An analysis of two-layer models for circumstellar disks

The two-layer disk models of Chiang & Goldreich (1997, henceforth CG) and its derivatives are popular among astronomers because of their simplicity and the clear predictions they make for the SEDs of T Tauri stars and Herbig Ae/Be stars. Moreover, they can be computed quickly, which is a great advantage when fitting observations using automated procedures. In this paper we wish to assess the accuracy and reliability of 2-layer models, by comparing them to detailed vertical structure models with accurate 1+1D radiative transfer. We focus on the shape of the SED, and the predicted height and "flaring index" of the disk. We first consider models where scattering is set to zero. We find that 2-layer models overestimate significantly the near-infrared flux, and we suggest a simple way of correcting this effect, at least in part. At longer wavelengths, the SED of two-layer models often show a two-bump structure, which is absent in 1+1D models. Nevertheless, overall agreement is reasonably good, and the differences are in most cases within 30%. At (sub)-mm wavelengths the differences may even be less. The shape of the disk, as measured by its pressure and surface scale height and by the flaring angle are also well reproduced by two-layer models. When scattering is included in the 1+1D models, the differences become larger, especially in the near-infrared. We suggest simple ways to include scattering in two-layer models and discuss their reliability. We do not compare the two-layer models to full 2D/3D models, so the conclusions remain valid only within the annulus-by-annulus approximation.