Astron. Astrophys. 362, 921-936 (2000)

3. Model results for abundance gradients

We calculated the evolution of the abundances of all elements between H and Zn with the WW95 metallicity dependent yields in all the zones of our model disk. In Fig. 4 we present the results concerning all elements with measured abundance gradients in the Milky Way. We notice that, since we did not include yields from IMS in our calculation, our results for He, C and N represent rather lower limits. We shall discuss the comparison to observations in the next section, where we shall also explore the role of massive, mass losing stars to the abundance profiles of those elements. Here we focus on the model results, which may be summarised as follows:

Fig. 4. Evolution of abundance profiles in the Milky Way disk, in the framework of the model presented in Sect. 2 and with the WW95 metallicity dependent yields. Curves show results at 2, 4, 9 and 13.5 Gyr, respectively (as indicated in the lower right panel). Because of the metallicity dependence of the yields, some elements (N, Al) have steeper abundance profiles than e.g. O, at all times. This is also the case for Fe, but the reason is its production mostly by SNIa. C and N are underproduced with respect to their solar system values, because yields from intermediate mass stars are neglected in this calculation. Metallicity dependent massive star yields from M92 considerably improve the situation concerning carbon (see Fig. 7), but not nitrogen. Solar abundances () were taken from Grevesse & Sauval (1998).

i) Final values (at T = 13.5 Gyr) of the abundances at R₀ = 8 kpc are solar for O, Al, Si, S, Ar and Fe; they are slightly lower than solar for Ne and Mg; and they are considerably below solar for C and N. It may appear surprising that Ne and Mg do not reach their solar values, but this is a consequence of the adopted metallicity dependent yields of WW95 (Fig. 1): the average (i.e. over the disk's age) overproduction factors of Ne and Mg are lower than the one of e.g. O. It is not clear whether such a dependence is physical or just an artifact of the WW95 models. As for C and N, it is clear that massive stars with no mass loss cannot be the main sources of those elements (see also Sect. 4).

ii) The most prominent feature of the model is the prediction that abundance gradients flatten with time. This is a generic feature of all models forming the galactic disk "inside-out". Indeed, in that case, there is a rapid increase of the metal abundance at early times in the inner disk, leading to a steep abundance gradient. As time goes on, star formation "migrates" to the outer disk, producing metals there and flattening the abundance gradient.

iii) The final abundance profile (T = 13.5 Gyr) is, in general, flatter in the inner disk. As already described in Prantzos & Aubert (1995) this is due to the fact that in those regions the large populations of low-mass, long-lived stars that are formed early on in galactic history reject a lot of metal-poor gas at the end of their evolution, which dilutes the metal abundances; this effect is absent in the outer regions, where there are not very old stellar populations. Notice that the flattening seems to be more important in the case of N, Ne, Mg and Al. These elements show some metallicity dependence in their yields (at least according to WW95) which is difficult to understand in the case of Ne and Mg, but expected in the case of the secondary N and of the odd-Z Al. Since WW95 give yields only up to stellar metallicities of Z = , for higher metallicities we use their Z = yields. This means that in the inner disk, where metallicities higher than solar are reached, we underestimate the production of any element with metallicity dependent yield. If appropriate yields were used, the Al and N profiles in the inner disk would be steeper, not flatter, than the one of O.

The magnitude of the current abundance gradients in the Milky Way disk is one of the most important constraints in the models of the evolution of our Galaxy. Most of the proposed models reproduce it fairly well (e.g. Tosi 2000 and references therein), at least when no radial inflows are included. However, equally important is the question of the evolution of those gradients and, in particular, whether they flatten or steepen with time. We shall confront our models to the data and to other theoretical works in the next section. Here, we present the evolution of our model gradients in the 4-14 kpc region for a few selected elements (Fig. 5). All gradients were systematically larger in the past. The gradient of Fe is slightly larger than the one of O, because our adopted prescription for the SNIa rate produces a smaller O/Fe ratio in the inner disk than in the outer one. The gradient of secondary N is always steeper than the one of O, but since we do not include N production from intermediate mass stars or WR stars in this calculation, this result serves merely for illustration purposes.

Fig. 5. Evolution of abundance gradients (expressed in dex/kpc) in the Milky Way disk (range: 4-14 kpc from the centre), in the framework of the model presented in Sect. 2 and with the WW95 metallicity dependent yields. Because of the inside-out formation scheme adopted here, gradients were steeper in the past. Because of the metallicity dependence of the yields of WW95, some elements, like N or Mg, have larger abundance gradients (in absolute value) than O. This is also the case for Fe, but the reason is its production mostly by SNIa.

© European Southern Observatory (ESO) 2000

Online publication: October 30, 2000
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