Investigating tidal heating in neutron stars via gravitational Raman scattering

TL;DR

This paper develops a formalism combining effective field theory and stellar perturbation theory to analyze tidal heating and gravitational Raman scattering in neutron stars, providing new insights into their gravitational wave signatures.

Contribution

It introduces a novel scattering amplitude approach to study tidal heating and gravitational Raman scattering in neutron stars, including analytical solutions and dissipation estimates.

Findings

Derived master perturbation equations for fluid perturbations in neutron stars.

Calculated gravitational wave scattering amplitudes and Love numbers.

Estimated tidal heating effects on gravitational wave cycles during inspiral.

Abstract

We present a scattering amplitude formalism to study the tidal heating effects of nonspinning neutron stars incorporating both worldline effective field theory and relativistic stellar perturbation theory. In neutron stars, tidal heating arises from fluid viscosity due to various scattering processes in the interior. It also serves as a channel for the exchange of energy and angular momentum between the neutron star and its environment. In the interior of the neutron star, we first derive two master perturbation equations that capture fluid perturbations accurate to linear order in frequency. Remarkably, these equations receive no contribution from bulk viscosity due to a peculiar adiabatic incompressibility which arises in stellar fluid for non-barotropic perturbations. In the exterior, the metric perturbations reduce to the Regge-Wheeler (RW) equation which we solve using the analytical Mano-Suzuki-Takasugi (MST) method. We compute the amplitude for gravitational waves scattering off a neutron star, also known as gravitational Raman scattering. From the amplitude, we obtain expressions for the electric quadrupolar static Love number and the leading dissipation number to all orders in compactness. We then compute the leading dissipation number for various realistic equation-of-state(s) and estimate the change in the number of gravitational wave cycles due to tidal heating during inspiral in the LIGO-Virgo-KAGRA (LVK) band.