The gravitational-wave story of a neutron-star merger

by Jocelyn Read, California State University Fullerton

With several binary black hole mergers observed in the past two years, astronomers and relativists have become familiar with their general features: a quick chirp signal lasting seconds or less, a familiar inspiral-merger-ringdown pattern of waves, and a dark event in a distant galaxy, billions of light-years away.

GW170817 is a little bit different.

We’ve already seen systems like its presumed antecedent in our galaxy, where pulsars with neutron-star companions precisely map out their hours-long orbits with radio blips. We can imagine, then, the last 80 million or so years of GW170817’s source. Two neutron stars, in a galaxy only 40 Mpc away, driven through a slow but steady inspiral by gravitational radiation. For us distant observers, things become more interesting when the increasing orbital frequency sends the emitted gravitational waves into the sensitive range of our ground-based detectors.


Dr. Jocelyn Read explains gravitational waves to undergraduate students Isabella Molina and Erick Leon.

I wanted to take this opportunity to give a sense of scale, so consider this a tour of some interesting way-points along the signal’s path through that sensitive range of frequencies. Many thanks to my colleagues in the LIGO and Virgo collaborations who’ve helped lay out these markers over the last weeks – and of course, any remaining errors are my own.

10 Hz: Calibration of gravitational-wave detector data starts at frequencies of 10 Hz. A Keplerian orbit with a total mass of 2.74 solar masses (compatible with GW170817) has a separation somewhat over 700 km at the corresponding orbital frequency. Be patient: the neutron-star binary has more than 17 minutes left in its inspiral.

15 Hz: The automated template-based search that triggered LIGO’s transient notification for GW170817 started its comparison with incoming data at this frequency. This turns out to be roughly where the signal amplitude began to compare with background fluctuations from terrestrial sources. The source’s corresponding Keplerian orbital separation hasn’t changed too dramatically—the stars would have been roughly 550 km apart—but the inspiral has been slow: about 6 minutes remain.

20 – 24 Hz: Some analyses, like offline searches that determine the signal’s significance and parameter estimation, that checks what we can say about the masses and spins of a precessing system, doesn’t begin until later frequencies like these. This is because of computational and technical constraints. Only a very small fraction of the signal-to-noise has accumulated so far, and there are about 100 seconds to go.

30 Hz: Our core parameter estimation analysis for the gravitational-wave observation paper only started to compare signal models with the data at 30 Hz [1]. Tens of millions of waveforms need to be generated and compared to the data for each configuration, and the lower the starting frequency, the longer the waveform. Determining the properties of the component neutron stars takes a lot longer than determining the properties of a binary black hole merger, though folks are already thinking up ways to make this go faster the next time around. About a minute of signal remains.

40 Hz: The signal begins to be visible by eye in the graphical representations of the data that you’ll see in all the gravitational-wave papers today. But there’s a lot of signal power that was hidden from view, contributing to the computational analysis before our eyes can pick out the chirp. It’s easily possible that a future neutron-star signal, confidently detected, would be entirely invisible. The 22-solar-mass GW151226 is already hard to pick out of the data by eye, and its strain amplitude is much larger than an equivalently significant neutron-star binary would produce. Still 30 seconds before the end of the chirp.

60 Hz: By the time the signal reaches this gravitational-wave frequency, the chirp mass has been pinned down by the low-frequency evolution, which has so far been very much determined by that leading-order post-Newtonian dynamics. Roughly half of the signal-to-noise ratio should have accumulated in most analyses. There are about 9 seconds remaining.

100 Hz: A Keplerian estimate has the stars moving at more than 10% the speed of light, and higher order terms in the post-Newtonian expressions for the orbital evolution are coming into play. The mass ratio and spin parameters of the stars are measured through these higher order terms, with an impact on the signal that can be frustratingly correlated. The uncertainties of how dense matter behaves in the cores of neutron stars has so far been cloaked by their compactness, and the system has behaved like a pair of point masses. But things are going to get even more interesting in the final two seconds before the stars collide.

450 Hz: The size of the orbits approaches the size of the stars in these final orbits. At 450 Hz, the Keplerian separation estimate has the stars’ centres 57 kilometres apart, but each star’s radius should be somewhere between 9 and 15 km, together covering almost half that distance. Each neutron star is tidally deformed by its companion, inducing a mass quadrupole moment that depends on the equation of state describing dense matter inside the star. The impact of this deformation on the orbital dynamics will the system to merge earlier than equivalent black holes or point masses. There are 30 ms remaining.

600 Hz: We stopped our estimate of the radiated energy here, as the leading-order amplitude of the post-Newtonian waveform model used becomes unreliable. Since parameter information comes mostly from the phase evolution, we could ignore amplitude effects from mass ratio, spin, and tides when determining their likely values. The details of the gravitational wave are starting to become uncertain; the ranges of masses, spins, and tides compatible with the data allow for a spread of possibilities. Something like 16 milliseconds remain before the stars collide.

1024 Hz: The final milliseconds of the inspiral and merger (exactly how many of them they are will depend on the details of the stars’ properties) have little impact on the overall strength of the signal. The searches no longer bother resolving the detail at this level, but the highest frequencies still contribute information about the parameters of the source system. With a gravitational wave this strong, even a small fraction of the overall signal-to-noise ratio can make a difference.

1300 Hz: The Keplerian estimate, which is becoming increasingly inappropriate, indicates the stars are 28 kilometres apart and travelling at 0.38 times the speed of light. This would seem to be a problem for component stars with radii greater than 14 km, but those are disfavoured by the current comparison of waveform models with GW170817 data. So, probably, the stars have not quite yet collided.

1500 Hz: Roughly the innermost stable circular orbit for a Schwarzschild black hole with the total mass of GW170817. Some of the post-Newtonian waveforms used in our analyses truncate themselves here, but phenomenological or effective-one-body models, with tides calibrated to numerical relativity simulations, continue undaunted.

2048 Hz: Our current parameter estimation stops, as the rising high-frequency noise of the current detector configurations overwhelms the signal. Have the neutron stars merged? Might they continue to orbit a little bit longer before colliding? The answer is lost to the noise, and is likely to remain a mystery for GW170817. But the analysis of this signal will certainly undergo refinements in the future.

2000-3000 Hz: Did you think the story was over? The gravitational-wave signal from binary neutron stars may not end shortly after merger like it does when a black hole is involved. It’s possible some hypermassive neutron-star remnant may oscillate for tens of milliseconds or more after the collision, emitting a high-frequency post-merger signal. The existence and frequency of such a signal would also be able to tell us about matter in its densest forms, but its presence after GW170817 has, with the analysis done so far, neither been detected nor excluded.

~6000 Hz: If there was a merger of non-spinning black holes, continuing to orbit without the impediments of matter, tides, and all those other fascinating details, the signal would continue to chirp up to approximately this frequency, where it would then ring down. A post-merger remnant might also eventually collapse to a black hole and ring down as perturbed black holes tend to do. It’s also possible that neutron stars collided and collapsed very quickly to a black hole. In the second two scenarios, the smearing of matter before the black hole forms would tend to damp the signal significantly compared to the ringdown seen in a binary black hole.

The gravitational-wave story ends as the final object, whatever it may be, settles down to a steady long-term stable configuration. Of course, as we now know, the gravitational-wave story is only the first volume. This gravitational-wave leftover is the incipit of electromagnetic drama to come: matter accreting onto the central remnant is about to launch the jet of a short gamma ray burst, and matter ejected during the final moments of the collision is now flying outward, to glow for days as a kilonova, ready to spark hundreds of astronomical investigations across the electromagnetic spectrum.

[1] B. P. Abbott et al. “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral”, (LIGO Scientific Collaboration and Virgo Collaboration),Phys. Rev. Lett. 119, 161101

Read more on gravitational waves in our focus issue: Gravitational Waves.

This YouTube video shows the last 30 milliseconds of inspiral (with waveform) plus post-merger.

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