  The low water content of the terrestrial planets in the solar system suggests
that the protoplanets formed within the water snow line. Accurate prediction of
the snow line location moving with time provides a clue to constrain the
formation process of the planets. In this paper, we investigate the migration
of the snow line in protoplanetary disks whose accretion is controlled by
laminar magnetic fields, which have been proposed by various nonideal
magnetohydrodynamic (MHD) simulations. We propose an empirical model of the
disk temperature based on our nonideal MHD simulations, which show that the
accretion heating is significantly less efficient than in turbulent disks, and
calculate the snow line location over time. We find that the snow line in the
magnetically accreting laminar disks moves inside the current Earth's orbit
within 1 Myr after star formation, whereas the time for the conventional
turbulent disk is much longer than 1 Myr. This result suggests that either the
rocky protoplanets formed in such an early phase of the disk evolution, or the
protoplanets moved outward to the current orbits after they formed close to the
protosun.
