Dust distribution in gas disks: A model for the ring around HR 4796A

There have been several model analyses of the near- and mid-IR flux from the circumstellar ring around HR 4796A. In one set of models, the 10 and 18 mum IR flux has been attributed to the reprocessing of stellar radiation by micron-size particles. Since these particles are being blown away, on a dynamical timescale, by the radiation pressure of HR 4796A, they must be continually replenished by the collisional fragments of larger particles. If the ring appearance persisted for the life span (8 x 10(6) yr) of HR 4796A, a parent-particle reservoir with a total mass greater than 300 M-circle plus would be needed. In order to avoid being conspicuous at longer wavelengths, most of the mass must be contained in parent particles larger than 20-40 cm. In other models, it has been suggested that the IR flux from the rings is emitted by sufficiently large particles that survive the radiative blowout by their host star. In a gas-free ring, greater than 3.2 mum size particles would survive radiative blowout and a total of 10(-2) M-circle plus would be adequate to account for the observed IR flux. But, in the vicinity of a young star, the possibility that the dust ring is embedded within a residual protostellar gas disk cannot be ruled out. In a gas-rich environment, larger sizes (>100 mum) are needed for the particles to survive the radiative blowout. The total dust mass required to account for the IR flux is less than 10(-1) M-circle plus. The combined influence of gas and stellar radiation may also account for the observed sharp inner boundary and rapidly fading outer boundary of the ring. The pressure gradient induced by a small (10%) amplitude variation in the surface density distribution of a low-mass gaseous disk would be sufficient to modify the rotation speed of the gas. The resulting hydrodynamic drag on modest-size (>100 mum) particles would be adequate to compensate for the turbulent stirring, radiative drag, and radiation pressure such that they remain gravitationally bound to the system. The required surface density variation of the gas may be induced by (1) the perturbation of a low-mass planet or the binary companion HR 4796B, (2) the photoevaporation of the disk, or (3) the variations in the viscous angular momentum transport and mass diffusion rate in the disk. We show that the structure of the dust ring is preserved during and after the gas is being depleted such that similar rings may be common among early-type stars.