A Conserved Quantity at Stellar Photospheres

We report a universal stellar equilibrium constant, I = 4πGσ/c⁴, that governs all thermal photospheres. This invariant emerges from the intersection of radiative equilibrium, Newtonian gravity, and relativistic compactness, yielding the identity I = (Φβ²)/(T⁴R²) = 4πGσ/c⁴, where Φ = L/(Mg) and β = GM/(Rc²). 

The constant depends only on fundamental constants (G, σ, c), reducing stellar observables (L, M, R, T) from four to three independent parameters. Classical relations—Eddington luminosity, Kelvin-Helmholtz timescale, radiation pressure—emerge as algebraic projections of this single identity rather than independent laws.

Numerical verification across the Sun, Sirius A, Vega, and WR 124 confirms I_left/I_right = 1.000±10⁻¹⁶. Empirically, the photogravitational parameter Φ clusters by Wolf-Rayet spectroscopic subtype (±10%), enabling direct mass determination from (L, R) alone with ~1-2% accuracy. Applied to 46 WR stars, this reveals a systematic ~43% mass deficit relative to evolutionary tracks—evidence of missing physics in massive star models.

The invariant establishes photospheres as critical geometric-thermodynamic boundaries where nature's constants enforce a universal constraint, providing falsifiable diagnostics (ΔI, ΔSB) for detecting non-thermal departures in any self-luminous system.