The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution

Abstract

Context. Exoplanets in the mass range between Earth and Saturn show a large radius, and thus density, spread for a given mass. Aims. We aim at understanding to which extent the observed radius spread is affected by the specific planetary parameters at formation and by planetary atmospheric evolution, respectively. Methods. We employ planetary evolution modeling to reproduce the mass-radius (MR) distribution of the 198 so far detected planets with mass and radius measured to the ≤45% and ≤15% level, respectively, and less massive than 108 M ⊕ . We simultaneously account for atmospheric escape, based on the results of hydrodynamic simulations, and thermal evolution, based on planetary structure evolution models. Since the high-energy stellar radiation affects atmospheric evolution, we account for the entire range of possible stellar rotation evolution histories. To set the planetary parameters at formation, we use analytical approximations based on formation models. Finally, we build a grid of synthetic planets with parameters reflecting those of the observed distribution.Results. The predicted radius spread reproduces well the observed MR distribution, except for two distinct groups of outliers (≈10% of the population). The first group consists of very close-in Saturn-mass planets with Jupiter-like radii for which our modeling underpredicts the radius likely because it lacks additional (internal) heating similar to that responsible for inflation in hot Jupiters. The second group consists of warm (∼400-800 K) sub-Neptunes, which should host massive primordial hydrogen-dominated atmospheres, but instead present high densities indicative of small gaseous envelopes (<1-2%). This suggests that their formation, internal structure, and evolution is different from that of atmospheric evolution through escape of hydrogen-dominated envelopes accreted onto rocky cores. On average the observed characteristics of low-mass planets (≤10-15 M ⊕ ) strongly depend on the impact of atmospheric escape, and thus of the evolution of the host star's activity level, while primordial parameters are less relevant. Instead, for more massive planets, the parameters at formation play the dominant role in shaping the final MR distribution. In general, the intrinsic spread in the evolution of the activity of the host stars can explain just about a quarter of the observed radius spread.

Conclusive Evidence for a Population of Water Worlds around M Dwarfs Remains Elusive

“…We find that planets with different equilibrium temperatures and atmospheric masses for a given core mass yield a natural spread in the mass-radius relation (see Figure 1) that does not vary dramatically for different stellar types. We do note that other factors that we have not taken into account, such as high-energy stellar luminosity variability (Kubyshkina & Fossati 2022) and observational uncertainty, will act to increase the spread in the sub-Neptune mass-radius relation. Nevertheless, we note that many high-mass planets 10M ⊕ in the sample from Luque & Pallé (2022), including GJ 436 b, GJ 3470 b, and GJ 1214, which have confirmed escaping H/He atmospheric detections, sit well above the mass-radius relations for both water-world and hydrogen atmosphere models that assume an initial boil-off scenario.…”

“…additional factors that can contribute to the mass-radius distribution spread, which we have not included in our models. As highlighted in Kubyshkina & Fossati (2022), variability in high-energy stellar luminosity (e.g., Tu et al 2015;Johnstone et al 2021;Ketzer & Poppenhaeger 2022) can increase the range in planet sizes since stars of different initial rotation rates will produce different X-ray/EUV flux and thus different massloss rates for the orbiting planets. In addition, observational uncertainties in planet radii will increase the spread in the mass-radius distribution due to purely statistical scatter.…”

Non-LTE effects in atmospheres of warm and hot Neptunes: implications for the atmospheric mass loss

“…Weiss and Marcy 2014;Hatzes and Rauer 2015;Ulmer-Moll et al 2019). Consideration in terms of atmospheric mass loss indicates that the mass-radius distribution is likely shaped by the atmospheric escape processes for low-mass planets (M pl <∼ 10 − 20 M ⊕ ) and retains the imprints of primordial parameters for more massive planets; furthermore, a significant fraction of planets with masses of a few tens of M ⊕ appear too dense to be explained in frame of the classic atmospheric evolution approach described in this chapter implying the planets starting with substantial hydrogen-helium atmospheres (Kubyshkina and Fossati 2022). These planets could be explained assuming the formation with water-rich composition (e.g.…”

“…Such an evolutionary path is typical for closein sub-giant planets, though it was shown that under more extreme conditions the Saturn-like planets can lose a considerable fraction of their atmospheres through the atmospheric mass loss (e.g. Pezzotti et al 2021a;Hallatt and Lee 2022;Kubyshkina and Fossati 2022).…”

LHS 1903 provides evidence for gas-depleted formation of planets around M-dwarfs

“…3, we plot the orbital periods of the LHS 1903 planets against their bulk densities normalised to an Earth-like density [49] and find that LHS 1903 e is nominally above the density valley [14]. Studies comparing well-characterised planets to formation and evolution [48,50] models concluded that planets with low equilibrium temperatures, such as LHS 1903 e, cannot evolve from a gaseous planet into a high-density state and thus must be formed rocky or water-rich. Therefore, the radius, density, and internal structure of planet e provides evidence that the numerous exoplanets in this intermediate radius range between rocky super-Earths and gaseous sub-Neptunes could have formed water-rich in a gasdepleted environment.…”