Does Cumulative XUV Unify the Neptunian Desert?

Abstract

The architecture of close-in planetary systems includes a conspicuous scarcity of Neptune-size worlds, known as the Neptunian desert. The deficit spans roughly $2$--$10\,R_{\oplus}$ at orbital periods of a few days. Atmospheric erosion by stellar X-rays and extreme-ultraviolet (XUV) radiation may shape its lower boundary, while the strong mass dependence of stellar activity complicates comparisons across spectral type. We test whether standardized cumulative XUV exposure places the lower boundaries around M-dwarf and F-, G-, and K-type (FGK) hosts on a common scale. The analysis uses 1850 Kepler and TESS planets; the primary fit contains 677 planets with $2.24 < R_p/R_{\oplus} < 7.48$. For a 5 Gyr median-rotation history, the fitted M-minus-FGK offset changes from $-1.06$ dex in present bolometric flux to $-0.37$ dex in cumulative XUV. This corresponds to $65.4\%$ compression in the point estimate and a host-bootstrap median of $73.4\%$. The convergence persists under host deletion, survey separation, unit weighting, alternative boundary definitions, and nine stellar age--rotation histories. A common-period null produces a median compression of $59.1\%$ in 2000 realizations, with $38.9\%$ at least as convergent as the data; an absolute offset-reduction statistic gives $p=0.522$. Cumulative XUV is a substantially more uniform empirical coordinate than present bolometric flux. Comparable uniformity follows from mapping a common period edge through Keplerian geometry and mass-dependent stellar activity, leaving a universal XUV erosion threshold unconstrained by the present sample.