On the core-mass-shell-luminosity relation for shell-burning stars

Core-mass–shell-luminosity relations for several types of shell-burning star have been calculated using simultaneous differential equations derived from simple homology approximations. The principal objective of obtaining a mass–luminosity relation for helium giants was achieved. This relation gives substantially higher luminosities than the equivalent relation for H-shell stars with core masses greater than 1 $$M_\odot$$. The algorithm for calculating mass–luminosity relations in this fashion was investigated in detail. Most of the assumptions regarding the physics in the shell do not play a critical role in determining the core-mass–shell-luminosity relation. The behaviour of the core-mass–core-radius relation for a growing degenerate core as a single unique function of mass and growth rate needs to be defined before a single core-mass–shell-luminosity relation for all H-shell stars can be obtained directly from the homology approximations.