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

1. Introduction

The evolution of a star is made of a succession of "controlled" thermonuclear burning stages interspersed with phases of gravitational contraction. The latter stages are responsible for a temperature increase, the former ones producing nuclear energy and composition changes.

As is well known, hydrogen and helium burning in the central regions or in peripheral layers of a star are key nuclear episodes, and leave clear observables, especially in the Hertzsprung-Russell diagram, or in the stellar surface composition. These photospheric abundance signatures may result from so-called "dredge-up" phases, which are expected to transport the H- or He-burning ashes from the deep production zones to the more external layers. This type of surface contamination is encountered especially in low- and intermediate-mass stars on their first or asymptotic giant branches, where two to three dredge-up episodes have been identified by stellar evolution calculations. Nuclear burning ashes may also find their way to the surface of non-exploding stars by rotationally-induced mixing, which has been started to be investigated in some detail (Heger 1998), or by steady stellar winds, which have their most spectacular effects in massive stars of the Wolf-Rayet type.

The confrontation between the wealth of observed elemental or isotopic compositions and calculated abundances can provide essential clues on the stellar structure from the main sequence to the red giant phase, and much has indeed been written on this subject. Of course, the information one can extract from such a confrontation is most astrophysically useful if the discussion is freed from nuclear physics uncertainties to the largest possible extent.

Thanks to the impressive skill and dedication of some nuclear physicists, remarkable progress has been made over the years in our knowledge of reaction rates at energies which are as close as possible to those of astrophysical relevance (e.g. Rolfs & Rodney 1988). Despite these efforts, important uncertainties remain. This relates directly to the enormous problems the experiments have to face in this field, especially because the energies of astrophysical interest for charged-particle-induced reactions are much lower than the Coulomb barrier energies. As a consequence, the corresponding cross sections can dive into the nanobarn to picobarn abyss. In general, it has not been possible yet to measure directly such small cross sections. Theoreticians are thus requested to supply reliable extrapolations from the lowest energies attained experimentally to those of most direct astrophysical relevance.

Recently, a new major challenge has been taken up by a consortium of European laboratories with the build-up of well documented and evaluated sets of experimental data or theoretical predictions for a large number of astrophysically interesting nuclear reactions (Angulo et al. 1999). This compilation of reaction rates, referred to as NACRE (Nuclear Astrophysics Compilation of REaction rates; see Sect. 2 for some details), comprises in particular the rates for all the charged-particle-induced nuclear reactions involved in the "cold" pp-, CNO, NeNa and MgAl chains, the first two burning modes being essential energy producers, all four being important nucleosynthesis agents. It also includes the main reactions involved in non-explosive helium burning.

The aim of this paper is to calculate with the help of the NACRE data the abundances of the different isotopes of the elements from C to Al involved in the non-explosive H (Sects. 3-5) and He (Sect. 6) burnings, special emphasis being put on the impact of the reported remaining rate uncertainties on the derived abundances. The yields from the considered burning modes are calculated by combining in all possible ways the lower and upper limits of all the relevant reaction rates. One "reference" abundance calculation is also performed with all the recommended NACRE rates. Note that the pp-chains are not considered here. A solar neutrino analysis based on preliminary NACRE data for the pp reactions can be found in Castellani et al. (1997).

Our extensive abundance uncertainty analysis is performed in the framework of a parametric model assuming that H burning takes place at a constant density  g cm^-3 and at constant temperatures between and 80 ( is the temperature in units of ). The corresponding typical values adopted for He burning are  g cm^-3 and and 3.5. These ranges encompass typical burning conditions in a large variety of realistic stellar models. For the study of H-burning, initial abundances are assumed to be solar (Anders & Grevesse 1989). For He-burning, we adopt the abundances resulting from H burning at and  g cm^-3 calculated with the use of the NACRE recommended rates. The H- and He-burning nucleosynthesis is followed until the H and He mass fractions drop to .

In spite of its highly simplistic aspect, this analysis provides results that are of reasonable qualitative value, as testified by their confrontation with detailed stellar model predictions. Most significant, these parametric calculations have the virtue of identifying the rate uncertainties whose impact may be of significance on abundance predictions at temperatures of stellar relevance. They thus serve as a guide in the selection of the nuclear uncertainties that have to be duly analyzed in detailed model stars, particularly in order to perform meaningful confrontations between abundance observations and predictions. They are also hoped to help nuclear astrophysicists pinpointing the rate uncertainties that have to be reduced most urgently.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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