Empirical Constraints on Photoevaporation from the Stellar Flux Dependence of the Exoplanet Radius Valley

The radius valley separating rocky super-Earths from volatile-rich sub-Neptunes remains a key observable for understanding atmospheric evolution in close-in planets. While photoevaporation and core-powered mass loss both predict this bimodality, they differ fundamentally in their dependence on stellar irradiation. We analyze 5,987 confirmed exoplanets to measure the valley's response to incident flux. The valley location shifts from 1.51 ± 0.08 R⊕ at low flux (S < 20 S⊕) to 2.25 ± 0.12 R⊕ at high flux (S > 200 S⊕), a 49% migration significant at 6.8σ. Power-law fitting yields R_valley ∝ S^(0.37±0.04), bracketing the energy-limited prediction of S^(1/3). This flux-driven migration provides direct empirical evidence for photoevaporation as the primary atmospheric removal mechanism in close-in planetary systems.