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Figure 6.6. Upper panel: abundance gradients along the disk of the Milky Way. The lines are the models from Chiappini et al. (2003a): these models differ in terms of the nucleosynthesis prescriptions. In particular, the dash-dotted line represents a model with van den Hoeck & Groenewegen (1997) (hereafter HG97) yields for low- to intermediate-mass stars with n (the mass-loss parameter) constant and Thielemann et al.'s (1996) yields for massive stars, the long-dashed thick line has HG97 yields with variable n and Thielemann et al. yields, and the long-dashed thin line has HG97 yields with variable n but WW95 yields for massive stars. It is interesting to note that in all of these models the yields of 12 C in stars of masses > 40M0 have artificially been increased by a factor of three relative to the yields of WW95. Lower panel: the temporal behavior of abundance gradients along the disk as predicted by the best model of Chiappini et al. (2001). The upper lines in each panel represent the present-day gradient, whereas the lower ones represent the gradient a few Gyr ago. It is clear that the gradients tend to steepen with time, which is a still-controversial result.

As an example of abundance gradients in a spiral galaxy we show in Figure 6.7 the observed and predicted gas distribution and abundance gradients for the disk of M101. In this case the gas distribution and the abundance gradients are reproduced with systematically smaller timescales for disk formation relative to the Milky Way (M101 formed faster), and the difference between the timescales of formation of the internal and external regions is smaller, tmioi = 0.75^ — 0.5 Gyr (Chiappini et al. 2003a).

To conclude this section, we would like to recall a paper by Boissier et al. (2001), where a detailed study of the properties of disks is presented. They conclude that more-massive disks are redder, metal-richer, and gas-poorer than smaller ones. On the other hand, their estimated SF efficiencies for various (defined as the SFR per unit mass of gas) spirals seem to be similar: this leads them to conclude that more-massive disks are older than less-massive ones.

6.2.6 How to model the Hubble sequence The Hubble sequence can be simply thought of as a sequence of objects for which SF proceeds faster in the early than in the late types. See also Sandage (1986).

We take the Milky Way galaxy, whose properties are best known, as a reference galaxy and we change the SFR relatively to the Galactic one, for which we adopt Equation (6.6). The quantity v in Equation (6.6) is the efficiency of SF, which we assume to be characteristic of each Hubble type. In the two-infall model for the Milky Way we adopt vhaio = 2.0 Gyr—1 and vd;sk = 1.0 Gyr—1 (see Figure 6.1). The choice of adopting a dependence on the total surface mass density for the Galactic disk is due to the fact that it helps in producing a SFR that is strongly varying with the galactocentric distance, as required by the observed SFR and gas-density distribution as well as by the abundance gradients. In fact, the inside-out scenario influences the rate at which the gas mass is accumulated by infall at each galactocentric distance and this in turn influences the SFR.

For bulges and ellipticals we assume that the SF proceeds as in a burst with very high SF efficiency, namely

with k = 1.0 for the sake of simplicity; v = 10-20 Gyr—1 (Matteucci 1994; Pipino & Matteucci 2004).

For irregular galaxies, on the other hand, we assume that SF proceeds more slowly and less efficiently than that in the Milky Way disk; in particular, we assume the same SF law as for spheroids but with 0.01 < v (Gyr—1) < 0.1. Among irregular galaxies, a special position is taken by the blue compact galaxies (BCGs), namely galaxies that have blue colors as a consequence of the fact that they are forming stars at the present time, and have small masses, large amounts of gas, and low metallicities. For these galaxies, we assume that they suffered on average from one to seven short bursts, with the SF efficiency mentioned above (Bradamante et al. 1998).

Finally, dwarf spheroidals are also a special category, characterized by having old stars, no gas, and low metallicities. For these galaxies we assume that they suffered one long starburst lasting 7-8 Gyr or at most a couple of extended SF periods, in agreement with their measured color-magnitude diagram. It is worth noting that both ellipticals and dwarf spheroidals should lose most of their gas and therefore one may conclude that galactic winds should play an important role in their evolution, although ram pressure stripping cannot be excluded as a mechanism for gas removal. Also for these galaxies we assume the previous SF law with k = 1 and v = 0.01-1.0 Gyr—1. Lanfranchi & Matteucci

Figure 6.7. Upper panel: predicted and observed gas distribution along the disk of M101. The observed H I, H2, and total gas are indicated. The large open circles indicate the models: in particular, the open circles connected by a continuous line refer to a model with central surface mass density of 1000M0 pc-2, while the dotted line refers to a model with 800M0 pc-2 and the dashed to a model with 600M0 pc-2. Lower panel: predicted and observed abundance gradients of C, N, O elements along the disk of M101. The models are the lines and differ for a different threshold density for SF, being larger in the dashed model. All the models are by Chiappini et al. (2003a).

Figure 6.7. Upper panel: predicted and observed gas distribution along the disk of M101. The observed H I, H2, and total gas are indicated. The large open circles indicate the models: in particular, the open circles connected by a continuous line refer to a model with central surface mass density of 1000M0 pc-2, while the dotted line refers to a model with 800M0 pc-2 and the dashed to a model with 600M0 pc-2. Lower panel: predicted and observed abundance gradients of C, N, O elements along the disk of M101. The models are the lines and differ for a different threshold density for SF, being larger in the dashed model. All the models are by Chiappini et al. (2003a).

Figure 6.8. Predicted SFRs in galaxies of various morphological types, from Calura (2004). Note that for the elliptical galaxy the SF stops abruptly as a consequence of the galactic wind.
Figure 6.9. Predicted Type Ia SN rates for the SFRs of Figure 6.8. Figure from Calura (2004). Note that for the irregular galaxy here the predictions are for the LMC, where a recent SF burst is assumed.

(2003, 2004) developed more-detailed models for dwarf spheroidals by adopting the SF history suggested by the color-magnitude diagrams of single galaxies, with the same efficiency of SF as above. In Figure 6.8 we show the SFRs adopted for various types of galaxy and in Figure 6.9 the corresponding predicted Type Ia SN rates. For the irregular galaxy, the predicted Type Ia SN rate refers to a specific galaxy, the Lesser Magellanic Cloud (LMC), with a SFR taken from observations (Calura et al. 2003) with an early and a late burst of SF and low SF in between.

6.2.7 Type Ia SN rates in various types of galaxy Following Matteucci & Recchi (2001), we define the typical timescale for Type Ia SN enrichment as the time taken for the SN rate to reach the maximum. In the following we will always adopt the SDS for the progenitors of Type Ia SNe. A point that is not often understood is that this timescale depends upon the progenitor lifetimes, IMF, and SFR and therefore is not universal. Sometimes in the literature the typical Type Ia SN timescale is quoted as being universal and equal to 1 Gyr, but this is just the timescale at which the Type Ia SNe start to be important in the process of Fe enrichment in the Solar vicinity.

Matteucci & Recchi (2001) showed that for an elliptical galaxy or a bulge of a spiral with a high SFR the timescale for Type Ia SN enrichment is quite short, in particular tSNIa = 0.3-0.5 Gyr. For a spiral like the Milky Way, in the two-infall model, a first peak is reached at 1.0-1.5 Gyr (the time at which SNe Ia become important as Fe producers) (Matteucci and Greggio 1986) and a second, less-important, peak occurs at tSN Ia = 4-5 Gyr. For an irregular galaxy with a continuous but very low SFR the timescale is tSNIa > 5 Gyr.

6.2.8 A time-delay model for galaxies of various types As we have already seen, the time delay between the production of oxygen by Type II SNe and that of Fe by Type Ia SNe allows us to explain the [X/Fe] versus [Fe/H] relations in an elegant way. However, the [X/Fe] versus [Fe/H] plots depend not only on nucleosynthesis and IMF but also on other model assumptions, such as the SFR, through the absolute Fe abundance ([Fe/H]). Therefore, we should expect different behaviors in galaxies with different SF histories. In Figure 6.10 we show the predictions of the time-delay model for a spheroid like the Bulge, for the Solar vicinity, and for a typical irregular Magellanic galaxy.

As one can see in Figure 6.10, we predict a long plateau, well above the Solar value, for the [a/Fe] ratios in the Bulge (and ellipticals), owing to the fast Fe enrichment reached in these systems by means of Type II SNe: when the Type Ia SNe start enriching the ISM substantially, at 0.3-0.5 Gyr, the gas Fe abundance is already Solar. The opposite occurs in irregulars, where the Fe enrichment proceeds very slowly so that when Type Ia SNe start restoring the Fe in a substantial way (> 3 Gyr) the Fe content in the gas is still well below Solar. Therefore, here we observe a steeper slope for the [a/Fe] ratio. In other words, we have below-Solar [a/Fe] ratios at below-Solar [Fe/H] ratios. This diagram is very important since it allows us to recognize a galaxy type solely by means of its abundances, and therefore it can be used to understand the nature of high-redshift objects.

6.3. Interpretation of abundances in dwarf irregulars

They are rather simple objects with low metallicity and large gas content, suggesting that they are either young or have undergone discontinuous SF activity (bursts) or a continuous but not efficient SF. They are very interesting objects for studying galaxy evolution. In fact, in "bottom-up" cosmological scenarios they should be the first self-gravitating systems to form and could also be important contributors to the population of systems giving rise to QSO absorption lines at high redshift (Matteucci et al. 1997; Calura et al. 2002).

6.3.1 Properties of dwarf irregular galaxies Among local star-forming galaxies, sometimes referred to as H II galaxies, most are dwarfs. Dwarf irregular galaxies can be divided into two categories: dwarf irregular

Figure 6.10. Predicted [a/Fe] ratios in galaxies with different SF histories. The top line represents the predictions for the Bulge or for an elliptical galaxy of the same mass 1O1OM0), the next line down represents the prediction for the Solar vicinity, and the lowest line shows the prediction for an irregular Magellanic galaxy. The differences among the various models are in the efficiency of star formation, this being quite high for spheroids (v = 20 Gyr-1), moderate for the Milky Way (v = 1-2 Gyr-1), and low for irregular galaxies (v = 0.1 Gyr-1). The nucleosynthesis prescriptions are the same for all objects. The time delay between the production of a-elements and that of Fe coupled with the different SF histories produces the differences among the plots. Data for damped-Lyman-a systems (DLA), the LMC, and the Bulge are shown for comparison.

Figure 6.10. Predicted [a/Fe] ratios in galaxies with different SF histories. The top line represents the predictions for the Bulge or for an elliptical galaxy of the same mass 1O1OM0), the next line down represents the prediction for the Solar vicinity, and the lowest line shows the prediction for an irregular Magellanic galaxy. The differences among the various models are in the efficiency of star formation, this being quite high for spheroids (v = 20 Gyr-1), moderate for the Milky Way (v = 1-2 Gyr-1), and low for irregular galaxies (v = 0.1 Gyr-1). The nucleosynthesis prescriptions are the same for all objects. The time delay between the production of a-elements and that of Fe coupled with the different SF histories produces the differences among the plots. Data for damped-Lyman-a systems (DLA), the LMC, and the Bulge are shown for comparison.

galaxies (DIGs) and blue compact galaxies (BCGs). The latter have very blue colors due to active SF at the present time.

Chemical abundances in these galaxies are derived from optical emission lines in H II regions. Both DIGs and BCGs show a distinctive spread in their chemical properties, although this spread is decreasing in the new, more-accurate, data, but also a definite mass-metallicity relation.

From the point of view of chemical evolution, Matteucci and Chiosi (1983) first studied the evolution of DIGs and BCGs by means of analytical chemical-evolution models including either outflow or infall and concluded that closed-box models cannot account for the Z-log G (G = Mgas/Mtot) distribution even if the number of bursts varies from galaxy to galaxy and suggested possible solutions to explain the observed spread. In other words, the data show a range of values of metallicity for a given G ratio, and this means that the effective yield is lower than that of the simple model and varies from galaxy to galaxy.

The possible solutions suggested to lower the effective yield were

(a) different IMFs,

(b) different amounts of galactic wind, and

(c) different amounts of infall.

In Figure 6.11 we show graphically the solutions (a), (b), and (c). Concerning the solution (a), one simply varies the IMF, whereas solutions (b) and (c) have already been described (Equations (1.21) and (1.23)).

Later on, Pilyugin (1993) put forward the idea that the spread observed also in other chemical properties of these galaxies such as in the He/H versus O/H and N/O versus O/H relations could be due to self-pollution of the H ii regions, which do not mix efficiently with the surrounding medium, coupled with "enriched" or "differential" galactic winds, namely different chemical elements are lost at different rates. Other models (Marconi et al. 1994; Bradamante et al. 1998) followed the suggestions of differential winds and introduced the novelty of the contribution to the chemical enrichment and energetics of the ISM by SNe of different types (II, Ia, and Ib).

Another important feature of these galaxies is the mass-metallicity relation.

The existence of a luminosity-metallicity relation in irregulars and BCGs was suggested first by Lequeux et al. (1979), then confirmed by Skillman et al. (1989), and extended also to spirals by Garnett & Shields (1987). In particular, Lequeux et al. suggested the relation with Z being the global metal content. Recently, Tremonti et al. (2004) analyzed 53000 local star-forming galaxies (irregulars and spirals) in the SDSS. Metallicity was measured from the optical nebular emission lines. Masses were derived from fitting spectral-energy-distribution (SED) models. The strong optical nebular lines of elements other than H are produced by collisionally excited transitions. Metallicity was then determined by fitting simultaneously the most-prominent emission lines ([O iii], Hp, [O ii], Ha, [N ii], and [S ii]). Tremonti et al. (2004) derived a relation indicating that 12 + log(O/H) is increasing steeply for M* going from 108 5 to 1010 5 but flattening for M* > 1010 5.

In particular, the Tremonti et al. relation is

This relation extends to higher masses the mass-metallicity relation found for star-forming dwarfs and contains very important information on the physics governing galactic evolution. Even more recently, Erb et al. (2006) found the same mass-metallicity relation for star-forming galaxies at redshift z > 2, with an offset from the local relation of >0.3dex. They used Ha and [N ii] spectra. In Figure 6.12 we show the figure from Erb et al. (2006) for the mass-metallicity relation at high redshift which includes the relation of Tremonti et al. (2004) for the local mass-metallicity relation.

The simplest interpretation of the mass-metallicity relation is that the effective yield increases with galactic mass. This can be achieved in several ways, as shown in Figure 6.11: by changing the IMF or the stellar yields as a function of galactic mass, or by assuming that the galactic wind is less efficient in more-massive systems, or that the infall rate is less efficient in more-massive systems. One of the commonest interpretations of the mass-metallicity relation is that the effective yield changes because of the occurrence of galactic winds, which should be more important in small systems. There is evidence that galactic winds exist for dwarf irregular galaxies, as we will see in the following section.

12 + log(O/H) = —1.492+ 1.847(log M*) — 0.08026(log M*)2.

Figure 6.11. The Z-log G diagram. Solutions (a), (b), and (c) to lower the effective yield in DIGs and BCGs by Matteucci & Chiosi (1983). Solution (a) consists in varying the yield per stellar generation, here indicated by pZ, just by changing the IMF. Solutions (b) and (c) correspond to Equations (6.21) and (6.23), respectively.

Figure 6.11. The Z-log G diagram. Solutions (a), (b), and (c) to lower the effective yield in DIGs and BCGs by Matteucci & Chiosi (1983). Solution (a) consists in varying the yield per stellar generation, here indicated by pZ, just by changing the IMF. Solutions (b) and (c) correspond to Equations (6.21) and (6.23), respectively.

Figure 6.12. Figure 3 from Erb et al. (2006), showing the mass-metallicity relation for star-forming galaxies at high redshift. The data from Tremonti et al. (2004) are also shown.

6.3.2 Galactic winds

Papaderos et al. (1994) estimated a galactic wind flowing at a velocity of 1320 km s-1 for the irregular dwarf VIIZw403. The escape velocity estimated for this galaxy is ~50 km s-1. Lequeux et al. (1995) suggested a galactic wind in Haro2=MKn33 flowing at a velocity of ^200 km s-1, also larger than the escape velocity of this object. More recently, Martin (1996, 1998) found supershells as well in 12 dwarfs, including IZw18, which imply gas outflow. Martin (1999) concluded that the galactic-wind rates are several times the SFR. Finally, the presence of metals in the ICM (revealed by X-ray observations) and in the IGM (Ellison et al. 2000) constitutes a clear indication of the fact that galaxies lose their metals. However, we cannot exclude the possibility that the gas with metals is lost also by ram pressure stripping, especially in galaxy clusters.

In models of chemical evolution of dwarf irregulars (e.g. Bradamante et al. 1998) the feedback effects are taken into account and the condition for the development of a wind is

namely, that the thermal energy of the gas is larger than or equal to its binding energy. The thermal energy of gas due to SN and stellar-wind heating is

with the contribution of SNe being

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