Observational breakthrough has been achieved in characterizing the properties of protoplanetary disks and extrasolar planets in the last decade. We thus gain a better understanding on both the birth conditions and the end products of planets. Meanwhile, more advanced theoretical and numerical models are required to establish the bridge between these two based on evolving planet formation theories. We develop the pebble-driven core accretion model to study the formation and evolution of planets around stars in the range of 0.08 M⊙ and 1 M⊙. By Monte Carlo sampling of their initial conditions, the growth and migration of a large number of individual protoplanetary embryos are simulated in a population synthesis mannar. Two hypothesis are proposed for the birth locations of embryos, at the water ice line or log-uniformly distributed over distance in protoplanetary disks. Two types of disks with different turbulent viscous parameters at of 10−3 and 10−4are also investigated.
Our model shows that 1) the characteristic planet mass is set by the pebble isolation mass. It increases linearly with the stellar mass, corresponding to one Earth mass around a Trappist-1 star and 20 Earth mass around a solar-mass star. 2) The low-mass planets up to 20 Earth mass can form around stars with a wide range of metallicities, while massive gas giant planets are preferred to grow around metal rich stars. 3) The super-Earth planets mainly composed of silicates with relatively low water fractions can form from the seeds at the water ice line in less turbulent disks. However, if the embryos are formed over a wide range of radial distances, they would end up into distinctive, bimodal composition in water mass. Altogether, the model succeeds in quantitatively reproducing several important observed properties and correlations among exoplanets.
