Leading-order post-Newtonian inspiral of a compact binary: f(τ) ∝ τ^(−3/8), strain h(t) ∝ M_c^(5/3) f^(2/3) / D_L. Tune component masses m₁, m₂ and luminosity distance D_L; live h(t) and f(t) traces with the orbiting bodies on the side. The chirp mass M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5) is the very quantity LIGO/Virgo measures from the early inspiral; the frequency freezes at the Schwarzschild ISCO.
About this model
Leading-order post-Newtonian inspiral of a compact binary radiates gravitational waves with frequency f(τ) ∝ τ^(−3/8) and strain amplitude h(t) ∝ M_c^(5/3) f^(2/3) / D_L, where τ is time to coalescence and M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5) is the chirp mass. The lab shows live h(t) and f(t) traces beside orbiting bodies; frequency freezes at the Schwarzschild ISCO as a simple cutoff for this inspiral-only model. Assumptions: circular leading-order PN inspiral, no merger/ringdown waveform, no spin effects. Tune component masses m₁, m₂ and luminosity distance D_L to see how chirp rate and strain scale—the same M_c LIGO/Virgo infer from early inspiral.
Who it's for: Advanced gravitational-wave astronomy, relativity, and compact-object courses.
Key terms
gravitational wave chirp
chirp mass
post-Newtonian inspiral
strain amplitude
luminosity distance
compact binary
How it works
Compact binary inspiral chirp at leading post-Newtonian order: frequency f(τ) ∝ τ^(−3/8), strain h(t) ∝ M_c^(5/3) f^(2/3) / D_L, animated orbit and live h(t) / f(t) traces. The chirp mass M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5) and luminosity distance D_L are exactly the quantities LIGO/Virgo measures from a binary black-hole or neutron-star event; the animation freezes at the Schwarzschild ISCO frequency.
Frequently asked questions
Why is chirp mass what detectors measure first?
To leading order the phase evolution depends on the combination M_c, not on m₁ and m₂ separately. Matching f(t) during early inspiral therefore constrains M_c tightly. Individual masses need higher-order terms, spin, or the merger to break the degeneracy—students often think each mass is read off independently from the start.
How does distance affect the signal?
Strain h scales as 1/D_L while the frequency chirp f(τ) does not; a farther binary looks quieter but chirps similarly if masses match. Confusing amplitude distance with a change in chirp rate is a common mistake.
Why freeze frequency at the ISCO?
This teaching model stops the PN inspiral near the Schwarzschild ISCO instead of attaching a full merger-ringdown waveform. Real LIGO templates continue through merger; here the freeze marks where the simple inspiral approximation ends for non-spinning holes.