When stars form within small groups (with N Ã % 100 500 members), their circumstellar disks are exposed to relatively little extreme-ultraviolet (EUV; h > 13:6 eV) radiation but a great deal of far-ultraviolet (FUV; 6 eV < h < 13:6 eV) radiation ($10 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 r g k 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 k 0:1 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 Ã P 0:5 M , are evaporated and shrink to disk radii r d P15 AU on short timescales t P10 Myr when exposed to moderate FUV fields with G 0 ¼ 3000 (where G 0 ¼ 1:7 for the local interstellar FUV field). The disks around solar-type stars are more durable. For intense FUV radiation fields with G 0 ¼ 30; 000, however, even these disks shrink to r d P 15 AU on timescales t $ 10 Myr. Such fields exist within about 0.7 pc of the center of a cluster with N Ã % 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.

From the masses of planets orbiting our Sun, and relative elemental abundances, it is estimated that at birth our Solar System required a minimum disk mass of ∼0.01 M within ∼100 AU of the star 1-4 . The main constituent, gaseous molecular hydrogen, does not emit from the disk mass reservoir 5 , so the most common measure of the disk mass is dust thermal emission and lines of gaseous carbon monoxide 6 . Carbon monoxide emission generally probes the disk surface, while the conversion from dust emission to gas mass requires knowl-1

Using Keck/HIRES spectra (Δ v∼7 km s −1 ) we analyze forbidden lines of [OI] 6300 Å, [OI] 5577 Åand [SII] 6731 Åfrom 33 T Tauri stars covering a range of disk evolutionary stages. After removing a high-velocity component (HVC) associated with microjets, we study the properties of the low-velocity component (LVC). The LVC can be attributed to slow disk winds that could be magnetically (magnetohydrodynamic) or thermally (photoevaporative) driven. Both of these winds play an important role in the evolution and dispersal of protoplanetary material. LVC emission is seen in all 30 stars with detected [OI] but only in two out of eight with detected [SII], so our analysis is largely based on the properties of the [OI] LVC. The LVC itself is resolved into broad (BC) and narrow (NC) kinematic components. Both components are found over a wide range of accretion rates and their luminosity is correlated with the accretion luminosity, but the NC is proportionately stronger than the BC in transition disks. The full width at half maximum of both the BC and NC correlates with disk inclination, consistent with Keplerian broadening from radii of 0.05 to 0.5 au and 0.5 to 5 au, respectively. The velocity centroids of the BC suggest formation in an MHD disk wind, with the largest blueshifts found in sources with closer to face-on orientations. The velocity centroids of the NC, however, show no dependence on disk inclination. The origin of this component is less clear and the evidence for photoevaporation is not conclusive.

We calculate the rate of photoevaporation of a circumstellar disk by energetic radiation (FUV, 6eV < hν <13.6eV; EUV, 13.6eV < hν <0.1keV; and Xrays, hν > 0.1keV) from its central star. We focus on the effects of FUV and X-ray photons since EUV photoevaporation has been treated previously, and consider central star masses in the range 0.3 − 7M ⊙ . Contrary to the EUV photoevaporation scenario, which creates a gap at about r g ∼ 7 (M * /1M ⊙ ) AU and then erodes the outer disk from inside out, we find that FUV photoevaporation predominantly removes less bound gas from the outer disk. Heating by FUV photons can cause significant erosion of the outer disk where most of the mass is typically located. X-rays indirectly increase the mass loss rates (by a factor ∼ 2) by ionizing the gas, thereby reducing the positive charge on grains and PAHs and enhancing FUV-induced grain photoelectric heating. FUV and X-ray photons may create a gap in the disk at ∼ 10 AU under favourable circumstances. Photoevaporation timescales for M * ∼ 1M ⊙ stars are estimated to be ∼ 10 6 years, after the onset of disk irradiation by FUV and X-rays. Disk lifetimes do not vary much for stellar masses in the range 0.3 − 3M ⊙ . More massive stars ( 7M ⊙ ) lose their disks rapidly (in ∼ 10 5 years) due to their high EUV and FUV fields. Disk lifetimes are shorter for shallow surface density distributions and when the dust opacity in the disk is reduced by processes such as grain growth or settling. The latter suggests that the photoevaporation process may accelerate as the dust disk evolves.