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

Heartbeat Stars, Tidally Excited Oscillations, and Resonance Locking