# Heartbeat Stars, Tidally Excited Oscillations, and Resonance Locking

## TL;DR

This paper develops advanced methods to analyze tidally excited oscillations in heartbeat stars, enhancing understanding of tidal interactions and resonance locking in eccentric binary systems.

## Contribution

It introduces comprehensive computational techniques for modeling tidally excited oscillations, including effects of rotation, non-adiabaticity, and spin-orbit misalignment, with applications to resonance locking analysis.

## Key findings

- Methods improve modeling of tidal oscillations in eccentric binaries.
- Hot stars with surface temperatures above 6500 K show more visible oscillations.
- Statistical framework helps distinguish chance resonances from resonance locking.

## Abstract

Heartbeat stars are eccentric binary stars in short period orbits whose light curves are shaped by tidal distortion, reflection, and Doppler beaming. Some heartbeat stars exhibit tidally excited oscillations and present new opportunities for understanding the physics of tidal dissipation within stars. We present detailed methods to compute the forced amplitudes, frequencies, and phases of tidally excited oscillations in eccentric binary systems. Our methods i) factor out the equilibrium tide for easier comparison with observations, ii) account for rotation using the traditional approximation, iii) incorporate non-adiabatic effects to reliably compute surface luminosity perturbations, iv) allow for spin-orbit misalignment, and v) correctly sum over contributions from many oscillation modes. We also discuss why tidally excited oscillations are more visible in hot stars with surface temperatures $T \! \gtrsim \! 6500 \, {\rm K}$, and we derive some basic probability theory that can be used to compare models with data in a statistical manner. Application of this theory to heartbeat systems can be used to determine whether observed tidally excited oscillations can be explained by chance resonances with stellar oscillation modes, or whether a resonance locking process is operating.