On the validity of the adiabatic approximation in compact binary inspirals

TL;DR

This paper investigates the validity of the adiabatic approximation in modeling tidal effects during compact binary inspirals, finding it generally reliable with minor impacts on gravitational waveforms.

Contribution

It provides a semi-analytical method to evaluate the adiabatic approximation's accuracy and derives an expression for the Love number consistent with numerical results.

Findings

The Love number increases during inspiral but minimally affects gravitational waveforms.

The tidal component is well described within a specific frequency range using the stationary phase approximation.

The semi-analytical Love number closely matches numerical relativistic calculations.

Abstract

Using a semi-analytical approach recently developed to model the tidal deformations of neutron stars in inspiralling compact binaries, we study the dynamical evolution of the tidal tensor, which we explicitly derive at second post-Newtonian order, and of the quadrupole tensor. Since we do not assume a priori that the quadrupole tensor is proportional to the tidal tensor, i.e. the so called "adiabatic approximation", our approach enables us to establish to which extent such approximation is reliable. We find that the ratio between the quadrupole and tidal tensors (i.e., the Love number) increases as the inspiral progresses, but this phenomenon only marginally affects the emitted gravitational waveform. We estimate the frequency range in which the tidal component of the gravitational signal is well described using the stationary phase approximation at next-to-leading post-Newtonian order, comparing different contributions to the tidal phase. We also derive a semi-analytical expression for the Love number, which reproduces within a few percentage points the results obtained so far by numerical integrations of the relativistic equations of stellar perturbations.