Photoevaporation of circumstellar disks due to external far-ultraviolet radiation in stellar aggregates

When stars form within small groups (with N-* approximate to 100-500 members), their circumstellar disks are exposed to relatively little extreme-ultraviolet (EUV; hv > 13: 6 eV) radiation but a great deal of far-ultraviolet (FUV; 6 eV < hv < 13.6 eV) radiation (similar to10(3) times the local interstellar FUV field) from the most massive stars in the group. This paper calculates the mass-loss rates and evaporation timescales for circumstellar disks exposed to external FUV radiation. Previous work treated large disks and/or intense radiation fields in which the disk radius r(d) exceeds the critical radius r(g) where the sound speed in the FUV heated surface layer exceeds the escape speed; it has often been assumed that photoevaporation occurs for r(d) > r(g) and is negligible for r(d) < r(g). Since rg greater than or similar to 100 AU for FUV heating, this would imply little mass loss from the planet-forming regions of a disk. In this paper we focus on systems in which photoevaporation is suppressed because r(d) < r(g) and show that significant mass loss still takes place as long as r(d)/r(g) greater than or similar to0.1-0.2. Some of the gas extends beyond the disk edge ( or above the disk surface) to larger distances where the temperature is higher, the escape speed is lower, and an outflow develops. The resulting evaporation rate is a sensitive function of the central stellar mass and disk radius, which determine the escape speed, and the external FUV flux, which determines the temperature structure of the surface layers and outflowing gas. Disks around red dwarfs, low-mass stars with M-* less than or similar to0.5 M-circle dot, are evaporated and shrink to disk radii r(d) less than or similar to15 AU on short timescales t less than or similar to10 Myr when exposed to moderate FUV fields with G(0) = 3000 (where G(0) = 1.7 for the local interstellar FUV field). The disks around solar-type stars are more durable. For intense FUV radiation fields with G0 30; 000, however, even these disks shrink to r(d) less than or similar to15 AU on timescales t similar to 10 Myr. Such fields exist within about 0.7 pc of the center of a cluster with N-* approximate to 4000 stars. If our solar system formed in the presence of such strong FUV radiation fields, this mechanism could explain why Neptune and Uranus in our solar system are gas-poor, whereas Jupiter and Saturn are relatively gas-rich. This mechanism for photoevaporation can also limit the production of Kuiper Belt objects and can suppress giant planet formation in sufficiently large clusters, such as the Hyades, especially for disks associated with low-mass stars.