An Analytic Model for an Evolving Protoplanetary Disk with a Disk Wind

Abstract

We describe an analytic model for an evolving protoplanetary disk driven by viscosity and a disk wind. The disk is heated by stellar irradiation and energy generated by viscosity. The evolution is controlled by three parameters: (i) the inflow velocity toward the central star at a reference distance and temperature, (ii) the fraction of this inflow caused by the disk wind, and (iii) the mass-loss rate via the wind relative to the inward flux in the disk. The model gives the disk midplane temperature and surface density as a function of time and distance from the star. It is intended to provide an efficient way to calculate conditions in a protoplanetary disk for use in simulations of planet formation. In the model, disks dominated by viscosity spread radially while losing mass onto the star. Radial spreading is the main factor reducing the surface density in the inner disk. The disk mass remains substantial at late times. Temperatures in the inner region are high at early times due to strong viscous heating. Disks dominated by a wind undergo much less radial spreading and weaker viscous heating. These disks have a much lower mass at late times than purely viscous disks. When mass loss via a wind is significant, the surface density gradient in the inner disk becomes shallower, and the slope can become positive in extreme cases.