Improved gravitational radiation timescales II: Spinorbit contributions and environmental perturbations
Abstract
Peters' formula is an analytical estimate of the timescale of gravitational wave (GW)induced coalescence of binary systems. It is used in countless applications, where the convenience of a simple formula outweighs the need for precision. However, many promising sources of the Laser Interferometer Space Antenna (LISA), such as supermassive black hole binaries and extreme massratio inspirals (EMRIs), are expected to enter the LISA band with highly eccentric (e ≳ 0.9) and highly relativistic orbits. These are exactly the two limits in which Peters' estimate performs the worst. In this work, we expand upon previous results and give simple analytical fits to quantify how the inspiral timescale is affected by the relative 1.5 postNewtonian (PN) hereditary fluxes and spinorbit couplings. We discuss several cases that demand a more accurate GW timescale. We show how this can have a major influence on quantities that are relevant for LISA eventrate estimates, such as the EMRI critical semimajor axis. We further discuss two types of environmental perturbations that can play a role in the inspiral phase: the gravitational interaction with a third massive body and the energy loss due to dynamical friction and torques from a surrounding gas medium ubiquitous in galactic nuclei. With the aid of PN corrections to the timescale in vacuum, we find simple analytical expressions for the regions of phase space in which environmental perturbations are of comparable strength to the effects of any particular PN order, being able to qualitatively reproduce the results of much more sophisticated analyses.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2021
 DOI:
 10.1093/mnras/stab1818
 arXiv:
 arXiv:2102.00015
 Bibcode:
 2021MNRAS.506.1007Z
 Keywords:

 black hole physics;
 gravitational waves;
 methods: analytical;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 Accepted for publication in MNRAS. Comments welcome!