Heartbeat Stars, Tidally Excited Oscillations, and 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 $T\gtrsim 6500\mathrm{K}$, 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.

Published in MNRAS

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• The effect of tides on near-core rotation: analysis of 35 Kepler $\gamma$ Doradus stars in eclipsing and spectroscopic binaries
• Tidally Trapped Pulsations in Binary Stars
• Tidally Excited Oscillations in Heartbeat Binary Stars: Pulsation Phases and Mode Identification
• Internal circulation in tidally locked massive binary stars -- Consequences for double black hole formation
• $\epsilon$ Lupi: measuring the heartbeat of a doubly-magnetic massive binary with BRITE-Constellation
• Polygram Stars: Resonant Tidal Excitation of Fundamental Oscillation Modes in Asynchronous Stellar Coalescence
• Finding the Needle in a Haystack: Detrending Photometric Timeseries Data of Strictly Periodic Astrophysical Objects