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 { 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 .