A unified normal mode approach to dynamic tides and its application to rotating Sun-like stars

TL;DR

This paper develops a unified normal mode approach to analyze the response of rotating Sun-like stars to tidal forces, accounting for energy and angular momentum transfer, applicable to various stellar structures and orbital configurations.

Contribution

It introduces a comprehensive formalism for tidal interactions in rotating stars, including both radiative and convective regions, with detailed calculations for Sun-like stars in slow rotation regimes.

Findings

Good agreement between WKBJ and numerical methods.

Derived expressions for energy and angular momentum transfer for arbitrary eccentricity.

Estimated evolution timescales for planetary orbits around Sun-like stars.

Abstract

We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low frequency modes, such as gravity modes and evaluate it in the limit of very weak dissipation. Our formalism may be applied both to Sun-like stars with radiative cores and convective envelopes and to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum valid for an orbit with any eccentricity. Detailed calculations are made for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a WKBJ procedure and direct numerical evaluation which are found to be in good agreement for regimes of interest. Finally we use our formalism to determine the evolution time scales for an object, in an orbit of small eccentricity, around a Sun-like star in which the tidal response is assumed to occur. Systems with either no rotation or synchronous rotation are considered. Only rotationally modified gravity modes are taken into account under the assumption that wave dissipation occurs close to the stellar centre.