The Photogravitational Parameter Φ: A Surface-First Diagnostic for Luminous Stars

This paper introduces the photogravitational parameter Φ = L/(Mg) - a new diagnostic tool for studying the most luminous stars in the universe. Instead of relying on complex interior models, this simple surface-based parameter uses only observable quantities: how bright a star is (L), how massive it is (M), and how strong its surface gravity feels (g). Inspired by recent advances in black hole thermodynamics, where boundary physics encodes system information without interior details, this work extends similar surface-first principles to stellar astrophysics. The framework reveals surprising connections between stellar photospheres and horizon thermodynamics, suggesting that fundamental physics principles apply across vastly different scales. This approach allows astronomers to check the consistency of stellar data directly, helping identify when observations are reliable and when hidden systematics may be present. By including relativistic corrections, the framework provides a clear upper bound on how unstable stellar envelopes can expand. The method is applied to some of the most extreme stars known—Wolf-Rayet stars and Luminous Blue Variables—where radiation nearly overpowers gravity. The results show how this simple diagnostic Φ can complement traditional stellar models, offering a new lens for understanding stellar evolution at its most extreme.