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Astron. Astrophys. 358, L67-L70 (2000)

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2. Input physics

The calculations reported here are based on a model for a [FORMULA] 8 [FORMULA] helium star already considered by RAHPN. It corresponds to a main sequence mass of about 25 [FORMULA] and is evolved from the beginning of core helium burning to the supernova explosion. Details about this model can be found in Hashimoto (1995), and are summarized in RAHPN. As in RAHPN, 20 O/Ne-rich layers with explosion temperatures peaking in the (1.8-3.3)[FORMULA] K range are selected as the P-Process Layers (PPLs). Their total mass is approximately 0.58 [FORMULA]. The deepest PPL is located at a mass of about 1.94 [FORMULA], which is far enough from the mass cut for all the nuclides produced in this region to be ejected during the explosion.

The p-process reaction network and its numerical solver are described by RAHPN. A series of their selected nuclear reaction rates are updated, however. In particular, the NACRE `adopted' rates are used for charged particle captures by nuclei up to [FORMULA]. For heavier targets, the rates predicted by the Hauser-Feshbach code MOST (Goriely 1997) are used, except for the experimentally-based neutron capture rates provided by Beer et al. (1992)1

As already pointed out in Sect. 1, we turn our special attention to the impact of the uncertainties remaining in the rate of [FORMULA]. For temperatures of about [FORMULA] K at which the s-process typically develops during core He burning in massive stars (e.g. Rayet & Hashimoto 2000), the NACRE upper limit on this rate is 50-500 times larger than the `adopted' value (see Angulo et al. 1999 for details). In order to quantify the consequences of this situation for the predicted abundance distribution of the s-nuclide seeds for the p-process, and ultimately for the p-nuclide yields themselves, we perform nucleosynthesis calculations for five different rates ranging from the NACRE adopted value to its upper limit. These rates, labelled Ri (i=1 to 5) in the following, are defined and displayed in Fig. 12 They are used in the [FORMULA] 25 [FORMULA] star referred to above to calculate the abundances of the s-process nuclides at the end of core He burning. The results are shown in Fig. 2 for the s-only nuclides. Use of R1 leads to the classical `weak' s-process component pattern (e.g. Rayet & Hashimoto 2000), exhibiting a decrease of the overproduction (with respect to solar) of the s-nuclides by a factor ranging from [FORMULA]100 to about unity when the mass number A increases from about 70 to 100. In the heavier mass range, the s-process `main component' supposed to originate from low- or intermediate-mass stars takes over. This `canonical' picture changes gradually with an increase of the [FORMULA] rate, more [FORMULA] having time to burn, releasing more neutrons, before He exhaustion in the core. The direct result of this is a steady increase of the overproduction of heavier and heavier s-nuclides. For example, with the extreme R5 rate, the overproduction factor increases from [FORMULA] to [FORMULA] for A varying from about 70 to 90, before decreasing to a value around unity for [FORMULA] only.

[FIGURE] Fig. 1. The five [FORMULA] rates Ri used in our calculations for temperatures of relevance for core He burning in massive stars. All rates are normalized to R1, which is the NACRE `adopted' rate. R5 corresponds to the NACRE upper values. R3, R2 and R4 are the geometrical means between R1 and R5, R1 and R3, and R3 and R5, respectively (see also footnote 2)

[FIGURE] Fig. 2. Distribution of the abundances, normalized to solar values, of the s-only nuclides at the end of core He burning in the considered [FORMULA] 25 [FORMULA] model star, for the [FORMULA] rates Ri (i = 1 to 5) defined in Fig. 1, all the other ingredients of the model being kept unchanged (see Rayet & Hashimoto 2000). The dashed line is the distribution adopted by RAHPN for their p-process calculations

At first sight, it might be felt that the s-process abundance distributions obtained with large enough Ri values exhibit some unwanted or embarrassing features. One of these concerns the underproduction of the [FORMULA] s-nuclides relative to the [FORMULA] ones. Another one relates to the fact that a more or less substantial production of heavy s-nuclides (like in the Ba region) would screw up the pattern of the s-process main component ascribed to lower-mass stars. In our opinion, none of these predictions can really act as a deterrent to [FORMULA] rates substantially in excess of R1. On the one hand, the absence of ab initio self-consistent calculations of the s-process in low- and intermediate mass stars does not allow at this time to predict the exact shape of the main s-process component which is classically assigned to these stars. As a consequence, a contribution to the main component by massive stars cannot be excluded, even if it may disturb some traditional views on the subject. On the other hand, the reduction of the light s-process nuclide production by massive stars could well be compensated by their increased synthesis by some low- or intermediate-mass stars when rates larger than R1 are considered (Goriely & Mowlavi 2000). The classical [FORMULA] overproduction problem found in the massive star s-process (e.g. Rayet & Hashimoto 2000) could also be eased with increased [FORMULA] rates, as demonstrated by Fig. 2. For these same rates, note that [FORMULA] is not overproduced either in some of the calculations of Goriely & Mowlavi (2000) which predict high yields of the other light s-nuclides.

Fig. 2 also suggests that a discrepancy, if any, between the observed Ba overabundance in the SN1987A ejecta and the model predictions could be cured in a natural way by increasing the adopted [FORMULA] rate. The [Ba/Fe]SN/[Ba/Fe]LMC ratio is observationally still quite uncertain, values between about 5 and 20 having been reported (e.g. Mazzali & Chugai 1995). Prantzos et al. (1988) have calculated lower values of 2.6 to 4.7 with the [FORMULA] rate of Fowler et al. (1975). This rate is on average comparable to R1 in the temperature range of relevance to the s-process. We have not conducted any new s-process calculation in a specific SN1987A progenitor model. Instead, some rough estimates based on the procedure of Prantzos et al. (1988) in which their adopted s-process Ba mass fraction is replaced by the one calculated for the model star adopted here have been made. Assuming that the LMC metallicity is one third of the solar one, we predict [Ba/Fe]SN/[Ba/Fe]LMC ratios from 3 to 14 for rates increasing from R1 to R5. Theory could thus account for quite substantial SN1987A Ba productions with high enough [FORMULA] rates (compatible with the NACRE data).

As discussed by RAHPN, it is a fair approximation to adopt the s-process abundance distributions of Fig. 2 as seeds for the p-process. For the [FORMULA] species, the initial abundances in the PPLs are taken from the detailed stellar models. Although these models have been obtained with rates that may differ from the NACRE ones adopted here, this inconsistency is certainly not responsible for any intolerable distorsion in the predicted s-process seeds or p-process yields.

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Online publication: June 20, 2000