Gyroscopic Gravitational Memory from quasi-circular binary systems

TL;DR

This paper analyzes gyroscopic gravitational memory effects in quasi-circular binary systems within the post-Newtonian framework, identifying the dominant contributions and their angular dependence, with implications for gravitational wave observations.

Contribution

It computes the leading gyroscopic precession and memory effects at post-Newtonian orders for binary systems, highlighting the significance of subleading adiabatic effects.

Findings

Gyroscopic memory involves a 1.5PN effect enhanced by velocity to the fifth power.

The spin memory is a 2PN oscillatory effect, while nonlinear helicity flux is 4PN adiabatic.

Explicit angular dependence of the memory on the celestial sphere is derived.

Abstract

Gravitational waves cause freely falling spinning objects to precess, resulting in a net orientation change called gyroscopic memory. In this paper, we will consider isolated gravitational sources in the post-Newtonian framework and compute the gyroscopic precession and memory at leading post-Newtonian (PN) orders. We compare two competing contributions: the spin memory and the nonlinear helicity flux. At the level of the precession rate, the former is a 2PN oscillatory effect, while the latter is a 4PN adiabatic effect. However, the gyroscopic memory involves a time integration, which enhances subleading adiabatic effects by the fifth power of the velocity of light, leading to a 1.5PN memory effect. We explicitly compute the leading effects for a quasi-circular binary system and obtain the angular dependence of the memory on the celestial sphere.