Coupling of solar p modes: quasi-degenerate perturbation theory

The interaction of a large-scale stationary poloidal velocity field (as a simple model for possibly existing giant cells) with solar p-mode oscillations is described by quasi-degenerate perturbation theory, as proposed by Lavely & Ritzwoller (1992). For oscillations of low degree (l ≤ 12) and sectoral velocity fields we obtain numerical solutions of the eigenvalue problem, and derive an approximate formula for the ensuing frequency splitting. The coupling of the oscillation modes leads to asymmetric frequency multiplets, with splittings of up to ≈ 100 nHz for a velocity with amplitude v = 100m s−1. The splitting scales with v2, with the oscillation frequency itself, and with the inverse difference of the squared frequencies of the coupling partners. Possible observable effects are briefly discussed.