Tidal interaction in compact binaries: a post-Newtonian affine framework

TL;DR

This paper introduces a semi-analytical post-Newtonian affine model to simulate tidal deformations in neutron stars during compact binary coalescences, integrating orbital evolution and stellar deformation.

Contribution

It presents a unified framework combining post-Newtonian expansion and affine approximation to model neutron star tidal deformation and orbital dynamics in binary mergers.

Findings

The model accurately predicts neutron star deformation up to mass shedding.

Results agree with fully relativistic numerical simulations.

The approach includes spin effects at 1/c^3 order.

Abstract

We develop a semi-analytical approach, based on the post-Newtonian expansion and on the affine approximation, to model the tidal deformation of neutron stars in the coalescence of black hole-neutron star or neutron star-neutron star binaries. Our equations describe, in a unified framework, both the system orbital evolution, and the neutron star deformations. These are driven by the tidal tensor, which we expand at 1/c^3 post-Newtonian order, including spin terms. We test the theoretical framework by simulating black hole-neutron star coalescence up to the onset of mass shedding, which we determine by comparing the shape of the star with the Roche lobe. We validate our approach by comparing our results with those of fully relativistic, numerical simulations.