Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals

TL;DR

This paper assesses the significance of second order self-forces on gravitational wave phase evolution from extreme mass-ratio inspirals, proposing new methods to estimate their impact and suggesting they may be captured by 3PN energy flux calculations.

Contribution

It introduces a novel exponential resummation technique and a scaling analysis to estimate second order self-force effects on gravitational wave dephasing.

Findings

Second order self-forces may cause measurable dephasing in gravitational waves.

The dephasing can be approximated by 3PN energy flux calculations with spin considerations.

The new resummation method ensures positive energy flux estimates.

Abstract

The accurate calculation of long-term phase evolution of gravitational wave (GW) forms from extreme (intermediate) mass ratio inspirals (E(I)MRIs) is an inevitable step to extract information from this system. Achieving this goal, it is believed that we need to understand the gravitational self-forces. However, it is not quntatively demonstrated that the second order self-forces are necessary for this purpose. In this paper we revisit the problem to estimate the order of magnitude of the dephasing caused by the second order self-forces on a small body in a quasi-circular orbit around a Kerr black hole, based on the knowledge of the post-Newtonian (PN) approximation and invoking the energy balance argument. In particular, we focus on the averaged dissipative part of the self-force, since it gives the leading order contribution among the various components of them. To avoid the possibility that the energy flux of GWs becomes negative, we propose a new simple resummation called exponential resummation, which assures the positivity of the energy flux. In order to estimate the magnitude of the yet unknown second order self-forces, here we point out the scaling property in the absolute value of the PN coefficients of the energy flux. Using these new tools, we evaluate the expected magnitude of dephasing. Our analysis indicates that the dephasing due to the second order self-forces for quasi-circular E(I)MRIs may be well captured by the 3PN energy flux, once we obtain all the spin dependent terms, except for the case with an extremely large spin of the central Kerr black.