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

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.”

💡 Research Summary

This paper investigates the long‑term dynamical evolution of planetary systems that contain close‑in sub‑Neptunes (SNs) and a population of high‑eccentricity planetary embryos residing near 1 au after the protoplanetary gas disc has dissipated. The authors aim to determine whether collisions between the inner SNs and the outer embryos can erode the SNs’ hydrogen‑rich envelopes enough to populate the observed “radius gap” (a dearth of planets around 2 R⊕) and to explain the “radius cliff,” i.e., the scarcity of sub‑Neptunes with atmospheric mass fractions above ~10 %.

Methodology
Three SNs are placed at 0.1–0.5 au with masses drawn from a log‑normal distribution (mean ≈ 3 M⊕) and modest initial eccentricities (e ≈ 0.02). Their orbital spacing is set to 30 mutual Hill radii, reproducing the observed log‑uniform period distribution beyond ~20 days. A swarm of low‑mass embryos (M ≈ 0.05 M⊕) is distributed uniformly between 1 and 2 au. The embryos are assigned initial eccentricities of 0.7, 0.8, or 0.9 and numbers of 60, 80, or 100, yielding nine distinct initial configurations; each is simulated 20 times for statistical robustness.

The N‑body integrations are performed with the REBOUND code using the MERCURIUS hybrid integrator, with a timestep of 1/40 of the orbital period at 0.1 au, and run for 50 Myr (extended to 100 Myr for a test case). Embryos are treated as test particles (mutual embryo‑embryo gravity ignored) to accelerate the calculations, but a subset of full‑gravity runs confirms that this approximation does not qualitatively alter the outcomes. Collisions are detected when the distance between two bodies falls below the sum of their radii; grazing impacts that affect only the atmosphere are not modelled. After a collision, the embryo’s mass is added to the SN, and the updated mass is used for subsequent dynamics.

Atmospheric loss model
For each impact, the relative velocity (v_imp) and impact geometry are recorded. The fraction of atmospheric mass lost (X) is estimated using the scaling law derived by Kegerreis et al. (2020), which was calibrated on SPH simulations of giant impacts:

X ≈ 0.64 (v_imp/v_esc)² (M_emb/M_tot)¹ᐟ² (ρ_emb/ρ_core)¹ᐟ² f_M⁰·⁶⁵

where v_esc is the mutual escape speed, M_emb and M_tot are the embryo and total (embryo + core) masses, ρ denotes densities, and f_M is a volume‑weighted mass‑fraction term. The initial atmospheric mass fraction of each SN follows a log‑normal distribution with mean 3 % and σ = 0.3. The cumulative loss from successive impacts is applied sequentially, and the final planetary radius is computed using the Lopez & Fortney (2014) mass‑radius‑atmosphere relation.

Results

• Collision timing and frequency: High‑eccentricity embryos rapidly intersect the inner region; the first SN‑embryo impact typically occurs within ~2 Myr, and most collisions happen within the first 10 Myr. Higher initial embryo eccentricities and larger embryo populations increase the number of impacts per SN.
• Impact velocities: Because embryos approach on highly eccentric orbits, impact speeds range from 2 to 5 times the mutual escape velocity, well above the low‑velocity regime typical of planet‑planet mergers.
• Atmospheric erosion per impact: The kinetic‑only scaling predicts loss of 15–30 % of the SN’s envelope per collision. After 3–6 such events, the remaining atmospheric mass is roughly one‑third of the original value.
• Implications for the radius gap: Starting from an atmospheric mass fraction of ~3 %, the cumulative loss shrinks the planetary radius to ≲ 2 R⊕, placing the planet inside the observed gap. Even SNs that begin with larger envelopes (>5 %) can be driven into the gap after a modest number of impacts, offering a natural explanation for the gap’s presence at orbital periods where stellar irradiation is weak and photoevaporation is inefficient.
• Explanation of the radius cliff: Planets with initial atmospheric fractions >10 % experience severe erosion; after a few collisions their envelopes fall below the 10 % threshold, reproducing the observed paucity of large‑radius sub‑Neptunes (“radius cliff”).

Discussion and Limitations
The authors compare their impact‑erosion scenario with photoevaporation and core‑powered mass loss, emphasizing that the latter mechanisms depend strongly on stellar XUV flux and are most effective at short orbital periods. The impact mechanism, by contrast, is driven by the dynamical architecture (embryo eccentricities and numbers) and can operate at larger distances, potentially accounting for a radius gap that persists out to periods of several hundred days.

Key caveats include: (1) neglect of embryo‑embryo gravitational interactions in most runs, which could alter collision rates; (2) omission of grazing impacts that strip only the atmosphere without merging cores; (3) exclusion of thermal effects such as magma‑ocean formation and post‑impact outgassing, which may either enhance or mitigate atmospheric loss. The authors suggest that future work should incorporate full N‑body dynamics, SPH‑based thermodynamic impact modeling, and a broader exploration of initial embryo mass distributions.

Conclusions
The study demonstrates that a modest population of high‑eccentricity embryos can, through a series of high‑velocity impacts, remove a substantial fraction of the hydrogen envelopes of close‑in sub‑Neptunes. This process naturally produces planets inside the radius gap and explains the observed scarcity of sub‑Neptunes with atmospheric mass fractions above 10 %. The impact‑erosion pathway provides a complementary, dynamical route to sculpt the exoplanet radius distribution, especially at orbital distances where irradiation‑driven mechanisms are weak. The work opens new avenues for linking planetary system dynamics with atmospheric evolution and underscores the need for integrated N‑body and hydrodynamic impact simulations to fully capture the complexity of planet formation and evolution.