Adiabatic high degree modes of a rotating star

Abstract

Aims. The influence of the rotation of the Sun on non-radial p-modes with high wave numbers l is studied. To investigate and understand the basic properties of these modes, it is sufficient to consider only the outer layers of the Sun, which can be approximated by a plane layer with constant gravity. Methods. We use a model with a smooth transition between a polytropic convection zone and an isothermal atmosphere. The rotation is simulated by a constant horizontal wind. For this model, using the column mass instead of the geometrical height, the adiabatic wave equation of the pressure perturbation can be reduced to Whittaker’s differential equation. From boundary conditions we obtain the dispersion relation. The geometrical height is a simple elementary function of the column mass. Results. The dispersion relation F(ω,k) = 0 is a higher order algebraic equation in both frequency and horizontal wave number, which must be solved numerically. We analyze the behavior of the dispersion curves of modes with an adiabatic exponent γ = 5/ 3f or layers with polytropic indices n = 3a ndn = 3/2. The f-mode is considered separately. For the understanding of the results we also consider modes of a homogeneous gas. We compare the k − ω diagram of our idealized model with the k − ω diagram of a real solar model.