In astrophysics, the chirp mass of a compact binary system determines the leading-order orbital evolution of the system as a result of energy loss from emitting gravitational waves.
Because the gravitational wave frequency is determined by orbital frequency, the chirp mass also determines the frequency evolution of the gravitational wave signal emitted during a binary's inspiral phase.
and other common mass parameters: In general relativity, the phase evolution of a binary orbit can be computed using a post-Newtonian expansion, a perturbative expansion in powers of the orbital velocity
are the speed of light and Newton's gravitational constant, respectively.
of a gravitational wave signal, the chirp mass can be determined.
[4][5][note 1] To disentangle the individual component masses in the system one must additionally measure higher order terms in the post-Newtonian expansion.
[1] One limitation of the chirp mass is that it is affected by redshift; what is actually derived from the observed gravitational waveform is the product where
This is usually resolved by using the observed amplitude to find the chirp mass divided by distance, and solving both equations using Hubble's law to compute the relationship between distance and redshift.
[note 3] Xian Chen has pointed out that this assumes non-cosmological redshifts (peculiar velocity and gravitational redshift) are negligible, and questions this assumption.
[9][10] If a binary pair of stellar-mass black holes merge while closely orbiting a supermassive black hole (an extreme mass ratio inspiral), the observed gravitational wave would experience significant gravitational and doppler redshift, leading to a falsely low redshift estimate, and therefore a falsely high mass.
He suggests that there are plausible reasons to suspect that the SMBH's accretion disc and tidal forces would enhance the merger rate of black hole binaries near it, and the consequent falsely high mass estimates would explain the unexpectedly large masses of observed black hole mergers.
(The question would be best resolved by a lower-frequency gravitational wave detector such as LISA which could observe the extreme mass ratio inspiral waveform.)
, the chirp mass can be calculated from the slope of the line fitted through the data points (x, y).