Initial-Final Mass Relationship for Stars of Different Metallicities

TL;DR

This paper models the initial-final mass relationship (IFMR) for stars across various metallicities, revealing a strong dependence on metallicity and matching observational data, with implications for white dwarf populations.

Contribution

It introduces a metallicity-dependent IFMR based on envelope binding energy assumptions, extending previous models and aligning with observational evidence.

Findings

IFMR varies significantly with metallicity, up to 0.4 solar masses difference.

The model matches well with observed white dwarf mass distributions.

Metal-rich stars tend to produce under-massive white dwarfs.

Abstract

Following Paczy\'{n}ski & Zi\'{o}lkowski (1968) and Han et al. (1994), 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.We find that the IFMRs 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 of the final mass due to the metallicity may be up to 0.4 $M_{\odot}$. A linear fit of the initial-final mass relationship in NGC 2099 (M37) shows a potential evidence of the effect of metallicity on the IFMR. The IFMR for stars of $Z=0.02$ obtained in the paper matches well with those inferred observationally in the Galaxy. For $Z\geq 0.02$, helium WDs are obtained from the stars of $M_{\rm i}\leq 1.0 M_{\odot}$ and this result is upheld 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 in the paper, we have reproduced the mass distribution of DA WDs in Sloan DR4 except for some ultra-massive white dwarfs. The trend that the mean mass of WDs decreases with effective temperature may originate from the increase of the initial metallicities of stars. We predict that metal-rich low-mass stars may become under-massive white dwarfs.