The Importance of Berry Phase in Solar Acoustic Modes

Abstract An analytic expression for the frequencies of standing waves in stars, applicable to any radial order n , is derived from ray-tracing equations by the mean of Wigner–Weyl calculus. A correction to previous formulas currently employed in asteroseismology is identified as the Berry phase, which accounts for the vectorial nature of wave propagation in stars. Accounting for this quantity significantly improves upon previous laws for low n modes of the Sun, and we show that the Berry phase is indeed present in the available observational data of solar modes. This phase is due to inhomogeneities of the medium.