The Stellar Equilibrium Constant: Unifying Radiation, Gravity, and Thermodynamics

We introduce two new stellar parameters, Φ and I, that establish a universal law connecting stellar light, heat, and gravity. The photogravitational parameter is defined as: Φ = L / (M g) = (L R²) / (G M²), quantifying the radiation–gravity balance. The relativistic compactness is: β = G M / (R c²). The Stefan–Boltzmann relation is: L = 4π R² σ T⁴. Combining these yields the invariant: I = (Φ β²) / (T⁴ R²) = (4π G σ) / c⁴. The right-hand side involves only the fundamental constants G, σ, and c, while the left uses observable stellar quantities L, M, R, and T. This identity reduces stellar structure from three observables to two and provides a unique dimensional link between radiation, gravity, relativity, and thermodynamics. Classical relations including the Eddington ratio, Kelvin–Helmholtz timescale, and radiation pressure emerge as limiting cases, and a GR-consistent local form is derived for compact objects. Observational consistency includes a Solar test at parts-per-million precision and Wolf–Rayet stars, where Φ clusters by subtype with about 10% scatter and indicates a robust ~43% mass deficit relative to evolutionary tracks. By introducing Φ and I, we establish a new stellar law with falsifiable predictions, offering both conceptual unification and practical diagnostics across the stellar mass spectrum.