Why Massive Rocky Planets Tend Toward Hydrogen Atmospheres

Abstract

msf:48280 v2.0 rebuilds the atmospheric-retention problem for massive rocky planets as a conditional evolutionary framework rather than a single mass threshold. The central proposition is: given access to hydrogen-bearing gas, increasing planetary gravitational binding generally enlarges the region of parameter space in which low-molecular-weight H/H₂/He inventories can survive. This is not a deterministic composition law. Planetary mass alone does not determine whether a rocky planet ends with a hydrogen-rich atmosphere. The final state depends on several coupled processes: gas supply, disk timing, nebular capture, interior–atmosphere chemistry, upper-atmosphere heating, Jeans escape, hydrodynamic escape, diffusion-limited transport, chemical fractionation, nonthermal loss, impacts, secondary outgassing, and long-term replenishment. The relevant thermal escape variable is the exobase Jeans parameter: λ_s,exo = G M_p m_s / (k_B T_exo r_exo). This uses the upper-atmosphere temperature and exobase radius rather than surface temperature. Hydrogen has the smallest Jeans parameter among common atmospheric species and is therefore among the easiest constituents to lose thermally. Greater gravity does not “lock hydrogen first.” It instead makes hydrogen progressively harder to remove as the gravitational potential deepens. When strong XUV heating produces a collisional expanding atmosphere, hydrodynamic escape can replace the simple Jeans regime. A commonly used limiting scaling is: Ṁ_EL ≈ η π R_p R_XUV² F_XUV / (G M_p K_tide), but this is treated only as a regime-dependent benchmark, not as a universal atmospheric-loss law. Hydrogen escape can also become limited by upward diffusion through heavier atmospheric species. The manuscript therefore separates: total atmospheric loss from species-selective loss and fractionation. The long-term hydrogen inventory is represented schematically as: dM_H/dt = nebular supply + outgassing + recycling − thermal loss − nonthermal loss − impact loss. This ledger makes clear why similar planetary masses can produce very different atmospheric endpoints. Formation history is equally important. A massive rocky core may efficiently capture nebular gas when gas is available. Models also show that continued H₂ accretion can outlast the finite oxygen inventory available for converting incoming hydrogen into water. But a planet forming in a gas-depleted environment may remain hydrogen-poor even when its gravity would otherwise favor retention. The manuscript therefore uses a four-stage logic: supply → capture → interior processing → survival or replenishment. Exoplanet population statistics are treated carefully. The radius valley provides important evidence for atmospheric evolution but is not used as a direct composition classifier. A planet above the radius valley is not automatically H/He dominated. Water/steam-world pathways, volatile-rich interiors, secondary H₂ atmospheres, and gas-poor formation histories can overlap in radius with primordial-envelope planets. Direct atmospheric escape measurements provide stronger constraints. Ly-α observations demonstrate active hydrogen escape in some systems. He I 1083 nm measurements provide another upper-atmosphere tracer, but detections and nondetections depend on epoch, stellar activity, atmospheric composition, and model assumptions. One transit or one tracer is therefore not treated as a bulk-composition measurement. The USP layer is introduced only after the complete planetary-science baseline. A standard retention statistic may be defined as: R_H = ln(τ_loss,H / t_ref), with: τ_loss,H = M_H / Ṁ_H,loss. A local USP Level-B translation may then map this standard quantity into an operational Δf coordinate. Such a coordinate is a representation of standard physics. It is not a new microscopic planetary frequency. A genuine USP test has the form: y_i = y_std(θ_i) - A_USP F_USP(z_i; φ) - ε_i. The exact additional-physics null is: A_USP = 0. No present atmospheric dataset in msf:48280 v2.0 requires a nonzero USP term. *SHORT ZENODO SUMMARY A conditional atmospheric-evolution framework showing why stronger planetary binding can improve the survival of hydrogen-bearing gas while mass alone does not determine atmospheric composition. Supply, formation, exobase physics, hydrodynamic and diffusion-limited escape, fractionation, outgassing, and evolutionary history remain primary. USP is restricted to calibrated residual testing under the exact null A_USP = 0.