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

August 23, 2016October 8, 2016 / CPLB / Leave a comment

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

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

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

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

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

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

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

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

The science

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

0. The Boxing Day Discovery Paper

Title: GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole
arXiv: 1606.04855 [gr-qc]
Journal: Physical Review Letters; 116(24):241103(14)
LIGO science summary: GW151226: Observation of gravitational waves from a 22 solar-mass binary black hole (by Hannah Middleton and Carl-Johan Haster)

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

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

More details: The Boxing Day Discovery Paper summary

1. The O1 Binary Black Hole Paper

Title: Binary black hole mergers in the first Advanced LIGO observing run
arXiv: 1606.04856 [gr-qc]
Journal: Physical Review X; 6(4):041015(36)
Posterior samples: Release v1.0

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

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

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

More details: The O1 Binary Black Hole Paper summary

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

The Boxing Day Discovery Paper

Synopsis: Boxing Day Discovery Paper
Read this if: You are excited about the discovery of GW151226
Favourite part: We’ve done it again!

The signal

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

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

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

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

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

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

The source

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

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

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

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

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

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

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

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

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

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.

Searches

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

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

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

Search results and GW150914, GW151226 and LVT151012

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

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

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

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

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

Parameter estimation

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

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

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

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

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

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

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

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

Estimated masses $M_\mathrm{f}^\mathrm{source}$ and spins $a_\mathrm{f}$ of the remnant black holes for each of the events in O1. The contours mark the 50% and 90% credible regions. Part of Figure 4 of the O1 Binary Black Hole Paper.

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

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

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

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

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

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

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

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

Sky localization in equatorial coordinates

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

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

Tests of general relativity

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

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

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

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

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

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

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

Rates

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

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

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

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

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

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

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

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

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

Astrophysical implications

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

Bonus notes

Christmas cease-fire

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

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

Naming

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

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

Matched filtering

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

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

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

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

The figure below shows how effective matched filtering can be.

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

The effectiveness of matched filtering for GW151226

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

Electromagnetic and neutrino follow-up

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

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

Reports by neutrino astronomers are:

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

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

Rounding

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

Black holes are massive

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

Maximum minimum spin

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

Just one more thing…

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

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

June 4, 2016August 27, 2016 / CPLB / Leave a comment

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

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

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

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

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

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

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

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

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

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

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

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

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

Intermediate-mass black hole probability

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

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

arXiv: 1511.01431 [astro-ph.HE]
Journal: Monthly Notices of the Royal Astronomical Society; 457(4):4499–4506; 2016
Birmingham science summary: Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes (by Carl)
Other collectables: Breakthrough, Gruber, Shaw, Kavli, …

Bonus notes

Jargon

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

Parameter-estimation runs

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

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

May 30, 2016October 8, 2016 / CPLB / Leave a comment

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.

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

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

Niceness

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.

All-sky search for long-duration gravitational wave transients with LIGO

April 2, 2016June 5, 2016 / CPLB / 5 Comments

It’s now about 7 weeks since the announcement, and the madness is starting to subside. Although, that doesn’t mean things aren’t busy—we’re now enjoying completely new forms of craziness. In mid March we had our LIGO–Virgo Collaboration Meeting. This was part celebration, part talking about finishing our O1 analysis and part thinking ahead to O2, which is shockingly close. It was fun, there was cake.

Celebratory cake from the March LIGO–Virgo Meeting. It was delicious and had a fruity (strawberry?) filling. The image is February 11th’s Astronomy Picture of the Day. There was a second cake without a picture, that was equally delicious, but the queue was shorter.

All the business means that I’ve fallen behind with my posts, and I’ve rather neglected the final paper published the week starting 8 February. This is perhaps rather apt as this paper has the misfortune to be the first non-detection published in the post-detection world. It is also about a neglected class of signals.

Long-duration transients

We look for several types of signals with LIGO (and hopefully soon Virgo and KAGRA):

Compact binary coalescences (like two merging black holes), for which we have templates for the signal. High mass systems might only last a fraction of a second within the detector’s frequency range, but low mass systems could last for a minute (which is a huge pain for us to analyse).
Continuous waves from rotating neutron stars which are almost constant throughout our observations.
Bursts, which are transient signals where we don’t have a good model. The classic burst source is from a supernova explosion.

We have some effective search pipelines for finding short bursts—signals of about a second or less. Coherent Waveburst, which was the first code to spot GW150914 is perhaps the best known example. This paper looks at finding longer burst signals, a few seconds to a few hundred seconds in length.

There aren’t too many well studied models for these long bursts. Most of the potential sources are related to the collapse of massive stars. There can be a large amount of matter moving around quickly in these situations, which is what you want for gravitational waves.

Massive stars may end their life in a core collapse supernova. Having used up its nuclear fuel, the star no longer has the energy to keep itself fluffy, and its core collapses under its own gravity. The collapse leads to an explosion as material condenses to form a neutron star, blasting off the outer layers of the star. Gravitational waves could be generated by the sloshing of the outer layers as some is shot outwards and some falls back, hitting the surface of the new neutron star. The new neutron star itself will start life puffed up and perhaps rapidly spinning, and can generate gravitational waves at it settles down to a stable state—a similar thing could happen if an older neutron star is disturbed by a glitch (where we think the crust readjusts itself in something like an earthquake, but more cataclysmic), or if a neutron star accretes a large blob of material.

For the most massive stars, the core continues to collapse through being a neutron star to become a black hole. The collapse would just produce a short burst, so it’s not what we’re looking for here. However, once we have a black hole, we might build a disc out of material swirling into the black hole (perhaps remnants of the outer parts of the star, or maybe from a companion star). The disc may be clumpy, perhaps because of eddies or magnetic fields (the usual suspects when astrophysicists don’t know exactly what’s going on), and they rapidly inspiralling blobs could emit a gravitational wave signal.

The potential sources don’t involve as much mass as a compact binary coalescence, so these signals wouldn’t be as loud. Therefore we couldn’t see them quite as far way, but they could give us some insight into these messy processes.

The search

The paper looks at results using old LIGO data from the fifth and sixth science runs (S5 and S6). Virgo was running at this time, but the data wasn’t included as it vastly increases the computational cost while only increasing the search sensitivity by a few percent (although it would have helped with locating a source if there were one). The data is analysed with the Stochastic Transient Analysis Multi-detector Pipeline (STAMP); we’ll be doing a similar thing with O1 data too.

STAMP searches for signals by building a spectrogram: a plot of how much power there is at a particular gravitational wave frequency at a particular time. If there is just noise, you wouldn’t expect the power at one frequency and time to be correlated with that at another frequency and time. Therefore, the search looks for clusters, grouping together times or frequencies closer to one another where there is more power then you might expect.

The analysis is cunning, as it coherently analysis data from both detectors together when constructing the spectrogram, folding in the extra distance a gravitational wave must travel between the detectors for a given sky position.

The significance of events is calculated is a similar way to how we search for binary black holes. The pipeline ranks candidates using a detection statistic, a signal-to-noise ratio for the cluster of interesting time–frequency pixels $\mathrm{SNR}_\Gamma$ (something like the amount of power measured divided by the amount you’d expect randomly). We work out how frequently you’d expect a particular value of $\mathrm{SNR}_\Gamma$ by analysing time-shifted data: where we’ve shifted the data from one of the detectors in time relative to data from the other so that we know there can’t be the same signal found in both.

The distribution of $\mathrm{SNR}_\Gamma$ is shown below from the search (dots) and from the noise background (lines). You can see that things are entirely consistent with our expectations for just noise. The most significant event has a false alarm probability of 54%, so you’re better off betting it’s just noise. There are no detections here.

False alarm rate (FAR) distribution of triggers from S5 (black circles) and S6 (red triangles) as a function of the
signal-to-noise ratio. The background S5 and S6 noise distributions are shown by the solid black and dashed red lines respectively. An idealised Gaussian noise background is shown in cyan. There are no triggers significantly above the expected background level. Fig. 5 from Abbott et al. (2016).

Since the detectors are now much more sensitive, perhaps there’s something lurking in our new data. I still think this in unlikely since we can’t see sources from a significant distance, but I guess we’ll have to wait for the results of the analysis.

arXiv: 1511.04398 [gr-qc]
Journal: Physical Review D; 93(4):042005(19); 2016
Science summary: Stuck in the middle: an all-sky search for gravitational waves of intermediate duration
Favourite (neglected) middle child: Lisa Simpson

Sunset over the Grand Canyon. One of the perks of academia is the travel. A group of us from Birmingham went on a small adventure after the LIGO–Virgo Meeting. This is another reason why I’ve not been updating my blog.

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

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

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

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

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

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

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

The Observing Scenarios

The paper is divided up into four sections.

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

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

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

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

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

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

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

The path to publication

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

In the beginning

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

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

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

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

Updating sky localization

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

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

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

Saying yes is a slippery slope.

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

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

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

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

The review

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Good things come…

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

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

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

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

— Christopher Berry (@cplberry) January 14, 2016

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

Looking forward

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

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

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

arXiv IDs

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

The next version

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

GW150914—The papers

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

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

The papers

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

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

0. The Discovery Paper

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

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

More details: The Discovery Paper summary

1. The Detector Paper

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

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

More details: The Detector Paper summary

2. The Compact Binary Coalescence Paper

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

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

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

More details: The Compact Binary Coalescence Paper summary

3. The Parameter Estimation Paper

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

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

More details: The Parameter Estimation Paper summary

4. The Testing General Relativity Paper

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

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

More details: The Testing General Relativity Paper summary

5. The Rates Paper

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

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

More details: The Rates Paper summary

6. The Burst Paper

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

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

More details: The Burst Paper summary

7. The Detector Characterisation Paper

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

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

More details: The Detector Characterisation Paper summary

8. The Calibration Paper

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

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

More details: The Calibration Paper summary

9. The Astrophysics Paper

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

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

More details: The Astrophysics Paper summary

10. The Stochastic Paper

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

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

More details: The Stochastic Paper summary

11. The Neutrino Paper

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

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

More details: The Neutrino Paper summary

12. The Electromagnetic Follow-up Paper

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

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

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

More details: The Electromagnetic Follow-up Paper summary

BEST. ARXIV. EVER!

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

— Christopher Berry (@cplberry) February 12, 2016

The Discovery Paper

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

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

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

The Detector Paper

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

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

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

The Compact Binary Coalescence Paper

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

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

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

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

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

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

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

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

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

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

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

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

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

The Parameter Estimation Paper

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Testing General Relativity Paper

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

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

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

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

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

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

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

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

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

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

The Rates Paper

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

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

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

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

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

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

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

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

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

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

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

The Burst Paper

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

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

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

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

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

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

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

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

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

Estimated waveforms from different models

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

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

The Detector Characterisation Paper

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

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

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

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

Sources of uncorrelated noise include:

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

Correlated noise can be caused by:

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

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

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

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

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

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

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

The Calibration Paper

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

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

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

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

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

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

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

The Astrophysics Paper

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

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

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

The Stochastic Paper

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

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

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

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

Models for a binary black hole stochastic background

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

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

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

The Neutrino Paper

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

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

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

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

The Electromagnetic Follow-up Paper

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

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

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

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

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

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

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

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

Observations have been reported (via GCN notices) by

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

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

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

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

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

Bonus notes

Naming The Event

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

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

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

Publishing in Physical Review Letters

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

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

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

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

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

Referee B wrote

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

and Referee C wrote

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

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

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

Publishing the Parameter Estimation Paper

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

This is a beautiful paper on a spectacular result.

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

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

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

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

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

Publishing the Rates Paper

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

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

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

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

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

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

Second, we were lacking in references to existing literature

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

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

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

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

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

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

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

LIGO Document Control Center

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

The überbank

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

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

Alphabet soup

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

Multi-band gravitational wave astronomy

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

Binary black hole mergers across the eLISA and LIGO frequency bands

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

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

The LALInference sky map

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

Searches for continuous gravitational waves from nine young supernova remnants

November 7, 2015October 1, 2016 / CPLB / Leave a comment

The LIGO Scientific Collaboration is busy analysing the data we’re currently taking with Advanced LIGO at the moment. However, the Collaboration is still publishing results from initial LIGO too. The most recent paper is a search for continuous waves—signals that are an almost constant hum throughout the observations. (I expect they’d be quite annoying for the detectors). Searching for continuous waves takes a lot of computing power (you can help by signing up for Einstein@Home), and is not particularly urgent since the sources don’t do much, hence it can take a while for results to appear.

Supernova remnants

Massive stars end their lives with an explosion, a supernova. Their core collapses down and their outer layers are blasted off. The aftermath of the explosion can be beautiful, with the thrown-off debris forming a bubble expanding out into the interstellar medium (the diffuse gas, plasma and dust between stars). This structure is known as a supernova remnant.

The youngest known supernova remnant, G1.9+0.3 (it’s just 150 years old), observed in X-ray and optical light. The ejected material forms a shock wave as it pushes the interstellar material out of the way. Credit: NASA/CXC/NCSU/DSS/Borkowski et al.

At the centre of the supernova remnant may be what is left following the collapse of the core of the star. Depending upon the mass of the star, this could be a black hole or a neutron star (or it could be nothing). We’re interested in the case it is a neutron star.

Neutron stars

Neutron stars are incredibly dense. One teaspoon’s worth would have about as much mass as 300 million elephants. Neutron stars are like giant atomic nuclei. We’re not sure how matter behaves in such extreme conditions as they are impossible to replicate here on Earth.

If a neutron star rotates rapidly (we know many do) and has an uneven or if there are waves in the the neutron star that moves lots of material around (like Rossby waves on Earth), then it can emit continuous gravitational waves. Measuring these gravitational waves would tell you about how bumpy the neutron star is or how big the waves are, and therefore something about what the neutron star is made from.

Neutron stars are most likely to emit loud gravitational waves when they are young. This is for two reasons. First, the supernova explosion is likely to give the neutron star a big whack, this could ruffle up its surface and set off lots of waves, giving rise to the sort of bumps and wobbles that emit gravitational waves. As the neutron star ages, things can quiet down, the neutron star relaxes, bumps smooth out and waves dissipate. This leaves us with smaller gravitational waves. Second, gravitational waves carry away energy, slowing the rotation of the neutron star. This also means that the signal gets quieter (and harder) to detect as the neutron star ages.

Since young neutron stars are the best potential sources, this study looked at nine young supernova remnants in the hopes of finding continuous gravitational waves. Searching for gravitational waves from particular sources is less computationally expensive than searching the entire sky. The search included Cassiopeia A, which had been previously searched in LIGO’s fifth science run, and G1.9+0.3, which is only 150 years old, as discovered by Dave Green. The positions of the searched supernova remnants are shown in the map of the Galaxy below.

The nine young supernova remnants searched for continuous gravitational waves. The yellow dot marks the position of the Solar System. The green markers show the supernova remnants, which are close to the Galactic plane. Two possible positions for Vela Jr (G266.2−1.2) were used, since we are uncertain of its distance. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

Gravitational-wave limits

No gravitational waves were found. The search checks how well template waveforms match up with the data. We tested that this works by injecting some fake signals into the data. Since we didn’t detect anything, we can place upper limits on how loud any gravitational waves could be. These limits were double-checked by injecting some more fake signals at the limit, to see if we could detect them. We quoted 95% upper limits, that is where we expect that if a signal was present we could see it 95% of the time. The results actually have a small safety margin built in, so the injected signals were typically found 96%–97% of the time. In any case, we are fairly sure that there aren’t gravitational waves at or above the upper limits.

These upper limits are starting to tell us interesting things about the size of neutron-star bumps and waves. Hopefully, with data from Advanced LIGO and Advanced Virgo, we’ll actually be able to make a detection. Then we’ll not only be able to say that these bumps and waves are smaller than a particular size, but they are this size. Then we might be able to figure out the recipe for making the stuff of neutron stars (I think it might be more interesting than just flour and water).

arXiv: 1412.5942 [astro-ph.HE]
Journal: Astrophysical Journal; 813(1):39(16); 2015
Science summary: Searching for the youngest neutron stars in the Galaxy
Favourite supernova remnant: Cassiopeia A

Parameter estimation for binary neutron-star coalescences with realistic noise during the Advanced LIGO era

May 14, 2015February 9, 2020 / CPLB / Leave a comment

The first observing run (O1) of Advanced LIGO is nearly here, and with it the prospect of the first direct detection of gravitational waves. That’s all wonderful and exciting (far more exciting than a custard cream or even a chocolate digestive), but there’s a lot to be done to get everything ready. Aside from remembering to vacuum the interferometer tubes and polish the mirrors, we need to see how the data analysis will work out. After all, having put so much effort into the detector, it would be shame if we couldn’t do any science with it!

Parameter estimation

Since joining the University of Birmingham team, I’ve been busy working on trying to figure out how well we can measure things using gravitational waves. I’ve been looking at binary neutron star systems. We expect binary neutron star mergers to be the main source of signals for Advanced LIGO. We’d like to estimate how massive the neutron stars are, how fast they’re spinning, how far away they are, and where in the sky they are. Just published is my first paper on how well we should be able to measure things. This took a lot of hard work from a lot of people, so I’m pleased it’s all done. I think I’ve earnt a celebratory biscuit. Or two.

When we see something that looks like it could be a gravitational wave, we run code to analyse the data and try to work out the properties of the signal. Working out some properties is a bit trickier than others. Sadly, we don’t have an infinite number of computers, so it means it can take a while to get results. Much longer than the time to eat a packet of Jaffa Cakes…

The fastest algorithm we have for binary neutron stars is BAYESTAR. This takes the same time as maybe eating one chocolate finger. Perhaps two, if you’re not worried about the possibility of choking. BAYESTAR is fast as it only estimates where the source is coming from. It doesn’t try to calculate a gravitational-wave signal and match it to the detector measurements, instead it just looks at numbers produced by the detection pipeline—the code that monitors the detectors and automatically flags whenever something interesting appears. As far as I can tell, you give BAYESTAR this information and a fresh cup of really hot tea, and it uses Bayes’ theorem to work out how likely it is that the signal came from each patch of the sky.

To work out further details, we need to know what a gravitational-wave signal looks like and then match this to the data. This is done using a different algorithm, which I’ll refer to as LALInference. (As names go, this isn’t as cool as SKYNET). This explores parameter space (hopping between different masses, distances, orientations, etc.), calculating waveforms and then working out how well they match the data, or rather how likely it is that we’d get just the right noise in the detector to make the waveform fit what we observed. We then use another liberal helping of Bayes’ theorem to work out how probable those particular parameter values are.

It’s rather difficult to work out the waveforms, but some our easier than others. One of the things that makes things trickier is adding in the spins of the neutron stars. If you made a batch of biscuits at the same time you started a LALInference run, they’d still be good by the time a non-spinning run finished. With a spinning run, the biscuits might not be quite so appetising—I generally prefer more chocolate than penicillin on my biscuits. We’re working on speeding things up (if only to prevent increased antibiotic resistance).

In this paper, we were interested in what you could work out quickly, while there’s still chance to catch any explosion that might accompany the merging of the neutron stars. We think that short gamma-ray bursts and kilonovae might be caused when neutron stars merge and collapse down to a black hole. (I find it mildly worrying that we don’t know what causes these massive explosions). To follow-up on a gravitational-wave detection, you need to be able to tell telescopes where to point to see something and manage this while there’s still something that’s worth seeing. This means that using spinning waveforms in LALInference is right out, we just use BAYESTAR and the non-spinning LALInference analysis.

What we did

To figure out what we could learn from binary neutron stars, we generated a large catalogue of fakes signals, and then ran the detection and parameter-estimation codes on this to see how they worked. This has been done before in The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo which has a rather delicious astrobites write-up. Our paper is the sequel to this (and features most of the same cast). One of the differences is that The First Two Years assumed that the detectors were perfectly behaved and had lovely Gaussian noise. In this paper, we added in some glitches. We took some real data™ from initial LIGO’s sixth science run and stretched this so that it matches the sensitivity Advanced LIGO is expected to have in O1. This process is called recolouring [bonus note]. We now have fake signals hidden inside noise with realistic imperfections, and can treat it exactly as we would real data. We ran it through the detection pipeline, and anything which was flagged as probably being a signal (we used a false alarm rate of once per century), was analysed with the parameter-estimation codes. We looked at how well we could measure the sky location and distance of the source, and the masses of the neutron stars. It’s all good practice for O1, when we’ll be running this analysis on any detections.

What we found

The flavour of noise (recoloured or Gaussian) makes no difference to how well we can measure things on average.
Sky-localization in O1 isn’t great, typically hundreds of square degrees (the median 90% credible region is 632 deg²), for comparison, the Moon is about a fifth of a square degree. This’ll make things interesting for the people with telescopes.
Probability that of a gravitational-wave signal coming from different points on the sky. The darker the red, the higher the probability. The star indicates the true location. This is one of the worst localized events from our study for O1. You can find more maps in the data release (including 3D versions), this is Figure 6 of Berry et al. (2015).
BAYESTAR does just as well as LALInference, despite being about 2000 times faster.
Sky localization (the size of the patch of the sky that we’re 90% sure contains the source location) varies with the signal-to-noise ratio (how loud the signal is). The approximate best fit is $\log_{10}(\mathrm{CR}_{0.9}/\mathrm{deg^2}) \approx -2 \log_{10}(\varrho) +5.06$ , where $\mathrm{CR}_{0.9}$ is the 90% sky area and $\varrho$ is the signal-to-noise ratio. The results for BAYESTAR and LALInference agree, as do the results with Gaussian and recoloured noise. This is Figure 9 of Berry et al. (2015).
We can’t measure the distance too well: the median 90% credible interval divided by the true distance (which gives something like twice the fractional error) is 0.85.
Because we don’t include the spins of the neutron stars, we introduce some error into our mass measurements. The chirp mass, a combination of the individual masses that we’re most sensitive to [bonus note], is still reliably measured (the median offset is 0.0026 of the mass of the Sun, which is tiny), but we’ll have to wait for the full spinning analysis for individual masses.
Fraction of events with difference between the mean estimated and true chirp mass smaller than a given value. There is an error because we are not including the effects of spin, but this is small. Again, the type of noise makes little difference. This is Figure 15 of Berry et al. (2015).

There’s still some work to be done before O1, as we need to finish up the analysis with waveforms that include spin. In the mean time, our results are all available online for anyone to play with.

arXiv: 1411.6934 [astro-ph.HE]
Journal: Astrophysical Journal; 904(2):114(24); 2015
Data release: The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo
Favourite colour: Blue. No, yellow…

Notes

The colour of noise: Noise is called white if it doesn’t have any frequency dependence. We made ours by taking some noise with initial LIGO’s frequency dependence (coloured noise), removing the frequency dependence (making it white), and then adding in the frequency dependence of Advanced LIGO (recolouring it).

The chirp mass: Gravitational waves from a binary system depend upon the masses of the components, we’ll call these $m_1$ and $m_2$ . The chirp mass is a combination these that we can measure really well, as it determines the most significant parts of the shape of the gravitational wave. It’s given by

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

We get lots of good information on the chirp mass, unfortunately, this isn’t too useful for turning back into the individual masses. For that we next extra information, for example the mass ratio $m_2/m_1$ . We can get this from less dominant parts of the waveform, but it’s not typically measured as precisely as the chirp mass, so we’re often left with big uncertainties.

Directed search for gravitational waves from Scorpius X-1 with initial LIGO

April 24, 2015May 30, 2016 / CPLB / Leave a comment

A new paper from the LIGO Scientific Collaboration has snuck out. It was actually published back in March but I didn’t notice it, nearly risking my New Year’s resolution. This is another paper on continuous waves from rotating neutron stars, so it’s a little outside my area of expertise. However, there is an official science summary written by people who do know what they’re talking about.

The paper looks at detecting gravitational waves from a spinning neutron star. We didn’t find any. However, we have slightly improved our limit for how loud they need to be before we would have detected them, which is nice.

Neutron stars can rotate rapidly. They can be spun up if they accrete material from a disc orbiting them. If they neutron star has an asymmetry, if it has a little bump, as it rotates it emits gravitational waves. The gravitational waves carry away angular momentum, which should spin down the neutron star. This becomes more effective as the angular velocity increases. At some point you expect that the spin-up effect from accretion balances the spin-down effect of gravitational waves and you are left with a neutron star spinning at pretty constant velocity. We have some evidence that this might happen, as low-mass X-ray binaries seem to have their spins clustered in a small range of frequencies. Assuming we do have this balance, we are looking for a continuous gravitational wave with constant frequency, a rather dull humming.

Scorpius X-1 is the brightest X-ray source in the sky. It contains a neutron star, so it’s a good place to check for gravitational waves from neutron stars. In this case, we’re using data from initial LIGO’s fifth science run (4 November 2005–1 October 2007). This has been done before, but this paper implements some new techniques. I expect that the idea is to test things out ahead of getting data with Advanced LIGO.

Swift X-ray Telescope image of Scorpius X-1 and the X-ray nova J1745-26 (a stellar-mass black hole), along with the scale of moon, as they would appear in the field of view from Earth. Credit: NASA/Goddard Space Flight Center/S. Immler and H. Krimm.

A limit of 10 days’ worth of data is used, as this should be safely within the time taken for the rotational frequency to fluctuate by a noticeable amount due to variation in the amount of accretion. In human terms, that would be the time between lunch and dinner, where your energy levels change because of how much you’ve eaten. They picked data from 21–31 August 2007, as their favourite (it has the best noise performance over the frequency range of interest), and used two other segments to double-check their findings. We’d be able to use more data if we knew how the spin wandered with time.

We already know a lot about Scorpius X-1 from electromagnetic observations (like where it is and its orbital parameters). We don’t know its spin frequency, but we might have an idea about the orientation of its spin if this coincides with radio jets. The paper considers two cases: one where we don’t know anything about the spin orientation, and one where we use information from the jets. The results are similar in both cases.

As the neutron star orbits in its binary system, it moves back and forth which Doppler shifts the gravitational waves. This adds a little interest to the hum, spreading it out over a range of frequencies. The search looks for gravitational waves over this type of frequency range, which they refer to as sidebands.

There are a few events where it looks like there is something, but after carefully checking, these look like they are entirely consistent with noise. I guess this isn’t too surprising. Since they didn’t detect anything, they can only impose an upper limit. This is stronger than the previous upper limit, but only by a factor of about 1.4. This might not sound too great, but the previous analysis used a year of data, whereas this only used 10 days. This method therefore saves a lot on computational time.

The result of the paper is quite nice, but not too exciting. If it were a biscuit, it’d probably be a rich tea. It’s nice to have, but it’s not a custard cream.

arXiv: 1412.5942 [astro-ph.HE]
Journal: Physical Review D; 91(6):062008(20); 2015
Science summary: Combing Initial LIGO Data for the Potentially Strong Continuous Wave Emitter Scorpius X-1
Biscuit rating: Rich tea

Bonus note

Magnetism and astrophysics

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The science

0. The Boxing Day Discovery Paper

1. The O1 Binary Black Hole Paper

The Boxing Day Discovery Paper

The signal

The source

The O1 Binary Black Hole Paper

Searches

Parameter estimation

Tests of general relativity

Rates

Astrophysical implications

Conclusion

Bonus notes

Christmas cease-fire

Naming

Other searches

Matched filtering

Electromagnetic and neutrino follow-up

Rounding

Black holes are massive

Maximum minimum spin

Just one more thing…

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Bonus notes

Jargon

Parameter-estimation runs

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Bonus note

Niceness

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Long-duration transients

The search

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The Observing Scenarios

The path to publication

In the beginning

Updating sky localization

The review

Good things come…

Looking forward

arXiv IDs

The next version

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The papers

0. The Discovery Paper

1. The Detector Paper

2. The Compact Binary Coalescence Paper

3. The Parameter Estimation Paper

4. The Testing General Relativity Paper

5. The Rates Paper

6. The Burst Paper

7. The Detector Characterisation Paper

8. The Calibration Paper

9. The Astrophysics Paper

10. The Stochastic Paper

11. The Neutrino Paper

12. The Electromagnetic Follow-up Paper

The Discovery Paper

The Detector Paper

The Compact Binary Coalescence Paper

The Parameter Estimation Paper

The Testing General Relativity Paper

The Rates Paper

The Burst Paper

The Detector Characterisation Paper

The Calibration Paper

The Astrophysics Paper

The Stochastic Paper

The Neutrino Paper

The Electromagnetic Follow-up Paper