Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation
Abstract
Context. Largescale Rossby waves have recently been discovered based on measurements of horizontal surface and nearsurface solar flows.
Aims: We are interested in understanding why it is only equatorial modes that are observed and in modelling the radial structure of the observed modes. To this aim, we have characterised the radial eigenfunctions of r modes for slowly rotating polytropes in uniform rotation.
Methods: We followed Provost et al. (1981, A&A, 94, 126) and considered a linear perturbation theory to describe quasitoroidal stellar adiabatic oscillations in the inviscid case. We used perturbation theory to write the solutions to the fourth order in the rotational frequency of the star. We numerically solved the eigenvalue problem, concentrating on the type of behaviour exhibited where the stratification is nearly adiabatic.
Results: We find that for freesurface boundary conditions on a spheroid of nonvanishing surface density, r modes can only exist for ℓ = m spherical harmonics in the inviscid case and we compute their depth dependence and frequencies to leading order. For quasiadiabatic stratification, the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as r^{m}. For all r modes, except the zero radial order sectoral ones, nonadiabatic stratification plays a crucial role in the radial force balance.
Conclusions: The lack of quasitoroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the need for both horizontal and radial force balance. In the absence of super or subadiabatic stratification and viscosity, both the horizontal and radial parts of the force balance independently determine the pressure perturbation. The only quasitoroidal cases in which these constraints on the pressure perturbation are consistent are the special cases where ℓ = m and the horizontal displacement scales with r^{m}.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 May 2020
 DOI:
 10.1051/00046361/201936251
 arXiv:
 arXiv:2003.05276
 Bibcode:
 2020A&A...637A..65D
 Keywords:

 Sun: oscillations;
 methods: analytical;
 stars: oscillations;
 stars: rotation;
 stars: interiors;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 10 pages, 8 figures, accepted in A&