🌌 Gravitational Wave Chirp
Two compact objects spiral inward under gravitational radiation reaction. Watch the strain waveform h(t) sweep from low to high frequency as the binary loses energy, just like GW150914 at LIGO. Set individual masses and adjustthe luminosity distance.
Binary system
Chirp parameters
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(G𝓅/c³)⁵/⁸·(t_c-t)⁻³/⁸
𝓅=(m₁m₂)³/⁵/(m₁+m₂)¹/⁵
h≈(4/r)(G𝓅/c²)⁵/³(πf)²/³
Gravitational Wave Physics
The Inspiral Phase
Two masses orbiting each other continuously lose energy to gravitational radiation (quadrupole formula: P = −32/5 · G&sup4;/c&sup5; · (m1m2)2(m1+m2)/r&sup5;). As the orbit shrinks, the orbital frequency rises — producing the characteristic “chirp” signal. LIGO detected GW150914 (30 + 36 M☉ black holes at 440 Mpc) on 14 September 2015.
Chirp Mass & Parameter Estimation
The chirp mass 𝓅 = (m1m2)3/5/(m1+m2)1/5 is the best-measured parameter from the inspiral phase; it controls the frequency evolution f(t). Individual masses and spin are harder to measure (require higher-order PN terms). The luminosity distance is measured from the amplitude h ∝ 𝓅5/3/r, making gravitational wave sources “standard sirens” for independent cosmology (H0 measurement).
Merger & Ringdown
Near coalescence (r → RISCO = 3rs) the post-Newtonian approximation breaks down. Numerical relativity is required. After merger, the remnant black hole rings like a bell — quasinormal modes with characteristic damped-sinusoid frequencies determined by mass and spin (Kerr). The ringdown frequency for GW150914 was ≈150 Hz with a damping time ≈4 ms.
LIGO Detection
LIGO uses 4 km Michelson interferometer arms. For h ∼ 10−²¹ (GW150914’s peak), the arm-length change is ΔL ∼ 4 × 10−¹&sup8; m — one-thousandth the diameter of a proton. The signal is extracted from detector noise (seismic, thermal, quantum shot noise) using matched filtering: cross-correlate the data with template waveforms from a bank spanning 𝓅 and η = m1m2/(m1+m2)2.