chirp mass

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.

Mc = ( m1 m2 )3/5 / ( m1 + m2 )1/5

• M_c - chirp mass.
• m₁, m₂ - 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:

Mc = c³(5/96π-8/3f-11/3df/dt)3/5/G

• c - speed of light in a vacuum.
• G - gravitational constant.
• f - GW frequency.
• t - time.
• df/dt - rate at which frequency changes with time.

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, most significant term of a multi-term equation modeling the chirp's frequency-increase. Other mass-related quantities associated with GWs:

• mass ratio: q = m₁/m₂
• symmetric mass ratio: η = m₁m₂/(m₁+m₂)²

These can be determined by higher-order terms of the above-mentioned multi-term equation, but they cannot be determined with the same accuracy (from observation data) as the chirp mass. Because of known relationships between the chirp mass and these quantities, the individual masses of the two bodies can be determined from them to some limited accuracy.