Rotating Love: The dynamical tides of spinning Newtonian stars

TL;DR

This paper develops a detailed Newtonian framework to model the dynamical tidal response of spinning neutron stars, including mode decomposition and rotational corrections to Love numbers, advancing understanding of tidal interactions in binary systems.

Contribution

It introduces a comprehensive mode-based approach to dynamical tides in spinning stars, accounting for rotational effects and clarifying mode orthogonality issues, which improves upon previous models.

Findings

Effective Love number is valid for any rotation rate.

Dynamical tide corrections are first order in rotation.

Static Love number corrections appear at second order.

Abstract

We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilising a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order.