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

TL;DR

The paper addresses modeling tidal deformation of neutron stars in black hole–neutron star and neutron star–neutron star binaries during inspiral. It combines a post-Newtonian two-body metric with an affine ellipsoidal description of the star, yielding a semi-analytic framework that evolves both orbital dynamics and stellar deformation through a tidal tensor of order $O(1/c^3)$ including spin effects. Key contributions include deriving the tidal tensor in harmonic coordinates with spinning terms, implementing Hadamard regularization to handle point-particle divergences, and validating the approach against fully relativistic simulations and Love-number calculations. This framework enables efficient exploration of parameter space, tests the limits of tidal adiabaticity, and can aid in generating initial data and GW models for compact-binary coalescences.

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.

Figures (3)

• Figure 1: (Color online) We plot the gravitational wave frequency $\Omega_{GW}$ versus time, both normalized to the total mass of the binary. The URB, KT data are indicated by a solid line, and our data by a dashed line. The dashed lines stop at $r_{12}=r_{shed}$, where the deformed star touches the Roche lobe.
• Figure 2: (Color online) The NS central density (normalized to the squared total mass of the binary) is plotted, as a function of time (normalized to the binary total mass), for the AEI simulations (solid line) and for our simulations (dashed line).
• Figure 3: (Color online) Snapshots corresponding to $t=t_{shed}$ which we evaluate integrating our equations. Upper panels: URB simulations with $C=0.145$, $\tilde{a}=0,0.75$, $q=3$. Lower panels: KT simulations with $C=0.145$, $\tilde{a}=0$, $q=2,3$.