4. Estimate of the contribution of WR stars to the galactic fluorine
In order to evaluate the level of contamination by the winds of WR stars on a galactic scale, we use the yields [Eq. (1)] in a very simple model of galactic chemical evolution making use of the closed box and instantaneous recycling approximations. We also suppose that only WR stars are able to affect the galactic budget through their winds, all other possible production or destruction sites being neglected.
In such conditions, the mass fraction in the galactic gas at time t is equal to (e.g. Tinsley 1980)
where is the mass fraction of the gas in the Galaxy at time t, and is a representative time-independent approximation of the net yield of a stellar generation defined by
where R is the "returned fraction", and the lowest and highest mass of the stars going through the WR phase, and the initial mass function (IMF). It has to be noted that Eq. (2) would break down if the true time- (or Z-)dependent yields were used instead of . In order to evaluate the latter quantity, we notice that values of about , and are obtained for , 0.02 and 0.04 if use is made of the values reported in Sect. 3 and of the (properly normalized) IMF derived by Kroupa et al. (1993). On such grounds, we just adopt the rough estimate .
If this approximation is used in conjunction with the value considered to characterize the solar neighbourhood at the time of the solar system formation 4.5 billion years ago (see Prantzos & Aubert 1995, and references therein), Eq. (2) leads to in the local interstellar medium (to be compared with the solar system abundance of 4 10-7). Thus, our simple estimate predicts that WR stars might account for most of the solar system content . Even larger quantities would be predicted with the use of the rate of Koehler & O'Brien (1989)! After having faced for long the problem of the underproduction of , the theory of nucleosynthesis might now live with the danger of its predicted overabundance. If this is confirmed by further studies, constraints will obviously have to be put on one model or another.
© European Southern Observatory (ESO) 2000
Online publication: March 17, 2000