Long-Term Evolution of Close-in Sub-Neptunes and Outer Planetary Embryos: Atmospheric Mass Loss and Origin of Planets Inside and Outside the Radius Gap

TL;DR

This paper demonstrates that late-stage collisions between inner close-in sub-Neptunes and outer high-eccentricity planetary embryos can strip substantial atmospheric mass, producing planets with radii inside the observed radius gap and shaping the radius distribution. Using N-body simulations with post-processed atmospheric-loss calculations, the authors show collision velocities of roughly 2–5 times the escape speed, per-collision losses of about 15–30%, and cumulative losses that commonly reduce atmospheres from a few percent to well below 1%. The results yield bimodal radius distributions with gap-forming peaks near 1.5 R⊕ and 2.7 R⊕ under plausible initial conditions, and they remain robust to full N-body dynamics and to variations in initial atmospheric fractions. Collectively, the work provides a viable, gravity-driven mechanism for creating planets inside and near the radius gap, and it offers testable predictions about eccentricities and period–radius correlations that complement irradiation-driven models of atmospheric escape.

Abstract

As a byproduct of sub-Neptune formation, planetary embryos with high eccentricity can remain in outer orbits, near 1 au from the star. In this work, we investigate the long-term evolution of systems consisting of close-in sub-Neptunes (SNs) and outer high-eccentricity embryos. Our analysis focuses on collisions between SNs and embryos, particularly their atmospheric mass loss. We performed N-body simulations for various initial eccentricities and numbers of embryos. We analyzed the impact-induced atmospheric loss using post-processing methods, finding that the embryos and SNs collide at high speeds on timescales of several million years, leading to the loss of the SNs' atmospheres. Depending on the embryos' eccentricity and the orbital radius of the SNs, the impact velocity can be quite high, ranging from 2 to 5 times the escape velocity. On average, about 15%-30% of the atmosphere is dissipated per collision, so after 3-6 collisions, the atmospheric mass of an SN is reduced to about 1/3 of its initial value. Collisions between SNs and embryos can thus explain the presence of planets within the radius gap. Depending upon the initial eccentricity and the number of remaining embryos, additional collisions can occur, potentially accounting for the formation of the radius gap. This study also indicates that collisions between remaining embryos and SNs may help to explain the observed rarity of SNs with atmospheric mass fractions greater than 10%, commonly termed the "radius cliff."

Figures (8)

• Figure 1: Time evolution of our typical simulation for $N_{\text{ini}} = 80$ with $e_{\text{ini}} = 0.8$. (a) The blue line represents the collisions between SNs and embryos, the red line represents the ejection of embryos, and the purple line represents the remaining embryos. (b) The impact velocities between SNs and embryos. (c) The atmospheric mass fractions of the innermost, middle, and outermost SNs are represented by the blue, green, and red lines, respectively. (d) Time intervals between successive SN–embryo collisions for the three SNs (blue, green, and red circles), showing that the impact intervals increase over time, indicating longer impact-erosion timescales at later stages.
• Figure 2: Summary of collisions between SNs and embryos in all simulations with $N_{\text{ini}}$=80 and different initial embryo eccentricities. (a)--(c) Impact velocities when SNs collide with embryos. The dashed line is a rough estimate of the maximum impact velocity. (d)--(f) Fractional atmospheric mass loss during collisions between SNs and embryos. The same colors represent collisions within the same system.
• Figure 3: Relationship between the positions of SNs and (a)--(c) the number of collisions experienced, and (d)--(f) the remaining atmospheric mass fraction. In panel (d), a value of $10^{-4}$ corresponds to complete atmospheric stripping. The dashed horizontal line marks a remaining atmospheric mass equal to 10% of the initial atmospheric mass.
• Figure 4: The initial radius distribution (thick orange histogram) and final radius distribution (thick black histogram) of SNs after 50 Myr across different models. Histograms of different colors represent SNs with different final atmosphere fractions. (a)--(c) $N_\text{ini} = 60, 80,$ and 100 and $e_\text{ini} = 0.9$. (d)--(f) $N_\text{ini} = 60, 80,$ and 100 and $e_\text{ini} = 0.8$. (g)--(i) $N_\text{ini} = 60, 80,$ and 100 and $e_\text{ini} = 0.7$. The green, blue, and gray dashed lines represent the observed peak for super-Earths (1.5 $R_\oplus$), the position of the radius valley, and the peak for SNs (2.7 $R_\oplus$), respectively. The color indicates the atmospheric percentages (see color bar).
• Figure 5: The same as Figure \ref{['fig:fig4']}, but showing the occurrence of planets by combining the initial and final distributions in the orbital-period--planet-radius plane. Contours in these plots connect points of equal probability density. The densities shown, estimated using kernel-density estimation, represent statistical probability densities that indicate the likelihood of finding planets with specific combinations of orbital period and radius. The integral of the density over any region gives the probability of finding planets within that area. The unit area is defined in logarithmic space, where the units are $\log_{10}$(days) for the orbital period and $\log_{10}$($R_{\oplus}$) for the planet radius. The density is therefore expressed in units of 1/[$\log_{10}$(days) $\times$$\log_{10}$($R_{\oplus}$)], and the integral over the entire space is normalized to unity.