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Astron. Astrophys. 356, 873-887 (2000)

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3. SN II yields and their uncertainties

In the present investigation we make use of the nucleosynthesis results by Thielemann et al. (1996) and Nomoto et al. (1997). Here we want to give a short summary of the key features together with an assessment of the uncertainties by comparing with available independent calculations. The synthesized elements form three different classes which are sensitive to different aspects of the stellar models and supernovae explosion mechanism: (1) stellar evolution, (2) stellar evolution plus the explosion energy, and (3) details of the explosion mechanism which includes aspects of stellar evolution determining the size of the collapsing Fe-core. Due to reaction equilibria obtained in explosive burning, the results do not show a strong sensitivity to the applied reaction rate library (Hoffman et al. 1999).

1: The abundances of C, O, Ne, and Mg originate from the unaltered (essentially only hydrostatically processed) C-core and from explosive Ne/C-burning. They are mainly dependent on the structure and zone sizes of the pre-explosion models resulting from stellar evolution. These zones and therefore the amount of ejected mass varies strongly over the progenitor mass range. O, Ne, and Mg vary by a factor of 10-20 between a [FORMULA] and a [FORMULA] progenitor star. This behaviour can vary with the treatment of stellar evolution and is strongly related to the amount and method of mixing in unstable layers. Woosley & Weaver (1995) employ the Ledoux criterion with semiconvection for Schwarzschild-unstable but Ledoux-stable layers. Nomoto & Hashimoto (1988) make use of the Schwarzschild criterion for convection (neglecting composition gradients) which ensures mixing over more extended regions than the Ledoux criterion. The Schwarzschild criterion causes larger convective cores (see also Chieffi et al. 1998) which leads to larger 16O, 20Ne, and 24Mg yields, the latter being also dependent on the 12C([FORMULA] rate (Langer & Henkel 1995). In addition, it is important to know the mixing velocity in unstable regions. Recent calculations by Umeda et al. (1999), within the diffusion approximation for mixing (Spruit 1992; Saio & Nomoto 1998) but with a remaining free parameter - permitted to vary between 0 and 1 - show that the Woosley & Weaver (1995) results can be reproduced with a small choice of this parameter of 0.05. A further effect is due to rotation. When also treating rotation correctly (Langer et al. 1997; Talon et al. 1997; Meynet & Maeder 1997; Heger et al. 1999), rotational instabilities lead to additional mixing which can bring the models making use of the Ledoux criterion closer to those evolved with the Schwarzschild criterion and the compositions closer to those obtained with instantaneous mixing (high mixing velocities). Thus, the amount of mixing (being influenced by the mixing criterion utilized, the mixing velocity, and rotation) determines in stellar evolution the size of the C/O core. While the yield of O can be fixed with a combination of the still uncertain 12C([FORMULA] rate (Buchmann 1996, 1997) and a mixing description, the yields of Ne and Mg depend on the extent of mixing. Recent galactic chemical (but not dynamic) evolution calculations (Thomas et al. 1998; Matteucci et al. 1999; Chiappini et al. 1999) prefer apparently a larger extent of mixing (caused by either of the effects mentioned above) in order to reproduce the observed Mg in low metallicity stars.

2: The amount of mass for the elements Si, S, Ar and Ca, originating from explosive O- and Si-burning, is almost the same for all massive stars in the Thielemann et al. (1996) models. They do not show the strong progenitor mass dependence of C, O, Ne, and Mg. Si has some contribution from hydrostatic burning and varies by a factor of 2-3. Thus, the first set of elements (C, O, Ne, Mg) tests the stellar progenitor models, while the second set (Si, S, Ar, Ca) tests the progenitor models and the explosion energy, because the amount of explosive burning depends on the structure of the model plus the energy of the shock wave which passes through it. Present models make use of an artificially induced shock wave via thermal energy deposition (Thielemann et al. 1996) or a piston (Woosley & Weaver 1995) with shock energies which lead, after the reduction of the gravitational binding of ejected matter, to a given kinetic energy. In our models this is an average energy of [FORMULA] erg, known from remnant observations, which does not reflect possible explosion energy variations as a function of progenitor mass. The apparent underproduction of Ca seen in some chemical evolution calculations (e.g. Thomas et al. 1998; Matteucci et al. 1999; Chiappini et al. 1999) could apparently be solved by a progenitor mass dependent explosion mechanism and energy.

3: 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, connected also to the size of the collapsing Fe-core. Observational checks of individual supernovae are presently still required to test the detailed working of a supernova. The present situation is still uncertain and depends on Fe-cores from stellar evolution, the supranuclear equation of state and maximum neutron star mass, related to the total amount of gravitational binding energy release of the collapsed protoneutron star, the resulting total amount of neutrinos, and the time release (luminosity), dependent on neutrino transport via numerical treatment, convective transport, and opacities (Burrows 1990; Herant et al. 1994; Janka & Müller 1995, 1996; Keil & Janka 1995; Burrows et al. 1995; Burrows 1996; Reddy & Prakash 1997; Burrows & Sawyer 1998; Mezzacappa et al. 1998; Messer et al. 1998; Yamada et al. 1999; Pons et al. 1999). Three types of uncertainties are inherent in the Fe-group ejecta, related to (i) the total amount of Fe (-group) nuclei ejected and the mass cut between neutron star and ejecta, mostly measured by 56Ni decaying to 56Fe, (ii) the total explosion energy which influences the entropy of the ejecta and with it the degree of alpha-rich freeze-out from explosive Si-burning and the abundances of radioactive 44Ti as well as 48Cr, the latter decaying later to 48Ti and being responsible for elemental Ti, and (iii) finally the neutron richness or [FORMULA]=[FORMULA] of the ejecta, dependent on stellar structure and the delay time between collapse and explosion. [FORMULA] influences strongly the ratios of isotopes 57/56 in Ni (Co, Fe) and the overall elemental Ni/Fe ratio. The latter being dominated by 58Ni and 56Fe. The position of the mass cut has also a side effect (besides determining the total amount of 56Ni/Fe), it influences the ratio of abundances from alpha-rich freeze-out and incomplete Si-burning, affecting in this way the abundances of the elements Mn (55Co decay), Cr (52Fe decay) and Co (59Cu decay) as discussed in Nakamura et al. (1999).

There is limited direct observational information from individual supernovae with known progenitors (SN 1987A, SN 1993J, 1997D?, 1996N?, 1994I) and possible hypernovae (SN1997ef, 1998bw), leading to direct O, Ti or Fe (Ni) observations (e.g. Shigeyama & Nomoto 1990; Iwamoto et al. 1994, 1998; Iwamoto 1999a, 1999b; Turatto et al. 1998; Sollerman et al. 1998; Kozma & Fransson 1998; Bouchet et al. 1991; Suntzeff et al. 1992). As explosive nucleosynthesis calculations cannot presently rely on self-consistent explosion models, the position of the mass cut is in all cases an assumption and has mostly been normalized to observations of SN 1987A. Whether there is a decline in Fe-ejecta as a function of progenitor mass (as assumed in Thielemann et al. 1996) or actually an increase (Woosley & Weaver 1995) or a more complex rise, maximum and decline (Nakamura et al. 1999) is not really understood. Thus, the results by Thielemann et al. (1996) utilized here are showing the correct IMF integrated behaviour of e.g. Si/Fe, but one has to keep in mind that e.g. O/Fe, Mg/Fe, Si/Fe, Ca/Fe yields of individual supernovae could be quite uncertain and even show an incorrect progenitor mass dependence or a larger scatter than (yet unknown) realistic models. Ratios within the Fe-group (like e.g. Ni/Fe) have been obtained by mass cut positions which reproduce the solar ratios. Thus, the theoretical yields might show already the average values and a much smaller scatter than some observations (see e.g. Henry 1984). Later work attempted to choose mass cuts in order to represent some specific element trends like e.g. in Cr/Fe, Co/Fe or Mn/Fe (Nakamura et al. 1999).

In general we should keep in mind that as long as the explosion mechanism is not completely and quantitatively understood yet, one has to assume a position of the mass cut. Dependent on that position, which is a function of explosion energy and the delay time between collapse and final explosion, the total amount of Fe-group matter can vary strongly, Ti-yields can vary strongly due to the attained explosion energy and entropy, and the ejected mass zones will have a variation in neutron excess which automatically changes relative abundances within the Fe-group, especially the Ni/Fe element ratio.

4: r-Process Yields. SNe II have long been expected to be the source of r-process elements. Some recent calculations seemed to be able to reproduce the solar r-process abundances well in the high entropy neutrino wind, emitted from the hot protoneutron star after the SN II explosion (Takahashi et al. 1994; Woosley et al. 1994). If the r-process originates from supernovae, a specific progenitor mass dependence has to be assumed in order to reproduce the r-process abundances in low metallicity stars as a function of [Fe/H] (Mathews et al. 1992; Wheeler et al. 1998). Such a "hypothetical" r-process yield curve has been constructed by Tsujimoto & Shigeyama (1998), in agreement with ideas of Ishimaru & Wanajo (1999) and Travaglio et al. (1999), and is used in the present galactic evolution calculation. However, we should keep in mind that present-day supernova models have difficulties to reproduce the entropies required for such abundance calculations. In addition, they could exhibit the incorrect abundance features of lighter r-process nuclei (Freiburghaus et al. 1999a), we know by now that at least two r-process sources have to contribute to the solar r-process abundances (Wasserburg et al. 1996; Cowan et al. 1999), and that possible other sources exist (Freiburghaus et al. 1999b). A larger scatter in the r/Fe ratio in low metallicity stars than predicted by the constructed supernova yields would also indicate the need of such another r-process source.

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Online publication: April 17, 2000