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

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4. The [FORMULA] -ray connection

The Comptel imaging telescope aboard the Compton Gamma-Ray Observatory (CGRO) has demonstrated that the emission of the 1.8 MeV line associated with the decay of [FORMULA] originates in rather localized regions along the galactic plane that are not necessarily concentrated in the inner disk of the Galaxy (Diehl et al. 1995a). In particular, some bright [FORMULA] emission features might be associated with the galactic inner-arm edges at [FORMULA]. This might support the idea that massive stars are significant contributors to the 1.8 MeV [FORMULA] -ray line, as suggested by Prantzos (1993).

On the other hand, a fraction of the 1.8 MeV emission could originate from localized foreground regions, as suggested by the recent detection of an emission peak in the direction of the Vela supernova remnant (Diehl et al. 1995b). In such conditions, as stressed by Diehl et al. (1995a), the present galactic mass [FORMULA] of [FORMULA] could be lower than the canonical [FORMULA] derived from the HEAO-C (Mahoney et al. 1984) and SMM (Share et al. 1985) measurements. However, the present inability to disentangle the contributions of foreground and background sources leaves a large uncertainty on [FORMULA]. In the following, we adopt [FORMULA].

4.1. Contribution of the WR population to the galactic [FORMULA]

Early estimates of the contribution of WR stars to the galactic [FORMULA] content (e.g. Prantzos et al. 1985; Prantzos and Cassé 1986) are based on an evaluation of their total number and distribution in the Galaxy. The estimate of these quantities is made uncertain by the fact that the inner galactic regions are obscured by dust, so that the WR catalogues are complete only at distances [FORMULA] from the Sun, where [FORMULA] WR stars have been observed up to now (van der Hucht 1995).

From an extrapolation of the data concerning the WR density in low-metallicity regions like the Large and Small Magellanic Clouds and in the solar neigborhood, the number of galactic WR stars can be roughly estimated from [FORMULA], where [FORMULA] is the galactocentric distance of the Sun. This leads to [FORMULA], corresponding to a galactic frequency [FORMULA], since the average WR lifetime is of the order of 0.5 My. Let us note that these numbers are likely to be lower limits, since the star formation rate and the ratio of the number of WR to O-type stars increase significantly in the inner galactic regions.

An estimate of the galactic frequency of WR stars may also rely on the use of a stellar initial mass function (IMF), and on the current rate [FORMULA] of massive star supernovae in the Milky Way (Prantzos & Diehl 1996). Observations of external spiral galaxies lead to the expectation that [FORMULA] supernovae explode per century in our Galaxy, 85% of them being considered to involve massive stars (Tammann et al. 1994). From this, we assume that [FORMULA] per century. We also adopt a power-law IMF [FORMULA] with [FORMULA] [Note that the value [FORMULA] of the Salpeter IMF was derived for [FORMULA] stars. For larger masses, [FORMULA] seems to be more appropriate (e.g. Scalo 1986; Kroupa et al. 1993)].

In such conditions, [FORMULA] relates to [FORMULA] by


where [FORMULA] and [FORMULA] are the lower limits to the masses of the stars that may become supernovae and WR. The former is [FORMULA], while the latter depends on the adopted mass loss rates and on metallicity. More specifically, our calculations predict that [FORMULA] for [FORMULA], while [FORMULA] for [FORMULA]. This Z value represents a present-day average galactic metallicity if one relies on the relatively large galactic metallicity gradient [FORMULA] dex/kpc suggested by the observations of HII regions (Shaver et al. 1983).

With these estimates, Eq. (3) leads to [FORMULA], depending on the adopted x and [FORMULA] values. This translates into 3000-10 000 WR stars per My. The lower value corresponds to [FORMULA] WR stars currently present in the Galaxy, while the latter leads to the rather extreme number [FORMULA]. On the other hand, from the yields of Fig. 3 and our adopted IMF, an average WR yield [FORMULA] can be defined for [FORMULA] stars.

With these estimates, the rate of [FORMULA] production by WR stars in the Galaxy amounts to


More formally, the [FORMULA] production rate from galactic WR stars may be evaluated from


In this expression, [FORMULA] is the galactocentric-dependent distribution of WR stars in the Galaxy, and the dependence of [FORMULA] and of [FORMULA] [Eq. (1)] on the metallicity [FORMULA] is explicitly taken into account.

The calculation of Eq. (5) is performed with the help of the following assumptions:

(1) the integral [FORMULA] is normalized to [FORMULA] per century in the Galaxy;

(2) in the whole [FORMULA] kpc, the metallicity gradient is [FORMULA] under the constraint that [FORMULA]. For [FORMULA] kpc, [FORMULA] ;

(3) [FORMULA] follows the observed surface density of giant molecular clouds as given by Scoville and Sanders (1987), except for [FORMULA] kpc, where 5 times lower values are adopted. This accounts for a possible overestimate of the number of [FORMULA] molecular clouds and of the star formation rate in the central parts of our Galaxy (see Prantzos 1991).

In such conditions, Eq. (5) leads to [FORMULA], in agreement with the approximate estimate provided by Eq. (4). The lower and upper limits are obtained with [FORMULA] and [FORMULA], respectively. These values are higher than previous estimates. For example, Signore and Dupraz (1993), Prantzos (1991, 1993) and Meynet (1994) evaluate the WR contribution to lie between 0.1 - 0.35, 0.2 - 0.5 and [FORMULA], respectively. Our larger production rates result mainly from the higher mass loss rates considered here. Indeed, as shown in Sect. 3.2, the adoption of previously used standard mass loss rates reduces the [FORMULA] masses obtained here by a factor of about two. At this point, it is important to emphasize again that the choice of higher than standard mass loss rates is not arbitrary, but improves the agreement between model predictions and observations.

The mass [FORMULA] of present-day galactic [FORMULA] can be obtained trivially from Eqs. (4) or (5) by noting that [FORMULA] in a steady-state regime. Thus, numerically, [FORMULA] if M and [FORMULA] are expressed in [FORMULA] and [FORMULA], respectively.

The preceding discussion puts forth that the estimates of [FORMULA] are sensitive to the galactic metallicity gradient, the precise value of which is still uncertain. In particular, observations of B stars up to about 15 kpc from the galactic center do not confirm the existence of an important gradient (Kaufer et al. 1994, and references therein). In order to evaluate the impact of a change in the adopted [FORMULA] value on the predicted [FORMULA], let us assume that [FORMULA] in the whole [FORMULA] kpc region. In such a case, the WR contribution amounts to [FORMULA] if [FORMULA], [FORMULA] and [FORMULA]. The results are also directly proportional to the adopted supernova rate. If [FORMULA] instead of 3, [FORMULA] is lowered from the (0.7 - 1.4) [FORMULA] range mentioned above to about (0.5 - 0.9) [FORMULA].

All in all, for reasonable values of the IMF, metallicity gradient, SN rate and star formation rates in the Galaxy, our stellar models predict that the contribution of the WR stars to the present-day galactic [FORMULA] production amounts to [FORMULA]. The WR stars might thus account for 20 to 70% of the approximate [FORMULA] of [FORMULA] present nowadays in the Galaxy, and are thus far from being negligible contributors.

4.2. The case of [FORMULA] Velorum

As already mentioned above, an enhanced 1.8 MeV [FORMULA] -ray line emission has been detected in the direction of the Vela supernova remnant by the CGRO, the measured flux having values between 2.3 and [FORMULA] (Diehl et al. 1995b). The one steradian field of view of the instruments not only contains the Vela remnant, but also [FORMULA] Velorum, the nearest known WR star (WR 11). Other sources, such as the Gum nebula and novae, also lie in the same direction.

While the general 1.8 MeV emission from the Galaxy likely results from a complex population of stellar objects, this observation gives an opportunity of constraining the yield from a few stellar sources, and even possibly from a single one. Unfortunately, our ignorance of the distance(s) of the emitting source(s) makes a reliable interpretation of this observation difficult (see Oberlack et al. 1994, Prantzos & Diehl 1996).

If it is assumed that [FORMULA] Vel lies 300 to 450 pc away (van der Hucht 1992), and if it is considered in addition that it can be represented reasonably well by our [FORMULA] model star, its maximum 1.8 MeV [FORMULA] -ray flux is expected to range from about 0.7 to about [FORMULA]. This falls short of accounting for the observed flux. This discrepancy might be even more severe if due consideration is taken of the fact that [FORMULA] Vel is a double line spectroscopic binary with a period of about 78 d (Niemela & Sahade 1980). Indeed, Braun & Langer (1995) estimate that the [FORMULA] yield from a WR star in a binary system undergoing Roche lobe overflow might be smaller than the one of a single star with the same initial mass if [FORMULA], which may well be the case of [FORMULA] Vel.

On the other hand, if the Vela supernova remnant is located at about 500 pc, as usually estimated (Milne 1968), its 1.8 MeV [FORMULA] -ray flux amounts to [FORMULA] if use is made of the [FORMULA] yield predictions of Timmes et al. (1995) for a [FORMULA] supernova with initial solar composition. This flux is comparable to the one for [FORMULA] Vel estimated above. However, this conclusion is quite uncertain in view of the poor knowledge of the distance of the Vela remnant and of the initial supernova mass. It has been proposed recently (Oberlack et al. 1994) that the distance to Vela may be as low as [FORMULA]. In such a case, the 1.8 MeV [FORMULA] -ray flux from the Vela remnant would likely exceed the one from [FORMULA] Vel.

In conclusion, various uncertainties prevent the unambiguous identification of the source(s) responsible for the observed [FORMULA] -ray flux increase in the direction of Vela. More sensitive detectors with better angular resolution might bring some light on this interesting issue (see below).

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Online publication: June 30, 1998