Analytical protostellar disk models 1: the effect of internal dissipation and surface irradiation on the structure of disks and the location of the snow line around Sun-like stars

Abstract

We construct a new set of self-consistent analytical disk models by taking into account both viscous and radiative sources of thermal energy. We analyze the non-isothermal structure of the disk across the mid-plane for optically thick disks, and use the standard two-temperature model in the case of optically thin disks. We deduce a set of general formula for the relationship between the mass accretion rate and the surface density profile. Our results recover those of Chiang & Goldreich in the optically thin regions, but extend their work for the opaque regions of the disk. For the purpose of illustration, we apply our theory in this paper to determine the structure of protostellar disks around T Tauri stars under a state of steady accretion and derive the corresponding radial distribution function of various disk properties such as surface density and temperature near the mid-plane. We calculate the position of the snow line around a sun-like T Tauri star, and deduce that it can evolve from well outside 10 AU during FU Orionis outbursts, to about 4 AU during passive accretion phase, to the present-day orbital radius of Venus and finally re-expand to over 2.2 AU during the protostellar- to-debris disk transition. This non-monotonous evolution of the snow line may provide some novel and deterministic explanation for the total water content and its isotopic composition of both Venus and the Earth. In the optically thin, outermost regions of the disk we find that the surface density profile of the dust varies roughly as 1/r, which is consistent with mm observations of spatially resolved disk of Mundy et al. (2000).