Assessment of Critical Convection and Associated Rotation States in Models of Sun-like Stars Including a Stable Layer

Abstract

Abstract Recent numerical simulations of rotating stellar convection have suggested the possible existence of retrograde (slow equator, fast poles) or so-called antisolar differential rotation states in slowly rotating stars possessing a large Rossby number. We aim to understand whether such rotational states exist from the onset of convective instability or are the outcome of complex nonlinear interactions in the turbulent convective envelope. To this end, we have made a systematic linear analysis of the critical state of convection in a series of 15 numerical simulations published in Brun et al. We have assessed their degree of supercriticality and most-unstable mode properties, and computed the second-order mean zonal flow response. We find that none of the linear critical cases show a retrograde state at the onset of convection even when their nonlinear counterparts do. We also find that the presence of a stably stratified layer coupled to the convectively unstable upper layer leads to interesting gravity-wave excitation and angular momentum transport. We conclude that retrograde states of differential rotation are probably the outcome of complex mode–mode interactions in the turbulent convection layer and are, as a consequence, likely to exist in real stars.