  Population synthesis studies into planet formation have suggested that
distributions consistent with observations can only be reproduced if the actual
Type I migration timescale is at least an order of magnitude longer than that
deduced from linear theories. Although past studies considered the effect of
the Type I migration of protoplanetary embryos, in most cases they used a
conventional formula based on static torques in isothermal disks, and employed
a reduction factor to account for uncertainty in the mechanism details.
However, in addition to static torques, a migrating planet experiences dynamic
torques that are proportional to the migration rate. These dynamic torques can
impact on planet migration and predicted planetary populations. In this study,
we derived a new torque formula for Type I migration by taking into account
dynamic corrections. This formula was used to perform population synthesis
simulations with and without the effect of dynamic torques. In many cases,
inward migration was slowed significantly by the dynamic effects. For the
static torque case, gas giant formation was effectively suppressed by Type I
migration; however, when dynamic effects were considered, a substantial
fraction of cores survived and grew into gas giants.
