# GW170608—The underdog

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

The growing family of black holes. From Dawn Finney.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Bonus notes

#### Detector engineering

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

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

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

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

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

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

#### Parameter estimation rota

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

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

• CALET—a gamma-ray search. This paper includes upper limits for GW151226, GW170104, GW170608, GW170814 and GW170817.
• DLT40—an optical search designed for supernovae. This paper covers the whole of O2 including GW170104GW170814, GW170817 plus GW170809 and GW170823.
• Mini-GWAC—a optical survey (the precursor to GWAC). This paper covers the whole of their O2 follow-up (including GW170104).
• NOvA—a search for neutrinos and cosmic rays over a wide range of energies. This paper covers all the events from O1 and O2, plus triggers from O3.
• The VLA and VLITE—radio follow-up, particularly targeting a potentially interesting gamma-ray transient spotted by Fermi.

#### Virgo?

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

#### Journal

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

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

# Parameter estimation on gravitational waves from neutron-star binaries with spinning components

blIn gravitation-wave astronomy, some parameters are easier to measure than others. We are sensitive to properties which change the form of the wave, but sometimes the effect of changing one parameter can be compensated by changing another. We call this a degeneracy. In signals for coalescing binaries (two black holes or neutron stars inspiralling together), there is a degeneracy between between the masses and spins. In this recently published paper, we look at what this means for observing binary neutron star systems.

### History

This paper has been something of an albatross, and I’m extremely pleased that we finally got it published. I started working on it when I began my post-doc at Birmingham in 2013. Back then I was sharing an office with Ben Farr, and together with others in the Parameter Estimation Group, we were thinking about the prospect of observing binary neutron star signals (which we naively thought were the most likely) in LIGO’s first observing run.

One reason that this work took so long is that binary neutron star signals can be computationally expensive to analyse [bonus note]. The signal slowly chirps up in frequency, and can take up to a minute to sweep through the range of frequencies LIGO is sensitive to. That gives us a lot of gravitational wave to analyse. (For comparison, GW150914 lasted 0.2 seconds). We need to calculate waveforms to match to the observed signals, and these can be especially complicated when accounting for the effects of spin.

A second reason is shortly after submitting the paper in August 2015, we got a little distracted

This paper was the third of a trilogy look at measuring the properties of binary neutron stars. I’ve written about the previous instalment before. We knew that getting the final results for binary neutron stars, including all the important effects like spin, would take a long time, so we planned to follow up any detections in stages. A probable sky location can be computed quickly, then we can have a first try at estimating other parameters like masses using waveforms that don’t include spin, then we go for the full results with spin. The quicker results would be useful for astronomers trying to find any explosions that coincided with the merger of the two neutron stars. The first two papers looked at results from the quicker analyses (especially at sky localization); in this one we check what effect neglecting spin has on measurements.

### What we did

We analysed a population of 250 binary neutron star signals (these are the same as the ones used in the first paper of the trilogy). We used what was our best guess for the sensitivity of the two LIGO detectors in the first observing run (which was about right).

The simulated neutron stars all have small spins of less than 0.05 (where 0 is no spin, and 1 would be the maximum spin of a black hole). We expect neutron stars in these binaries to have spins of about this range. The maximum observed spin (for a neutron star not in a binary neutron star system) is around 0.4, and we think neutron stars should break apart for spins of 0.7. However, since we want to keep an open mind regarding neutron stars, when measuring spins we considered spins all the way up to 1.

### What we found

Our results clearly showed the effect of the mass–spin degeneracy. The degeneracy increases the uncertainty for both the spins and the masses.

Even though the true spins are low, we find that across the 250 events, the median 90% upper limit on the spin of the more massive (primary) neutron star is 0.70, and the 90% limit on the less massive (secondary) neutron star is 0.86. We learn practically nothing about the spin of the secondary, but a little more about the spin of the primary, which is more important for the inspiral. Measuring spins is hard.

The effect of the mass–spin degeneracy for mass measurements is shown in the plot below. Here we show a random selection of events. The banana-shaped curves are the 90% probability intervals. They are narrow because we can measure a particular combination of masses, the chirp mass, really well. The mass–spin degeneracy determines how long the banana is. If we restrict the range of spins, we explore less of the banana (and potentially introduce an offset in our results).

Rough outlines for 90% credible regions for component masses for a random assortments of signals. The circles show the true values. The coloured lines indicate the extent of the distribution with different limits on the spins. The grey area is excluded from our convention on masses $m_1 \geq m_2$. Figure 5 from Farr et al. (2016).

Although you can’t see it in the plot above, including spin does also increase the uncertainty in the chirp mass too. The plots below show the standard deviation (a measure width of the posterior probability distribution), divided by the mean for several mass parameters. This gives a measure of the fractional uncertainty in our measurements. We show the chirp mass $\mathcal{M}_\mathrm{c}$, the mass ratio $q = m_2/m_1$ and the total mass $M = m_1 + m_2$, where $m_1$ and $m_2$ are the masses of the primary and secondary neutron stars respectively. The uncertainties are small for louder signals (higher signal-to-noise ratio). If we neglect the spin, the true chirp mass can lie outside the posterior distribution, the average is about 5 standard deviations from the mean, but if we include spin, the offset is just 0.7 from the mean (there’s still some offset as we’re allowing for spins all the way up to 1).

Fractional statistical uncertainties in chirp mass (top), mass ratio (middle) and total mass (bottom) estimates as a function of network signal-to-noise ratio for both the fully spinning analysis and the quicker non-spinning analysis. The lines indicate approximate power-law trends to guide the eye. Figure 2 of Farr et al. (2016).

We need to allow for spins when measuring binary neutron star masses in order to explore for the possible range of masses.

Sky localization and distance, however, are not affected by the spins here. This might not be the case for sources which are more rapidly spinning, but assuming that binary neutron stars do have low spin, we are safe using the easier-to-calculate results. This is good news for astronomers who need to know promptly where to look for explosions.

arXiv: 1508.05336 [astro-ph.HE]
Journal: Astrophysical Journal825(2):116(10); 2016
Authorea [bonus note]: Parameter estimation on gravitational waves from neutron-star binaries with spinning components
Conference proceedings:
Early Advanced LIGO binary neutron-star sky localization and parameter estimation
Favourite albatross:
Wilbur

### Bonus notes

#### How long?

The plot below shows how long it took to analyse each of the binary neutron star signals.

Distribution of run times for binary neutron star signals. Low-latency sky localization is done with BAYESTAR; medium-latency non-spinning parameter estimation is done with LALInference and TaylorF2 waveforms, and high-latency fully spinning parameter estimation is done with LALInference and SpinTaylorT4 waveforms. The LALInference results are for 2000 posterior samples. Figure 9 from Farr et al. (2016).

BAYESTAR provides a rapid sky localization, taking less than ten seconds. This is handy for astronomers who want to catch a flash caused by the merger before it fades.

Estimates for the other parameters are computed with LALInference. How long this takes to run depends on which waveform you are using and how many samples from the posterior probability distribution you want (the more you have, the better you can map out the shape of the distribution). Here we show times for 2000 samples, which is enough to get a rough idea (we collected ten times more for GW150914 and friends). Collecting twice as many samples takes (roughly) twice as long. Prompt results can be obtained with a waveform that doesn’t include spin (TaylorF2), these take about a day at most.

For this work, we considered results using a waveform which included the full effects of spin (SpinTaylorT4). These take about twenty times longer than the non-spinning analyses. The maximum time was 172 days. I have a strong suspicion that the computing time cost more than my salary.

Waiting for LALInference runs to finish gives you some time to practise hobbies. This is a globe knitted by Hannah. The two LIGO sites marked in red, and a typical gravitational-wave sky localization stitched on.

In order to get these results, we had to add check-pointing to our code, so we could stop it and restart it; we encountered a new type of error in the software which manages jobs running on our clusters, and Hannah Middleton and I got several angry emails from cluster admins (who are wonderful people) for having too many jobs running.

In comparison, analysing GW150914, LVT151012 and GW151226 was a breeze. Grudgingly, I have to admit that getting everything sorted out for this study made us reasonably well prepared for the real thing. Although, I’m not looking forward to that first binary neutron star signal…

#### Authorea

Authorea is an online collaborative writing service. It allows people to work together on documents, editing text, adding comments, and chatting with each other. By the time we came to write up the paper, Ben was no longer in Birmingham, and many of our coauthors are scattered across the globe. Ben thought Authorea might be useful for putting together the paper.

Writing was easy, and the ability to add comments on the text was handy for getting feedback from coauthors. The chat was going for quickly sorting out issues like plots. Overall, I was quite pleased, up to the point we wanted to get the final document. Extracted a nicely formatted PDF was awkward. For this I switched to using the Github back-end. On reflection, a simple git repo, plus a couple of Skype calls might have been a smoother way of writing, at least for a standard journal article.

Authorea promises to be an open way of producing documents, and allows for others to comment on papers. I don’t know if anyone’s looked at our Authorea article. For astrophysics, most people use the arXiv, which is free to everyone, and I’m not sure if there’s enough appetite for interaction (beyond the occasional email to authors) to motivate people to look elsewhere. At least, not yet.

In conclusion, I think Authorea is a nice idea, and I would try out similar collaborative online writing tools again, but I don’t think I can give it a strong recommendation for your next paper unless you have a particular idea in mind of how to make the most of it.