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.本研究报道了一个普适恒星平衡常数$I = 4pi Gsigma/c^4$，该常数支配所有热光球层。该不变量源自辐射平衡、牛顿引力与相对论紧致度的结合，由此得到恒等式$I = (Phieta^2)/(T^4R^2) = 4pi Gsigma/c^4$，其中$Phi = L/(Mg)$，$eta = GM/(Rc^2)$。 该常数仅由基本物理常数（引力常数$G$、斯特藩-玻尔兹曼常数$sigma$、光速$c$）决定，可将恒星的四个可观测物理量（光度$L$、质量$M$、半径$R$、温度$T$）缩减为三个独立参数。经典关系——包括爱丁顿光度（Eddington luminosity）、开尔文-亥姆霍兹时标（Kelvin-Helmholtz timescale）与辐射压（radiation pressure）——均可由该单一恒等式通过代数投影导出，而非独立的物理定律。 通过对太阳、天狼星A（Sirius A）、织女星（Vega）与沃尔夫-拉叶星WR 124（Wolf-Rayet 124）进行数值验证，结果证实恒等式两侧的比值$I_ ext{左}/I_ ext{右} = 1.000pm10^{-16}$。经验上，光引力参量$Phi$会按照沃尔夫-拉叶星光谱亚型（Wolf-Rayet spectroscopic subtype）聚类，偏差为$pm10\%$，由此可仅通过光度$L$与半径$R$直接测定恒星质量，精度可达$sim1\%$-$2\%$。将该方法应用于46颗沃尔夫-拉叶星后，研究发现相较于恒星演化轨迹（evolutionary tracks），这些恒星存在系统性的$sim43\%$质量亏损——这表明现有大质量恒星模型（massive star models）中存在缺失的物理机制。 该不变量将光球层确立为关键的几何热力学边界，在此处自然常数施加了普适约束，并提供了可证伪诊断量（$Delta I$、$Delta SB$），用于探测任何自发光系统中的非热偏离现象。