Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources. Issue 2 (20th May 2020) - Zwick, Lorenz; Capelo, Pedro R; Bortolas, Elisa; Mayer, Lucio; Amaro-Seoane, Pau
ABSTRACT: We present a revised version of Peters' 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)= 8^1-1-e_0 and Q f ( p 0 ) = exp (2.5( r S / p 0 )), where e 0 and p 0 are the initial eccentricity and periapsis, respectively, and r 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. We apply the revised time-scales to a set of typical sources for existing ground-based laser interferometers and for the future Laser Interferometer Space Antenna (LISA), at the onset of their GW-driven decay. We argue that our more accurate model for the orbital evolution will affect current event- and detection-rate estimates for mergers of compact object binaries, with stronger deviations for eccentric LISA sources, such as extreme and intermediate mass-ratio inspirals. We propose the correction factors R and Q f as a simple prescription to quantify decay time-scales more accurately in future population synthesis models. We also suggest that the corrected time-scale may be used as a computationally efficient alternative to numerical integration in other applications that include the modelling of radiation reaction for eccentric sources.