The r-modes of slowly rotating, stratified neutron stars. Issue 2 (2nd March 2023) - Gittins, Fabian; Andersson, Nils
ABSTRACT: The only r -modes that exist in a globally barotropic, rotating, Newtonian star are the fundamental l = | m | solutions, where l and m are the indices of the spherical harmonic Y_l^m that describe the mode's angular dependence. This is in stark contrast to a stellar model that is non-barotropic throughout its interior, which hosts all the l ≥ | m | perturbations including radial overtones. In reality, neutron stars are stratified with locally barotropic regions. Therefore, we explore how stratification alters a star's ability to support r -modes. We consider the globally stratified case and examine the behaviour of the modes as the star gets close to barotropicity. In this limit, we find that all but the fundamental l = | m | perturbations change character and become generic inertial modes. Restricting the analysis to l = | m | perturbations, we develop the r -mode equations in order to consider stellar models that exhibit local barotropicity. Our results for such models show that the r -mode overtones diverge and join the inertial modes. In order to see which r -modes persist and retain their character in realistic neutron stars, these calculations will need to be brought into full general relativity.