Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits

TL;DR

This paper compares the computational efficiency of frequency- and time-domain methods for calculating gravitational waveforms from extreme mass-ratio inspirals, finding that the time-domain approach is more efficient for high eccentricity equatorial orbits.

Contribution

It provides a detailed analysis of mode requirements and computation times, proposing a hybrid approach for optimal efficiency in modeling black hole inspirals.

Findings

Time-domain methods are more efficient for high eccentricity orbits.

Low-m modes are best computed with frequency-domain methods.

High-m modes are more efficiently computed with time-domain methods.

Abstract

Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be computed using time--domain methods with accuracy that is fast approaching that of frequency--domain methods. We study in detail the computational efficiency of these methods for equatorial orbits of fast spinning Kerr black holes, and find the number of modes needed in either method --as functions of the orbital parameters-- in order to achieve a desired accuracy level. We then estimate the total computation time and argue that for high eccentricity orbits the time--domain approach is more efficient computationally. We suggest that in practice low--$m$ modes are computed using the frequency--domain approach, and high--$m$ modes are computed using the time--domain approach, where $m$ is the azimuthal mode number.