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

## TL;DR

This study uses disc models with irradiation and viscous heating to explore how stellar mass and disc size influence super-Earth formation and migration, revealing that heating mechanisms significantly affect planet populations.

## Contribution

It introduces a comprehensive simulation combining irradiation and viscous heating effects to explain observed variations in super-Earth and giant planet occurrence around different stellar masses.

## Key findings

- Inward migration dominates with pure irradiation heating.
- Viscous heating can cause outward migration, delaying inward movement.
- Higher stellar mass correlates with fewer close-in super-Earths and more giants.

## Abstract

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 both the stellar mass, the size of the protoplanetary disc, and viscous heating. We utilise 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, inwards 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 outwards migration, delaying migration to the inner edge of the protoplanetary disc, which causes a fraction of super-Earth planets to grow to become 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 time-scale. We also test a model when we inject protoplanets at a fixed time early on in the disc lifetime. In this case, 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 allows for planets to grow into giants instead of super-Earths for most injection locations.