# Observation of Gravitional waves by LIGO from binary black hole merger

I read the paper "Observation of Gravitational Waves from a Binary Black Hole Merger" https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102

I tried to understand all the graphs and data observed in the paper. I am curious how these data and graphs conclude that the gravitational waves observed were because of binary black holes merger? Also what calculations and equations led to the same? Also how will the calculations and equations look if neutron stars were there instead of black hole in the same merger?

(graphs and data can be seen in the observation section in the paper)

Neutron stars are less massive but larger than black holes. The frequency of the gravitational waves is due to the orbital period of the objects as they spiral together. A neutron star merger would have a different orbital speed, so the frequency would be different and lower. It would rise at a different rate. The signal from neutron stars is also much weaker, so couldn't be detected from the same range.

Prior to the detection of the signal, numerical simulations of merging black holes of various sizes were done, so the theoretical shape of the waveform expected from the merger of black holes (and neutron stars) was known. It was possible from this theoretical work to estimate the mass of the two black holes taking part in the merger by matching the observed signal to a theoretical one. You can see the theoretical signal for black holes with 36 and 29 in the diagrams labelled as "numerical relativity"

• Thank you for a really good and simple answer, it cleared all the doubts but I am still curious to enjoy the beauty of how those equations governing the same would look like. Please give equations for the same it would be really helpful. Commented Apr 11, 2017 at 18:25
• Numerical relativity is heavy duty number crunching. The Ligo team use supercomputer time to run the simulations. The basic equations are the Einstein field equations en.wikipedia.org/wiki/Einstein_field_equations but the solutions are anything but trivial. Commented Apr 11, 2017 at 19:46
• The wrong way around. The inspiral frequency varies inversely with mass of the coalescing objects. Commented Apr 15, 2017 at 9:00

This is to supplement @JamesK's very clear answer. From the oscillations shown in Figure 1, one can estimate a period of the of the measured gravitational wave of about 5 milliseconds, which would correspond to an estimated frequency of the wave of about 200 Hz. Because the phenomenon is binary - a "wave" will come from each of the two objects, one can estimate the instantaneous orbital frequency at this moment to be half that, or about 100 Hz.

The discussion at the end of Section II mentions that in this case an orbital frequency reaching 75 Hz before contact could only be produced by two compact massive objects — black holes.

The annotations indicate an estimation from the figures only. An accurate analysis would require modeling the original data set.

From P. B. Abbott et al. PRL 116, 061102 (2016), section II and Figure 1:

To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) the objects must have been very close and very compact; equal Newtonian point masses orbiting at this frequency would be only ≃350 km apart. A pair of neutron stars, while compact, would not have the required mass, while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency. This leaves black holes as the only known objects compact enough to reach an orbital frequency of 75 Hz without contact. Furthermore, the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration.