The Stellar Equilibrium Constant: connecting 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 represents a previously unrecognized universal constant for thermal stellar objects. When combined with empirical clustering of Φ (as demonstrated for Wolf–Rayet stars), it reduces the effective degrees of freedom from three 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 for stellar masses.