Importance of relativistic pericenter precession in identifying the presence of a third body near eccentric binaries

TL;DR

This paper demonstrates that including relativistic pericenter precession in timing models of eccentric binaries is crucial for detecting third bodies via gravitational wave burst timing, significantly improving accuracy over Newtonian models.

Contribution

The paper introduces an improved timing model that incorporates conservative post-Newtonian corrections, notably 1PN precession, to better detect and characterize third bodies in eccentric binary systems.

Findings

1PN precession causes distinctive modulation features in orbital parameters.

Including PN corrections reduces bias in estimating third body properties.

PN effects are essential for accurate modeling of hierarchical triple systems.

Abstract

Many astrophysical processes can produce gravitational wave (GW) sources with significant orbital eccentricity. These binaries emit bursts of gravitational radiation during each pericenter passage. In isolated systems, the intrinsic timing of these bursts is solely determined by the properties of the binary. The presence of a nearby third body perturbs the system and alters the burst timing. Accurately modeling such perturbations therefore offers a novel approach to detecting the presence of a nearby companion. Existing timing models account for Newtonian dynamics and leading-order radiation reaction effects but neglect the higher order post-Newtonian (PN) contributions to the inner binary. In this paper, we present an improved timing model that incorporates conservative PN corrections that lead to the precession of the binary's pericenter. We find that these PN corrections significantly impact the binary's orbital evolution and the timing of the GW burst. In particular, 1PN precession gives rise to distinctive modulation features in the binary's semilatus rectum and eccentricity. These modulations encode valuable information about the presence and properties of the third body, including its mass and distance. Furthermore, unmodeled 1PN effects significantly bias the tertiary's mass and distance. Finally we assess the detectability of GW bursts from such perturbed systems and demonstrate that the inclusion of PN corrections is crucial for accurately capturing the orbital dynamics of hierarchical triples.