Corecollapse supernovae

Observations reveal typical kinetic energies of 1051 erg in supernova remnants. This permits one to perform light-curve as well as explosive-nucleosynthesis calculations by introducing a shock of appropriate energy into the pre-collapse stellar model (Woosley and Weaver 1995; Thielemann et al. 1996; Nomoto et al. 1997; Hoffman et al. 1999; Nakamura et al. 1999; Rauscher et al. 2002; Umeda and Nomoto 2005). Such induced calculations lack self-consistency and cannot predict the masses of 56Ni ejected from the innermost explosive Si-burning layers (powering the supernova light curves by the decay chain 56Ni—56Co—56Fe) due to our lack of knowledge about the detailed explosion mechanism and therefore the partition of mass between the neutron star and supernova ejecta. However, the amounts of intermediate-mass elements Si—Ca produced are dependent solely on the explosion energy and the stellar structure of the progenitor star, whereas abundances for elements like O and Mg are essentially determined by the evolution of the stellar progenitor. Thus, on moving in from the outermost to the innermost ejecta of an SN II explosion, we see an increase in the complexity of our understanding, this depending (a) only on stellar evolution, (b) on the stellar evolution and explosion energy, and (c) on stellar evolution and the complete explosion mechanism.

Stellar Collapse Supernova

Figure 37.3. Left panel: results for the composition of supernova ejecta from an induced-explosion calculation for a 20M© star (Thielemann et al. 1996). The change of the Fe-group composition in the innermost ejecta is due to the change in the Ye of the pre-collapse stellar model. Right panel: Comparison of these abundances (open squares; Thielemann et al. 1996) with abundance observations of low-metallicity stars (triangles; Gratton & Sneden 1991; Cayrel etal. 2004) that reflect average Type-II supernova ejecta. Calculations that include also neutrino interactions during the explosion (open circles; Frohlich et al. 2006a) lead to proton-rich conditions in the innermost zones and an improved description of the iron-group abundances (see Sc and Zn). Copper is an s-process element and originates from other sources.

Figure 37.3. Left panel: results for the composition of supernova ejecta from an induced-explosion calculation for a 20M© star (Thielemann et al. 1996). The change of the Fe-group composition in the innermost ejecta is due to the change in the Ye of the pre-collapse stellar model. Right panel: Comparison of these abundances (open squares; Thielemann et al. 1996) with abundance observations of low-metallicity stars (triangles; Gratton & Sneden 1991; Cayrel etal. 2004) that reflect average Type-II supernova ejecta. Calculations that include also neutrino interactions during the explosion (open circles; Frohlich et al. 2006a) lead to proton-rich conditions in the innermost zones and an improved description of the iron-group abundances (see Sc and Zn). Copper is an s-process element and originates from other sources.

The correct prediction of the amount of Fe-group nuclei ejected (which includes also one of the so-called alpha-elements, i.e. Ti) and their relative composition depends directly on the explosion mechanism and the size of the Fe core. Three types of uncertainties are inherent in consideration of the Fe-group ejecta, related to (i) the total amount of Fe-group nuclei ejected and the partition of mass between neutron star and ejecta, mostly measured in terms of 56Ni decaying to 56Fe, (ii) the total explosion energy, which influences the entropy of the ejecta and with it the amount of radioactive 44Ti as well as 48Cr (decaying to 48Ti and being responsible for production of elemental Ti), and (iii) finally the neutron richness or Ye = (Z / A) of the ejecta, which depends on stellar structure, electron captures, and neutrino interactions (Frohlich et al. 2006a). The electron fraction Ye strongly influences the overall Ni/Fe ratio.

An example for the composition after explosive processing due to an (induced) shock wave is shown in the left panel of Figure 37.3 (Thielemann et al. 1996). The outer ejected layers (M(r) > 2M©) are unprocessed by the explosion and contain results of prior H-, He-, C-, and Ne-burning during the stellar evolution. The interior parts of SNe II contain products of explosive Si-, O-, and Ne-burning. In the inner ejecta, which experience explosive Si-burning, Ye changes from 0.4989 to 0.494. The Ye originates from beta-decays and electron captures in the pre-explosive hydrostatic fuel in these layers. Neutrino reactions during the explosion have not yet been included in these induced-explosion calculations utilizing a thermal-bomb prescription. Huge changes occur in the Fe-group composition for mass zones below M(r) = 1.63M0. There the abundances of 58Ni and 56Ni become comparable. Amounts of all neutron-rich isotopes (57Ni, 58Ni, 59Cu, 61Zn, 62Zn) increase, the effect being strongest for the even-mass isotopes (58Ni, 62Zn). One can also recognize the increase in production of 40Ca, 44Ti, 48Cr, and 52Fe for the inner high-entropy zones, but a decrease in production of the N = Z nuclei in the more neutron-rich layers. More details can be found in extended discussions (Thielemann etal. 1996; Nakamura et al. 1999).

Recent core-collapse supernova simulations with accurate modeling of neutrino transport (Liebendorfer et al. 2001; Buras et al. 2003; Thompson et al. 2005) show the presence of proton-rich neutrino-heated matter, both in the inner ejecta (Liebendorfer et al. 2001; Buras et al. 2003) and in the early neutrino wind from the proto-neutron star (Buras et al. 2003). This matter, part of the initially shock-heated material located between the surface of the proto-neutron star and the shock front expanding through the outer layers, is subjected to a large deposition of neutrino energy, heating the matter. This and the expansion, lifting the electron degeneracy, make it possible for the reactions ve + n ^ p + e- and p + Ve ^ n + e+ (i.e. neutrino and antineutrino captures on free nucleons and their inverse reactions, electron and positron capture) to drive the composition proton-rich (Frohlich et al. 2005; Pruet et al. 2005; Frohlich et al. 2006a), i.e. the electron fraction Fe > 0.5. This effect will always occur in a successful explosion with ejected matter irradiated by a strong neutrino flux, irrespective of the details of the explosion. While this matter expands and cools, nuclei can form. This results in a composition dominated by N = Z nuclei, mainly 56Ni and 4He, and protons. Without the further inclusion of neutrino and antineutrino reactions the composition of this matter will finally consist of protons, alpha-particles, and heavy (Fe-group) nuclei, i.e. a proton- and alpha-rich freeze-out that results in enhanced abundances of 45 Sc, 49Ti, and 64Zn (Frohlich et al. 2005; Pruet et al. 2005; Frohlich et al. 2006a).

Traditional explosive (supernova)-nucleosynthesis calculations did not include interactions with neutrinos and antineutrinos. The heaviest nuclei synthesized in these calculations have a mass number A = 64. The matter flow stops at the nucleus 64Ge, which has a small proton-capture probability and a beta-decay half-life (64 s) that is much longer than the expansion timescale (10 s) (Pruet et al. 2005). When reactions with neutrinos and antineutrinos are considered for both free and bound nucleons the situation becomes dramatically different (Frohlich et al. 2006b; Pruet et al. 2006; Wanajo 2006).

The N ~ Z nuclei are practically inert to neutrino capture (i.e. converting a neutron into a proton) because such reactions are endoergic for neutron-deficient nuclei located away from the valley of stability. The situation is different for antineutrinos, which are captured in a typical time of a few seconds, both by protons and by nuclei, at the distances at which nuclei form (~ 1,000 km). Since protons are more

Figure 37.4. Left panel: the evolution of the abundances of neutrons, protons, alpha-particles, and 56Ni in a nucleosynthesis trajectory resulting from model B07 (Frohlich et al. 2006a). Right panel: isotopic abundances for model B07 relative to Solar abundances (filled circles; Lodders 2003) compared with earlier predictions (open circles; Thielemann et al. 1996). The filled circles represent results from calculations in which (anti)neutrino-absorption reactions are included in the nucleosynthesis, whereas for the open circles neutrino interactions are neglected. The effect of neutrino interactions is clearly seen for nuclei above A > 64, for which enhanced abundances are obtained.

Figure 37.4. Left panel: the evolution of the abundances of neutrons, protons, alpha-particles, and 56Ni in a nucleosynthesis trajectory resulting from model B07 (Frohlich et al. 2006a). Right panel: isotopic abundances for model B07 relative to Solar abundances (filled circles; Lodders 2003) compared with earlier predictions (open circles; Thielemann et al. 1996). The filled circles represent results from calculations in which (anti)neutrino-absorption reactions are included in the nucleosynthesis, whereas for the open circles neutrino interactions are neglected. The effect of neutrino interactions is clearly seen for nuclei above A > 64, for which enhanced abundances are obtained.

abundant than heavy nuclei, antineutrino capture occurs predominantly on protons, causing a residual density of free neutrons of 1014 —1015 cm-3 for several seconds when the temperatures are in the range (1-3) x 109 K. This effect is clearly seen in Figure 37.4 (left panel), where the time evolution of the abundances of protons, neutrons, alpha-particles, and 56Ni is shown for a trajectory of the model B07 (Frohlich et al. 2006a). The solid (dashed) lines display the nucleosynthesis results which include (omit) neutrino- and antineutrino-absorption interactions after nuclei are formed. The abundance of 56Ni serves to illustrate when nuclei are formed. The difference in proton abundances between these two calculations is due to antineutrino captures by protons, producing neutrons that drive the vp process. Without the inclusion of antineutrino captures the neutron abundance soon becomes too small to allow any capture by heavy nuclei.

The neutrons produced via antineutrino absorption by protons can easily be captured by neutron-deficient N ~ Z nuclei (for example 64Ge) that have large neutron-capture cross sections. While proton capture, (p, y), on 64Ge takes too long or is impossible, the (n, p) reaction dominates, permitting the matter flow to continue to nuclei heavier than 64Ge via subsequent proton captures with freeze-out at close to 1 x 109 K.

Figure 37.4 (right panel) shows the results for the composition of supernova ejecta from one hydrodynamical model (Frohlich et al. 2006a) that includes neutrinoabsorption reactions in the nucleosynthesis calculations (filled circles) that lead initially to proton-rich conditions in the innermost zones, which experience afterwards the vp process. These abundances are compared with those from an older set of nucleosynthesis calculations (open circles) by Thielemann et al. (1996) that did not include neutrino interactions and therefore did not produce the proton-rich matter resulting in models with accurate modeling of neutrino transport (Liebendorfer et al. 2001; Buras et al. 2003; Thompson et al. 2005). In later phases of the cooling proto-neutron star, neutrino interactions will cause the emission of neutron-rich ejecta. Whether this permits a weak or strong r-process is still being debated (Thompson 2003).

High-mass stars (as discussed in Section 1) will undergo direct black-hole formation or black-hole formation via fallback onto the initially formed neutron star. Accretion onto stellar-mass black holes (if the surroundings are of sufficiently low density) can cause a fireball behavior and be related to gamma-ray bursts or the collapsar/hypernova phenomenon (Woosley 1993; Paczynski 1998; Nomoto et al. 2006). They indicate the occurence of higher explosion energies beyond 1052 erg and that large masses of 56Ni are ejected (e.g. Nakamura et al. 2001; Umeda and Nomoto 2005). While the general explosive-nucleosynthesis behavior is similar to that of supernovae (see Figure 37.3), the higher explosion energy of hypernovae shifts both the complete Si-burning region (Tpeak > 5 x 109 K with Co, Zn, V, and some Cr as products) and the incomplete Si-burning region (4 x 109 K > Tpeak > 5 x 109 K with Cr and Mn as products after decay) outwards in mass. With this outward shift of the boundary the ratio of complete to incomplete Si-burning becomes larger and therefore higher [(Zn, Co, V)/Fe] ratios and lower [(Mn, Cr)/Fe] ratios are obtained (Nomoto et al. 2006). Which fraction of high-mass stars leads to such events is still unknown and depends on rotation and magnetic-field effects.

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