Multi-cavity gravito-acoustic oscillation modes in stars

Asteroseismology has proven to be a powerful method for probing stellar interiors. Analytical descriptions of the global oscillation modes, in combination with pulsation codes, have provided valuable help processing and interpreting large amount seismic data collected by CoRoT, $Kepler$, TESS missions. These prior results paved way more in-depth analyses spectra stars, which requires innovative theoretical oscillations. In this paper, we aim analytically express resonance condition spheroidal adiabatic modes very general way, applicable at different evolutionary stages. present formulation, star is represented as an acoustic interferometer composed multitude resonant cavities where waves can propagate short-wavelength JWKB approximation met. Each cavity separated from adjacent ones barriers, corresponds regions either are evanescent or fails. The stationary computed using two physical representations: 1) infinite-time reflections picture 2) linear boundary value problem picture. Both provide same condition, ultimately turns out depend on number parameters: reflection transmission phase lags introduced each barrier, coupling factor associated wave integral over cavity. Using such retrieve usual forms derived previous works (e.g., mixed three cavities, low- large-amplitude glitches). This provides new tool that useful predicting interpret observations Practical applications left future work.