Young Planets around Young Accreting Stars: I. Migration and Inner Stalling Orbits

Abstract

Planet migration within inner protoplanetary disks significantly influences exoplanet architectures. We investigate various migration mechanisms for young planets close to young stars. To quantify the stochastic migration driven by turbulent disks, we incorporate planets into existing 3-D MHD disk simulations of magnetospheric accretion. Besides the stochastic torque, we identify periodic torques from slowly evolving disk substructures farther out. We quantify these turbulent torques analytically using a modified Gaussian process. Then, using the disk structure in our simulation, we calculate migration timescales of various processes, including the smooth Type I/II migration, planet-star tidal interaction, magnetic dipole-dipole interaction, unipolar induction, and aerodynamical drag with the magnetosphere. Since our inner MHD turbulent disk reveals a very low surface density ($\sim 0.01$ g/cm$^{2}$), the resulting disk migration is significantly slower than previously estimated. Earth-mass planets have the migration timescale in the inner MHD turbulent disk exceeding the Hubble time, effectively stalling at the deadzone inner boundary ($R_{\mathrm{DZIB}}$). Only giant planets could migrate inward within the turbulent disk, and may stall at the magnetospheric truncation radius ($R_T$). A simplified planet population synthesis demonstrates that, at the end of the disk phase, all planets around solar-mass stars typically stall at $\lesssim$0.1 au since $R_T\sim R_{\mathrm{DZIB}}$. However, around 2 $M_{\odot}$ stars, higher-mass planets stall significantly closer to the star compared to low-mass planets, due to $R_T\ll R_{\mathrm{DZIB}}$. These results are consistent with recent observations on exoplanet demographics around different types of stars. Finally, turbulence in the low-density disk is unable to break the resonant planets, and thus young planets in resonances may be abundant.