Post-Newtonian templates for phase evolution of spherical extreme mass ratio inspirals

TL;DR

This paper develops and compares various post-Newtonian models for the phase evolution of extreme mass ratio inspirals in Kerr spacetime, highlighting the accuracy and analytical advantages of different approximants.

Contribution

It introduces high-order 12PN analytic formulas for phase evolution and evaluates the convergence and performance of different PN approximants for EMRI modeling.

Findings

TaylorT1 model performs best among time-domain models.

TaylorF2 model has comparable performance to TaylorT2.

Fully analytical models are useful for exploring effects beyond general relativity.

Abstract

We present various post-Newtonian (PN) models for the phase evolution of compact objects moving along quasi-spherical orbits in Kerr spacetime derived by using the 12PN analytic formulas of the energy, angular momentum and their averaged rates of change calculated in the framework of the black hole perturbation theory. To examine the convergence of time-domain PN models (TaylorT families), we evaluate the dephasing between approximants with different PN orders. We found that the TaylorT1 model shows the best performance and the performance of the TaylorT2 is the next best. To evaluate the convergence of frequency-domain PN models (TaylorF families), we evaluate the mismatch between approximants with different orders. We found that the performance of the TaylorF2 model is comparable with the TaylorT2 model. Although the TaylorT2 and TaylorF2 models are not so accurate as the TaylorT1, the fully analytical expressions give us easy-to-handle templates and are useful to discuss effects beyond general relativity.