A Conserved Quantity at Stellar Photospheres

We identify and empirically validate a boundary-closure condition for stable radiative-gravitational systems. A scalar invariant, X = (L G M) / (g R^4 c^4 T^4), is formed solely from independently measured boundary observables (luminosity L, effective temperature T, surface gravity g, mass M, and radius R), with G and c included to place radiative and gravitational inputs on a common metrological footing. Using the Sun and two benchmark samples of detached eclipsing-binary components with geometry-based M and R and spectroscopic T and g, we find that X converges to a single value, X ≈ X_0 ≡ 4πσ/c^4, with a dispersion of 0.13% in the high-precision sample, consistent with measurement limits. In natural units (c=ħ=k_B=1, σ=π^2/60) this closure corresponds to the third-order Bose-Einstein integral, X_0 = π^3/15 ≃ 2.067. Scrambling boundary observables between systems destroys the closure, demonstrating that the result reflects a physical boundary constraint rather than a definitional identity. The closure is interpreted as a consequence of radiative decoupling: the surface where photon degrees of freedom detach from an optically thick interior and become defined as free-streaming radiation at the boundary.我们识别并实证验证了稳定辐射引力系统的边界闭合条件。我们构造了一个仅由独立测量的边界可观测量构建的标量不变量（scalar invariant）$X = frac{LGM}{gR^4c^4T^4}$，其中L为光度（luminosity）、T为有效温度（effective temperature）、g为表面重力加速度（surface gravity）、M为质量（mass）、R为半径（radius），引入引力常数（gravitational constant）G与光速（speed of light）c，以统一辐射与引力相关物理量的计量基准。我们利用太阳以及两个分离食双星（detached eclipsing binary）子星的基准样本，该样本中质量M与半径R由几何方法测定，有效温度T与表面重力加速度g由光谱方法测定，发现X收敛至唯一值$X approx X_0 equiv frac{4pisigma}{c^4}$，在高精度样本中其离散度仅为0.13%，与测量极限相符。在自然单位制（natural units，$c=hbar=k_B=1，sigma=frac{pi^2}{60}$）下，其中$hbar$为约化普朗克常数（reduced Planck constant），$k_B$为玻尔兹曼常数（Boltzmann constant），该闭合条件对应三阶玻色-爱因斯坦积分（Bose-Einstein integral），即$X_0=frac{pi^3}{15} simeq 2.067$。将不同系统的边界可观测量随机打乱后，该闭合条件便不再成立，这表明该结果反映的是物理边界约束，而非定义上的恒等式。该闭合条件可被解释为辐射退耦（radiative decoupling）的结果：在该边界表面处，光子自由度（degrees of freedom）从光学致密（optically thick）的内部脱离，并在边界处被定义为自由流辐射（free-streaming radiation）。