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

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

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


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—GW170714. 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.

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].

Signal and glitch

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.


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.

Normalised spectrograms for GW170817

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).

Binary neutron star masses

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 don’t yet have good model waveforms including tides, so for now we’ve just done a preliminary analysis. 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. 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.

GW170817 Hubble constant

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!


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

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.

Nobel medal

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



GW170814—Enter Virgo

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

A new foe appeared

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

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

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

Three different ways of visualising GW170814: an SNR time series, a spectrogram and a waveform reconstruction

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

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

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

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

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

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

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

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

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

Sky localization of GW170814

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

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

Plus and cross polarizations

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

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

The siz gravitational wave polarizations

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

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

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

Bonus notes

Signs of paranoia

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

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

Signal hunting

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

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

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

In conclusion: Virgo works. Probably.


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

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

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

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

Perfect advice

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

One more thing

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

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

Observing run 1—The papers

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

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

Transient searches

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

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

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

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

The O1 Gamma-Ray Burst Paper

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

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

More details: O1 Gamma-Ray Burst Paper summary

The O1 Intermediate Mass Black Hole Binary Paper

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

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

More details: O1 Intermediate Mass Black Hole Binary Paper summary

The O1 Burst Paper

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

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

More details: O1 Burst Paper summary

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

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

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

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

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

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

\Lambda = R \langle VT \rangle

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

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

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

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

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

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

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

Upper merger rate limits for binary neutron stars

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

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

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

Comparison of merger rates

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

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

The O1 Gamma-Ray Burst Paper

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

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

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

We used two search algorithms:

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

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

GRB 150906B sky location

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

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

The O1 Intermediate Mass Black Hole Binary Paper

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

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

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

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

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

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

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

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

Intermediate mass black hole binary search results

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

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

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

The O1 Burst Paper

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

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

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

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

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

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

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

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

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

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

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

Upper limits on energy at different frequencies

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

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

GW170104 and me

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

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

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

Normalised spectrograms for GW170104

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 tail 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…

Looking east across Lake Annecy, France

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.

Binary black hole masses

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.

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. Part of Figure 3 of the GW170104 Discovery Paper.

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

Final black hole mass and spin

Estimated mass M_\mathrm{f} and spina_\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.


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.

Effective inspiral spin parameters

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).
  • 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 GRB170105A.
  • ATLAS and Pan-STARRS—optical follow-up. They identified a bright optical transient 23 hours after GW170104, ATLAS17aeu. This could be a counterpart to GRB170105A. 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.
  • 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.

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.


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

Bonus notes


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.

Distance and inclination

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.


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

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
 1608.01940 [gr-qc]
 Annalen der Physik529(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
 1606.01210 [gr-qc]
 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
 1611.07531 [gr-qc]
Classical & Quantum Gravity; 34(10):104002(48); 2017

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
 1606.01262 [gr-qc]
 Physical Review D; 94(6):064035(30); 2016

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 LIGO Open Science Center (LOSC), has put together a selection of tutorials to show you some of the basics of analysing signals. 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 LOSC 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 LOSC 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, I would prefer the results in the O1 Binary Black Hole Paper, even though this doesn’t use the fully precessing EOBNR waveform, because we do use an updated calibration of the detector data. Neither the choice of waveform or the calibration make much of an impact on the results, so for most uses it shouldn’t matter too much.

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


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 O1 Binary Black Hole Paper) would be 30.6^{+1.9}_{-1.6} 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 28.1^{+1.8}_{-1.5} 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.

First low frequency all-sky search for continuous gravitational wave signals

It is the time of year for applying for academic jobs and so I have been polishing up my CV. In doing so I spotted that I had missed the publication of one of the LIGO Scientific–Virgo Collaboration papers. In my defence, it was published the week of 8–14 February, which saw the publication of one or two other papers [bonus note]. The paper I was missing is on a search for continuous gravitational waves.

Continuous gravitational waves are near constant hums. Unlike the chirps of coalescing binaries, continuous signals are always on. We think that they could be generated by rotating neutron stars, assuming that they are not perfectly smooth. This is the first search to look for continuous waves from anywhere on the sky with frequencies below 50 Hz. The gravitational-wave frequency is twice the rotational frequency of the neutron star, so this is the first time we’ve looked for neutron stars spinning slower than 25 times per second (which is still pretty fast, I’d certainly feel more than a little queasy). The search uses data from the second and fourth Virgo Science Runs (VSR2 and VSR4): the detector didn’t behave as well in VSR3, which is why that data isn’t used.

The frequency of a rotating neutron star isn’t quite constant for two reasons. First, as the Earth orbits around the Sun it’ll move towards and away from the source. This leads to the signal being Doppler shifted. For a given position on the sky, this can be corrected for, and this is done in the search. Second, the neutron star will slow down (a process known as spin-down) because it looses energy and angular momentum. There are various processes that could slow a neutron star, emitting gravitational waves is one, some form of internal sloshing around is another which could also cause things to speed up, or perhaps some braking from its magnetic field. We’re not too sure exactly how quickly spin down will happen, so we search over a range of possible values from -1.0\times10^{-10}~\mathrm{Hz\,s^{-1}} to +1.5\times10^{-11}~\mathrm{Hz\,s^{-1}}.

The particular search technique used is called FrequencyHough. This chops the detector output into different chunks of time. In each we calculate how much power is at each frequency. We then look for a pattern, where we can spot a signal across different times, allowing for some change from spin-down. Recognising the track of a signal with a consistent frequency evolution is done using a Hough transform, a technique from image processing that is good at spotting lines.

The search didn’t find any signals. This is not too surprising. Therefore, we did the usual thing of setting some upper limits. The plot below shows 90% confidence limits (that is where we’d expect to detect 9/10 signals) on the signal amplitude at different frequencies.

Upper limits at different frequencies

90% confidence upper limits on the gravitational-wave strain at different frequencies. Each dot is for a different 1 Hz band. Some bands are noisy and feature instrumental artefacts which have to be excluded from the analysis, these are noted as the filled (magenta) circles. In this case, the upper limit only applies to the part of the band away from the disturbance. Figure 12 of Aasi et al. (2016).

Given that the paper only reports a non-detection, it is rather lengthy. The opening sections do give a nice introduction to continuous waves and how we hunt for them, so this might be a good paper is you’re new to the area but want to learn some of the details. Be warned that it does use \jmath = \sqrt{-1} for some reason. After the introduction, it does get technical, so it’s probably only for insomniacs. However, if you like a good conspiracy and think we might be hiding something, the appendices go through all the details of removing instrumental noise and checking outliers found by the search.

In summary, this was the first low-frequency search for continuous gravitational waves. We didn’t find anything in the best data from the initial detector era, but the advanced detectors will be much more sensitive to this frequency range. Slowly rotating neutron stars can’t hide forever.

arXiv: 1510.03621 [astro-ph.IM]
Journal: Physical Review D; 93(4):042007(25); 2016
Science summary: First search for low frequency continuous gravitational waves emitted by unseen neutron stars
Greatest regret:
 I didn’t convince the authors to avoid using “air quotes” around jargon.

Bonus note

Better late than never

I feel less guilty about writing a late blog post about this paper as I know that it has been a long time in the making. As a collaboration, we are careful in reviewing our results; this can sometimes lead to delays in announcing results, but hopefully means that we get the right answer. This paper took over three years to review, a process which included over 85 telecons!

Comprehensive all-sky search for periodic gravitational waves in the sixth science run LIGO data

The most recent, and most sensitive, all-sky search for continuous gravitational waves shows no signs of a detection. These signals from rotating neutron stars remain elusive. New data from the advanced detectors may change this, but we will have to wait a while to find out. This at least gives us time to try to figure out what to do with a detection, should one be made.

New years and new limits

The start of the new academic year is a good time to make resolutions—much better than wet and windy January. I’m trying to be tidier and neater in my organisation. Amid cleaning up my desk, which is covered in about an inch of papers, I uncovered this recent Collaboration paper, which I had lost track of.

The paper is the latest in the continuous stream of non-detections of continuous gravitational waves. These signals could come from rotating neutron stars which are deformed or excited in some way, and the hope that from such an observation we could learn something about the structure of neutron stars.

The search uses old data from initial LIGO’s sixth science run. Searches for continuous waves require lots of computational power, so they can take longer than even our analyses of binary neutron star coalescences. This is a semi-coherent search, like the recent search of the Orion spur—somewhere between an incoherent search, which looks for signal power of any form in the detectors, and a fully coherent search, which looks for signals which exactly match the way a template wave evolves [bonus note]. The big difference compared to the Orion spur search, is that this one looks at the entire sky. This makes it less sensitive in those narrow directions, but means we are not excluding the possibility of sources from other locations.

Part of the Galaxy searched

Artist’s impression of the local part of the Milky Way. The yellow cones mark the extent of the Orion Spur spotlight search, and the pink circle shows the equivalent sensitivity of this all-sky search. Green stars indicate known pulsars. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

The search identified 16 outliers, but an examination of all of these showed they could be explained either as an injected signal or as detector noise. Since no signals were found, we can instead place some upper limits on the strength of signals.

The plot below translates the calculated upper limits (above which there would have been a ~75%–95% chance of us detected the signal) into the size of neutron star deformations. Each curve shows the limits on detectable signals at different distance, depending upon their frequency and the rate of change of their frequency. The dotted lines show limits on ellipticity \varepsilon, a measure of how bumpy the neutron star is. Larger deformations mean quicker changes of frequency and produce louder signals, therefore they can can be detected further away.

Limits on detectable signals and ellipticities

Range of the PowerFlux search for rotating neutron stars assuming that spin-down is entirely due to gravitational waves. The solid lines show the upper limits as a function of the gravitational-wave frequency and its rate of change; the dashed lines are the corresponding limits on ellipticity, and the dotted line marks the maximum searched spin-down. Figure 6 of Abbott et al. (2016).

Neutron stars are something like giant atomic nuclei. Figuring the properties of the strange matter that makes up neutron stars is an extremely difficult problem. We’ll never be able to recreate such exotic matter in the laboratory. Gravitational waves give us a rare means of gathering experimental data on how this matter behaves. However, exactly how we convert a measurement of a signal into constraints on the behaviour of the matter is still uncertain. I think that making a detection might only be the first step in understanding the sources of continuous gravitational waves.

arXiv: 1605.03233 [gr-qc]
Journal: Physical Review D; 94(4):042002(14); 2016
Other new academic year resolution:
 To attempt to grow a beard. Beard stroking helps you think, right?

Bonus note

The semi-coherent search

As the first step of this search, the PowerFlux algorithm looks for power that changes in frequency as expected for a rotating neutron star: it factors in Doppler shifting due to the motion of the Earth and a plausible spin down (slowing of the rotation) of the neutron star. As a follow up, the Loosely Coherent algorithm is used, which checks for signals which match short stretches of similar templates. Any candidates to make it through all stages of refinement are then examined in more detail. This search strategy is described in detail for the S5 all-sky search.

Search for transient gravitational waves in coincidence with short-duration radio transients during 2007–2013

Gravitational waves give us a new way of observing the Universe. This raises the possibility of multimessenger astronomy, where we study the same system using different methods: gravitational waves, light or neutrinos. Each messenger carries different information, so by using them together we can build up a more complete picture of what’s going on. This paper looks for gravitational waves that coincide with radio bursts. None are found, but we now have a template for how to search in the future.

On a dark night, there are two things which almost everyone will have done: wondered at the beauty of the starry sky and wondered exactly what was it that just went bump… Astronomers do both. Transient astronomy is about figuring out what are the things which go bang in the night—not the things which make suspicious noises, but objects which appear (and usually disappear) suddenly in the sky.

Most processes in astrophysics take a looooong time (our Sun is four-and-a-half billion years old and is just approaching middle age). Therefore, when something happens suddenly, flaring perhaps over just a few seconds, you know that something drastic must be happening! We think that most transients must be tied up with a violent event such as an explosion. However, because transients are so short, it can difficult to figure out exactly where they come from (both because they might have faded by the time you look, and because there’s little information to learn from a blip in the first place).

Radio transients are bursts of radio emission of uncertain origin. We’ve managed to figure out that some come from microwave ovens, but the rest do seem to come from space. This paper looks at two types: rotating radio transients (RRATs) and fast radio bursts (FRBs). RRATs look like the signals from pulsars, except that they don’t have the characteristic period pattern of pulsars. It may be that RRATs come from dying pulsars, flickering before they finally switch off, or it may be that they come from neutron stars which are not normally pulsars, but have been excited by a fracturing of their crust (a starquake). FRBs last a few milliseconds, they could be generated when two neutron stars merge and collapse to form a black hole, or perhaps from a highly-magnetised neutron star. Normally, when astronomers start talking about magnetic fields, it means that we really don’t know what’s going on [bonus note]. That is the case here. We don’t know what causes radio transients, but we are excited to try figuring it out.

This paper searches old LIGO, Virgo and GEO data for any gravitational-wave signals that coincide with observed radio transients. We use a catalogue of RRATs and FRBs from the Green Bank Telescope and the Parkes Observatory, and search around these times. We use a burst search, which doesn’t restrict itself to any particular form of gravitational-wave; however, the search was tuned for damped sinusoids and sine–Gaussians (generic wibbles), cosmic strings (which may give an indication of how uncertain we are of where radio transients could come from), and coalescences of binary neutron stars or neutron star–black hole binaries. Hopefully the search covers all plausible options. Discovering a gravitational wave coincident with a radio transient would give us much welcomed information about the source, and perhaps pin down their origin.

Results from search for gravitational waves conicident with radio transients

Search results for gravitational waves coincident with radio transients. The probabilities for each time containing just noise (blue) match the expected background distribution (dashed). This is consistent with a non-detection.

The search discovered nothing. Results match what we would expect from just noise in the detectors. This is not too surprising since we are using data from the first-generation detectors. We’ll be repeating the analysis with the upgraded detectors, which can find signals from larger distances. If we are lucky, multimessenger astronomy will allow us to figure out exactly what needs to go bump to create a radio transient.

arXiv: 1605.01707 [astro-ph.HE]
Journal: Physical Review D; 93(12):122008(14); 2016
Science summary: Searching for gravitational wave bursts in coincidence with short duration radio bursts
Favourite thing that goes bump in the night: Heffalumps and Woozles [probably not the cause of radio transients]

Bonus note

Magnetism and astrophysics

Magnetic fields complicate calculations. They make things more difficult to model and are therefore often left out. However, we know that magnetic fields are everywhere and that they do play important roles in many situations. Therefore, they are often invoked as an explanation of why models can’t explain what’s going on. I learnt early in my PhD that you could ask “What about magnetic fields?” at the end of almost any astrophysics seminar (it might not work for some observational talks, but then you could usually ask “What about dust?” instead). Handy if ever you fall asleep…

The Boxing Day Event

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

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

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

A Christmas gift

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

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

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

The science

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

0. The Boxing Day Discovery Paper

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

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

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

More details: The Boxing Day Discovery Paper summary

1. The O1 Binary Black Hole Paper

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

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.

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!

Binary black hole masses

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.

Orientation and magnitudes of the two spins

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.


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.

All binary black hole masses

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.

All mass ratios and effective spins

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.

All final masses and spins

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).

All luminosity distances

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.

Sky localization relative to Earth.

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.

O1 testing general relativity bounds

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.


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

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

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

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

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

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

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

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

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

Astrophysical implications

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

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

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

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

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


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.


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

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

Other searches

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

Matched filtering

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

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

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

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

The figure below shows how effective matched filtering can be.

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

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.

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


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.

Search of the Orion spur for continuous gravitational waves using a loosely coherent algorithm on data from LIGO interferometers

A cloudy bank holiday Monday is a good time to catch up on blogging. Following the splurge of GW150914 papers, I’ve rather fallen behind. Published back in February, this paper is a search for continuous-wave signals: the almost-constant hum produced by rapidly rotating neutron stars.

Continuous-wave searches are extremely computationally expensive. The searches take a while to do, which can lead to a delay before results are published [bonus note]. This is the result of a search using data from LIGO’s sixth science run (March–October 2010).

To detect a continuous wave, you need to sift the data to find a signal that present through all the data. Rotating neutron stars produce a gravitational-wave signal with a frequency twice their orbital frequency. This frequency is almost constant, but could change as the observation goes on because (i) the neutron star slows down as energy is lost (from gravitational waves, magnetic fields or some form of internal sloshing around); (ii) there is some Doppler shifting because of the Earth’s orbit around the Sun, and, possibly, (iii) the there could be some Doppler shifting because the neutron star is orbiting another object. How do you check for something that is always there?

There are two basic strategies for spotting continuous waves. First, we could look for excess power in a particular frequency bin. If we measure something in addition to what we expect from the detector noise, this could be a signal. Looking at the power is simple, and so not too expensive. However, we’re not using any information about what a real signal should look like, and so it must be really loud for us to be sure that it’s not just noise. Second, we could coherently search for signals using templates for the expected signals. This is much more work, but gives much better sensitivity. Is there a way to compromise between the two strategies to balance cost and sensitivity?

This paper reposts results of a loosely coherent search. Instead of checking how well the data match particular frequencies and frequency evolutions, we average over a family of similar signals. This is less sensitive, as we get a bit more wiggle room in what would be identified as a candidate, but it is also less expensive than checking against a huge number of templates.

We could only detect continuous waves from nearby sources: neutron stars in our own Galaxy. (Perhaps 0.01% of the distance of GW150914). It therefore makes sense to check nearby locations which could be home to neutron stars. This search narrows its range to two directions in the Orion spur, our local band with a high concentration of stars. By focussing in on these spotlight regions, we increase the sensitivity of the search for a given computational cost. This search could possibly dig out signals from twice as far away as if we were considering all possible directions.

Part of the Galaxy searched

Artist’s impression of the local part of the Milky Way. The Orion spur connects the Perseus and Sagittarius arms. The yellow cones mark the extent of the search (the pink circle shows the equivalent all-sky sensitivity). Green stars indicate known pulsars. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

The search found 70 interesting candidates. Follow-up study showed that most were due to instrumental effects. There were three interesting candidates left after these checks, none significant enough to be a detection, but still worth looking at in detail. A full coherent analysis was done for these three candidates. This showed that they were probably caused by noise. We have no detections

arXiv: 1510.03474 [gr-qc]
Journal: Physical Review D; 93(4):042006(14); 2016
Science summary: Scouting our Galactic neighborhood
Other bank holiday activities:

Scrabble board

Bank holiday family Scrabble game. When thinking about your next turn, you could try seeing if your letters match a particular word (a coherent search which would get you the best score, but take ages), or just if your letters jumble together to make something word-like (an incoherent search, that is quick, but may result in lots of things that aren’t really words).

Bonus note


The Continuous Wave teams are polite enough to wait until we’re finished searching for transient gravitational-wave signals (which are more time sensitive) before taking up the LIGO computing clusters. They won’t have any proper results from O1 just yet.