AN ANALYTIC MODEL FOR THE EVOLUTION OF A VISCOUS, IRRADIATED DISK

We describe an analytic model for the evolution of a protoplanetary disk heated by viscous accretion and radiation from the central star. The disk is assumed to be flared and viscosity is assumed to follow an alpha model, where viscosity is proportional to the local sound speed and scale height. In the inner disk, the midplane temperature is mainly determined by the energy released by the viscous accretion of material through the disk and onto the star. In the outer disk, stellar irradiation is the dominant heat source. A third regime is present in the innermost part of the disk, where viscous heating dominates but the opacity declines rapidly with increasing temperature due to dust grain sublimation. Changes in the protostellar radius and luminosity over time are readily incorporated into the model, although these have a relatively minor effect on the disk evolution. The model yields the surface density and midplane temperature at any point in space and time during the lifetime of the disk. It is especially suited to studies of planet formation that require a self-consistent model of disk evolution with minimal computational expense.