How stellar mass and disc size shape the formation and migration of super-Earths

The occurrence rate of close-in super-Earths is higher around M-dwarfs compared to stars of higher masses. In this work, we aim to understand how the super-Earth population is affected by the stellar mass, the size of the protoplanetary disc, and viscous heating. We utilised a standard protoplanetary disc model with both irradiated and viscous heating, together with a pebble accretion model, to simulate the formation and migration of planets. We find that if the disc is heated purely through stellar irradiation, inward migration of super-Earths is very efficient, resulting in the close-in super-Earth fraction increasing with increasing stellar mass. In contrast, when viscous heating is included, planets can undergo outward migration, delaying migration to the inner edge of the protoplanetary disc, which causes a fraction of super-Earth planets to grow into giant planets instead. This results in a significant reduction of inner super-Earths around high-mass stars and an increase in the number of giant planets, both of which mirror observed features of the planet population around high-mass stars. This effect is most pronounced when the protoplanetary disc is large, since such discs evolve over a longer timescale. We also tested a model when we injected protoplanets at a fixed time early on in the disc lifetime. In this case, we find that the fraction of close-in super-Earths decreases with increasing stellar mass in both the irradiated case and viscous case, since longer disc lifetimes around high-mass stars allow for planets to grow into giants instead of super-Earths for most injection locations.