Models of the Structure and Evolution of Protoplanetary Disks

We review advances in the modeling of protoplanetary disks. This review will focus on the regions of the disk beyond the dust sublimation radius, i.e. beyond 0.1 - 1 AU, depending on the stellar luminosity. We will be mostly concerned with models that aim to fit spectra of the dust continuum or gas lines, and derive physical parameters from these fits. For optically thick disks, these parameters include the accretion rate through the disk onto the star, the geometry of the disk, the dust properties, the surface chemistry and the thermal balance of the gas. For the latter we are mostly concerned with the upper layers of the disk, where the gas and dust temperature decouple and a photoevaporative flow may originate. We also briefly discuss optically thin disks, focusing mainly on the gas, not the dust. The evolution of these disks is dominated by accretion, viscous spreading, photoevaporation, and dust settling and coagulation. The density and temperature structure arising from the surface layer models provide input to models of photoevaporation, which occurs largely in the outer disk. We discuss the consequences of photoevaporation on disk evolution and planet formation.