LIGO-PENR

GW150914 was produced by the coalescence of two black holes, in good agreement with the predictions of general relativity, as estimated by full numerical simulations of Einstein’s equations. To infer the properties of GW150914, however, the LIGO Scientific Collaboration previously made systematic comparisons between the data and semianalytic models, tuned to these full numerical simulations. In a new paper, GW150914 is compared directly against a large suite of numerical simulations of Einstein’s equations. These comparisons enable a completely independent reconstruction of GW150914’s properties, without recourse to these approximations. Though these simulations include new physics not previously incorporated in our analysis, we find reassuringly similar conclusions regarding the source properties.

For nonexperts: The process of solving Einstein’s equations on a supercomputer is called numerical relativity. All the understanding we have about the coalescence of binary black holes comes, in the end, from numerical relativity simulations. However, these simulations are notoriously challenging, requiring weeks to months of time on the world’s fastest supercomputers.
Working with four teams of experts in numerical relativity, including my RIT colleagues, we assembled a large collection of more than one thousand of their simulations of binary black holes.

Fortunately, because Einstein’s theory of gravity works the same way for all objects, no matter their mass, we can scale each simulation to larger or smaller black holes. In other words, for every simulation, we can pick any total binary mass we want. Still, we only have one thousand simulations to cover all the other parameters needed to describe a binary black hole: the ratio between the two black hole masses, and any other intrinsic properties (spin) the black holes have.

The problem of reconstructing the black hole’s properties turns into a jigsaw puzzle: we have only some of the pieces, but from experience we know the picture was drawn with a broad brush. We can boil the comparison between the data and a particular simulation and mass down to one number. This number (the marginalized likelihood) tells us the color of each piece of the puzzle. For an object like GW150914, with very few gravitational wave cycles, the colors of neighboring pieces of the puzzle are necessarily similar. So even though we’re missing most of the pieces, we can still figure out what the whole puzzle looked like. Or, at least, the most important part of the puzzle: the part that describes black holes most like GW150914.

In our original analysis, which you can read about here, we were excited to identify the masses and spins of the two black holes. These provide pieces of another jigsaw puzzle: how do we make binary black holes in the first place? Our new analysis teased out a little more information about the two black holes that merged to form GW150914, using information uniquely available from numerical relativity simulations.

Perhaps most important, however, we found similar conclusions using an independent analysis that incorporated simulations of binary black hole coalescence.

This work also more explicitly illustrated a result we learned in our initial interpretation of GW150914: how binary black holes with very different dynamics can, under suitable circumstances, produce gravitational waves like GW150914. Some of the simulations which fit the data were simple, with the inspiral occurring entirely within one plane. In others, the orbital plane slews strongly (precesses) through the merger. The movies below illustrate the range of possible sources of GW150914.

Finally, by measuring how similar each simulation was to this event, we can now figure out where new simulations would fill in the gaps, for this and future events.

For experts: When higher harmonics are included (l=3), we can place tighter constraints on the mass ratio.

For more information, see the links below, and prior posts

• LIGO Science Summaries (summary on this article here)

• Abbott et al, Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence, available here.

• APS April meeting presentation