The Mass-Luminosity Relationship (MLR)

Abstract

The names of Hertzsprung and Russell are immortalized by the well-known spectrumluminosity diagram of stars. Some years later, in 1923, the same authors discovered empirically the relation connecting stellar masses and luminosities. Eddington’s work then was so far advanced that he showed shortly thereafter the theoretical basis for the existence of a relationship of this kind. The empirical finding became a weighty support of the theory, as is demonstrated in his 1926 classic ‘The Internal Constitution of the Stars’, and it also provided the first grave objection against the then widely held hypothesis of stellar evolution from giants to dwarfs. As the pressure and, hence, the energy generation increase with the mass, the MLR is a consequence of the pressure and temperature gradient inside the stars, and its validity extends beyond Eddington’s special star models to all stars with a chemically homogeneous interior composition.With the usual assumptions on the mean particle weightµ, the opacity, etc., a relationship of the form L = M^K R^x µ ^y can always be derived. The mass exponent k is about 4, the exponent x of the radius Ronly — $\frac{1}{2}$ Though µ enters with the high power y&j it does not dominate over the mass dependence, buty suffices to prevent a representation of the form L ~ M^k (solely as a function of the mass) with a single value for k.