  We investigate the conditions under which the regular satellites of Jupiter
and Saturn formed. The final stage of giant planet accretion is thought to
occur slowly over a relatively long, 10 Myr, timescale. Gas accretion during
this stage, through a completely or partially opened gap in the solar nebula,
occurs slowly allowing for the condensation of ices, and incomplete
differentiation, seen in the regular satellites of the giant planets.
Furthermore, the dichotomy seen in the Jovian and Saturnian systems may be
explained as this infall wanes or is completely shutoff as a result of gap
opening or global depletion of gas in the solar nebula. We present
one-dimensional simulations of circumplanetary disks that couple the viscous
transport of material with the loss of mass at the disk outer edge by
ultraviolet photoevaporation as well as the infall of material from the solar
nebula. We find that the circumplanetary disks of these protoplanets are
truncated, as a result of photoevaporation, at a range of values with the mean
corresponding to $\approx$ 0.16 Hill radii. These truncation radii are broadly
consistent with the current locations of the regular satellite systems of
Jupiter and Saturn. We also find that photoevaporation can successfully act as
a clearing mechanism for circumplanetary nebulae on the potentially short
timescales, 100-10,000 yr, over which mass accretion from the solar nebula
wanes as a result of gap opening. Such a rapid clearing of the circum-Jovian
disk may be required to explain the survival of the Galilean satellites.
