### chirp mass

**(M**_{c}, ℳ)
(a reduced-mass-like quantity that relates to gravitational waves)

The **chirp mass** (**M**_{c} or **ℳ**)
is a function of the masses of two
orbiting bodies that is related to the rate of energy transferred
away through gravitational waves. Its role is somewhat like reduced mass:
it encapsulates some useful calculation and
constitutes a relation between masses that some observations reveal.

M_{c} = ( m_{1} m_{2} )^{3/5} / ( m_{1} + m_{2} )^{1/5}

- M
_{c} - chirp mass.
- m
_{1}, m_{2} - masses of the co-orbiting bodies.

The following differential equation approximately relates this
value to the orbit's GW frequency and its rate of change:

M_{c} = c³/G(5/96π^{-8/3}f^{-11/3}df/dt)^{3/5}

This is the equation solved for M_{c}
in terms of f and df/dt, the latter two being
the values that can be measured from observation.
(I assume the name is *chirp mass* because these two values are evident
from a GW chirp.)
It is approximate because
it is based upon the first term of a multi-term equation modeling
the chirp's frequency increase.
Other mass-related quantities associated with GWs:

- mass ratio:
**q** = m_{1}/m_{2}
**symmetric mass ratio**: **η** = m_{1}m_{2}/(m_{1}+m_{2})²

These can be determined by higher order terms of the same equation,
and the accuracy of the determination is lower. Because of known
relationships between the chirp mass and these quantities,
the individual masses of the two bodies can be determined
(to some limited accuracy) from them.

(*physics,mass,relativity*)
**Further reading:**

https://en.wikipedia.org/wiki/Chirp_mass

https://ui.adsabs.harvard.edu/abs/2016CQGra..33aLT01T/abstract

https://ui.adsabs.harvard.edu/abs/1994PhRvD..49.2658C/abstract

**Referenced by pages:**

GW detection (GW)

pulsar timing array (PTA)

Index