The evolution of single stars can be followed in the Hertzsprung-Russell (HR) diagram (e.g. Iben 1991). Their fate is mainly determined by the initial mass and composition. This implies in principle also the history of mass loss, but in theoretical modeling the mass-loss prescription adds a degree of freedom. Rotation can drastically affect the evolutionary track of a star in the HR diagram due to modification of the surface composition, induced by rotational diffusion, which directly affects the mass loss by stellar winds. The mass-loss rates depend on metallicity via the interaction of radiation transport with the surface composition. The present theoretical and observational knowledge was recently summarized by Meynet and Maeder (2005). In general this leads to low-metallicity stars experiencing less mass loss than high metallicity stars do and therefore possessing larger He cores and H envelopes at the ends of their lives. The same applies to the C-O core size after He-burning, which determines the final fate of the star, due to the much shorter burning timescales of the later burning stages (see Figure 37.1, left panel).
For different initial masses and metallicities, different end stages such as planetary nebulae, supernovae, and hypernovae/gamma-ray bursts can be expected. The lower boundary for stars to form cores massive enough to undergo core collapse is at ~9M©. For stars of masses above 10M© core collapse is the only possible fate. In between, stars form O-Ne-Mg cores, which can either collapse and form neutron stars or lose their envelopes and result in white dwarfs. While the size of the C-O core determines the final stellar fate, its relation to the progenitor mass depends on the metallicity. At low metallicities massive stars end their lives as neutron stars (for initial mass of ~10M© to ~25M©), as black holes through fallback onto the neutron star (initial mass between ~25M© and ~40M©), or directly as black holes (initial mass above ~40M©). At higher metallicities mass loss becomes more important, producing smaller He and C-O cores for a given initial mass. For very massive stars the metallicity dependence can be so strong that, with increasing metallicity, the mass loss during stellar evolution is large enough to exclude the possibility of black-hole formation, permitting neutron stars as the only possible type of remnant.
Core collapse with neutron-star formation leads to supernovae. Figure 37.1 (right panel) shows the resulting explosion energy for Solar metallicities from calculations discussed in Section 3 (Liebendorfer et al. 2003). If the star still possesses a hydrogen envelope it is visible as a Type-II supernova (containing H lines in its spectra), whereas if the hydrogen envelope was lost this leads to a Type-Ib supernova (no H lines but still He lines). If also the He envelope is lost a Type-Ic supernova (also no He lines) results. For a recent summary see e.g. Heger et al. (2003).
Type-Ia SNe exhibit, in addition to the absence of hydrogen in their optical spectra, a specific Si line. They are the only type of supernovae observed in elliptical galaxies and therefore have to originate from an older (revived) stellar population. Their origin is explained in terms of carbon-oxygen white dwarfs in binary stellar systems exploding after having accreted sufficient matter from the companion star for them to undergo thermonuclear runaway. Details are discussed in Section 2.
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