The Evolution and Internal Structure of Neptunes and Sub-Neptunes: The importance of thermal conductivity in non-convective regions

TL;DR

The paper investigates how composition gradients and non-convective layers influence the thermal evolution and interior structure of Neptunes and sub-Neptunes. It develops a non-adiabatic planetary evolution framework in MESA that includes radiative, vibrational, and electronic conductivities and tests two gradient profiles across masses $5$, $10$, and $15$ $M_$ with three primordial entropies. Key results show that the assumed conductivity can shift the radius by up to about $20\%$ and that the primordial entropy can alter radii by about $25\%$, often larger than observational errors. The work emphasizes the need for more laboratory and ab initio data on thermal conductivities of planetary mixtures at relevant pressures and temperatures, and tighter constraints on initial thermal states to enable reliable exoplanet characterization in this mass regime.

Abstract

Neptunes and sub-Neptunes are typically modeled under the assumption that the interior is adiabatic and consists of distinct layers. However, formation models indicate that composition gradients can exist. Such composition gradients can significantly affect the planetary thermal evolution. In non-convective layers, the heat transport is governed by multiple processes. 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 simulate the planetary evolution by considering thermal transport via radiation, electrons, and vibrational conductivity. We consider planetary masses of 5, 10 and 15 ME, three different initial energy budgets, and two different primordial composition profiles. 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. 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.

Figures (14)

• Figure 1: Initial profiles for the wide composition gradient, showing specific entropy, temperature, and composition as functions of normalized mass. The colors blue, orange, and yellow correspond to different primordial entropies. The dotted, solid, and dashed lines correspond to planets with a mass of 5 M$_\oplus$, 10 M$_\oplus$, and 15 M$_\oplus$, respectively. Top: Specific entropy vs. normalized mass of the initial model for the wide composition profile. The metallicity of the composition profile is shown by a black line, with its y-axis on the right-hand side. Bottom: Temperature vs. normalized mass of the initial model for the wide composition profile. The black line corresponds to the metallicity.
• Figure 2: Total conductivity vs. radius at $t=5$ Gyr for the warm $M_\text{p}$=10 M$_\oplus$ planet. The blue, green, and red curves represent Cond-1, Cond-2, and Cond-3, respectively. The largest contribution to the conductivity is shown by the line styles with solid, dotted, and dashed for radiation (opacity), vibration, and electron-dominated, respectively.
• Figure 3: Temperature and conductivity as a function of the radius at $t=5$ Gyr for our three cases of the "warm" planet with $M_\text{p}=10$ M$_\oplus$. In each panel, the temperature is shown in the left half of the cone, colored in blue, red, and yellow from cold to hot. The order of magnitude of the conductivity is shown in the right half of each cone, colored in different shades of brown. The areas with circular arrows indicate convective regions within the planet. The 1 bar radius is also indicated.
• Figure 4: Radius vs. time for a planet with $M_\text{p}=10$ M$_\oplus$. The solid, dashed, and dotted lines correspond to Cond-1, Cond-2, and Cond-3, respectively. The different colors correspond to the different initial energy states.
• Figure 5: The planetary temperature profile at various times. The three different conductivity cases are shown in the panels from left to right for the warm $M_\text{p}=10$ M$_\oplus$ model. The color indicated the planetary age, while the style of the line indicates whether the zone is convective (solid) or non-convective (dotted).