An Empirical Photospheric Boundary Closure Relation from Detached Eclipsing Binaries

Using a benchmark sample of 190 stellar components in detached eclipsing binary systems, we examine whether independently measured surface observables—luminosity, radius, mass, surface gravity, and effective temperature—satisfy a closure condition at the photospheric boundary.

We evaluate the combination directly from these measurements. When radiative, gravitational, and geometric effects jointly balance at a stable photospheric boundary, this combination reduces algebraically to the constant scale .

The ratio is found to remain invariant across the full stellar mass range of the sample, with a mean value of 0.996585 and a dispersion of 0.001293. No dependence on stellar mass is observed. In Planck units, corresponds to the geometric realization of equilibrium photon statistics at a radiating boundary.