2. Composition of the EPs
2.1. Mean-wind compositions
Leaving aside selective effects at the acceleration related to the different mass-to-charge ratios of the ions (Ellison et al. 1997, Meyer et al. 1997), we assume that the composition of the accelerated nuclei reflects the Wolf-Rayet stellar wind supplying the acceleration process. However, since we adopt the steady-state approximation, we must average the wind composition over the entire life of the star, weighting each instantaneous composition by the current mass loss rate. The total mass of the nuclear species i blown by the star during its life is given by:
where and are respectively the stellar mass loss rate and the mass fraction of element i in the wind at time t.
We have estimated in this way the mean wind composition for stars with zero-age-main-sequence (ZAMS) masses , 60, 85 and , using the massive star evolutionary models of the Geneva group (Schaller et al. 1992, Meynet et al. 1994), either with `standard' mass loss rates (models C), mass-loss rates twice as large after the main-sequence phase (models D), or mass-loss rates twice as large during the main-sequence and the late WN phases (models E). Some of the resulting compositions, normalised to O, are shown in Table 1.
In the special case of Orion, the study of the stellar content of the molecular complex has been carried out in great detail (e.g. Brown et al. 1994). Blaauw (1964) divided the Orion OB1 association into four subgroups: 1a, 1b, 1c and 1d, whose respective ages have been re-estimated recently to be ( Myr), ( Myr), ( Myr) and ( Myr) respectively (Brown et al. 1994). The most recent intense activity is expected to be related mainly to subgroup 1c. Indeed, the most massive stars (with lifetimes years) of subgroup 1a have exploded some 5- years ago, while the subgroups 1b and 1d are too young for even their most massive stars to have evolved up to the WC stage. Subgroup 1b actually contains the most massive stars known in Orion OB1, namely Ori A (), Ori A () and Ori A (), which are not observed as Wolf-Rayet stars. By contrast, subgroup 1c has just the age required for the stars of ZAMS mass (if any) to have exploded, but not the stars of (see Table 2). The most massive stars in OB1c are indeed Ori A () and Ori () (Lamers & Leitherer 1993; Vilkoviskij & Tambovtseva 1992). We conclude that the composition of the Orion EPs is likely to be of the mean-wind type.
Other compositions have been investigated in previous works. Ramaty et al. (1996) (hereafter RKL96) have discussed in detail the cases of solar system composition (SS), cosmic-ray source (CRS), supernova ejecta from stars of (SN35) and (SN60), dust grains (GR) and Wolf-Rayet (W-R) stars of spectral type WC. We also used these compositions comparison, and obtained identical results for both gamma-ray line and LiBeB production, except in the calculation of the (1-3 MeV)/(3-7 MeV) band ratio, to be discussed in Sect. 5.2.
It can be seen in Table 1 that the abundances of 1 H and 4 He are between one and two orders of magnitude lower in the `WC' composition than in our mean-wind compositions (depending on the model used). This is because Ramaty et al. use the extreme late phase wind of a W-R star, whereas we use averaged abundances. However, the late WC composition should not reflect the mean EP composition, since the mass ejected from the star during the final episode is negligible with respect to the total mass of the wind. Indeed, the mass loss rate is highest at the onset of the W-R phase, when the wind is still rich in helium. Afterwards, the 4 He abundance in the wind continues to decrease, to the benefit of 16 O. As a consequence, the C/O ratio decreases by about a factor of 4 from the onset of the W-R phase to its very end, which also explains why our mean wind compositions have a higher C/O ratio than the `late-WC' composition used by RKL96. This constitutes a second distinctive feature whose observational consequences, together with those of the higher 1 H and 4 He abundances, are discussed below.
2.2. Mean-OB compositions
In the general situation where nuclei are accelerated from the hot plasma filling a bubble (or superbubble) created by joint stellar winds and multiple SNe, as possibly in Orion (Cowie et al. 1979, Burrows et al. 1993, Bykov & Bloemen 1994), the mean wind compositions of individual stars are probably not appropriate. Rather we have to consider a global mean composition, arising from an evolved OB association. To obtain such a `mean-OB' composition, we must weight the mean-wind composition of each star in a given range of ZAMS mass according to its total ejected mass and to its probability of occurrence among the association, which is given by the initial mass function (IMF). Indeed, the most massive stars supply the bubble with more enriched material than the lighter ones, but on the other hand they are less numerous.
The mean OB compositions are thus obtained from the total ejected mass of isotope i:
where is the IMF, and . A few examples of total mass loss , taken from the Geneva group calculations, are shown in Table 2.
The resulting compositions are quite independent of , the mass of the heaviest stars which contribute, because these stars are very rare, even in the case of a hard IMF with index . Here we set . Concerning , we argue that most of the energy released within superbubbles comes from stars with mass greater than . Since less massive stars have longer lifetimes, the contribution of their winds is expected to come too late to participate to the acceleration process. We thus assume here that , and argue that, accordingly, the OB associations should not be active as gamma-ray line sources during more than Myr, the lifetime of stars (see Table 2).
However, we also investigated as an `extreme case' various EP compositions obtained with . In a general way, these compositions are poorer in C and O, with respect to H and He, and have a smaller C/O abundance ratio than the `standard' compositions obtained with . Both cases are compared in Sect. 8. However, our main conclusions are found to be insensitive to such a change in .
In Table 1 we show mean-OB compositions calculated for solar and twice solar metallicities, recalling that the first composition applies to Orion and the second one to OB associations in the inner Galaxy. The assumed IMF index is , which is the value estimated for the Orion OB1 association (Brown et al. 1994). The stellar evolutionary models that we use are again those of the Geneva group, and the compositions shown in Table 1 correspond to standard mass loss rates (models C). Other models and IMF indices have been investigated, but we do not show them here.
It is worth noting that: i) as Z increases, the WC-O phase arises earlier and earlier in the stellar evolution, when 4 He has only burned partially in the core. In our example of a star, only of the core 4 He has burned at the onset of the WC phase (i.e. when the mass loss rate is highest) for , and only for . As a consequence, the metals are relatively less abundant in the winds of twice solar metallicity stars than in the winds of solar metallicity stars. ii) a higher C/O ratio occurs for ; not as much carbon is burned into oxygen, since some of it is expelled - and thus saved - in the wind. Some implications of these pecularities are analysed below.
2.3. Remark on the W-R models
We have assumed that the EP composition reflects essentially that of the winds of massive stars, neglecting in particular the supernovae ejecta contribution. This is justified in the case of Orion, since the total mass lost by a massive star during its life is much larger than the mass ejected in its final explosion (see Table 2). We also compare in Table 3 the masses of the most relevant nuclei expelled in the wind and in the explosion by a star, using the wind model C and the explosion model WRA of Woosley et al. (1993). Note that the SN ejecta are very rich in 16 O, and might enhance somewhat the oxygen abundance in the EPs, and in turn lower slightly the 12 C /16 O emission line ratio.
© European Southern Observatory (ESO) 1997
Online publication: March 24, 1998