Semiclassical approximation for low-degree stellar p modes — I. The classical eigenfrequency equation

A new eigenfrequency equation for low-degree solar-like oscillations in stars is developed, based on the assumption of purely classical propagation in the stellar interior of acoustic waves modified by buoyancy and gravity. Compared with high-frequency asymptotic analysis, the eigenfrequency equation has a new functional form, with expansion in powers of l(l+1) instead of 1/ω. Basic observable quantities, the ‘large’ and ‘small’ frequency separations, are interpreted as the dependence on frequency and refraction angle of a classical action integral for waves propagating close to the stellar diameter. The new eigenfrequency equation gives a significant improvement in accuracy over previous analyses when tested with solar p modes, suggesting this as an alternative and more powerful tool for applications in stellar seismology.