Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources

Understand

We present a revised version of Peters' (1964) time-scale for the gravitational-wave (GW) induced decay of two point masses.

• The new formula includes the effects of the first-order post-Newtonian perturbation and additionally provides a simple fit to account for the Newtonian self-consistent evolution of the eccentricity.
• The revised time-scale is found by multiplying Peters' estimate by two factors, $R(e_0)= 8^{1-\sqrt{1-e_0}}$ and $Q_{\rm f}(p_0) = \exp \left(2.5 (r_{\rm S}/p_0) \right)$, where $e_0$ and $p_0$ are the initial eccentricity and periapsis, respectively, and $r_{\rm S}$ the Schwarzschild radius of the system.
• Their use can correct errors of a factor of 1-10 that arise from using the original Peters' formula.