A Physical Upper Limit on Planetary Radius for Surface-Compatible Atmospheres

Exoplanet characterization studies frequently adopt empirical planetary radius thresholds, such as the 1.6R⊕ limit, to distinguish rocky worlds from volatile-rich sub-Neptunes. However, these static thresholds are largely derived from population statistics rather than fundamental physical constraints. This work derives a physics-based upper limit on planetary radius for sustaining surface-compatible atmospheres (i.e., stripped of primordial envelopes) by analyzing the competition between gravity and atmospheric escape. We employ three complementary analytical frameworks: thermal Jeans escape, energy-limited hydrodynamic escape, and core-powered mass loss. By coupling these escape mechanisms with a mass-radius scaling relation for rocky cores (M ∝ R3.7), we demonstrate that the critical radius for envelope retention is not constant but scales with equilibrium temperature. Our primary thermodynamic constraint yields a boundary of Rcrit ∝ T0.37. While energy-limited hydrodynamic models suggest a steeper dependence during early stellar activity, the shallower slope derived from Jeans escape provides a robust baseline for long-term stability. We compare this theoretical boundary with mass-radius data from 292 confirmed planets in the NASA Exoplanet Archive. The observed population exhibits a clear stratification consistent with our derived limit, where high-density cores populate the region below the curve and low-density volatile-rich worlds lie above it. Furthermore, our derived slope aligns remarkably well with recent observational constraints (dlogR / dlogT ≈ 0.40). We conclude that surface compatibility is governed by a continuous, temperature-dependent physical boundary rather than a universal radius cutoff. This framework offers a more precise tool for selecting terrestrial candidates from future surveys like PLATO and ARIEL.