Galactic Chemical Evolution
C. Chiappini* and F. Matteucci1^
*Osservatorio Astronomico di Trieste - Via G.B. Tiepolo 11 - Trieste -TS - 34131 - Italy
^Universita di Trieste - Via G. B. Tiepolo 11 - Trieste - TS - 34131 - Italy
Abstract. In this paper we review the current ideas about the formation of our Galaxy. In particular, the main
ingredients necessary to build chemical evolution models (star formation, initial mass function and stellar yields)
are described and discussed. A critical discussion about the main observational constraints available is also
presented. Finally, our model predictions concerning the evolution of the abundances of several chemical elements
(H, D, He, C, N, O, Ne, Mg, Si, Ca and Fe) are compared with observations relative to the solar neighborhood and
the whole disk. We show that from this comparison we can constrain the history of the formation and evolution
of the Milky Way as well as the nucleosynthesis theories concerning the Big Bang and the stars.
INTRODUCTION
In the past years a great deal of theoretical work has
appeared concerning the chemical evolution of the Milky
Way [59,10, 9, 95,99, 19,18, 13,71, 72, 8, 34, 17].
This is a consequence of the improvement of observations of chemical abundances in stars and gas, and the
progress in our understanding of stellar evolution processes. Stellar evolution models are now converging to
a more self-consistent description (see Thielemann this
conference) and several research groups in the world are
now able to compute one of the fundamental ingredients for chemical evolution models, the stellar yields.
Calculations are now available for an extended range of
stellar masses and for different initial metallicities [eg.
93, 50,102].
Different approaches have been used so far for the
description of the Milky Way formation and evolution.
The most common ones are: i) Serial Formation in which
the halo, thick and thin disk form in temporal sequence
[eg. 59]; ii) Parallel Formation in which the various
components start forming at the same time out of the
same gas but evolve at different rates [68]; iii) The twoinfall approach (see below).
As shown by Chiappini et al. [19], the most likely scenario, in the light of recent data, is the one where the
Galaxy forms as a result of two main infall episodes. The
serial approach predicts no overlapping in metallicities
between the different stellar populations, against observational evidence [6]. Both approaches i) and ii) are at
variance with the distribution of the angular momentum
of stars in different components [104], indicating that the
gas, out of which the stellar halo formed, did not partici-
pate in the formation of the disk. In the two-infall model,
the first episode forms the halo and the gas lost by the
halo rapidly (roughly 0.3-0.5 Gyr) accumulates at the
center with the consequent formation of the bulge. During the second episode, a much slower infall of primordial gas gives rise to the disk with the gas accumulating
faster in the inner than in the outer regions. In this scenario the formation of the halo and disk are almost completely disentangled although some halo gas eventually
falls into the disk. This mechanism for disk formation
is known as the "inside-out" scenario [49] and is quite
successful in reproducing the main features of the Milky
Way [19] as well as of external galaxies especially concerning abundance gradients [see 73]. In this paper we
show the model predictions once the two-infall approach
is adopted.
We believe that by improving the Milky Way model
we will provide a solid basis for a more detailed understanding of the history of chemical enrichment not only
of our Galaxy but also of other spirals. In particular, the
slow timescale for the formation of the Milky Way disk
implied by our chemical evolution model suggests that at
high redshifts we should see smaller disks. An important
aspect of this work will be to provide specific predictions
for galaxy sizes of Milky Way-like galaxies as a function
of redshift, which could in principle be tested against the
growing body of observational data on distant galaxies.
Although the interpretation of the observational data is
still controversial [see 88], they clearly represent a powerful test for disk formation models.
CP598, Solar and Galactic Composition, edited by R. F. Wimmer-Schweingruber
© 2001 American Institute of Physics 0-7354-0042-3/017$ 18.00
227
OBSERVATIONAL CONSTRAINTS: A
CRITICAL DISCUSSION
A good model of chemical evolution of the Galaxy
should reproduce a number of constraints which is larger
than the number of free parameters. Therefore, it is very
important to choose a high quality set of observational
data to be compared with model predictions. The set of
observations that should be explained by the models are
listed below. In what follows we comment on the most
important ones.
Solar Vicinity
TABLE 1. Observed and predicted quantities at RQ and
t = *Gal
Model A [17]
Observed*
Fraction of halo stars
10%
2—10 %
0.4
SNIa1"
0.3 ± 0.2
SNII
1.2 ± 0.8
0.8
2.6
2—10
oPiv(/vQ, tGal)
7.0
7—16
^g<3w\"Q» iGal)
36.3
35 ±5
%stars(R®, tGal)
0.13 0.05—0.20
^gasfatot (^0, tGai)
1.0
0.3—1.5
2<infall(R®>tGal^
AY/AZ
1—3
1.9
22
Nova outbursts (yr"1)
20—30
Dp/Dwow
1.5
<3
* References for the observed values can be found in [17,79]
t SN rates are given in units of century"1
** in units of M0 pc~2 Gyr"1
* in units of M0 pc~2
S in units of MQ pc~~2
' in units of MQ pc~"2 Gyr""1
* Observational constraints at solar vicinity (Table 1)
* Solar Abundances (Table 2)
* Abundance ratios as function of [Fe/H]
• Age-Metallicity relationship
• Current supernovae rates (Table 1)
• Metallicity distribution of G dwarf disk stars
TABLE 2. Solar abundances by mass
The solar abundances in principle should represent
the chemical composition of the interstellar medium in
the solar neighbourhood at the time of Sun formation
(4.5 Gyrs ago). However, the abundance of oxygen in
the Orion nebula is roughly solar when the new value
reported by Holweger (this conference) is taken as a
reference. This could be interpreted as an indication that
the evolution of the solar vicinity in the last 4.5 Gyrs
was very slow. In fact, when including the threshold
in the process of star formation, we predict a small
increase of the elements produced by massive stars (as
is the case of oxygen) as a consequence of the threshold
mechanism in the star formation rate. However, we have
to consider also the possibility that the solar composition
is not representative of the local ISM 4.5 Gyrs ago,
an alternative being that the Sun was born in a region
closer to the Galactic center and then moved to the
present region (but see Holweger, this conference). The
absolute solar values taken at a face value are not a very
tight constraint to chemical evolution models as they are
dependent on many model parameters.
The behaviour of the [oc/Fe] ratio as a function of
[Fe/H] is very useful to constrain chemical evolution
models. The a-elements (O, Ne, Mg, etc..) are produced
only by type II SNe (which have high mass progenitors
with short life time), whereas most of the iron is produced by type la SNe, which are believed to be the result of the explosion of C-O white dwarfs in binary systems. Iron release from type la SNe begins not before
several 107 years after the birth of a stellar generation,
and the bulk of iron enrichment takes up to some Gyrs,
depending on the assumptions on the binary system characteristics, explosion mechanism and star formation rate.
228
Model*
H
D
3
He
4
He
12
C
16Q
0.71
0.70
3.3 (-5)
4.8 (-5)
2.9 (-5)
2.2 (-5)
2.7 (-1)
3.5 (-3)
7.1 (-3)
14N
1.6 (-3)
13
C
4.7 (-5)
20
Ne
0.9 (-3)
24
2.4 (-4)
6.9 (-4)
3.0 (-4)
Mg
Si
S
Ca
3.9 (-5)
Fe
Cu
Zn
1.31 (-3)
7.7 (-7)
2.3 (-6)
1.6 (-2)
Z
AG89t
2.7 (-1)
3.0 (-3)
9.6 (-3)
1.1 (-3)
3.7 (-5)
1.6 (-3)
5.1 (-4)
7.1 (-4)
4.2 (-4)
6.2 (-5)
1.3 (-3)
8.4 (-7)
2.1 (-6)
1.9 (-2)
GS98** H2001*
2.7 (-1)
2.8 (-3)§ 3.3(-3)
7.7 (-3) 6.2(-3)
8.3 (-4) 8.5(-4)
1.6(-3)
5.9(-3)
7.1 (-4)
4.9 (-4)
7.2(-4)
6.5 (-5)
1.3 (-3)
7.3 (-7)
l.K-3)
1.9 (-6)
1.7 (-2)
* Model A of [17] at 4.5 Gyr ago
^ Anders and Grevesse [3] - meteoritic values
** Grevesse and Sauval [36] photospheric values. The meteoritic
values reported by [36] for Si, S, Ca, Fe, Cu, and Zn agree with the
photospheric ones except for S, Cu, and Zn, for which they report
3.6 (-4), 8.7 (-7), and 2.2 (-6), respectively. The value listed
here for the abundance by mass of 4He is that at the time of Sun
formation
* Holweger, this conference
§
The observed abundances of GS98 and H2001 are elemental thus
including different isotopes.
Therefore, the delayed arrival of the iron produced by
type la SNe is responsible for the observed decrease in
the [a/Fe] ratio as a function of the iron abundance in the
solar vicinity [58, 59]. This fact makes the [a/Fe] ratio a
very important tool to access the formation timescales of
different galactic components and can be used as a cosmic clock.
In particular, recent data by Gratton et al. [35] suggest
that there was a hiatus in the process of star formation
during the halo-thin disk transition. Such a hiatus seems
to be real since it is observed both in the plot of [Fe/O]
versus [O/H] [19, 35] and in the plot of [Fe/Mg] versus
[Mg/H] [32]. The evidence for this is shown by the steep
increase of [Fe/O] and [Fe/Mg] at a particular value
of [O/H] and [Mg/H], respectively, indicating that at a
certain epoch (coinciding with the halo-disk transition)
SNe II, responsible for the production of O and Mg,
stopped exploding while Fe, produced by the long living
SNe la, continued to be produced (see figure 4).
tometric system adopted in [64]. In particular, the new
data show a well-defined peak in metallicity (between
[Fe/H]=—0.3 and 0.), which was not evident in the previous data (see figure 1).
The age-metallicity relation [24] is not a strong constraint since it can be fitted by a variety of model assumptions and it shows a very large spread.
Radial Profiles - Disk
• Star Formation Rate profile
• Gas and Stars density distribution
• Radial Abundance Gradients
The observed (HI + H2) distribution is taken from [21].
The surface density distribution of the total gas £gas is
obtained from the sum of the HI and H2 distributions,
%Hi + £//2' accounting for the helium and heavy elements
fractions (thick line in the lower left panel of figure 2).
I 0.1
fi?
f
0
5
10
R (kpc)
15
20
2
0
5
10
R (Kpc)
15
20
-0.5
[Fe/H]
« 10
a.
FIGURE 1. G-dwarf metallicity distribution. The curve
shows the best model of Chiappini et al. [17].
Another fundamental constraint on chemical evolution
models is the metallicity distribution of the G-dwarfs for
the solar vicinity. The G-dwarf metallicity distribution is
representative of the chemical enrichment of the Galaxy
since these stars have lifetimes larger than or equal to
the age of the Galaxy and hence can provide a complete
record of its chemical history. Until 1995 the G-dwarf
metallicity distribution which was adopted to compare
with the models was the one published by Pagel and
Patchett [64] and revised by Pagel [66] and SommerLarsen [91]. Later on, two different groups using new observations and up to date techniques, published new data
on the G-dwarf distribution [77, 103]. The basic differences are in the new adopted catalog, namely, the Third
Gliese Catalog, and in the calibration used to determine
the metallicity. This calibration is based on Stromgren
photometry which allows a more reliable estimation of
the metallicity than does the one based on the UB V pho-
229
10
R (Kpc)
10
R (Kpc)
FIGURE 2. Predictions (thin lines) from the best model of
[17]. In the upper left panel the oxygen gradient is shown. The
upper right panel shows the radial profile of SFR (normalized
by the star formation rate at the solar vicinity). The left and
right lower panels show the gas and stellar surface densities
respectively (the thick lines enclose the areas where the observations lie).
The stellar profile is exponentially decreasing outwards, with characteristic scale length Rstars ~ 2.5-3
kpc [83, 30]. Moreover, COBE observations suggest that
the stellar disk has an outer edge of 4 kpc from the Sun
[30]. To compare our model predictions on the stellar
density profile along the Galactic disk to the observed
one we consider ^stars(R0^Gai) = 35 ± 5 M0 pc~2 [33]
and Rstars = 2.5 kpc (see lower right panel of figure 2).
The distributions of supernova remnants [37], of pulsars [51], of Lyman-continuum photons [40] and of
molecular gas [74] all can be used to derive an estimate for the SFR along the Galactic disk. Since these observables cannot directly provide the absolute SFR without further assumptions — e.g. on the IMF and mass
ranges for producing pulsars, supernovae, etc. [see 47],
it is common practice to normalize them to their values at the solar radius, and then to trace the radial profile SFR(tf )/SFR(^0) (the thick lines plotted in the upper
right panel of figure 2 refer to the upper and lower limits
obtained from the observational data listed above).
Among the radial constraints the most important and
precise are the abundance gradients.
However, over the past decade, different authors using
different observational tools often came to contradictory
views on both the shape, the magnitude and the evolution
of the abundance gradients along the disk. The controversial results originate from both theoretical and observational considerations.
Data from several sources, namely, HII regions [87,
29, 89, 1, 82]; PNe of type II [52, 53, 55] and B stars
[90, 38] suggest a value for the gradient of oxygen of the
order of ~ —0.07 dex/kpc in the galactocentric distance
range of 4-14 kpc (figure 2, upper left panel - gradients
of other abundance elements can be seen in [17]).
However, recently Deharveng et al. [22] analyzed a
new sample of 34 Hn regions located between 6.6 and
17.7 kpc from the Galactic center and after a careful
estimate of the electron temperatures in those objects
they obtained, using their best observations, an oxygen
abundance gradient which is flatter (by a factor of 2)
than the one obtained in previous works based on HII
regions. Their result seems to be in good agreement with
results by Esteban et al.[26, 27, 28]. Proposals for flatter
gradients or bimodal ones have also been made by works
based on open clusters [31,100] although the situation is
still very unclear.
Another open question related to the observed abundance gradients concerns their variation with time: do
the gradients steepen or flatten with time? This question
cannot be answered properly by the presently available
data [see 56]. However, PNe are the most promising objects to solve this problem. As it has been extensively
discussed in the past few years, PNe Galactic distribution, kinematics, chemical composition and morphology
clearly indicate that PNe comprise objects belonging to
different populations [69, 54]. Previous work has shown
that disk objects of type II are particularly useful in tracing the chemical enrichment of the interstellar medium at
the time of the formation of the PN progenitors [53, 52].
In a recent work, Maciel and Quireza [55] obtained
the gradients for a sample that includes the objects from
Maciel and Koppen [53], Maciel and Chiappini [52] and
Costa et al. [20] (the latter consists of a sample of PNe
230
near the anticentre direction intended to derive a better estimate of the gradients at Galactocentric distances
larger than the solar position). Their main conclusions
were: i) there is an average gradient of —0.04 to —0.07
dex/kpc for what they call "inner" Galaxy (between 4
and 10 kpc — those authors assume RQ = 7.6 kpc); ii)
the gradients show a small variation for the different element ratios (see their table 2); in) the PN gradients are
generally slightly flatter than those derived from younger
objects; iv) for larger galactocentric distances the PN gradients show some flattening. However, several uncertainties such as the small number of objects measured at
galactocentric distances larger than 12 kpc, the problem
of assigning precise ages to disk PNe, and the difficulties
in estimating the importance of dynamical effects still
prevent a definitive answer on the temporal variation of
the abundance gradients in the galactic disk.
Other constraints
• Relative ages of Globular Clusters:
In a recent work, Rosenberg et al. [81], based on two
new large homogeneous photometric databases of 35 and
15 globular clusters found that there is no age-metallicity
trend and no evidence of an age spread for clusters with
[Fe/H]< —1.2 and out to a galactocentric distance of
25kpc. This suggests that the globular cluster formation
process started at the same zero age throughout the "internal halo" (by "internal" we mean up to a galactocentric distance of 25kpc). Moreover they showed that a
fraction of the metal rich globular clusters were formed at
a later time and show a ^f 25% lower age. Those younger
clusters located at larger galactocentric distances have
typical halo kinematics. This is a very strong constraint
and suggests that the timescale for the formation of the
"inner-halo" was short, which is in agreement with the
abundance ratios of metal-poor stars [18].
• Abundances and metallicity distribution of Bulge:
Abundance ratios are sensitive to details of galaxy evolution, and therefore represent a powerful tool for the
study of the Galactic bulge formation. Recently, Barbuy
[5] presented abundance ratios for bulge stars belonging to globular clusters. Those data show that many aelements are overabundant suggesting a rapid bulge formation. Moreover, Matteucci et al. [60] suggested that in
order to fit the observed metallicity distribution of giant
bulge stars obtained by Rich [76] and Me William and
Rich [62], the bulge should have been formed in a short
timescale and probably with a top-heavy IMF. Those results are in agreement with the suggestion by Wyse and
Gilmore [104], from angular momentum arguments, that
the bulge formed out of the gas left from the halo formation [see also 25]. More data are needed, in particular to
investigate the possible existence of abundance gradients
in the bulge. In fact, the radial abundance gradients and
the overall metallicity distribution are very useful in discriminating between the main bulge formation scenarios
proposed so far, namely, monolithic or secular.
where £^ is the total surface mass density, £# is the
surface gas density, k\ = 1.5 and ki — 0.5. A threshold in
the surface gas density (^ 7 M0/?c~2) is also assumed;
when the gas density drops below this threshold the star
formation stops.
THE MODEL FOR THE MILKY WAY
The Initial Mass Function
In what follows the ingredients to build chemical evolution models and the specific choices that apply to our
two-infall model are discussed briefly.
There is at present no clear direct evidence that the
IMF in the Galaxy has varied with time. A detailed discussion about possible observed variations in the IMF in
different environments is given by Scalo [85], but such
variations are comparable with the uncertainties still involved in the IMF determinations. The present uncertainties in the observational results prevent any conclusion
concerning a universal IMF.
However, a variable IMF, which formed relatively
more massive stars during the earlier phases of the evolution of the Galaxy compared to the one observed today
in the solar vicinity, has often been suggested as being
one of the possible solutions for the G-dwarf problem
(namely the deficiency of metal-poor stars in the solar
neighborhood when compared with the number of such
stars predicted by the simple model). Such an IMF would
also be physically plausible from the theoretical point of
view if the IMF depends on a mass scale such as the Jeans
mass [48]. Given the uncertainties in both theoretical and
observational grounds, the proposed IMFs can in principle be tested only by means of a detailed chemical evolution model.
The effect of a variable IMF in a chemical evolution
model was studied by Chiappini et al. [15]. In this work
it was shown that a better agreeement with the observational constraints is obtained for a constant rather than
variable IMF and this conclusion is mostly based on
the abundance gradients and radial profiles of gas and
SFR. Therefore a constant IMF should still be preferred
when describing the evolution of the Galactic disk. In the
present model we adopt the Scalo [86] IMF, constant in
time.
Ingredients
Star formation Rate
The process of star formation is still not understood
and this is why we are forced to adopt a parametrization
for this function. Many are the parametrizations adopted
in the literature. A common approach is to use the so
called "Schmidt-law" in which the star formation rate
depends on a power between 1 and 2 of the volume or
surface gas density. However, a known result is that to
be able to reproduce the observed radial profiles (gas,
stars, star formation rate and abundances) it is not enough
to consider a radial variation of the thin disk formation
timescale, but a radial dependence of the star formation
itself is required [59].
Many are the parametrizations for such radial variation. One possibility is to assume that the star formation rate is not only a function of the gas density but
also of the angular rotation speed of the gas. Another approach is to consider that the SFR has also a dependence
on the total surface mass density (adopted in the present
model). This last parametrization accounts for the feedback mechanism between star formation and heating of
the interstellar medium, due to supernovae and stellar
winds [eg. 92, 59, 11]. Observational evidence for such
a law is provided by Dopita and Ryder [23]. Moreover,
Kennicutt [46] suggested that either a SFR dependence
on the total surface mass density or on the angular rotation speed of the gas leads to a good fit of the SFR
measured from the Ha emission in other spiral galaxies.
Kennicutt [45] (and more recently Martin and Kennicutt
[57]) has also suggested the existence of a threshold gas
density for the star formation of a few M©pc~2, below
which the star formation stops.
Our prescription for the star formation rate (SFR) is
[17]:
SFR
Nucleosynthesis Prescriptions
One of the most important ingredients for chemical
evolution models is the nucleosynthesis prescription and
the computation of stellar yields. Below we describe the
prescriptions adopted here:
• Light Elements produced during the Big Bang:
The elements formed during the Big Bang were H,
D, 3He, 4He and 7Li. Some of them were then consumed/produced by stars and hence what we observe today is a convolution of their primordial values with their
(1)
231
evolution due to stellar processes. In the case of D, the
primordial abundance value is an upper limit as this element is only consumed during stellar evolution. In fact
the D evolution represents a very important constraint to
chemical evolution models. As discussed in Tosi et al.
[98] chemical evolution models which can reproduce the
majority of observational constraints predict a depletion
of D abundance of no more than a factor of 2-3. This of
course can also be used to put limits on the D primordial abundance value. We assume primordial values for
each of those elements and then trace their evolution in
time. Our predictions for the evolution of D, 3He, 4He
and 7Li in the Galaxy can be found in the WG5 contribution [this conference and 16, 80]. In our model we have
included the extra-mixing process for the 3He production [14]. This "non-standard" convective mixing process
would occur in RGB stars further consuming 3He. In this
way we are able to explain the 3He observed in the interstellar medium and in the solar photosphere, overcoming the so called "helium-3 problem" (namely, the overproduction of this element by chemical evolution models
adopting standard yields for low mass stars).
• Low and Intermediate mass stars (0.8 < M/M0 < 8):
Single stars in this mass range contribute to the Galactic enrichment through planetary nebula ejection and quiescent mass loss. They enrich the interstellar medium
mainly in He, C and N. The adopted yields for the low
and intermediate mass range stars are taken from van den
Hoek and Groenewegen [101]. This new set of stellar
yields allows a better agreement between the predicted
C (and its isotopes) evolution with the observations (see
next section). Moreover, we have included the explosive
nucleosynthesis from nova outbursts (white dwarfs in binary systems giving rise to explosive nucleosynthesis and
contributing mainly for the enrichment of 7Li and of 13C;
[see 78].
• Type la Supernovae (0.8 < M/M0 < 8):
Type la SNe are thought to originate from Cdeflagration in C-O white dwarfs in binary systems. The
type la SNe contribute to a substantial amount of iron
(^ 0.6M0 per event) and to non-negligible quantities of
Si and S. They also contribute to other elements such as
C, Ne, Ca, Mg and Ni, but in negligible amounts when
compared with the masses of such elements ejected by
type II SNe. The adopted nucleosynthesis prescriptions
are from Thielemann et al. [94].
• Massive stars (8< M/M0 < 100):
These stars are the progenitors of type II SNe. For
this range of masses we adopt the yields computed by
Woosley and Weaver [102] for the following elements:
4
He, 12C, 13C, 14N, 160,20Ne, 24Mg, 28Si, 32S, 40Ca and
56
Fe. The major advantage of these calculations is that
explosive nucleosynthesis is taken into account.
232
RESULTS
Figures from 1 to 6 and tables 1 and 2 show the predictions of our best model both for the solar vicinity and the
whole disk.
The "two-Mall" model allowed us to fit the observed
metallicity distribution of the G-dwarfs by assuming a
long timescale for the thin-disk formation. In particular,
the fit of the G-dwarf [Fe/H] distribution requires that the
local disk formed by infall of gas on a time scale of the
order of 6-8 Gyr [see 19]. This long timescale for the
thin-disk formation at the solar vicinity was then suggested also by more recent chemical evolution models
[eg. 70, 13, 8, 42]. The same result is also suggested by
chemodynamical models [84,41].
A detailed discussion of the results can be found in
Chiappini et al. [17, 19]. Here we call attention to some
specific points.
What can we learn from the abundance
ratios ?
Secondary/primary and s-processlprimary ratios
Abundance ratios of a primary element over a secondary one are expected to decrease with time or metallicity [67] and to increase with the galactocentric distance when adopting the "inside-out" scenario. This fact
can be useful to understand the origin of different elements and to give us information on the timescale of formation of galaxies. One example is the 12C/13C ratio.
The temporal and spatial behaviour of the 12C/13C ratio
predicted by models adopting the standard nucleosynthesis are flatter than observations [see 97]. A steeper gradient for 12C/13C can be achieved either by assuming
that novae (white dwarfs in binary systems) are important producers of 13C (restored into the ISM on longer
timescales), or by adopting new C yields for low mass
stars including deep extra mixing during the red giant
phase associated with cool bottom processing [see 14].
For the 16O/18O ratio the problem resides in the fact
that its predicted value in the ISM is higher by a factor
1.6 than that inferred from molecular cloud observations.
Moreover, from the nucleosynthetic point of view 18O
is a neutron-rich element, namely an s-process element
which should show, as do all s-process elements, a sort
of secondary behaviour and, as a consequence, chemical
evolution models predict that the 16O/18O ratio should
decrease with time, being lower in the ISM than in the
Sun, contrary to what is observed [see WG5 contribution
and 97].
vicinity, as shown in Chiappini et al. [18]. Here we only
show the plot of [Fe/O] versus [O/H] which indicates the
existence of a gap in the SFR occurring at [O/H] ~ —0.2
dex (figure 4). In fact, if there is a gap in the SFR we
should expect both a steep increase of [Fe/O] at a fixed
[O/H] and a lack of stars corresponding to the gap period
(the gap in Chiappini et al. [17] is more pronounced
than in Chiappini et al. [18] given the lower value of
the threshold adopted for the halo) [see discussion in
17, 25]. This gap, suggested also by the [Fe/Mg] data of
Fuhrmann [32], in our models is due to the adoption of
the threshold in the star formation process coupled with
the assumption of a slow infall for the formation of the
disk.
1-0.
0.4
-0.8
0.4
-3.6
-3.4
log(0/H)
Gratton et al. 2000
0.2
FIGURE 3. The line shows our model prediction for
log(C/O) vs (O/H). The discontinuity seen in the model is the
result of the gap in the star formation occurring at the end of the
halo phase. The dots show the data by Gustafsson et al. [39].
The big simbols show the different location of the Sun in this
diagram when adopting Anders and Grevesse [3] (hexagon),
Grevesse and Sauval [36] (star) or Holweger (triangle - this
conference)
-0.2
-0.4
Ratio between primary elements produced on different
timescales
-0.6
The abundance ratio of two primary elements that are
restored into the interstellar medium by stars in different mass ranges, would show almost the same behavior discussed above. One example is the 16O/12C ratio. In this case both elements are primary but as 12C is
mainly restored into the interstellar medium by intermediate mass stars (and hence on larger timescales compared to the 16O enrichment which comes mainly from
massive stars), this ratio decreases as a function of metallicity. An important point about this abundance ratio is
that models adopting the yields of Renzini and Voli [75]
for low and intermediate mass stars could not reproduce
the steep rise of C/O vs. O/H and the solar value for
this ratio [19]. However, this problem is overcame once
the yields of van den Hoek and Groenewegen [101] are
adopted instead of the ones of Renzini and Voli [75], for
low and intermediate mass stars (see figure 3) and [78].
The [OIFe] vs [Fe/H] plot
It is worth noting that the two-Mail model provides a
good fit of the [oc/Fe] versus [Fe/H] relation in the solar
233
-2
-1.5
-1
[O/H]
-0.5
0.5
FIGURE 4. [Fe/O] vs [O/H] diagram. The data are from
Gratton et al. [35] and the curve shows the prediction of the
best model of Chiappini et al. [17].
Another interesting point about abundance ratios that
can be understood using the particular case of [O/Fe] is
discussed below. The data for oxygen from Gratton et al.
[35] (figures 4 and 6) show a slight increase of the [O/Fe]
ratio with decreasing [Fe/H] at variance with what happens for other a-elements which show a flatter plateau.
This slight slope is well reproduced by theoretical models [18, 17] owing to the fact that the O/Fe production
ratio from massive stars, in the adopted yields, is an increasing function of the initial stellar mass (figure 5). On
the other hand, other elements such as Si and S are not
predicted to have a large overabundance relative to Fe
in metal poor stars, owing to the fact that they are also
produced in a non-negligible way by type la SNe. The
change in the slope, occurring at roughly [Fe/H] =—1.0
dex, is due to the bulk of iron produced by type la SNe
which becomes important after a timescale of the order
of 1 Gyr. This change in slope corresponds also to the
0.9
10
20
30
40
Mi (M0)
[Fe/H]
FIGURE 5. Ejected masses of oxygen and iron computed
by stellar evolution models of massive stars Thielemann et
al. [TNH96 93] and Woosley and Weaver [WW95 102] as a
function of initial mass, MJ.
end of the halo phase and thus allows us to have an estimate for the duration of the halo-thick disk phase.
Our prediction for the [O/Fe] ratio, especially at very
low metallicities, is not in agreement with recent claims
of a linear rising of this ratio with decreasing [Fe/H] obtained from UV OH lines (e.g. data from Israelian et
al. [44] and Boesgaard et al. [7]). A detailed discussion
about this apparent controversy can be found in Melendez et al. [63]. Those authors obtained high-resolution infrared spectra in H-band in order to derive oxygen abundances from IR OH lines and found that for a sample
of stars in the -2.2 < [Fe/H] < -1.2, [O/Fe] ~ 0.4 ±
0.2 with no significant evidence for an increase of [O/Fe]
with decreasing metallicity. Moreover, as shown by Asplund et al. [4], the traditional ID LTE analyses of the
UV OH lines can overestimate the O/Fe ratio while when
adopting 3D analyses the results from UV OH lines are
consistent with the one obtained from forbidden lines.
Figure 6 shows our model predictions (thick solid
line) adopting the yields from Thielemann et al. [93] for
massive stars, which predict the highest [O/Fe] at low
metallicities, instead of Woosley and Weaver [102]. The
recent data of Melendez et al. [63] are also plotted (open
simbols) and the star shows the very metal poor object
recently measured by Cayrel et al. [12] from [OI] lines.
The dashed line represents a mean fit to the oxygen data
of Gratton et al. [35]. The triangles show the recent new
results of Israelian et al. [43] (here we took only their
measurements of the oxygen triplet lines with NLTE
corrections in the iron abundance). As it can be seen,
234
FIGURE 6. The solid line shows the predictions of Chiappini
et al. [18] (adopting the yields of [93] instead of [102], for
massive stars). The dashed line shows a fit to the data by
Gratton et al. [35]. The open simbols are the observations
reported by Melendez et al. [63]. The filled hexagons represent
the abundances obtained by Israelian et al. [44] from UV OH
lines. The filled triangles show the data from Israelian et al.
[43]. In particular, from [43] we ploted only the observations
obtained from oxygen triplet lines with NLTE corrections. It
can be seen that once the data of Israelian et al. [44] obtained
from UV OH lines are not considered [see 4] the models
provide a good fit to the most up to date observations.
the model seems to fit the data quite well (even those
of [43], whereas the previous data by the same authors filled hexagons - based only on OH lines measurements
cannot be explained by our models).
Solar Abundance Values
The solar abundances (by mass) predicted by our
model are compared with the observed ones [3, 36, Holweger this conference] in Table 2. Since we assume a
Galactic lifetime of 14 Gyrs the time of the Sun formation in our models corresponds to 9.5 Gyrs after the Big
Bang. Given the uncertainties involved either in the observed determinations and in some of the chemical evolution parameters (namely, galaxy age, stellar yields, etc)
we can consider that a model is in agreement with the observed values inside a factor 2 difference. From table 2
we can see that for most of the elements the observed and
predicted values agree inside a factor of 2. We note that
the values of Holweger and [36] for C, shown in table 2,
include both 12C and 13C.
The radial profiles
As can be seen in figure 2, our model demonstrates
a satisfactory fit to the elemental abundance gradients
and it is also in good agreement with the observed radial
profiles of the SFR, gas density and the number of stars in
the disk. As shown in the previous sections, a decoupling
between halo and disk phases is needed in order to best
fit all the solar neighborhood observational constraints.
However, the outer gradients are sensitive to the halo
evolution, in particular to the amount of halo gas which
ends up in the disk. This result is not surprising since
the halo density is comparable to that of the outer disk,
whereas it is negligible when compared to that of the
inner disk. Therefore, the inner parts of the disk (R <
RQ) evolve independently from the halo evolution in
agreement with Chiappini et al. [19].
Moreover, we predict that the abundance gradients
along the Galactic disk must have increased with time.
Other authors find a flattening of the gradients ([see 97]
for clear discussion on the possible scenarios for the evolution of the abundance gradients). In fact, different authors can fit the solar vicinity constraints and even the
present time abundance gradients, but the papers seem
to be divided into two groups concerning the evolution
of the abundance gradients: in some of them the gradients steepen with time [96, 19, 84] while in others the
abundance gradients flatten with time [2, 72, 42]. For
the models that predict a flattening of the gradients with
time, this can be explained as follows: in the inner parts
of the disk those models assume a very high efficiency
in the chemical enrichment process already in the earliest phases of the Galaxy evolution, thus soon reaching a maximum metallicity in the gas which then remains constant or decreases due to the gas recycled by
dying stars. At the same time, in the outermost disk regions the lack of any pre-enrichment from the halo phase
and the fact that those models do not include a threshold in the star formation process in the disk, produces a
growth of metallicity larger than the one we found. This
also explains an important difference between the results
shown by Chiappini et al. [17] and those of Hou et al.
[42]. As in Hou et al. [42] model the halo phase is completely decoupled from the disk evolution (even in the
outer parts), their initial metallicities at larger Galactocentric distances are very small. Moreover, since they do
not consider a threshold on the star formation process
in the disk, their predicted abundances in the outermost
parts of the disk keep increasing with time leading to a
flattening of the abundance gradients.
The lack of good data for the outer Milky Way disk
abundances still prevents us from testing the predictions
for the evolution of abundance gradients and represents
one of the main reasons for the non-uniqueness of the
various chemical evolution models (a discussion about
235
this specific problem can be found in Tosi [97]; and
a discussion about the possible reasons for the above
discrepancy can be found in Chiappini et al. [17]).
The gradients of different elements are predicted to be
slightly different, owing to their different nucleosynthesis histories. In particular, Fe and N, which are produced
on longer timescales than the a-elements, show steeper
gradients. Unfortunately, the available observations cannot yet confirm or disprove this, because the predicted
differences are below the limit of detectability.
DISCUSSION
We conclude this paper by discussing the scenario for the
formation of the Milky Way that emerges once the best
observables and the predictions of our detailed chemical
evolution model are put together.
What do the observables in the Milky Way
tell us ?
* The galactic disk formed inside-out and mainly out of
extragalactic gas.
* The SFR should be a strongly varying function of
radius.
* The solar vicinity region should have formed by slow
infall of primordial (or metal-poor) gas over a time scale
of the order of 7 Gyr.
* The bulge formed on a much shorter timescale than the
disk and from the same gas which formed the halo.
* The inner halo formed on a shorter timescale than the
outer halo.
* The SFR probably stopped for a certain period (<
IGyr) during the halo-thin disk transition.
* The majority of the a-elements should have been produced on short timescales relative to the age of the
Galaxy (~ 15 Gyr) (type II SNe) whereas the Fe-peak
elements should have been restored with a large delay by
type la SNe, in agreement with current ideas on nucleosynthesis and SN progenitors.
* The IMF should have been rather constant during the
galactic lifetime.
Finally we would like to conclude this paper by calling attention to a forthcoming new important observational constraint on chemical evolution models, namely,
the abundances in the interstellar medium (see WG3)
which will help to constrain the last 4.5 Gyrs of evolution of our Galaxy. The results shown in this conference (e.g. Gloeckler, Wiedenbeck, WG3), together with
the assumption that the sun represents the abundance of
the ISM 4.5 Gyrs ago, seem to suggest a slow evolution
for a-elements during this period. This leads to an in-
teresting final question: is this another indication of the
importance of the threshold in the process of star formation?
ACKNOWLEDGMENTS
C. Chiappini would like to thank the organizers of the
SOHO-ACE conference for the invitation and for the
very stimulating environment created during the meeting. This work was partially supported by the Bern University and ES A space agency.
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