Gravitational Wave: Binary Inspiral Chirp

Binary System

M₁ (solar masses): 30 M☉ M₂ (solar masses): 30 M☉ Initial separation: 200 km Simulation speed: 1.0×

Chirp mass M_c:—

Frequency f:—

Separation a:—

Strain h:—

Time to merge:—

h(t) ~ M_c^(5/3) f^(2/3)

ḟ = (96/5)π^(8/3)(GM_c/c³)^(5/3) f^(11/3)

The gravitational wave frequency chirps upward as the orbit decays. M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5) is the chirp mass — the primary observable.

GW150914 (LIGO 2015): first detection, M_c≈28.3 M☉, merge at ~150 Hz.

Gravitational Wave Inspiral

Binary System