# Gravitational waves: how can scientists derrive the sizes and spin and distance of two merging black holes?

After recording the ripples of passing gravity waves I would imagine that some high-power math would be required to derive information about the sizes, spin, and distance of the merging black holes. Is it possible to get some insight into how they figured out one was 31 solar masses and the other was 20? How do you "see" spin from a wave?

• There are some answers to this in this site and in Physics SE as well but I don't have time to search for them. Briefly, they run simulations with a large number of different starting conditions (masses, spins, etc.) and for each they calculate what the radiated gravitational waves would look like viewed from different directions relative to the pair's orbital plane, and for different orientations of the GW detectors. All of these get put into a big library of possible waveforms.
– uhoh
Commented Jun 26, 2019 at 8:30
• When a real gravitational wave is recorded, they search the library for the best fit as a first pass, and if there is anything even close they go on to refine the simulations to improve the fit. See for example What does “GPU-accelerated butterfly matched filtering over dense bank of time-symmetric chirp-like templates” mean? (GW170817)
– uhoh
Commented Jun 26, 2019 at 8:31
• – uhoh
Commented Jun 26, 2019 at 8:38
• I've edited the title: Gravity -> Gravitational. Gravity waves are an atmospheric/hydrodynamic phenomenon. The name is easily mixed up with gravitational waves, which are a GR phenomenon. Commented Jun 26, 2019 at 12:27
• Thanks so much for the answers and links. I will eagerly research them. Commented Jun 27, 2019 at 3:21

## 1 Answer

One element of the answer is that they do it in the other direction. They simulate many different possible black hole mergers and then look for the nearest matches to what they observe. I imagine there is some scope for interpolating between the simulations as well as running bespoke simulations to confirm the match. Spin affects the wave because the shape of space around a spinning black hole is different from that around a non-spinning one, which affects both the motion of the black holes and the processes by which the gravitational waves are radiated.