Passive Irradiated Circumstellar Disks with an Inner Hole

Abstract

A model for irradiated dust disks around Herbig Ae stars is proposed. The model is based on the flaring disk model given by Chiang and Goldreich in 1997, but with the central regions of the disk removed. The inner rim of the disk is puffed up and is much hotter than the rest of the disk because it is directly exposed to the stellar flux. If located at the dust evaporation radius, its reemitted flux produces a conspicuous bump in the spectral energy distribution (SED) that peaks at 2-3 μm. We propose that this emission is the explanation for the near-infrared bump observed in the SEDs of Herbig Ae stars. We study for which stellar parameters this bump would be observable and find that it is the case for Herbig Ae stellar parameters but not for T Tauri stars, confirming what is found from the observations. We also study the effects of the shadow cast by the inner rim over the rest of the flaring disk. The shadowed region can be quite large, and under some circumstances the entire disk may lie in the shadow. This shadowed region will be much cooler than an unshadowed flaring disk, since its only heating sources are radial radiative diffusion and possible indirect sources of irradiation. Under certain special circumstances the shadowing effect can suppress, or even completely eliminate, the 10 μm emission feature from the spectrum, which might explain the anomalous SEDs of some isolated Herbig Ae stars in the recent sample of Meeus and colleagues. At much larger radii the disk emerges from the shadow and continues as a flaring disk toward the outer edge. The emission from the inner rim contributes significantly to the irradiation of this flaring disk. The complete semianalytical model, including structure of the inner edge, the shadowed region, and the flared outer part, is described in detail in this paper, and we show examples of the general behavior of the model for varying parameters.