Relations of core mass-stellar luminosity and core mass-stellar radius for AGB and FGB stars

The relations between core mass and stellar luminosity and radius for AGB and FGB stars are systematically investigated with the latest stellar models. A single unique relation between the core mass and giant's luminosity is obtained. The core mass giant's radius relations are given for both Pop I and Pop II stars. The core mass giant's luminosity relation is almost independent of the stellar parameters, such as stellar metallicity, mixing length parameter α , and stellar winds. The core mass giant's radius relation is somewhat affected by the parameters. The giant's radius at an M c (core mass) for Pop II is smaller than that for Pop I (by a factor of ～1.5). A larger mixing length parameter α also tends to reduce the giant's radius.