Figure 6.5. Upper panel: predicted and observed [C/Fe] versus [Fe/H]. Models from Chiappini et al. (2003a). Lower panel: predicted and observed [N/Fe] versus [Fe/H]. For references to the data see the original paper. The thin and thick continuous lines in both panels represent models with standard nucleosynthesis, as described in the text, whereas the dashed line represents the predictions of a model in which N in massive stars has been considered as a primary element with "ad-hoc" stellar yields.

increased in Type Ia SNe, relative to the yields of I99, and decreased in stars in the range (10-20)MQ, relative to the yields of WW95. Finally, the yield of Ni should be decreased in Type Ia SNe.

• The yields of Cu and Zn from Type Ia SNe should be larger, relative to the standard yields, as already suggested by Matteucci et al. (1993).

6.2.3 Common conclusions from Milky Way models Most of the chemical-evolution models for the Milky Way in the literature lead to the following conclusions.

• The G-dwarf metallicity distribution can be reproduced only by assuming a slow formation of the local disk by infall. In particular, the timescale for the formation of the local disk should be in the range Td > 6-8 Gyr (Chiappini et al. 1997; Boissier and Prantzos 1999; Chang et al. 1999; Chiappini et al. 2001; Alibes et al. 2001).

• The relative abundance ratios [X/Fe] versus [Fe/H], interpreted as a time delay between Type Ia and II SNe, suggest a timescale for the halo-thick-disk formation of Th > 1.5-2.0 Gyr (Matteucci and Greggio 1986; Matteucci and Francois 1989; Chiappini et al. 1997). The external halo and thick disk probably formed more slowly or accreted (Chiappini et al. 2001).

• To fit the abundance gradients, SFR, and gas distribution along the Galactic thin disk we must assume that the disk formed inside-out (Matteucci & Francois 1989; Chiappini et al. 2001; Boissier & Prantzos 1999; Alibes et al. 2001). Radial flows can help in forming the gradients (Portinari & Chiosi 2000) but they are probably not the main cause for them. A variable IMF along the disk can in principle explain abundance gradients but it creates unrealistic situations: in fact, in order to reproduce the negative gradients one should assume that in the external and less-metal-rich parts of the disk low-mass stars form preferentially. See Chiappini et al. (2000) for a discussion on this point.

• The SFR is a strongly varying function of the galactocentric distance (Matteucci & Francois 1989; Chiappini et al. 1997, 2001; Goswami & Prantzos 2000; Alibes et al. 2001).

6.2.4 Abundance gradients from emission lines

There are two types of abundance determinations in H II regions: one is based on recombination lines, which should have a weak temperature dependence (He, C, N, and O); the other is based on collisionally excited lines, for which a strong dependence is intrinsic to the method (C, N, O, Ne, Si, S, Cl, Ar, Fe, and Ni). The second method has predominated until now. A direct determination of the abundance gradients from H II regions in the Galaxy from optical lines is difficult because of extinction, so usually the abundances for distances larger than 3 kpc from the Sun are obtained from radio and infrared emission lines.

Abundance gradients can also be derived from optical emission lines in planetary nebulae (PNe). However, the abundances of He, C, and N in PNe are giving information only on the internal nucleosynthesis of the star. So, to derive gradients one should look at the abundances of O, S, and Ne, which are unaffected by stellar processes. In Figure 6.6 we show theoretical predictions of abundance gradients along the disk of the Milky Way compared with data from H II regions and B stars. The model adopted is from Chiappini et al. (2001, 2003a) and is based on an inside-out formation of the thin disk with the inner regions forming faster than the outer ones, in particular t(R) = 0.875R - 0.75 Gyr. Note that, to obtain a better fit for 12 C, the yields of this element have been increased artificially relative to those of WW95.

As already mentioned, most of the models agree on the inside-out scenario for the disk formation; however, not all models agree on the evolution of the gradients with time. In fact, some models predict a flattening with time (Boissier and Prantzos 1998; Alibes et al. 2001), whereas others, such as that of Chiappini et al. (2001), predict a steepening. The reason for the steepening is that in the model of Chiappini et al. there is a threshold density for SF, which induces the SF to stop when the density decreases below the threshold. This effect is particularly strong in the external regions of the disk, thus contributing to a slower evolution and therefore to a steepening of the gradients with time, as shown in the bottom panel of Figure 6.6.

6.2.5 Abundance gradients in external galaxies Abundance gradients expressed in dex kpc-1 are found to be steeper in smaller disks but the correlation disappears if they are expressed in dex/Rd, which means that there is a universal slope per unit scale length (Garnett et al. 1997). The gradients are generally flatter in galaxies with central bars (Zaritsky et al. 1994). The SFR is measured mainly from Ha emission (Kennicutt 1998) and exhibits a correlation with the total surface gas density (H I plus H2), in particular the suggested law is that of Equation (6.5).

In the observed gas distributions, differences between field and cluster spirals are found in the sense that cluster spirals have less gas, probably as a consequence of stronger interactions with the environment. Integrated colors of spiral galaxies (Josey & Arimoto 1992; Jimenez et al. 1998; Prantzos & Boissier 2000) indicate inside-out formation, as has also been found for the Milky Way.

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