Gyroscopic Gravitational Memory from quasi-circular binary systems

Gravitational waves cause a precession in a freely falling spinning object and a net change of orientation after the passage of the wave, dubbed as the 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 make a comparison between 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.