  Evolution of a snow line in an optically-thick protoplanetary disk is
investigated with numerical simulations. The ice-condensing region in the disk
is obtained by calculating the temperature and the density with the 1+1D
approach. The snow line migrates as the mass accretion rate (\dot{M}) in the
disk decreases with time. Calculations are carried out from an early phase with
high disk accretion rates (\dot{M} \sim 10^{-7} M_sun/yr) to a later phase with
low disk accretion rates (\dot{M} \sim 10^{-12} M_sun/yr) using the same
numerical method. It is found that the snow line moves inward for \dot{M} >
10^{-10} M_sun/yr, while it gradually moves outward in the later evolution
phase with \dot{M} < 10^{-10} M_sun/yr. In addition to the silicate opacity,
the ice opacity is taken into consideration. In the inward migration phase, the
additional ice opacity increases the distance of the snow line from the central
star by a factor of 1.3 for dust grains < 10 micro-meter in size and 1.6 for >
100 micro-meter. It is inevitable that the snow line comes inside the Earth's
orbit in the course of the disk evolution, if the alpha viscosity parameter is
in a range 0.001-0.1, the dust-to-gas mass ratio is higher than a tenth of the
solar abundance value, and the dust grains are smaller than 1 mm. The formation
of water-devoid planetesimals in the terrestrial planet region seems to be
difficult throughout the disk evolution, which imposes a new challenge to
planet formation theory.
