Effect of Dust Evaporation and Thermal Instability on Temperature Distribution in a Protoplanetary Disk

The thermal instability of accretion disks is widely used to explain the activity of cataclysmic variables, but its manifestation in gas and dust disks in young stars has been studied in less detail. A semi-analytical stationary model is presented for calculating the equatorial temperature of a gas and dust disk around a young star. The model considers the opacity caused by dust and gas, as well as the evaporation of dust at temperatures above 1000 K. Using this model, the distributions of the equatorial temperature of the gas and dust disk are calculated under various assumptions on the source of opacity and the presence of dust. It is shown that when all the above processes are considered, the thermal balance equation in the region r<1 AU has multiple temperature solutions. Thus, the conditions for thermal instability are satisfied in this region. As an illustration of the possible influence of instability on the nature of accretion in a protoplanetary disk, we consider a viscous disk model with α-parametrization of turbulent viscosity. It is shown that in such a model a non-stationary mode of disk evolution is realized with alternating phases of accumulation of matter in the inner disk and phases of its rapid accretion onto the star, which leads to a burst character of accretion. The results obtained indicate the need to take this instability into account when modeling the evolution of protoplanetary disks.