Radial infall of two compact objects: 2.5PN linear momentum flux and associated recoil

TL;DR

This paper derives a 2.5PN analytical formula for the linear momentum flux in a binary system of compact objects undergoing radial infall, estimating the resulting recoil velocity during premerger evolution.

Contribution

It provides the first 2.5PN accurate analytical expressions for linear momentum flux in radially infalling binaries, including finite initial separation cases.

Findings

Derived 2.5PN formulas for momentum flux in radial infall

Estimated recoil velocities during premerger phase

Applicable to systems with finite and infinite initial separation

Abstract

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.