On the core mass luminosity relation.

A homology method for understanding the properties of a hydrogen shell burning around a degenerate helium core is presented. The method is compared to models developed by Refsdal and Weigert (R and W, 1970) and Paczynski (P, 1970), and it is noted that different slopes of the two relations in the two mass ranges are influenced by radiation pressure. The R and W homology is analytically extended by the method to higher core masses in a discussion limited to cases of constant opacity. It is shown that the luminosity of the shell becomes proportional to the core mass and independent of the core radius as soon as the radiation pressure becomes important. Differences observed from predictions by the method and the P curve from predictions by the R and W projections are shown to be due to the R and W figures being based on white dwarfs, which do not have totally degenerate cores, in addition to differences in estimates of the material weight outside the core.