Mass, Luminosity, Radius & Temperature: Physical Mechanisms

Luminosity can be related to radius and effective temperature through the Stefan-Boltzmann law, L = 4πR²σT⁴. For main-sequence stars, mass also correlates strongly with luminosity because greater gravity drives higher core pressure and temperature, though the exact relation changes across the mass range.

Increasing stellar mass raises central pressure and temperature, accelerating temperature-sensitive fusion reactions. A star can also change luminosity without changing mass by expanding or contracting and changing surface temperature. Consequently, two stars of similar temperature can have radically different luminosities if their radii differ.

Binary orbits provide stellar masses, parallax plus measured flux yields luminosity, interferometry and eclipsing binaries constrain radii, and spectra or colors constrain effective temperature. These independent measurements populate the observed mass-luminosity and radius-temperature relations.

Increasing stellar mass raises central pressure and temperature, causing fusion rate and luminosity to rise disproportionately. A star can cool at the surface while becoming more luminous if its radius expands enough, which is exactly what happens in many giant phases.