Radiatively heated, protoplanetary discs with dead zones. I. Dust settling and thermal structure of discs around M stars

The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between 2D self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes (N=15), the gravitational force of an embedded planet on the disc, and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an $r^{-3/5}$ distribution (well mixed dust models) toward an $r^{-3/4}$. The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin-Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is $\alpha=10^{-5}$.