The Chemical Evolution of our Galaxy

Milky Way Surveys: The Structure and Evolution of Our Galaxy ASP Conference Series, Vol. 317, 2004 Dan Clemens, Ronak Y. Shah, and Tereasa Brainerd

The Chemical Evolution of our Galaxy Francesca Matteucci Dipartimanto di Astronomia, Universita’ di Trieste, Via G.B. Tiepolo 11, 34124 Trieste Abstract. I first review the basic ingredients necessary to build chemical evolution models for the Milky Way galaxy. Then I discuss how to infer important constraints on the mechanisms of formation and evolution of our Galaxy by comparison between model results and observations. In particular, I focus on the stellar abundances which recently have reached an high level of accuracy. Both common and specific conclusions from the different chemical evolution models existing in the literature are presented. Common conclusions suggest that the Milky Way thin disk formed inside-out and on much longer timescales than the halo, the bulge and the thin disk. This implies that the gas forming the thin disk must have been accreted from the intergalactic medium. Some specific models predict a gap in the star formation rate just before the formation of the thin disk, as it seems to be indicated by a gap in some observed abundance ratios.

1.

Introduction

The Milky Way galaxy is ideal to test models of chemical evolution because of the large number of observational constraints available in comparison with external galaxies. In particular, for the solar vicinity (a cylinder of 1 kpc radius centered on the Sun) we have the majority of information. Abundances and abundance ratios of a large number of chemical elements are now available as well as estimates for the initial mass function (IMF) and the star formation rate (SFR). However, while the IMF and the SFR are still uncertain quantities, the chemical abundance measures have recently reached a high level of precision and extend towards very low metallicities (down to [Fe/H] =−4.0). This has also been possible thanks to a very recent spectroscopic survey carried out by Cayrel et al. (2003) with the VLT at E.S.O. In addition, we have information about the amount of gas in the solar vicinity and the whole disk as well as of the SN rates (II, Ia, Ib). All of these observational facts should be taken into account when building a model of chemical evolution for the Milky Way. In this paper I will recall the basic ingredients necessary to chemical evolution models and then I will discuss the model predictions in comparison to the data. In particular, I will discuss the chemical evolution of the halo, bulge and disk. 2.

Basic Ingredients

The main ingredients in chemical evolution models can be summarized as follows: • The initial conditions: a) chemical composition of the initial gas (primordial or pre-enriched by a pre-galactic stellar generation); b) whether we 337

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F. Matteucci consider the studied system as a closed box or an open system (infall and/or outflows). • The birthrate function, namely B(M, t) = ψ(t)ϕ(M )

(1)

ψ(t) = SF R

(2)

where the quantity: is called the star formation rate, namely the rate at which the gas is turned into stars, and the quantity: ϕ(M ) = IM F

(3)

is the initial mass function. The most common parametrization of the SFR is the Schmidt (1959) law: k SF R = νσgas ,

(4)

where k=1-2 with a preference for k=1.4, as suggested by Kennicutt (1998) for spiral disks, and ν is a parameter describing the star formation efficiency. Other common parameterizations include a dependence from the total surface mass density besides the surface gas density: k 1 k2 σgas , SF R = νσtot

(5)

as suggested by observational results by Dopita & Ryder (1974) and taking into account the influence of the potential well in the star formation process (i.e., feedback between SN energy input and star formation, see also Talbot & Arnett 1975). Other suggestions concern the star formation induced by spiral density waves (Wyse & Silk 1998) with expressions like (Prantzos, 2002): 1.5 SF R = νV (R)R−1 σgas , (6) or SF R = 0.017Ωgas σgas ∝ R−1 σgas

(7)

with Ωgas being the angular rotation speed of gas (Kennicutt 1989). The most common parametrization of the IMF is a one-slope (Salpeter 1955) or multi-slope (Scalo 1986,1998; Kroupa et al. 1993) power law: IM F = aM −(1+x)

(8)

generally defined in a mass range of 0.1-100 M⊙ , where a is the normalization constant. • Stellar nucleosynthesis: this includes the stellar yields, namely the amount of newly formed and pre-existing elements ejected by stars of all masses at their death.

The Chemical Evolution of Our Galaxy

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• Gas infall and gas outflows. Various parameterizations have been suggested for gas flows and the most common are an exponential law for the gas infall: IR ∝ e−t/τ (9) with the timescale τ being a free parameter, whereas for the galactic outflows the wind rate is generally assumed to be proportional to the SFR: W R = −λSF R

(10)

where λ is again a free parameter. Both τ and λ should be fixed by reproducing the majority of observational constraints. 2.1.

Stellar Yields

I recall here the various stellar mass ranges and their nucleosynthesis products. In particular: • Low and Intermediate mass stars (0.8 ≤ M/M⊙ ≤ 8.0). Calculations are available from Marigo et al. (1996), van den Hoeck & Groenewegen (1997), Marigo (2001), Meynet & Maeder (2002), Ventura et al. (2002), Siess et al. (2002). These stars produce mainly 4 He, C, N and s-process (A > 90) elements. • Massive stars (M > 8M⊙ ). Available calculations are from Woosley & Weaver (1995), Langer & Henkel (1995), Thielemann et al. (1996), Nomoto et al. (1997), Limongi & Chieffi (2003), Rauscher et al. (2002), Meynet & Maeder (2002). They produce mainly α-elements (O, Ne, Mg, Si, S, Ca), some Fe-peak elements, s-process elements (A < 90) and r-process elements. • Type Ia SNe (white dwarfs in binary systems, see later). Calculations are available from Nomoto et al. (1997), Iwamoto et al. (1999). They produce mainly Fe-peak elements. • Very massive objects (M > 100M⊙ ). Recent calculations are available from Portinari et al. (1998), Umeda & Nomoto (2001). They should produce mainly oxygen although many uncertainties are still present. 2.2.

Type Ia SN progenitors

Two main scenarios have been proposed for the progenitors of type Ia SNe, which are: • Single Degenerate (SD) scenario: the classical scenario of Whelan & Iben (1973), namely C-deflagration in a C-O WD reaching the Chandrasekhar mass MCh after accreting material from a red giant companion. More recently Hachisu et al. (1999) have proposed a similar scenario where the companion can be either a red giant or a main sequence star including a metallicity effect which suggests that no type Ia systems can form for [Fe/H]< −1.0.

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F. Matteucci • Double Degenerate (DD) scenario: the merging of two C-O white dwarfs, due to loss of angular momentum caused by gravitational wave radiation, which explode by C-deflagration when MCh is reached (Iben & Tutukov 1984).

Clearly these different scenarios predict different typical timescales for SN Ia enrichment. A way of defining the typical type Ia SN timescale is to assume it as the time when the maximum in the type Ia SN rate is reached (Matteucci & Recchi 2001). This timescale varies according to the chosen progenitor model and star formation history. For the Milky Way in the solar vicinity, this timescale is at least 1 Gyr, if the SD scenario is assumed (Matteucci & Greggio 1986; Matteucci & Recchi 2001). 3.

The Formation of the Milky Way

In a seminal paper, Eggen, Lynden-Bell & Sandage (1962) suggested a rapid collapse for the formation of the Galaxy lasting ∼ 3 × 108 years. This conclusion arose from the study of a kinematically selected sample of high velocity stars which indicated a correlation between the [Fe/H] abundance the orbital eccentricity and the height from the galactic plane of these stars. We know now that this picture could still hold for the inner halo but certainly it cannot reproduce the features of the stars in the thin disk. Later on, Searle & Zinn (1978) proposed a central collapse similar to that proposed by Eggen et al. (1962) but also that the outer halo formed by merging of large fragments taking place over a considerable timescale > 1 Gyr. More recently, Berman & Suchov (1991) proposed the “hot Galaxy picture”, namely an initial strong burst of star formation which inhibited further star formation for few Gyr while a strong galactic wind was created. The most realistic picture is probably a suitable combination of these three scenarios, where the Eggen et al. picture holds only for the inner halo and bulge, with the outer halo and the disk forming on relatively long timescales and with a gap in the star formation before the formation of the thin disk. From the point of view of modeling the chemical evolution of the Milky Way, different approaches have been followed in the past years: • SERIAL FORMATION: halo, thick and thin disk form in sequence as a continuous process and the local disk forms over a timescale of 3-4 Gyr (e.g., Matteucci & Fran¸cois 1989; Timmes et al. 1995). It does not predict any overlapping between stars belonging to different galactic components, which is instead observed. • PARALLEL FORMATION: the various Galactic components start collapsing at the same time and from the same gas but evolve at different rates (e.g., Pardi et al. 1995). It predicts overlapping of stars belonging to the different components but it cannot reproduce simultaneously the metallicity distributions in the halo, thick and thin disk. • TWO-INFALL FORMATION: halo and thin disk form out of two separate infall episodes (overlapping in metallicity is also predicted) (e.g., Chiappini, Matteucci & Gratton 1997; Chang et al. 1999; Alibès et al. 2000).


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The local disk forms over a timescale of 6-8 Gyr from extragalactic gas. It reproduces the majority of the observational constraints. • STOCHASTIC FORMATION: in the early halo phases, mixing was not efficient so that pollution from single SNe can be seen in the observed abundance patterns (Tsujimoto et al. 1999; Argast et al. 2000; Oey 2000). A large spread at low metallicities is predicted. For a more detailed and extensive discussion on the various approaches and their predictions see Matteucci (2001). 4.

Predictions of the two-infall model

Here I will recall the main results of a typical two-infall model, that of Chiappini et al. (1997; 2001; 2003). 4.1.

The SFR and SN rates

This model assumes the existence of a threshold gas density for the star formation process (∼ 7M⊙ pc−2 for the galactic disk) as suggested by studies of Kennicutt (1989) and Martin & Kennicutt (2001). In Figure 1 is shown the predicted star formation rate for the halo-thick disk and the thin disk phases, respectively. Note that in between the two phases there is a period (less than 1 Gyr) when the star formation rate is going to zero and this is a direct consequence of the threshold gas density. In fact, at the end of the halo -thick-disk phase the gas density is below the threshold and so is at the beginning of the thin disk formation. This gap has important consequences on the predicted [X/Fe] versus [Fe/H] relations in the solar vicinity, as we will see later. In Figure 2 we show the predicted type II and Ia SN rates. The type II SN rate follows the SFR, as expected, whereas the type Ia SN rate has a continuous behaviour due to the nature of type Ia SN progenitors, which here are assumed to be single degenerate systems. 4.2.

The G- and K- dwarf metallicity distribution

The dwarf metallicity distribution of the disk stars in the solar neighbourhood is a very important constraint since it contains all the star formation history of the local disk. In Figures 3 and 4 we show the predicted G-dwarf and K-dwarf metallicity distributions, respectively. Both distributions are very well fitted when a timescale for the formation of the thin disk τ = 7 − 8 Gyr is assumed. A shorter τ = 2 Gyr leads to predictions at variance with observations, as evident in Figure 4. The dwarf metallicity distribution is therefore an excellent test for establishing the time scale for the formation of the local disk. 4.3.

The element abundance patterns

One of the most important observational constraints is represented by the various relations between the abundances of metals (C, N, O, α-elements, Fe-peak elements and beyond) as functions of the [Fe/H] abundance. At the present time a large body of data of very high precision is available, especially at very low metallicities ([Fe/H] < − 3.0, Cayrel et al. 2003; Spite et al. 2003). Here we

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Figure 1. The SFR expressed in M⊙ pc−2 Gyr−1 , as predicted by the model of Chiappini et al. (1997).It is evident the gap in the SFR at the end of the halo- thick disk phase. The oscillations are due to the fact that at late times in the galactic disk the surface gas density is always close to the threshold density.

Figure 2.

Predicted SN (II and Ia) rates by the Chiappini et al. (1997) model.


Figure 3. The G-dwarf metallicity distribution. The model prediction is from Chiappini et al. (1997) and assumes a timescale for the formation of the local disk of 8 Gyr.

Figure 4. The figure is from Kotoneva et al. (2002) and shows the comparison between a sample of K-dwarfs and model predictions in the solar neighbourhood. The dotted curve refers to two-infall model with a timescale τ = 2 Gyr.

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Figure 5. The [X/Fe] vs. [Fe/H] relations for α-elements: black dots are the new data from Cayrel et al. (2003). The other data and the model predictions can be found in Fran¸cois et al. (2003). The predicted solar value for each [X/Fe], namely the value of each ratio 4.5 Gyr ago, is shown in each panel.

show the predictions of the two-infall model including yields from Woosley & Weaver (1995) (WW95) for massive stars, Iwamoto et al. (1999) for type Ia SNe and van den Hoeck & Groenewegen (1997) for low and intermediate mass stars. The yields of WW95 and Iwamoto et al. have been in some cases modified to obtain the best agreement with both the solar [X/Fe] ratio and the [X/Fe] vs. [Fe/H] relations (see Fran¸cois et al. 2003). In Figures 5, 6 and 7 are shown the comparisons between model predictions and data for α–elements and Fe–peak elements. In Figure 8 we show the predictions for C and N. Nitrogen is assumed either to be only secondary in massive stars or primary (see Chiappini et al. 2003 for details). In particular, the dashed curve in Figure 8 represents the predictions of the model assuming only primary N in massive stars. As evident from Figure 8, it is not clear which one of the two assumptions on N fits the data better and more observations at low metallicities are necessary before drawing firm conclusions. The majority of α-elements shows a typical behaviour represented by a plateau extending from [Fe/H] ∼ −4.0 up to [Fe/H]=−1.0 and a subsequent decrease, with increasing metallicity, of the [X/Fe] ratios until the solar value. This behaviour is well accounted for by the time-delay in the element production between type II and type Ia SNe. In the case of Mg the yields of WW95 as well as those for type Ia SNe had to be increased in order to achieve an acceptable solar Mg abundance (see Fran¸cois et al. 2003 for details). The most striking aspect of the new data at very low [Fe/H] (Cayrel et al. 2003) is the lack of spread, at variance with what assumed by stochastic models.


Figure 6.

The same as in Figure 5 but for Ni, Zn, K and Sc.

Figure 7.

The same as in Figure 5 but for Ti, Cr, Mn and Co.

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Figure 8. Models and data from Chiappini et al. (2003) where details can be found. The dashed line in the [N/Fe] vs. [Fe/H] plot refers to the case where it is assumed that massive stars produce primary nitrogen.

The information we get from the previous figures is therefore that the galactic halo was already well mixed at metallicities as low as [Fe/H]=−4.0. 4.4.

Chemical Evolution of the Bulge

Several different scenarios have been proposed so far for the formation of the galactic bulge (Wyse & Gilmore 1992): • Accretion of extant stellar systems which eventually settle in the center of the Galaxy. • Accumulation of gas at the center of the Galaxy and subsequent evolution with either fast or slow SFR. • Accumulation either rapid or slow of metal enriched gas from the halo or thick disk or thin disk in the Galaxy center. The metallicity distribution of stars in the bulge helps in selecting the most probable scenario (see Figure 9). In particular, detailed models of chemical evolution of the bulge indicate that the galactic bulge formed very quickly out of gas shed from the halo and that a Salpeter IMF should be preferred over the Scalo (1986) one (Matteucci & Brocato, 1990; Matteucci et al. 1999). These models assume that the SFR and the infall rate were much faster than in the solar neighbourhood, thus implying a timescale for the formation of the main stellar bulge component no longer than 1-1.5 Gyr and overabundances of αelements relative to Fe over the major part of the metallicity range, a prediction which seems to be confirmed by spectroscopic studies (see for example Barbuy et al. 1998).


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Figure 9. Predicted and observed metallicity distribution of bulge stars. The data are from McWilliam & Rich (1994) while the models, computed for different IMFs are from Matteucci et al. (1999). The best fit is obtained with a Salpeter (1955) IMF.

5.

Common conclusions from chemical evolution models

A good model for the chemical evolution of the Milky Way should reproduce a number of observational constraints much larger than the number of free parameters in the model. The observational constraints concern both the solar vicinity and the whole disk. In particular, the observational data in the disk are the abundance gradients of some α- elements and Fe (see Figure 10), the gas distribution (although uncertain) and the SFR distribution (also rather uncertain). Most of current chemical evolution models for the Galaxy agree on the following conclusions: • The G-dwarf metallicity distribution implies a slow formation of the local disk by infall of mainly extragalactic gas: the suggested time-scale for the formation of the local disk is τ ∼ 6 − 8 Gyr (Chiappini et al. 1997; Boissier & Prantzos 1999; Chang et al. 1999; Chiappini et al. 2001; Alibès et al. 2001). • The relative abundance ratio relations [X/Fe] vs. [Fe/H] can be well explained as due to the time-delay between type Ia and II SNe. The inferred timescale for the inner halo-thick disk formation is τ ∼ 1.5 − 2.0 Gyr, (Matteucci & Greggio 1986; Matteucci & Fran¸cois, 1989; Chiappini et al. 1997). The external halo and thick disk formed more slowly or have been partly or totally accreted.

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Figure 10. Abundance gradients of several heavy elements observed and predicted by the model of Chiappini et al. (2001). The lower curve in each panel corresponds to the predicted gradient at a thin disk age of ∼ 1 Gyr. References to the data can be found in Chiappini et al. (2001).

• The galactic bulge formed on a timescale τ = 1 − 1.5 Gyr. The expected [α/Fe] ratios are larger than zero over most of the [Fe/H] range (Matteucci & Brocato 1990; Matteucci et al. 1999). • To fit the abundance gradients, SFR and gas distribution along the galactic disk one should assume that the disk formed inside-out and the SFR is a strongly varying function of the galactocentric distance (Matteucci & Fran¸cois 1989; Chiappini et al. 1997, 2001; Hou et al. 2000; Alibès et al. 2001). This conclusion seems to apply also to other disk galaxies (Prantzos & Boissier 2000).

6.

Specific conclusions from chemical evolution models

Specific conclusions concern either the evolution in the solar vicinity or in the disk. In particular, in the solar vicinity the assumption of a threshold gas density in the star formation as in Chiappini et al. (1997; 2001) leads naturally to a halt in the SFR just between the end of the thick-disk phase and the beginning of the thin disk phase, as explained before. This gap in the SFR implies a gap in the


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[Fe/α] ratios around a specific [α/H] value and a subsequent steep increase of the [Fe/α] ratios (see Matteucci 2003). This effect is due to the fact that during the gap Fe is still produced whereas the α-elements are not. This behaviour has been observed in the [Fe/O] ratio (Gratton et al. 2000) and in the [Fe/Mg] ratio (Furhmann 1998). The adoption of a threshold acts also on the abundance gradients in the sense that it predicts less steep abundance gradients at large galactocentric distances. Another specific conclusion of the model of Chiappini et al. (2001) concerns the temporal evolution of the abundance gradients. In Figure 10 are shown the observed and predicted gradients by the above model. There are the predictions for the present time and for a thin disk age of ∼ 1 Gyr. The Chiappini et al. model predicts a steepening of the gradients with time. This is at variance with other models (e.g., Boissier & Prantzos 1998; Alibès et al. 2001), although they assume the same inside-out mechanism as in Chiappini et al. (2001) for the formation of the galactic disk. The reason for this discrepancy probably resides in the different SFRs used in the different approaches and in the adoption of a SF threshold. In fact, the gas density threshold produces a slower growth of the metal abundances at large galactocentric distances than models without the threshold. References Alibés, A., Labay, J., Canal, R. 2001, A&A, 370, 1103 Argast, D., Samland, M., Gerhard, O.E., Thielemann, F.-K. 2000, A&A, 356, 873 Barbuy, B., Ortolani, S., Bica, E. 1998, A&AS, 132, 333 Berman, B.C., Suchov, A.A. 1991, Ap&SS, 184, 169 Boissier, S., Prantzos, N. 1999, MNRAS, 307, 857 Cayrel, R., Depagne, E., Spite, M., Hill, V., Fran¸cois, P. et al. 2003, A&A, submitted Chang, R.X., Hou, J.L., Shu, C.G., Fu, C.Q. 1999, A&A, 350, 38 Chiappini, C., Matteucci, F., Gratton, R. 1997, ApJ, 477, 765 Chiappini, C., Matteucci, F., Romano, D. 2001, ApJ, 554, 1044 Chiappini, C., Romano, D., Matteucci, F. 2003, MNRAS, 339, 63 Dopita, M.A., Ryder, S.D. 1994, ApJ, 430, 163 Eggen, O.J., Lynden-Bell, D., Sandage, A.R. 1962, ApJ, 136, 748 Fran¸cois, P., Matteucci, F., Cayrel, R., Spite, M., Spite, F.. Chiappini, C. 2003, A&A, submitted Fuhrmann, K., 1998, A&A, 338, 161 Gratton, R.G., Carretta, E., Matteucci, F., Sneden, C. 2000, A&A, 358, 671 Kennicutt, R.C. Jr. 1989, ApJ, 344, 685 Kennicutt, R.C. Jr. 1998, ApJ, 498, 541 Kotoneva, E., Flynn, C., Chiappini, C., Matteucci, F. 2002, MNRAS, 336, 879 Kroupa, P., Tout, C.A., Gilmore, G. 1993, MNRAS, 262, 545 Hachisu, I, Kato, M., Nomoto, K. 1999, ApJ, 522, 487 Hou, J.L., Chang, R., Fu, C. 1998, ASP Conference Ser. Vol. 138, p. 143 Hou, J.L., Boissier, S., Prantzos, N. 2000, A&A, 362, 921 Iben, I.Jr., Tutukov, A.V. 1984, ApJS, 54, 335 Iwamoto, N., Brachwitz, F. et al. 1999, ApJS, 125, 439 Langer, N., Henkel, C. 1995, Space Sci. Rev. 74, 343

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