Fundamentals of interior modelling and challenges in the interpretation of observed rocky exoplanets

Abstract

Most our knowledge about rocky exoplanets is based on their measure of mass and radius. These two parameters are routinely measured and are used to categorise different populations of observed exoplanets. They are also tightly linked to the planet's properties, in particular those of the interior. As such they offer the unique opportunity to interpret the observations and potentially infer the planet's chemistry and structure. Required for the interpretation are models of planetary interiors, calculated a priori, constrained using other available data, and based on the physiochemical properties of mineralogical phases. This article offers an overview of the current knowledge about exoplanet interiors, the fundamental aspects and tools for interior modelling and how to improve the contraints on the models, along with a discussion on the sources of uncertainty. The origin and fate of volatiles, and their role in planetary evolution is discussed. The chemistry and structure of planetary interiors have a pivotal role in the thermal evolution of planets and the development of large scale properties that might become observables with future space missions and ground-based surveys. As such, having reliable and well constrained interior models is of the utmost importance for the advancement of the field.

Figures (9)

• Figure 1: Confirmed exoplanets with measured radius $<3\,R_\oplus$ and measured mass $<19\,M_\oplus$, excluding planets with mass uncertainty $>50\%$. Data are from the NASA Exoplanet Archive, accessed 05/12/2024, using the most recent entries for each planet. Effective blackbody temperature is calculated assuming 30% albedo. The $y$ axis shows bulk density normalised to the bulk density of an Earth-like composition at that planet mass, which is calculated using the scaling $R_p/R_\oplus = \left(M_p/M_\oplus\right)^{0.282}$zeng_growth_2019noack_parameterisations_2020. Marker size is proportional to planet radius. Bluer (redder) colours indicate radii further above (below) 1.6 $R_\oplus$, which is an illustrative radius often taken to separate rocky planets from volatile-rich ones rogers_most_2015. Nonetheless, the scatter of blue markers denser than the Earth composition line and red markers less dense than this line shows that this 1.6 $R_\oplus$ 'boundary' is not hard.
• Figure 2: Distribution of observed planets with orbital periods below 100 days as a function of received stellar flux (relative to Earth) and planet radius, showing two distinct populations of planets with a scarcity of planets between 1.5 and 2 R$_{\rm \Earth}$. The background shows the corresponding density distribution (arbitrary units) using a kernel density estimation algorithm. The histogram on the right side shows the marginal density distribution of planet radii. Data are from the NASA Exoplanet Archive, accessed Oct 29, 2025, using the most recent entries for each planet. Only planets with a relative radius error below 10% are shown here.
• Figure 3: The same as Figure \ref{['fig:temperature-density']}, but plotted in terms of planet mass. The coloured lines represent the density of a planet with constant composition: Mercury-like with a 70% iron core by mass (red, baumeister2023ExoMDNRapid); a theoretical pure-silicate body (yellow, baumeister2023ExoMDNRapid); a theoretical pure-water ice body (blue, zeng_growth_2019); and a theoretical Earth-like composition with 0.3% H2 by mass at 500K (green, zeng_growth_2019). The shaded area marks the location of the radius gap, assuming a nominal range between 1.5 and 2 R$_{\rm \Earth}$fulton_californiakepler_2017.
• Figure 4: Measured densities of seven different planets classified at least at some point in time as super-Mercuries in the literature, scaled to an Earth-like density and compared to a Mercury-like density (dotted lines). Labels on the x-axis refer to the respective publications; "M" refers to an update in the mass measurement and "R" for an update in the radius measurement.
• Figure 5: Pressure-temperature diagrams illustrating the ranges covered by the available experimental techniques along with some references for solar system planets and exoplanets. The figure on the right is modified from duffy_ultra-high_2019.