The effect of dynamic temperatures on pebble dynamics and planet formation

¹ Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
² Netherlands Space Research Institute (SRON), Leiden, The Netherlands
³ Centre for ExoLife Sciences, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

^★ Corresponding author; castrejon@astro.rug.nl

Received: 3 July 2023
Accepted: 2 September 2024

Abstract

Context. To date, more than 5000 exoplanets have been discovered. The large majority of these planets have a mass between 1 and 17 M_⊕, making them so-called super-Earths and mini-Neptunes. The exact formation process for this abundant planet population has not yet been fully constrained.

Aims. Recent studies on the formation of these planets make various assumptions with regard to the disk. The primary mass budget, held in pebbles, is either assumed to have a constant size or is parametrized as a flux. Simplifications of the temperature structure, in the form of a static power law, do not consider the temperature evolution and high magnitudes of heating in the inner part of the disk. In this study, we aim to investigate the effect these simplifications of temperature and pebble sizes have on the pebble densities and resulting planet populations.

Methods. To constrain the timescales needed to form super-Earths, we developed a model for exploring a large parameter space. We included the effect of two different temperature prescriptions on a viscously accreting and spreading disk. We formed a pebble reservoir utilizing a simplified conversion timescale with a time- and radially dependent Stokes number for the dust. We then tracked the temporal evolution of the surface densities of gas, dust, and pebbles. Pebbles were allowed to drift and be accreted onto a growing protoplanet. As a planet grows, it exerts a torque on the disk, carving out a gap and affecting the pebble drift, before halting the growth of the planet.

Results. We find that viscous heating has a significant effect on the resulting mass populations, with the static power law showing smaller planets within 10 AU. Inside the dust-sublimation line, usually within 0.5 AU, planet formation is reduced due to the loss of planet-forming material. Our model replicates observed planet masses between Earth and mini-Neptune sizes at all radial locations, with the most massive planets growing in the intermediate turbulence of α = 10⁻³.

Conclusions. We conclude that a self-consistent treatment of temperature, with the inclusion of a dust-sublimation line, is important and could explain the high occurrence of super-Earths at short orbital separations.