The chirp mass of a compact binary star system with component masses
m
1
and
m
2
is given by
M
=
(
m
1
m
2
)
3
/
5
(
m
1
+
m
2
)
1
/
5
. In general relativity, the chirp mass determines the leading-order amplitude and frequency evolution of the gravitational-wave signal emitted by the binary during its inspiral. To lowest order in a post-Newtonian expansion, the evolution of the waveform’s phase depends only on the chirp mass:
where
c
,
G
,
f
and
f
˙
are the speed of light, Newton's gravitational constant, orbital frequency and the first time derivative of f, respectively. Accordingly, in gravitational-wave astronomy, the chirp mass can be accurately measured by detectors from frequency and gravitational strain of gravitational wave.
Rewrite equation (1) to obtain the frequency evolution of gravitational waves from a coalescing binary:
Integrating equation (2) with respect to time gives:
where C is the constant of integration. Furthermore, on identifying
x
≡
t
and
y
≡
3
8
f
−
8
/
3
, the chirp mass can be calculated from the slope of the line fitted through the data points (x, y).
