probabilities calculated in the Rates Paper that the signal is astrophysical are really what you want.

p-values are often misinterpreted, but most scientists are aware of this, and so are cautious when they come across them

As a consequence of this complaint, the Collaboration is purging “false alarm probability” from our papers. It is used in most of the companion papers, as they were published before we got this report (and managed to convince everyone that it is important).

Second, we were lacking in references to existing literature

Regarding scholarship, the paper is quite poor. I take it the authors have written this paper with the expectation, or at least the hope, that it would be read […] If I sound frustrated, it’s because I am.

This is fair enough. The referee made some good suggestions to work done on inferring the rate of gamma-ray bursts by Loredo & Wasserman (Part I, Part II, Part III), as well as by Petit, Kavelaars, Gladman & Loredo on trans-Neptunian objects, and we made sure to add as much work as possible in revisions. There’s no excuse for not properly citing useful work!

Third, the referee didn’t understand how we could be certain of the distribution of signal-to-noise ratio $\rho$ without also worrying about the distribution of parameters like the black hole masses. The signal-to-noise ratio is inversely proportional to distance, and we expect sources to be uniformly distributed in volume. Putting these together (and ignoring corrections from cosmology) gives a distribution for signal-to-noise ratio of $p(\rho) \propto \rho^{-4}$ (Schulz 2011). This is sufficiently well known within the gravitational-wave community that we forgot that those outside wouldn’t appreciate it without some discussion. Therefore, it was useful that the referee did point this out.

Fourth, the referee thought we had made an error in our approach. They provided an alternative derivation which

if useful, should not be used directly without some kind of attribution

Unfortunately, they were missing some terms in their expressions. When these were added in, their approach reproduced our own (I had a go at checking this myself). Given that we had annoyed the referee on so many other points, it was tricky trying to convince them of this. Most of the time spent responding to the referees was actually working on the referee response and not on the paper.

Finally, the referee was unhappy that we didn’t make all our data public so that they could check things themselves. I think it would be great, and it will happen, it was just too early at the time.

LIGO Document Control Center

Papers in the LIGO Document Control Center are assigned a number starting with P (for “paper”) and then several digits. The Discover Paper’s reference is P150914. I only realised why this was the case on the day of submission.

The überbank

The set of templates used in the searches is designed to be able to catch binary neutron stars, neutron star–black hole binaries and binary neutron stars. It covers component masses from 1 to 99 solar masses, with total masses less than 100 solar masses. The upper cut off is chosen for computational convenience, rather than physical reasons: we do look for higher mass systems in a similar way, but they are easier to confuse with glitches and so we have to be more careful tuning the search. Since bank of templates is so comprehensive, it is known as the überbank. Although it could find binary neutron stars or neutron star–black hole binaries, we only discuss binary black holes here.

The template bank doesn’t cover the full parameter space, in particular it assumes that spins are aligned for the two components. This shouldn’t significantly affect its efficiency at finding signals, but gives another reason (together with the coarse placement of templates) why we need to do proper parameter estimation to measure properties of the source.

Alphabet soup

In the calculation of rates, the probabilistic means for counting sources is known as the FGMC method after its authors (who include two Birmingham colleagues and my former supervisor). The means of calculating rates assuming that the population is divided into one class to match each observation is also named for the initial of its authors as the KKL approach. The combined FGMCKKL method for estimating merger rates goes by the name alphabet soup, as that is much easier to swallow.

Multi-band gravitational wave astronomy

The prospect of detecting a binary black hole with a space-based detector and then seeing the same binary merger with ground-based detectors is especially exciting. My officemate Alberto Sesana (who’s not in LIGO) has just written a paper on the promise of multi-band gravitational wave astronomy. Black hole binaries like GW150914 could be spotted by eLISA (if you assume one of the better sensitivities for a detector with three arms). Then a few years to weeks later they merge, and spend their last moments emitting in LIGO’s band. The evolution of some binary black holes is sketched in the plot below.

Binary black hole mergers across the eLISA and LIGO frequency bands

The evolution of binary black hole mergers (shown in blue). The eLISA and Advanced LIGO sensitivity curves are shown in purple and orange respectively. As the black holes inspiral, they emit gravitational waves at higher frequency, shifting from the eLISa band to the LIGO band (where they merge). The scale at the top gives the approximate time until merger. Fig. 1 of Sesana (2016).

Seeing the signal in two bands can help in several ways. First it can increase our confidence in detection, potentially picking out signals that we wouldn’t otherwise. Second, it gives us a way to verify the calibration of our instruments. Third, it lets us improve our parameter-estimation precision—eLISA would see thousands of cycles, which lets it pin down the masses to high accuracy, these results can be combined with LIGO’s measurements of the strong-field dynamics during merger to give a fantastic overall picture of the system. Finally, since eLISA can measure the signal for a considerable time, it can well localise the source, perhaps just to a square degree; since we’ll also be able to predict when the merger will happen, you can point telescopes at the right place ahead of time to look for any electromagnetic counterparts which may exist. Opening up the gravitational wave spectrum is awesome!

The LALInference sky map

One of my jobs as part of the Parameter Estimation group was to produce the sky maps from our parameter-estimation runs. This is a relatively simple job of just running our sky area code. I had done it many times while were collecting our results, so I knew that the final versions were perfectly consistent with everything else we had seen. While I was comfortable with running the code and checking the results, I was rather nervous uploading the results to our database to be shared with our observational partners. I somehow managed to upload three copies by accident. D’oh! Perhaps future historians will someday look back at the records for G184098/GW150914 and wonder what was this idiot Christopher Berry doing? Probably no-one would every notice, but I know the records are there…

The papers

The O2 Catalogue Paper

The O2 Populations Paper

The O2 Catalogue Paper

The instruments

The searches

The source properties

Waveform reconstructions

Merger rates

The O2 Populations Paper

Masses

Spins

Redshift evolution

Bonus notes

Naming

Burning bright

August 2017—Something fishy or just Poisson statistics?

Sign errors

SEOBNRv3

Thanksgiving

Confession

New sources

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Commissioning and observing phases

Searches for gravitational-wave transients

Observing scenarios

Bonus notes

GW170817 announcement

Design sensitivity

Binary black holes vs binary neutron stars

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Bonus notes

Detector engineering

Parameter estimation rota

Alerts and follow-up

Virgo?

Journal

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Discovery

Science

Summary

Bonus notes

Inbox zero

Worst case scenario

Parameter estimation rota

Especially made

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Transient searches

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

The O1 Gamma-Ray Burst Paper

The O1 Intermediate Mass Black Hole Binary Paper

The O1 Burst Paper

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

The O1 Gamma-Ray Burst Paper

The O1 Intermediate Mass Black Hole Binary Paper

The O1 Burst Paper

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The story

The science

The searches

The source

Merger rates

Astrophysics

Tests of general relativity

The search for counterparts

Summary

Bonus notes

Naming

The 6 January sky map

Binary black hole waveforms

On distance

Time line

Detector status

Spin evolution

Footnotes