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Fe-peak elements are formed in the explosive burning of silicon, hence the physical conditions of their formation are similar except for the important fact that these elements are produced in separate regions. The regions are characterized by slightly different temperatures, so that the one with lowerT undergoes incomplete Si burning, whereascomplete Si burning occurs in the region

8.2 Explosive nucleosynthesis 99

with higherT. In short, the explosive nucleosynthesis proceeds as follows. As the burning becomes more extreme, it approaches nuclear statistical equilibrium, where the rates of all nuclear reactions are nearly compensated by the inverse. During the subsequent expansion and cooling of matter, all rates converting free particles to nuclei become too slow. So the nuclear abundances “freeze out” at some temperature characteristic of each nuclei. The resulting abundances ofneutron-richnuclei depend critically on the neutron excess prior to the freeze-out (Truran & Arnett 1971) because explosive nucleosynthesis does not allow a sufficient number ofβ-decays to change the neutron-to- proton ratio of a star from its initial value. What is also important for the final abundance pattern, is whether some extraα-particles are left after freezing. This could be a result of thetoo slowtriple- αreaction during the the decreasing temperatures in a low-density environment. This mechanism leaves a large number of freeα-particles, which are not in a complete equilibrium with the Fe-peak nuclei. The extraα-particles then recombine with other Fe-peak nuclei to form elementsheavier than Fe. For example, Co, being a product of the59_{Cu decay, is mostly synthesized during such an} α-rich freeze-outthat takes place in the complete Si-burning region. On the other side, Cr formed as 52_{Fe and Mn formed as} 55_{Co are typical elements of the incomplete Si-burning. Furthermore,} therelative amount of Mn, Cr, and Co ejected from a SN depends on the relative masses of regions, where they are produced. For a SN II, the latter is a sensitive function of the mass cut between the ejected material and the remnant, the explosion energy, and the neutron excess (Umeda & Nomoto 2002). The former two are ”free parameters“ even in modern calculations of massive star nucleosynthesis. Assuming a delayed detonation model for SN Ia (Iwamoto et al. 1999), in which a C-O white dwarf experiences an initial central deflagration followed by a detonation, a deflagration-detonation transition determines the contribution of complete and incomplete Si- burning regions.

Mn and Co are both neutron-rich elements; as noted above, their abundances must be sensitive to the neutron excess η available to the progenitor star in the explosive Si-burning phase. Obvi- ously, in environments with largeη odd-Z nuclei are produced more readily than the even-Z nuclei resulting in theodd-even effect. The neutron enrichment is determined by theinitial metal content of a star and by the previous hydrostatic burning stages. On the one side, creation of neutron-rich nuclei during the CNO cycle of H burning and subsequent He burning implies the dependency of the neutron excess on the initial stellar abundance of carbon, nitrogen, and oxygen, and hence, on the metallicity (Truran & Arnett 1971). For the solar metallicity star, this mechanism produces η≈0.0022. On the other side, neutron enrichment can result from thehydrostatic carbon burning stage, which occurs in stars with a mass >9M¯. According to Arnett (1971), the neutron excess

resulting from the complete C burning is ≥ 0.0009−0.002. Thus, Arnett concludes that the difference inη between an extreme Population II and a typical Population I star is probably not larger than 3, although the total metal content changes by a factor of 1000. A very important consequence is thatthe amount of heavy odd-Z elements produced in the Population II and I SNe would be nearly equal, and hence independent of metallicity at least for [Fe/H]≤ −0.5. This was confirmed by Woosley & Weaver (1982), who studied nucleosynthesis yields of two 25M¯ stars of

different populations.

In the past 15 years, several research groups published the results of explosive nucleosynthesis calculations for massive and intermediate-mass stars. Perhaps, the most widely-used are the yields of Woosley & Weaver (1995) for stars with 12. . .40M¯ and metallicities varying from 0 to solar.

For SN Ia, a standard reference is the metallicity-independent W7 model of Nomoto et al. (1984) in the more recent version of Iwamoto et al. (1999). The dependence of the Fe-peak on the neutron excess requires thatmetallicity-dependent yields are used in chemical evolution calculations. This is not critical for the SN Ia model, because the neutron excess in the regions where Fe-peak nuclei are produced is primarily determined by electron captures on 56Ni in the explosion (Thielemann et al. 2007). For the massive stars exploding as SN II, the neutron excess strongly depends on the β-decays in the pre-explosive hydrostatic burning stages.