Time evolution of a viscous protoplanetary disk with a free geometry: Toward a more self-consistent picture
Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as r {sup –1} or aspect ratios of about 0.03-0.23. Accretion rates are also recurrently found around 10{sup –8}-10{sup –6} M {sub ☉} yr{sup –1} for disks that have already evolved. Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major consequences for modeling the disk evolution over millions of years and consequently planet migration. In the present paper, we develop a viscous evolution hydrodynamical numerical code that simultaneously determines the disk photosphere geometry and the mid-plane temperature. We then compare our results of long-term simulations with similar simulations of disks with a constrained geometry along the Chiang and Goldreich prescription (d lnH/d lnr = 9/7). We find that the constrained geometry models provide a good approximation of the disk surface density evolution. However, they differ significantly regarding the temperature-time evolution. In addition, we find that shadowed regions naturally appear at the transition between viscously dominated and radiation-dominated regions that falls in the region of planetary formation. We show that χ (photosphere height to pressure scale height ratio) cannot be considered a constant, which is consistent with the findings of Watanabe and Lin. Comparisons with observations show that all disks naturally evolve toward a shallow surface density disk (Σ∝r {sup –1}). The mass flux across the disk typically stabilizes in about 1 Myr.