Chirp mass

The chirp mass is the quantity that governs the leading-order gravitational-wave signal from a compact binary. For two bodies of masses m₁ and m₂ it is defined as ℳ = (m₁ m₂)^{3/5} / (m₁ + m₂)^{1/5}. It is a weighted blend of the two masses, distinct from both the total mass m₁ + m₂ and the reduced mass; it carries the dimensions of mass and, for stellar-mass black holes and neutron stars, comes out in the range of roughly one to a few tens of solar masses.

Its importance is that the rate at which an inspiral's frequency sweeps upward — the chirp — depends on the masses only through this single combination. The frequency evolution obeys df/dt ∝ ℳ^{5/3} f^{11/3}, so measuring how the gravitational-wave frequency accelerates yields the chirp mass directly and with high precision, while the individual masses and mass ratio are far harder to extract. The same chirp mass also sets the wave's amplitude, making an inspiral a self-calibrating 'standard siren' whose distance can be read from its own waveform.

Because two very different mass pairs can share nearly the same chirp mass, early-inspiral waveforms are degenerate: an 18 + 50 solar-mass binary sounds almost identical to a 30 + 30 binary until higher-order, post-Newtonian corrections near merger break the degeneracy. For the first detected merger, GW150914, the chirp mass was pinned to within a few percent of about 28 solar masses long before the component masses were confidently separated.

The chirp mass emerged naturally from the post-Newtonian analysis of inspiralling binaries developed in the 1970s through 1990s, as theorists worked out the templates that gravitational-wave detectors would later use to dig signals out of noise. It became the headline observable of the LIGO–Virgo detections beginning in 2015.