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Astron. Astrophys. 346, 329-339 (1999)

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1. Introduction

There has recently been considerable interest in the Galactic evolution of the abundances of the light elements Li, Be and B (Feltzing & Gustafsson 1994; Reeves 1994; Cassé et al. 1995; Fields et al. 1994,1995; Ramaty et al. 1996,1997; Vangioni-Flam et al. 1998). The Be abundance is particularly interesting because this element is thought to be produced exclusively by spallation reactions involving collisions between nuclei of the CNO group of elements and protons or alpha particles at energies greater than about [FORMULA] per nucleon (MeV/n). Thus the evolution of the Be abundance contains information about the particle acceleration and cosmic ray history of the Galaxy.

The evolution of the Be abundance, and indeed the evolution of all elemental abundances, has to be deduced from observations of the fossil abundances preserved in the oldest halo stars. Advances in spectroscopy over the last decade have greatly improved the quality of the data available (Duncan et al. 1992,1997; Edvardsson et al. 1994; Gilmore et al. 1992; Kiselman & Carlsson 1996; Molaro et al. 1997; Ryan et al. 1994) and the main result is easily summarized: in old halo stars of low metallicity, the ratio of the Be abundance to the Iron (Fe) abundance appears constant, that is to say the Be abundance rises linearly with the Fe abundance.

This has been a surprising result. Naively one had expected that, because Be is a secondary product produced from the primary CNO nuclei, its abundance should vary quadratically as a function of the primary abundances at low metallicities. Indeed, considering that the cosmic rays (CRs) responsible for the Be production are somehow related to the explosion of supernovae (SNe) in the Galaxy, it is natural to assume that their flux is proportional to the SN rate, [FORMULA]. Now since the number of CNO nuclei present in the Galaxy at time t is proportional to the total number of SN having already exploded, [FORMULA], the Be production rate has to be proportional to [FORMULA]. Therefore, the integrated amount of Be grows as [FORMULA], that is quadratically with respect to the ambient metallicity (C,N,O or Fe, assumed to be more or less proportional to one another).

The above reasoning, however, relies on two basic assumptions that need not be fulfilled: i) the CRs recently accelerated interact with all the CNO nuclei already produced and dispersed in the entire Galaxy and ii) the CRs are made of the ambient material, dominated by H and He nuclei. Instead, it might be i) that the proton rich CRs recently accelerated interact predominantly with the freshly synthesized CNO nuclei near the explosion site and ii) that a significant fraction of the CNO rich SN ejecta are also accelerated. In both cases, a linear growth of the Be abundance with respect to Fe or O would arise very naturally, since the number of Be-producing spallation reactions induced by each individual supernova would be directly linked to its local, individual CNO supply, independently of the accumulated amount of CNO in the Galaxy.

In fact, as emphasised by Ramaty et al. (1997), the simplest explanation of the observational data is to assume that each core-collapse supernova produces on average [FORMULA] of Fe, one to few [FORMULA] of the CNO elements and [FORMULA] of Be, with no metallicity dependence . Clearly if this is the case and the production of Be is directly linked to that of the main primary elements, the observed linear relation between Be and Fe will be reproduced whatever the complications of infall, mixing and outflow required by the Galactic evolution models. On the other hand, although the simplest explanation of the data is clearly to suppose a primary behaviour for the Be production, it is possible that this could be an artifact of the evolutionary models (as argued, e.g., by Casuso & Beckman 1997).

Most work in this area has attempted to deduce information about cosmic ray (or other accelerated particle populations) in the early galaxy by working backwards from the abundance observations. While perfectly legitimate, our feeling is that the observational errors and the uncertainties relating to Galactic evolution in general make this a very difficult task. We have chosen to approach the problem from the other direction and ask what currently favoured models for particle acceleration in supernova remnants (SNRs) imply for light element production. This is in the general spirit of recent calculations of the [FORMULA]-decay gamma-ray luminosity of SNRs (Drury et al. 1994) and the detailed chemical composition of SNR shock accelerated particles (Ellison et al. 1997) where we look for potentially observable consequences of theoretical models for cosmic ray production in SNRs.

Interestingly enough, the study of particle acceleration in SNRs suggests that both alternatives to the naive scenario mentioned above do occur in practice, as demonstrated qualitatively in Sect. 2. The first of these alternatives, namely the local interaction of newly accelerated cosmic rays in the vicinity of SN explosion sites, has already been called upon by Feltzing & Gustaffson (1994), as well as the second, the acceleration of enriched ejecta through a SN reverse shock, by Ramaty et al. (1997). However, no careful calculations have yet been done, taking the dynamics of the process into account, notably the dilution of SN ejecta and the adiabatic losses. Yet we show below that they have a crucial influence on the total amount of Be produced, and that a time-dependent treatment is required. Indeed, the evolution of a SNR is essentially a dynamical problem in which the acceleration rate as well as the chemical composition inside the remnant are functions of time. The results of the full calculation of both processes and the discussion of their implications for the chemical evolution of the Galaxy will be found in an associated paper (Parizot & Drury 1999). Here we present simple analytical calculations which provide an accurate understanding of the dynamics of light element production in SNRs and elucidates the role and influence of the different parameters, notably the ambient density.

Although Li and B are also produced in the processes under study, we shall choose here Be as our `typical' light element, because nuclear spallation of CNO is thought to be its only production mechanism, while Li is also (and actually mainly) produced through [FORMULA] reactions, 7Li may be produced partly in AGB stars (Abia et al. 1993), and 11B neutrino spallation may be important as seems to be required by chemical evolution analysis (Vangioni-Flam et al. 1996). In order to compare our results with the observations, we simply note that, as emphasized in Ramaty et al. (1997), the data relating to the Galactic Be evolution as a function of [Fe/H] indicate that [FORMULA] nuclei of Be must be produced in the early Galaxy for each Fe nucleus. Therefore, if Be production is indeed induced, directly or indirectly, by SNe explosions, and since the average SN yield in Fe is thought to be [FORMULA], each supernova must lead to an average production of [FORMULA] nuclei (or [FORMULA]) of Be, with an uncertainty of about a factor of 2 (Ramaty et al. 1997). We adopt this value as the `standard needed number' of Be per supernova explosion. To state this again in a different way, for an average SN yield in CNO of, say, [FORMULA], the required spallation probability per CNO atom is [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999