Initial-final mass relationship for stars of different metallicities

Context. The initial-final mass relationship (IFMR) for stars is important in many astrophysical fields of study, such as the evolution of galaxies, the properties of type Ia supernovae (SNe Ia) and the components of dark matter in the Galaxy. Aims. The purpose of this paper is to obtain the dependence of the IFMR on metallicity. Methods. We assume that the envelope of an asymptotic giant branch (AGB) or a first giant branch (FGB) star is lost when the binding energy of the envelope is equal to zero (Delta W = 0) and the core mass of the AGB star or the FGB star at the point (Delta W = 0) is taken as the final mass. Using this assumption, we calculate the IFMRs for stars of different metallicities. Results. We find that the IFMR depends strongly on the metallicity, i.e. Z = 0.0001, 0.0003, 0.001, 0.004, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08 and 0.1. From Z = 0.04, the final mass of the stars with a given initial mass increases with increasing or decreasing metallicity. The difference in the final mass due to the metallicity may be up to 0.4 M-circle dot. A linear fit of the initial-final mass relationship in NGC 2099 (M37) shows the effect of metallicity on the IFMR. The IFMR for stars of Z = 0.02 obtained here matches well with those inferred observationally in the Galaxy. For Z >= 0.02, helium WDs are obtained from the stars of M-i <= 1.0 M-circle dot and this result is supported by the discovery of numerous low-mass WDs in NGC 6791, which is a metal-rich old open cluster. Using the IFMR for stars of Z = 0.02 obtained here, we have reproduced the mass distribution of DA WDs in Sloan DR4 except for some ultra-massive white dwarfs. Conclusions. The trend that the mean mass ofWDs decreases with effective temperature may originate from the increase of the initial metallicities of stars. We briefly discuss the potential effects of the IFMR on SNe Ia and at the same time, predict that metal-rich low-mass stars may become under-massive white dwarfs.