5PN eccentric waveforms for intermediate-mass-ratio-inspirals (IMRIs) from post-Newtonian and black hole perturbation theory

TL;DR

This paper develops a hybrid gravitational waveform model for intermediate-mass-ratio inspirals involving eccentric orbits, combining post-Newtonian and black hole perturbation theories up to high PN orders, to improve detection accuracy.

Contribution

It introduces a 3PN/5PN accurate hybrid waveform model incorporating high-order eccentricity corrections for IMRIs, enhancing gravitational wave analysis for future space detectors.

Findings

Significant increase in gravitational wave cycles when including higher eccentricity corrections.

Demonstrates importance of high PN order contributions from BHP theory.

Highlights the necessity of going beyond 5PN order in waveform modeling.

Abstract

Detection of gravitational waves from compact binaries involving at least one intermediate mass black hole, and component mass ratios in the range $0.1$-$10^{-4}$, are among the primary sources for future space detectors with target strain sensitivities in the deci-Hertz (dHz) band. Tuned to the waveform requirements for analyzing such sources, a hybrid model is obtained by combining waveforms from the post-Newtonian (PN) and black hole perturbation (BHP) theory. Components of the binary are assumed to be nonspinning and on eccentric orbits. This hybrid model is 3PN accurate in terms of results from PN theory and 5PN in results from BHP theory. In terms of eccentricity, corrections through the order $\mathcal{O}(e^{10})$ are included. Further, using number of gravitational wave cycles estimates for a few representative binaries observable in the dHz band, we demonstrate the significance of the mass ratio information from the PN approach, of contributions from the BHP theory at high PN orders, and also of higher order eccentricity corrections. In particular, we find an almost 10-fold increase in number of gravitational wave cycles for a fixed mass ratio of 0.1 and $e_0\sim0.3$ (evaluated at $0.01$Hz) when contributions beyond the leading order in eccentricity are accounted for. We also confirm the requirement to go beyond 5PN order in the circular part of the waveform from BHP theory.