Binary pulsar evolution

How does a neutron-star binary orbit shrink through gravitational waves? Choose an example or enter masses, initial period and eccentricity, then Calculate. Named examples use rounded initial values, not precise observational fits. Reset restores the Hulse–Taylor example, age and phase, stops playback and clears the output without calculating again.

Evolution: Model age selects 0–95% of the formal lifetime. Results and the curve marker describe the same instant. Myr means million years, Gm means million kilometres, and M☉ means solar masses. A negative period derivative means the orbital period is decreasing.

Orbit preview: Select a phase or start playback. Both stars move on their Kepler orbits around the barycentre while the evolutionary age stays fixed. Phase 1 equals 0; motion speeds up near periastron. Visual orbits per second set playback speed, not the physical orbital period. Equal axis scales and a fixed initial scale reveal shrinking; star sizes are schematic.

Limits: Semi-major axis and eccentricity evolve together using the orbit-averaged Peters model at leading quadrupole order. The supported range is 0.5–3 solar masses per star, 0.01–100 days and eccentricity 0–0.9. The formal lifetime extrapolates point masses to merger; that final stage is not reliably modelled. Spin, tides, mass transfer, relativistic periastron advance and pulse arrival times are excluded. Precise comparisons with measured period derivatives require a timing fit and Galactic/kinematic corrections.

Sources: Peters (1964), section V, equations 5.6–5.14; Weisberg & Huang (2016), table 2 and section 4.3; IAU 2015 B3 nominal constants; Kramer et al. (2021), double-pulsar timing.