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Astron. Astrophys. 320, 460-468 (1997)

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2. The WR model stars

Stars with initial masses [FORMULA] in excess of some critical value (around 25 to [FORMULA] for a Pop I composition) are expected to go through the WR phase. Due to strong winds, the original stellar envelope may be removed, so that the H-burning (CNO processed) core may appear at the stellar surface, leading to the development of the WN phase (comprising the WNL and WNE sub-phases). This stage is considered to start when the surface hydrogen mass fraction decreases below 0.4 and the effective temperature [FORMULA] exceeds about 4 (cf. Schaller et al. 1992). In at least certain cases, the further peeling-off of the star may transform the WN star into a WC-WO object. The WC phase starts when He-burning products appear at the surface. The star may then evolve into the WO phase when the ratio [FORMULA] increases above unity (Smith & Maeder 1991), [FORMULA], [FORMULA] and [FORMULA] being the carbon, oxygen and helium mass fractions. In the following, no distinction will be made between the WC and WO phases. The important WR enrichment of the interstellar medium with H-burning products (especially [FORMULA]), as well as with He-burning ashes, at least if the star can reach the WC-WO stage, may have important astrophysical consequences. This paper just deals with the possible contribution of WR stars to the galactic 1.8 MeV [FORMULA] -ray luminosity from the [FORMULA] decay.

2.1. Improved physical ingredients

There are some good reasons to update previous [FORMULA] yield predictions based on a large grid of WR models (Walter & Maeder 1989, Prantzos 1991). This comes about because of some important improvements brought recently to many key physical ingredients of the models. These are taken into account in the computations reported in this paper and are briefly described below:

(1) use is made of the new radiative opacity estimates provided by Iglesias & Rogers (1993);

(2) for consistency, our solar metallicity ([FORMULA]) models are assumed to have the same initial mixture of C to Fe elements as the one adopted for the opacity calculations (see Table 3 of Iglesias & Rogers 1993), while the H and He mass fractions are assumed to be [FORMULA] and [FORMULA]. In addition, the isotopic composition is adopted from Anders & Grevesse (1989). For [FORMULA], the metal abundances are just scaled by the factor [FORMULA] ;

(3) within the framework of the Schwarzschild criterion for convection and of a moderate core overshooting 1 adopted in this and previous work (e.g. Schaller et al. 1992), the models cannot account for several observed features if use is made of the pre-WR and WNL mass loss rates of de Jager et al. (1988) and Abbott and Conti (1987), respectively. A much better agreement between theory and observation is achieved when mass loss rates that are twice the values given by these authors are adopted (Meynet et al. 1994; Maeder & Meynet 1994). These enhanced stellar winds are also adopted in this paper. For WNE and WC stars, we adopt the mass dependence of [FORMULA] proposed by Langer (1989), as in Schaller et al. (1992).

The assumed metallicity dependence of the stellar wind has been shown to impact strongly on the calculated ratios WR/O and WC/WN of stellar types in galaxies of the Local Group (Maeder 1991). Following stellar wind model predictions (e.g. Kudritzki et al. 1987, 1991), the pre-WR mass loss rates are assumed here, as well as in the models of Schaller et al. (1992), to scale with metallicity Z as [FORMULA] ;

(4) The nuclear reaction network for hydrogen burning used by Meynet et al. (1994) has been extended to the NeNa and MgAl chains. It includes in particular the reactions leading to the production and destruction of the [FORMULA] ground ([FORMULA] [FORMULA]) and isomeric ([FORMULA] [FORMULA]) states, considered as two separate species at the temperatures of relevance to the WR model stars (Ward & Fowler 1980). Most of the H-burning rates are taken from Caughlan & Fowler (1988). When it appears, their (0-1) uncertainty factor is adopted equal to 0.1. Updated rates have, however, been used in some cases. The standard set includes the following rates: Landré et al. (1990) for [FORMULA] and [FORMULA], Kious (1990) for [FORMULA], Illiadis et al. (1990) for [FORMULA] and [FORMULA], Champagne et al. (1993) for [FORMULA], Champagne et al. (1988) for [FORMULA]. A limited analysis of the impact on the [FORMULA] yields of the remaining uncertainties in the rates of some of these reactions is presented in Sect. 4.3.

The rates of the He-burning reactions are those adopted by Meynet & Arnould (1993a, b), except that the rate proposed by Giesen et al. (1994) is adopted for [FORMULA]. In order to model correctly the s-process that develops during the WR core He-burning (to be discussed elsewhere), all the neutron sources and sinks up to [FORMULA] have been included in the nuclear network. The neutron poisoning by the heavier nuclides is approximated by an effective neutron sink (see e. g. Jorissen & Arnould 1989).

All the other physical ingredients are the same as in Meynet et al. (1994).

2.2. General characteristics of the models

The general properties of the present models do not differ substantially from those of Meynet et al. (1994). In particular, as in this earlier study, the "enhanced" stellar wind prescription mentioned above, leads to an improved agreement between predictions and several observed WR properties, as for instance their luminosities, their surface chemical composition, as well as the number ratio of WR to O type stars in zones of constant star formation rate and in starburst regions (Maeder & Meynet 1994; Meynet 1995).

Figs. 1 and 2 display the evolution of the total and convective core masses of various of the computed model stars. While Fig. 1 emphasizes the impact of a metallicity variation for [FORMULA], Fig. 2 describes the changes in the structural evolution when [FORMULA] varies at constant ([FORMULA]) metallicity. The different spectroscopic classes through which the displayed model stars evolve are also indicated.

[FIGURE] Fig. 1a-c. Evolution of the total mass [FORMULA], of the mass of the convective core [FORMULA], and of the central ([FORMULA]) and surface ([FORMULA]) [FORMULA] mass fractions for the 60 [FORMULA] model stars with metallicities [FORMULA] (a), 0.02 (b) and 0.008 (c). The central [FORMULA] abundance reaches a maximum at time [FORMULA]. The [FORMULA] surface enrichment starts at time [FORMULA]. The various spectroscopic types encountered during the evolution are indicated on the right of the figure: OV for O-type main sequence stars, LBV for Luminous Blue Variables, WNL, WNE and WC for the different classes of WR stars (see the main text). Note the different ordinate scales defined on the left of the figure.
[FIGURE] Fig. 2a-d. Same as Fig. 1, but for [FORMULA] and [FORMULA] = 120 (a), 85 (b), 60 (c) and 40 [FORMULA] (d).

For each of the computed model stars, Table 1 provides the lifetimes of the H- and He-burning phases, as well as of the WR stage and of the associated spectroscopic classes. The replacement of the opacities of Iglesias et al. (1992) used by Meynet et al. (1994) by those of Iglesias & Rogers (1993) used in the present models leads to somewhat shorter H-burning lifetimes due to slightly increased luminosities predicted during this burning phase. This reduction amounts to 20% and 10% for the 120 and [FORMULA] models with [FORMULA], but is limited to less than 4% for the other models. In contrast, the He-burning lifetimes found here are about 10 to 30 % longer than those found by Meynet et al. (1994). This is a direct consequence of the smaller total masses of the stars when they enter the He-burning phase, this mass reduction being implied by the larger prior mass losses associated with the previously mentioned higher luminosities experienced during the H-burning stage.


Table 1. Duration (in 106 y) of the various evolutionary phases of stars with metallicity Z and initial mass [FORMULA].

The fate of the 120 and [FORMULA] with [FORMULA] deserves some further comments. In these high metallicity cases, the peeling-off of the star by stellar winds is predicted to be so strong that these stars might end their lives as white dwarfs (Meynet et al. 1994). In addition, they spend their whole WR phase as WNL stars. This is also a consequence of the strong stellar winds. These indeed force such a drastic reduction of the main sequence convective core that the He-burning core becomes so small that it is never uncovered by the stellar winds.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998