Mass, Luminosity, Radius & Temperature: Structures & Vocabulary

A star's mass, luminosity, radius, and effective temperature are linked but not interchangeable. Mass strongly influences internal pressure and nuclear-burning rate, luminosity measures total power output, radius sets emitting area, and effective temperature describes the thermal spectrum emerging from the photosphere.

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.

The Stefan-Boltzmann relation L = 4πR²σT⁴ connects radius, effective temperature, and luminosity. Main-sequence stars also show a steep empirical mass-luminosity relation, but evolved stars can have the same mass and radically different radius and luminosity.