Population synthesis of planet formation using a torque formula with dynamic effects

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.