  We develop a pebble-driven model to study the formation and evolution of
planets around stars in the mass range of 0.08 and 1 solar mass. The growth and
migration of a large number of individual protoplanetary embryos are simulated
in a population synthesis manner. We test two hypotheses for the birth
locations of embryos: at the water ice line or log-uniformly distributed over
entire protoplanetary disks. Two types of disks with different turbulent
viscous parameters alpha of 1e-3 and 1e-4 are investigated, to shed light on
the role of outward migration of protoplanets. The forming planets are compared
with the observed exoplanets in terms of masses, semimajor axes, metallicities,
and water contents. We find that gas giant planets are likely to form when the
characteristic disk sizes are larger, the disk accretion rates are higher, the
disks are more metal-rich and/or their stellar hosts are more massive. Our
model shows that 1) the characteristic mass of super-Earth is set by the pebble
isolation mass. Super-Earth masses increase linearly with the mass of its
stellar host, corresponding to one Earth mass around a late M-dwarf star and 20
Earth masses around a solar-mass star. 2) The low-mass planets up to 20 Earth
masses can form around stars with a wide range of metallicities, while massive
gas giant planets are preferred to grow around metal-rich stars. 3) Super-Earth
planets that are mainly composed of silicates, with relatively low water
fractions can form from protoplanetary embryos at the water ice line in weakly
turbulent disks where outward migration is suppressed. However, if the embryos
are formed over a wide range of radial distances, the super-Earths would end up
having a distinctive, bimodal composition in water mass. Our model succeeds in
quantitatively reproducing several important observed properties of exoplanets
and correlations with their stellar hosts.
