Astron. Astrophys. 347, 572-582 (1999)

6. Helium burning

The NACRE compilation also provides recommended rates and their lower and upper limits for most of the -captures involved in the non-explosive burning of helium. The impact of the remaining rate uncertainties on the abundances of the elements up to Al affected by He burning is evaluated in our parametric model for two sets of conditions: (i)  g cm^-3 and , adopted to characterize the central or shell He-burning phases of intermediate-mass stars ( ), and (ii)  g cm^-3 and , which can be encountered at the end of the He burning phase in the core of massive stars or in AGB thermal pulses. The initial abundances used in these calculations are adopted as described in Sect. 1.

In contrast to the H-burning case, the abundances during He burning exhibit some sensitivity to density, as it enters differently the reaction rate and the other -capture rates. Consequently, the results presented here should not be used to infer abundances resulting from He burning in specific stellar models, where the time evolution of the temperature and the density may play an important role on the final He-burning composition. It has also to be noted that the neutrons produced by or during He burning lead us to extend the nuclear network to all (about 500) the s-process nuclides up to Bi.

Figs. 10 and 11 illustrate the evolution during He burning in the two situations mentioned above of the abundances of all the stable nuclides between and (plus ). At low temperature (; Figs. 10a and 11a), the main reaction flows are

a) , followed by at the very end of He burning. The factor of 2 uncertainty in the rate of (Fig. 12) is responsible for the error bars on the abundance;

Fig. 10a and b. Mass fractions of the stable C to F isotopes versus the amount of 4He burned at constant density and constant temperature (a left panel ) or (b right panel ). The 4He mass fraction is denoted X(He), the subscript 0 corresponding to its initial value

Fig. 11a and b. Same as Fig. 10 for the nuclides from Ne to Al

Fig. 12. Same as Fig. 4 for some -capture reactions

b) , followed by at the end of He burning. The resulting does not burn at the considered low temperature ³. The uncertainties of a factor of 1.5 and 5 at in the NACRE rates of and , respectively (Fig. 12), are responsible for the wide range of predicted and abundances. A much larger abundance at the end of He burning would result if use were made of the CF88 rate, which is about 220 times smaller than the NACRE one (Fig. 12).

The neutron density resulting from is shown in Fig. 13, along with its associated uncertainty. Albeit small, this neutron irradiation is responsible for the and abundance peaks seen in Fig. 10a. They result from , the protons originating from . Towards the end of He burning, is destroyed by . Shell He burning in AGB stars or central He burning in Wolf-Rayet stars have been proposed as a major site for the galactic production of (Goriely et al. 1989; Meynet & Arnould 1996, 1999; Mowlavi et al. 1998). For AGB stars, these predictions have been confirmed by the observation of overabundances in some of these objects (Jorissen et al. 1992). Incomplete He-burning (e.g. in Wolf-Rayet stars) may also contribute to the galactic enrichment in primary , as required by the observations of this nuclide in the interstellar medium (Güsten & Ungerechts 1985).

Fig. 13. Neutron density versus the amount of helium burned at and (solid line) or (dashed line). The initial mass fraction is adopted equal to , which is obtained at the end of the CNO cycle operating at and g cm-3 (Sect. 3)

The large abundance seen on Fig. 11a results from the particular choice of initial conditions (see Sect. 1), since is not produced in the conditions prevailing during He-burning. Its rapid drop close to the end of He burning results from the combined effect of -decay and making use of the few neutrons liberated by .

At higher temperatures (Figs. 10b and 11b), the He-burning nucleosynthesis of the elements up to about Al is essentially the same as in the low temperature case. The major differences are observed for , , , , , and , and are mainly due to a larger neutron production by , and . Note that is about 150 times slower than in these conditions, but is fast enough to keep the neutron density above (Fig. 13). These neutrons allow protons to be produced by the reactions and . Additional protons come from . As a result, is produced via , , and . The production of follows from . Since most of the involved reactions have better known rates at than at , the corresponding error bars on the abundances are smaller at higher temperature. Neutrons are also responsible for the destruction of any that may survive the former H-burning episode.

The operation of Mg at the end of He burning leads to a non-negligible neutron irradiation which triggers a weak s-process leading to the overproduction of the s-nuclei. Unfortunately, the rate of Mg remains quite uncertain (Fig. 12), even at temperatures as high as (in this case by a factor of 25). The resulting uncertainty on the neutron density amounts to a factor of 10 (Fig. 13), while the total neutron exposure spans the range 0.1-0.3 mbarn^-1. Finally, the -captures by the Ne isotopes are fast enough at temperatures to alter the Mg isotopic composition. This may provide a direct observational signature of the operation of the Mg neutron source in stars (e.g. Malaney & Lambert 1988). Large uncertainties remain, however, in these reaction rates at He-burning temperatures, except for the relatively well-determined rate.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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