Mass–luminosity relation

In astrophysics, the mass–luminosity relation is an empirical and theoretical relationship between a star's mass and its luminosity The relationship is represented by the equation: ${\frac {L}{L_{\odot }}}=\left({\frac {M}{M_{\odot }}}\right)^{a}$ where $L ⊙$ and $M ⊙$ are the luminosity and mass of the Sun and $1 < a < 6$ . The value $a = 3.5$ is commonly used for main-sequence stars. This equation and the usual value of $a = 3.5$ only applies to main-sequence stars with masses $2 M ⊙ < M < 55 M ⊙$ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then $a = 1$ .