Multi-Color Model for the Protoplanetary Disks HL Tau and HD142527

Protoplanetary disks are circumstellar disks of gas and dust, from which planets may eventually form or be in the process of forming. Recent direct imaging of them has enabled us to derive the density and temperature distributions. Interestingly they often show quite different features depending on the wavelength observed. The near-infrared emission is dominated by scattering of stellar light while the mm-and submm-wave emissions are dominated by thermal dust emission. Thus, the near-infrared emission traces a low density surface layer where stellar light is scattered toward us. The mm-and submm-wave emission trace the high density part of the disk near the mid plane. In order to explain the wavelength dependent images, we have constructed a passive disk model for HL Tau and HD142527. The former shows concentric rings in the ALMA image while the latter shows a highly asymmetric arc. Our models are based on the multi-color radiation transfer calculation. It takes account of radiation ranging from 100 nm to 3.16 mm. We used the M1 model to solve the radiative equilibrium. Our model gives some constraints on the optical properties of the dust.