Luminosity functions and the evolution of low-mass population I giants

Luminosity functions in terms of bolometric magnitudes are constructed for M67 and for two samples of old-disk field giants. These are compared with theoretical rates of evolution on the giant branch. M67 has too few stars to give a useful comparison. The field giants show good agreement with theory, and the number of stars at the ''clump'' suggests that core helium-burning is prolonged by overshoot with semiconvective mixing. The fuel consumption derived from the luminosity functions is consistent with core helium ignition at the theortically predicted core mass, and with a final core mass in agreement with observed white dwarf masses. Data are needed for a larger complete sample of field giants for the luminosity function to be better determined. Further details, especially for the variable M giants at the top of the giant branch, are needed for population syntheses of elliptical galaxies