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

TL;DR

This paper addresses why close-in super-Earths are more common around M-dwarfs and how disc structure and heating influence their formation and migration. It employs a population-synthesis framework based on pebble accretion in two disc heating regimes—pure irradiation and irradiation plus viscous heating—to track core growth, migration, and gas accretion across a range of stellar masses and disc sizes. The main finding is that irradiation-only discs drive strong inward migration, producing more close-in SE with increasing stellar mass, whereas viscous heating creates outward migration in parts of the disc, delaying inward migration and boosting giant-planet formation, especially in large discs; this reduces the inner SE population around higher-mass stars. The study highlights the importance of disc thermal physics, disc size, and injection timing in shaping planetary system architectures and provides testable predictions for future observations of planet populations and disc structures.

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.

Figures (16)

• Figure 1: Disc lifetimes (top) and disc-to-star mass ratios (bottom) for discs with varying stellar masses and initial disc sizes. For a fixed disc mass, the disc lifetime increases with increasing stellar mass, while a larger disc also results in longer disc lifetime. Large discs ($\gtrsim$100 AU) around stars more massive than $\sim$1.5 $M_\odot$ are gravitationally unstable in some regions of the discs. This region is marked by a hatched pattern.
• Figure 2: Migration coefficient, $f_{\rm I,visc}$, as a function of distance to the star and planet mass for a solar-mass star with a disc size of 71 AU at $t=0$. Inside of the transition radius ($\sim$5 AU), the disc is viscously heated, and for certain masses, the planet experiences outward migration. The sharp switch to inward migration at $\sim$0.2 AU is caused by the significant decrease in opacity due to the evaporation of silicate and metal grains, which occurs at $\sim$1000 K. We also show $f_{\rm I, visc}$ at different times and for different stellar masses and disc sizes in appendix \ref{['app:mig_coeff']}.
• Figure 3: Example of the resulting semi-major axes and masses of planets injected around a solar-mass star for two different initial disc sizes, 150 AU (top) and 50 AU (bottom). Here, only irradiation heating is considered. We indicate the planets that we define as close-in super-Earths (blue) and giants (red). The large disc forms significantly more giant planets due to having more available mass and a longer lifetime.
• Figure 4: The fraction of close-in super Earths ($r < 0.2$ AU) for a range of stellar masses (x-axis) and disc sizes (colours). In all cases, no super-Earths are formed around stars with a mass of $0.1\, M_\odot$. When only considering discs heated by irradiation (left), the fraction of super-Earths increases with increasing stellar mass regardless of disc size. In the viscously heated case (right), the fraction of super-Earths reaches a maximum at 0.5 $M_\odot$ and then declines slightly for large discs (90 AU or larger). For smaller discs (30 and 60 AU), the super-Earth fraction peaks at 1 $M_\odot$, while for larger discs it peaks at 0.5 $M_\odot$.
• Figure 5: Growth tracks of a single planet injected at $r=3$ AU and $t=10^4$ yr. In the irradiated case (left), this results in the formation of a super-Earth at the inner disc edge for all stellar masses and disc sizes. In the viscous heating case (right), the protoplanet grows into a giant planet for high stellar masses as well as for solar-mass stars with sufficiently large discs.