Heather Fong — a PhD candidate in Physics at the University of Toronto, who also loves travelling and gastronomy photography — gives us an insight into her group’s work on using numerical relativity simulations for the detection of gravitational waves.

Heather Fong, a PhD candidate in Physics at the University of Toronto.

Answer: quite a lot! Numerical relativity (NR) provides the most accurate solutions to the binary black hole problem, which is exactly the type of source LIGO wants to detect — and has succeeded at! Most of the time, LIGO’s data streams are overwhelmed with noise, and so we use a technique called matched-filtering to identify gravitational-wave signals. Finding and characterizing signals requires a massive amount of accurate waveforms, and we use semi-analytic waveform models as filters which are built using the results of NR simulations.

Why don’t we use NR alone to identify signals? It certainly would be ideal if the theoretical template waveforms were generated entirely from NR; not only would we be using the most accurate waveforms available, it would also allow us to extract the weaker harmonics of gravitational-wave signals that current semi-analytic waveform models do not encode. However, simulations are tricky to compute and despite significant advancements over the years, NR is still too slow to replace semi-analytic models in LIGO data analyses — in short, NR is too expensive!

On the other hand, the theoretical waveforms generated from analytic models are much faster to compute, which means they can densely sample the parameter space of compact binaries in a fraction of the time that NR simulations can — usually as small as 0.001%-0.01%! Still, because analytic models aren’t quite solutions to the field equations, they aren’t nearly accurate enough on their own. To make the models as reliable as possible, they are tuned to reproduce the waveforms generated from available NR simulations. That’s why it’s more correct to call the models ‘semi-analytic’.

Since the models can’t be tuned for systems where NR simulations don’t exist, we have to fill in the gaps with additional simulations. NR becomes especially challenging to simulate numerically when the black holes have high spin and the binary is high mass-ratio, and so, available simulations are still pretty sparse in these regimes. Waveform models have to be used outside their domain of construction, where it’s not 100% clear how well they perform. The addition of NR simulations that populate new areas in parameter space are used to test current semi-analytic models as well as to develop more accurate ones.

In our CQG paper, we present a new set of 95 non-precessing, binary black hole NR simulations. In particular, these simulations cover the full spin-spin plane, and each simulation includes all three stages (inspiral, merger, and ringdown) of the merger.

The waveforms of our set of simulations. The text in each panel specifies the source parameters of the binary black hole (from left to right): mass ratio, spin of first black hole, spin of second black hole. The zoomed-in simulations shows how different binary systems produce different-looking gravitational waves. Adapted from Figure 2 of our CQG paper. © 2016 IOP Publishing Ltd. All rights reserved.

We include a detailed explanation of the simulations and an error analysis of the extracted gravitational waveforms.

Summary of the main error analysis results of our set of simulations. Figure 9 of our CQG paper. © 2016 IOP Publishing Ltd. All rights reserved.

Coincidentally, this set of simulations precisely covers the parameter space of LIGO’s first detection event, GW150914. These simulations have been used in a subsequent analysis comparing GW150914 with numerical relativity waveforms (arxiv.org/abs/1606.01262). On the other hand, the second event, GW151226, is not covered by our simulations because its long inspiral phase well-exceeds the length of the simulations in our set. It’s an example of one of the many challenges that NR still faces; there’s certainly still lots to be done in this field!

What else is NR good for? Well, it’s also great for making really cool movies! NR simulations were used to create the binary black hole merger visualizations that were shown during the LIGO press conferences. In fact, two of the movies were made by researchers at the Canadian Institute for Theoretical Astrophysics (CITA) at the University of Toronto, which is home to a highly active numerical relativity research group and is also the only Canadian research facility currently affiliated with the LIGO Scientific Collaboration. Find out more on our group website and to watch some binary black holes in action, take a look at our movies of Warped Spacetime and Horizons of GW150914 and Inspiral and merger of binary black hole GW151226.

Read the full article for free* in Classical and Quantum Gravity:
On the accuracy and precision of numerical waveforms: effect of waveform extraction methodology
Tony Chu et al 2016 Class. Quantum Grav. 33 165001

*until 8 September 2016

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