Abstract
ABSTRACT Rossby wave instabilities (RWIs) usually lead to non-axisymmetric vortices in protoplanetary discs and some observed substructures of these discs can be explained well by RWIs. We explore how the cooling influences the growth rate of unstable RWI modes in terms of the linear perturbation analysis. The cooling associated with the energy equation is treated in two different ways. The first approach that we adopt is a simple cooling law. The perturbed thermal state relaxes to the initial thermal state on a prescribed cooling time-scale. In the second approach, we treat the cooling as a thermal diffusion process. The difference in the growth rate between the adiabatic and isothermal modes becomes more pronounced for discs with smaller sound speed. For the simple cooling law, the growth rates of unstable modes monotonically decrease with the shorter cooling time-scale in barotropic discs. However, the dependence of the growth rate with the cooling time-scale becomes non-monotonic in non-baratopic discs. The RWIs might even be enhanced in non-barotropic discs during the transition from the adiabatic state to the isothermal state. When the cooling is treated as thermal diffusion, even in barotropic discs, the variation of the growth rate with thermal diffusivity becomes non-monotonic. Furthermore, a maximum growth rate may appear with an appropriate value of thermal diffusivity. The angular momentum flux is investigated to understand the angular momentum transport by RWIs with cooling.
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