We calculate the rate of photoevaporation of a circumstellar disk by energetic radiation (FUV, 6eV $<h u<$13.6eV; EUV, 13.6eV $<h u<$0.1keV; and Xrays, $h u>0.1$keV) 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 $0.3-7 {rm M}_{odot}$. Contrary to the EUV photoevaporation scenario, which creates a gap at about $r_gsim 7 (M_*/1{rm M}_{odot})$ 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 $sim 2$) 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 $sim 10$ AU under favourable circumstances. Photoevaporation timescales for M$_* sim 1{rm M}_{odot}$ stars are estimated to be $sim 10^6$ years, after the onset of disk irradiation by FUV and X-rays. Disk lifetimes do not vary much for stellar masses in the range $0.3-3$M$_{odot}$. More massive stars ($gtrsim 7 {rm M}_{odot}$) lose their disks rapidly (in $sim 10^5$ 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.
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