The evolution and internal structure of Neptunes and sub-Neptunes

The importance of thermal conductivity in non-convective regions

Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

^★ Corresponding author: mark.eberlein@uzh.ch

Received: 21 July 2025
Accepted: 3 September 2025

Abstract

Context. Neptunes and sub-Neptunes are typically modeled under the assumption that the interior is adiabatic and consists of distinct layers. However, this assumption is oversimplified, as formation models indicate that composition gradients can exist. Such composition gradients can significantly affect the planetary thermal evolution by inhibiting convection. In non-convective layers, the heat transport is governed by multiple processes, and each is relevant in different regions within the planet.

Aims. We investigate how the evolution and internal structure of Neptunes and sub-Neptunes is affected when considering non-convective layers and the sensitivity of the results on the assumed thermal conductivity.

Methods. We simulated the planetary evolution of such objects with an appropriate implementation for the conductivity by considering thermal transport via radiation, electrons, and vibrational conductivity. We considered planetary masses of 5, 10, and 15 M_⊕; three different initial energy budgets; and two different primordial composition profiles.

Results. We find that the assumed conductivity significantly affects the planetary thermal evolution. We show that the commonly used conductivity assumption is inappropriate for modeling this planetary type. Furthermore, we find that the inferred radii deviate by ~20% depending on the assumed conductivity. The uncertainty on the primordial entropy in planets with non-convective layers leads to a difference of ~25% in the radii. This shows that the theoretical uncertainties are significantly larger than the observed ones and emphasizes the importance of these parameters.

Conclusions. We conclude that the characterization and modeling of intermediate-mass gaseous planets strongly depend on the modeling approach and the model assumptions. We demonstrate that the existence of composition gradients significantly affects the inferred radius. We suggest that more data on thermal conductivities, particularly for partially ionized material and mixtures, as well as better constraints on the primordial thermal state of such planets are necessary.