What planetary nebulae tell us about helium and CNO elements in Galactic bulge stars

The chemical composition and core masses of thermally pulsing asymptotic giant branch (TP-AGB) models of bulge stars are calculated using a synthetic model. The goal is to infer typical progenitor masses and compositions by reproducing the typical chemical composition and central star masses of planetary nebulae (PNe) in the Galactic bulge. The AGB-tip luminosity and the observed lack of bright carbon stars in the bulge are matched by the models. Five sets of Galactic bulge PNe were analysed to find typical abundances and masses of the central stars of planetary nebulae (CSPNs). These global parameters were matched by the AGB models. These sets are shown to be consistent with the most massive CSPNs having the largest abundances of helium and heavy elements. The CSPN masses of the most helium-rich (He/H greater than or similar to 0.130 or Y greater than or similar to 0.34) PNe are estimated to be between 0.58 and 0.62 M-circle dot. The oxygen abundance in the form log (O/H) + 12 of these highest-mass CSPNs is estimated to be similar to 8.85. TP-AGB models with zero-age main sequence (ZAMS) masses between 1.2 and 1.8 M-circle dot with Y-ZAMS approximate to 0.31-0.33 and Z(ZAMS) approximate to 0.019-0.022 fit the typical global parameters, mass and abundances of the highest-mass CSPNs. The inferred ZAMS helium abundance of the most metal-enriched stars implies that dY/dZ similar to 4 for the Galactic bulge. These models produce no bright carbon stars, in agreement with observations of the bulge. They produce an AGB-tip luminosity for the bulge in agreement with observations and suggest that the youngest main sequence stars in the Galactic bulge have an enhanced helium abundance (Y approximate to 0.32) and ages between 2 and 4 Gyr. The chemical evolution of nitrogen in the Galactic bulge inferred from the models is consistent with the cosmic evolution inferred from H II regions and unevolved stars. The inferred ZAMS N/O ratios (logN/O approximate to -0.35) of the bulge PNe with the largest CSPN masses are shown to be above the solar ratio. The inferred ZAMS N/O ratios of the entire range of PN metallicities is consistent with both primary and secondary production of nitrogen contributing to the chemical evolution of nitrogen in the Galactic bulge. The inferred ZAMS value of C/O is less than 1. This indicates that the masses of the PN progenitors are low enough (M less than or similar to 1.8 M-circle dot) that carbon stars are not produced via the third dredge-up.