Gravitational Waves¶
The LIGO project recently announced the results of their searches for gravitational waves:
On October 28, 2020, the LIGO Scientific Collaboration and the Virgo
Collaboration announced the results of their searches for
gravitational-waves from coalescing compact binaries during the first
half of their third observing run (O3a), spanning 1 April 2019 to 1
October 2019. 39 events are reported here; when added to the 11 events
in the first Gravitational-Wave Transient Catalog (GWTC-1), this
brings the total number of reported LIGO/Virgo gravitational-wave
detections to 50. Besides the paper discussing the new catalog,
companion papers discuss population properties of the catalog, tests
of general relativity, and a search for associated gamma-ray bursts.
https://www.ligo.org/detections/O3acatalog.php
Each of the companion papers comes with a science summary that gives a good overview of each paper. It is a great place to explore.
These papers are both fascinating.
There has been excitement about gamma ray bursts being associated with gravitational waves. More of this later.
The tests on general relativity is also, in some sense, a test on the whole theory that the causes of these gravitational waves is the coalescense of compact binary objects.
General relativity predicts how they will move as they coalesce.
The whole idea of gravitational waves came from general relativity. How to generate a wave big enough to travel billions of light years through space?
Mass on it’s own cannot do it, says the theory. Conservation of mass precludes it radiating away.
Momentum? That is conserved too, so cannot radiate.
The quadripole moment? That comes next and it turns out it can’t help but radiate, or so says the theory, along with an argument that the moment must vary over time.
So, if I am following correctly, the quadripole moment is what our detectors see. Plus higher order moments and noise of course.
One problem we are wrestling with here is that Einstein’s equations are not easy to solve.
We have several notable solutions, and these work extraordinarily well in all our observations up to now.
A key difference with these black hole mergers is we see speeds closer to the speed of light, where Einstein’s equations make a bigger difference compared to classical Newtonian dynamics. And giant masses where everything is so dense that space warps in on itself, again something Einstein modelled.
The initial gravitational wave detection is done in data processing chains which match templates for black hole mergers within the range of the detector sensitivity.
The follow-up work is able to look at the data in much more detail and fit more detailed models to each wave form.
Unfortunately, the extra freedom for models takes us well below the detector noise.
To offset that, we now have many observations which we can test in parallel.
This is essentially what is done in the paper. [1]
The paper notes:
... the statistical uncertainty can be reduced by combining the
results from multiple events.
Additional uncertainty will arise from systematic error in the
calibration of the detectors and power spectral density (PSD)
estimation, as well as errors in the modeling of GW waveforms in
GR;
unlike uncertainty induced by detector noise, such errors do
not improve when combining multiple events and therefore will
dominate the uncertainty budget for sufficiently large catalogs of
merger events.
So, errors in the modelling of gravitational waves in general relativity will eventually dominate the errors in this analysis.
The models are using a Bayesian approach, so priors should be examined carefully.
It looks like we are at that intriguing point. From the science summary:
The bottom line is that, when we take noise and inaccurate
approximations into account, everything we found is compatible with
general relativity. As we show in the figures, some of our tests do
not yield very strong results. In the future, we expect to detect many
more black hole mergers to help us give a more definitive answer.
The good news is we are likely to soon get more data soon, as there is more data to come from the O3 run, we are at the very beginning of this story.
Further, the theory passed all the tests in the meanwhile.
On to the search for hidden gravitational waves produced by gamma-ray burst events, in O3a [2].
The news here is that the search turned up a blank, but again it is early days and the general theory is that only mergers where one component is a neutron star will also generate a gamma-ray-burst.
These are at the smaller end of the spectrum of collisions that have been detected so far and it is expected that the majority of GRBs will originate beyond the distance our detectors can currently see, and events are believed to be directional, the burst and the wave along different axes.
So in this case, no news is just what you might expect.
I believe the search for coincident events at the same time as the O3a detections also turned a blank, but I have not seen a paper as yet.
This again is as expected, since the events detected in O3a did not include events where one component was definitively a neutron star.
References¶
[1] Tests of General Relativity with Binary Black Holes from the second LIGO–Virgo Gravitational-Wave Transient Catalog
https://dcc.ligo.org/public/0166/P2000091/010/o3a_tgr.pdf