The paper from LIGO's original gravitational wave detection (PRL 116, 061102 (2016)) defines the chirp mass as $$M=\frac{(m_1 m_2)^{3/5}}{(m_1+m_2)^{1/5}}=\frac{c^3}{G}\left[\frac{5}{96}\pi^{-8/3}f^{-11/3}\dot{f}\right]^{3/5}\approx 30M_{sun}$$

and states "a black hole neutron star binary with the deduced chirp mass would have a very large total mass..." I do not get this. I can get the deduced chirp mass with a neutron star mass of about 18 suns and a black hole mass of 70 suns, for a total mass of 98 suns. Why did they draw this conclusion?


1 Answer 1


The important thing to realize here is that neutron stars are limited to comparatively low masses. The classic mass of a "canonical" neutron star is $\sim1.4M_{\odot}$, and almost all observed examples fall into the $1.4\mathrm{-}2.0M_{\odot}$ range, with a few extremely tentative candidates approaching $2.5M_{\odot}$ (e.g. a possible $2.50\mathrm{-}2.67M_{\odot}$ compact object seen in GW190814, Abbott et al. 2020, which may or may not be a neutron star). The general relativistic bound is no higher than about $3.0M_{\odot}$, and an $18M_{\odot}$ neutron star is definitely out of the question.

With that in hand: Say GW 150914 was the result of a neutron star-black hole merger. If we take the neutron star to have the canonical mass of $1.4M_{\odot}$, the black hole would have to have a mass of $\sim3000M_{\odot}$ to produce the measured chirp mass. Even increasing the neutron star mass to $2.0M_{\odot}$ only reduces the black hole mass to a bit under $2000M_{\odot}$. It's certainly possible to have black holes in this mass range, but as the paper points out, this would lead to gravitational wave emission at a much lower frequency than was actually observed.

For comparison, the sources of the GW200105 and GW200115 detections, postulated to be neutron star-black hole mergers, had chirp masses of only $\sim3.41M_{\odot}$ and $\sim2.42M_{\odot}$, respectively, and total masses of $\sim10.8M_{\odot}$ and $\sim7.3M_{\odot}$. In both cases, the neutron stars appear to be comfortably within the observed range of neutron star masses.


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