Chemical Evolution
Francesca Matteucci
Department of Astronomy
University of Trieste
and Osservatorio Astronomico di Trieste (INAF)
Via G.B. Tiepolo, 11, 34124 Trieste
Italy
(matteucci@ts.astro.it)
http://arxiv.org/abs/0704.0770v1
Contents
1 Chemical Evolution page 1
1.1 Lecture I: basic assumptions and equations of chem-
ical evolution 1
1.1.1 The basic ingredients 1
1.1.2 The Star Formation Rate 2
1.1.3 The Initial Mass Function 3
1.1.4 The Infall Rate 4
1.1.5 The Outflow Rate 4
1.1.6 Stellar evolution and nucleosynthesis: the
stellar yields 5
1.1.7 Type Ia SN Progenitors 6
1.1.8 Yields per Stellar Generation 7
1.1.9 Analytical models 8
1.1.10 Numerical Models 9
1.2 Lecture II: the Milky Way and other spirals 11
1.2.1 The Galactic formation timescales 11
1.2.2 The two-infall model 12
1.2.3 Common Conclusions from MW Models 18
1.2.4 Abundance Gradients from Emission Lines 19
1.2.5 Abundance Gradients in External Galaxies 21
1.2.6 How to model the Hubble Sequence 21
1.2.7 Type Ia SN rates in different galaxies 24
1.2.8 Time-delay model for different galaxies 25
1.3 Lecture III: interpretation of abundances in dwarf
irregulars 27
1.3.1 Properties of Dwarf Irregular Galaxies 27
1.3.2 Galactic Winds 31
iv Contents
1.3.3 Results on DIG and BCG from purely
chemical models 32
1.3.4 Results from Chemo-Dynamical models: IZw18 34
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrich-
ment 38
1.4.1 Ellipticals 38
1.4.2 Chemical Properties 38
1.4.3 Scenarios for galaxy formation 39
1.4.4 Ellipticals-Quasars connection 41
1.4.5 The chemical evolution of QSOs 41
1.4.6 The chemical enrichment of the ICM 43
1.4.7 Conclusions on the enrichment of the ICM 46
References 48
Chemical Evolution
1.1 Lecture I: basic assumptions and equations of chemical
evolution
To build galaxy chemical evolution models one needs to elucidate a num-
ber of hypotheses and make assumptions on the basic ingredients.
1.1.1 The basic ingredients
• INITIAL CONDITIONS: whether the mass of gas out of which stars
will form is all present initially or it will be accreted later on. The
chemical composition of the initial gas (primordial or already enriched
by a pregalactic stellar generation).
• THE BIRTHRATE FUNCTION:
B(M, t) = ψ(t)ϕ(M) (1.1)
where:
ψ(t) = SFR (1.2)
is the star formation rate (SFR) and:
ϕ(M) = IMF (1.3)
is the initial mass function (IMF).
• STELLAR EVOLUTION AND NUCLEOSYNTHESIS: stellar yields,
yields per stellar generation
• SUPPLEMENTARY PARAMETERS : infall, outflow, radial flows.
2 Chemical Evolution
1.1.2 The Star Formation Rate
Here we will summarize the most common parametrizations for the SFR
in galaxies, as adopted by chemical evolution models:
• Constant in space and time and equal to the estimated present time
SFR. For example, for the local disk, the present time SFR is SFR=2-
5M⊙pc
−2Gyr−1 (Boissier& Prantzos, 1999).
• Exponentially decreasing:
SFR = νe−t/τ∗ (1.4)
with τ∗ = 5− 15 Gyr (Tosi, 1988). The quantity νis a parameter that
we call efficiency of SF since it represents the SFR per unit mass of
gas and is expressed in Gyr−1.
• The most used SFR is the Schmidt (1959) law, which assumes a de-
pendence on the gas density, in particular:
SFR = νσkgas (1.5)
where k = 1.4± 0.15, as suggested by a study of Kennicutt (1998)
of local star forming galaxies.
• Some variations of the Schmidt law with a dependence also on the
total mass have been suggested for example by Dopita & Ryder (1994).
This formulation takes into account the feedback mechanism acting
between supernovae ( SNe) and stellar winds injecting energy into the
interstellar medium (ISM) and the galactic potential well. In other
words, the SF process is regulated by the fact that in a region of
recent star formation the gas is too hot to form stars and it is easily
removed from that region. Before new stars could form the gas needs
to cool and collapse back into the star forming region and this process
depends on the potential well and therefore on the total mass density:
SFR = νσk1totσ
gas (1.6)
with k1 = 0.5 and k2 = 1.5.
• Kennicutt (1998) also suggested, as an alternative to the Schmidt law
to fit the data, the following relation:
SFR = 0.017Ωgasσgas ∝ R
−1σgas (1.7)
with Ωgas being the angular rotation speed of gas.
1.1 Lecture I: basic assumptions and equations of chemical evolution3
• Finally a SFR induced by spiral density waves was suggested by Wyse
& Silk (1989):
SFR = νV (R)R−1σ1.5gas (1.8)
with R being the galactocentric distance and V (R) the gas rotation
velocity.
1.1.3 The Initial Mass Function
The IMF is a probability function describing the distribution of stars
as a function of mass. The present day mass function is derived for
the stars in the solar vicinity by counting the Main Sequence stars as a
function of magnitude and then applying the mass-luminosty relation,
holding for Main Sequence stars, to derive the distribution of stars as
a function of mass. In order to derive the IMF one has then to make
assumptions on the past history of SF.
The derived IMF is normally approximated by a power law:
ϕ(M)dM = aM−(1+x)dM (1.9)
where ϕ(M) is the number of stars with masses in the interval M,
M+dM.
Salpeter (1955) proposed a one-slope IMF (x = 1.35) valid for stars
with M > 10M⊙. Multi-slope (x1, x2, ..) IMFs have been suggested
later on always for the solar vicinity (Scalo 1986,1998; Kroupa et al.
1993; Chabrier 2003). The IMF is generally normalized as:
∫ 100
Mϕ(M)dM = 1 (1.10)
where a is the normalization constant and the assumed interval of inte-
gration is 0.1− 100M⊙.
The IMF is generally considered constant in space and time with some
exceptions such as the IMF suggested by Larson (1998) with:
x = 1.35(1 +m/m1)
−1 (1.11)
where m1 is variable typical mass and is associated to the Jeans mass.
This IMF predicts then that m1 is a decreasing function of time.
4 Chemical Evolution
1.1.4 The Infall Rate
For the rate of gas accretion there are in the literature several parametriza-
tions:
• The infall rate is constant in space and time and equal to the present
time infall rate as measured in the Galaxy (∼ 1.0M⊙yr
• The infall rate is variable in space and time, and the most common
assumption is an exponential law (Chiosi 1980; Lacey & Fall 1985):
IR = A(R)e−t/τ(R) (1.12)
with τ(R) constant or varying with the galactocentric distance. The
parameter A(R) is derived by fitting the present day total surface
mass density, σtot(tG), at any specific galactocentric radius R.
• For the formation of the Milky Way two episodes of infall have been
suggested (Chiappini et al. 1997), where during the first infall episode
the stellar halo forms whereas during the second infall episode the
disk forms. This particular infall law gives a good representation of
the formation of the Milky Way. The proposed two-infall law is:
IR = A(R)e−t/τH(R) +B(R)e−(t−tmax)/τD(R) (1.13)
where τH(R) is the timescale for the formation of the halo which
can be costant or vary with galactocentric distance. The quantity
τD(R) is the timescale for the formation of the disk and is a function
of the galactocentric distance; in most of the models it is assumed to
increase with R (e.g. Matteucci & François, 1989).
• More recently, Prantzos (2003) suggested a gaussian law with a peak
at 0.1 Gyr and a FWHM of 0.04 Gyr for the formation of the stellar
halo.
1.1.5 The Outflow Rate
The so-called galactic winds occur when the thermal energy of the gas
in galaxies exceeds its potential energy. Generally, gas outflows are
called winds when the gas is lost forever from the galaxy. Only detailed
dynamical simulations can suggest whether there is a wind or just an
outflow of gas which will soon or later fall back again into the galaxy. In
chemical evolution models galactic winds can be sudden or continuous. If
they are sudden, the mass is assumed to be lost in a very short interval of
1.1 Lecture I: basic assumptions and equations of chemical evolution5
time and the galaxy is devoided from all the gas; if they are continuous,
one has to assume the rate of gas loss. Generally, in chemical evolution
models (Bradamante et al. 1998) and also in cosmological simulations
(Springel & Hernquist, 2003) it is assumed that the rate of gas loss is
several times the SFR:
W = −λSFR (1.14)
where λ is a free parameter with the meaning of wind efficiency. This
particular formulation for the galactic wind rate is confirmed by obser-
vational findings (see Martin, 1999).
1.1.6 Stellar evolution and nucleosynthesis: the stellar yields
Here we summarize the various contribution to the element production
by stars of all masses.
• Brown Dwarfs (M < ML, ML = 0.08 − 0.09M⊙) are objects which
never ignite H and their lifetimes are larger than the age of the Uni-
verse. They are contributing to lock up mass.
• Low mass stars (0.5 ≤ M/M⊙ ≤ MHeF ) (1.85-2.2M⊙) ignite He ex-
plosively but without destroying themselves and then become C-O
white dwarfs (WD). If M < 0.5M⊙ they become He WDs. Their
lifetimes range from several 109 years up to several Hubble times!
• Intermediate mass stars (MHeF ≤ M/M⊙ ≤ Mup) ignite He quies-
cently. The mass Mup is the limiting mass for the formation of a C-O
degenerate core and is in the range 5-9M⊙, depending on stellar evo-
lution calculations. Lifetimes are from several 107 to 109 years. They
die as C-O WDs if not in binary systems. If in binary systems they
can give rise to cataclysmic variables such as novae and Type Ia SNe.
• Massive stars (M > Mup). We distinguish here several cases:
-Mup ≤ M/M⊙ ≤ 10 − 12. Stars with Main Sequence masses in
this range end up as electron-capture SNe leaving neutron stars as
remnants. These SNe will appear as Type II SNe which show H in
their spectra.
-10 − 12 ≤ M/M⊙ ≤ MWR, (with MWR ∼ 20 − 40M⊙ being the
limiting mass for the formation of a Wolf-Rayet (WR) star). Stars in
this mass range end their life as core-collapse SNe (Type II) leaving a
neutron star or a black hole as remnants.
-MWR ≤ M/M⊙ ≤ 100. Stars in this mass range are probably
6 Chemical Evolution
exploding as Type Ib/c SNe which do not show H in their spectra.
Their lifetimes are of the order of ∼ 106 years.
• Very Massive Stars (M > 100M⊙), they should explode by means
of instability due to “pair creation” and they are called pair-creation
SNe. In fact, at T ∼ 2 · 109 K a large portion of the gravitational
energy goes into creation of pairs (e+, e−), the star becomes unstable
and explodes. They leave no remnants and their lifetimes are < 106
years. Probably these very massive stars formed only when the metal
content was almost zero (Population III stars, Schneider et al. 2004).
All the elements with mass number A from 12 to 60 have been formed
in stars during the quiescent burnings. Stars transform H into He and
then He into heaviers until the Fe-peak elements, where the binding
energy per nucleon reaches a maximum and the nuclear fusion reactions
stop.
H is transformed into He through the proton-proton chain or the CNO-
cycle, then 4He is transformed into 12C through the triple- α reaction.
Elements heavier than 12C are then produced by synthesis of α-
particles. They are called α-elements (O, Ne, Mg, Si and others).
The last main burning in stars is the 28Si -burning which produces
56Ni which then decays into 56Co and 56Fe. Si-burning can be quiescent
or explosive (depending on the temperature).
Explosive nucleosynthesis occurring during SN explosions mainly pro-
duces Fe-peak elements. Elements originating from s- and r-processes
(with A> 60 up to Th and U) are formed by means of slow or rapid (rel-
ative to the β- decay) neutron capture by Fe seed nuclei; s-processing
occurs during quiescent He-burning whereas r-processing occurs during
SN explosions.
1.1.7 Type Ia SN Progenitors
The Type Ia SNe, which do not show H in their spectra, are believed to
originate from WDs in binary systems and to be the major producers of
Fe in the Universe. The model proposed are basically two:
• Single Degenerate Scenario (SDS), with a WD plus a Main Se-
quence or Red Giant star, as originally suggested by Whelan and Iben
(1973). The explosion (C-deflagration) occurs when the C-O WD
reaches the Chandrasekhar mass, MCh =∼ 1.44M⊙, after accreting
material from thecompanion. In this model the clock to the explosion
is given by the lifetime of the companion of the WD (namely the less
1.1 Lecture I: basic assumptions and equations of chemical evolution7
massive star in the system). It is interesting to define the minimum
timescale for the explosion which is given by the lifetime of a 8M⊙
star, namely tSNIamin=0.03 Gyr (Greggio and Renzini 1983). Recent
observations in radio-galaxies by Mannucci et al. (2005;2006) seem to
confirm the existence of such prompt Type Ia SNe.
• Double Degenerate Scenario (DDS), where the merging of two C-
OWDs of mass∼ 0.7M⊙, due to loss of angular momentum as a conse-
quence of gravitational wave radiation, produces C-deflagration (Iben
and Tutukov 1984). In this case the clock to the explosion is given
by the lifetime of the secondary star, as above, plus the gravitational
time delay, namely the time necessary for the two WDs to merge. The
minimum time for the explosion is tSNIamin = 0.03+∆tgrav=0.04 Gyr
(see Tornambè 1989).
Some variations of the above scenarios have been proposed such as
the model by Hachisu et al. (1996; 1999), which is based on the sin-
gle degenerate scenario where a wind from the WD is considered. Such
a wind stabilizes the accretion from the companion and introduces a
metallicity effect. In particular, the wind, necessary to this model, oc-
curs only if the systems have metallicity ([Fe/H]< −1.0). This implies
that the minimum time for the explosion is larger than in the previous
cases. In particular, tSNIamin = 0.33 Gyr, which is the lifetime of the
more massive secondary considered (2.3M⊙) plus the metallicity delay
which depends on the assumed chemical evolution model.
1.1.8 Yields per Stellar Generation
Under the assumption of Instantaneous Recycling Approximation (IRA)
which states that all stars more massive than 1M⊙ die immediately,
whereas all stars with masses lower than 1M⊙ live forever, one can
define the yield per stellar generation (Tinsley, 1980);
mpimϕ(m)dm (1.15)
where pim is the stellar yield of the element i, namely the newly formed
and ejected element i by a star of mass m.
The quantity R is the so-called Returned Fraction:
(m−Mrem)ϕ(m)dm (1.16)
8 Chemical Evolution
and is the total mass of gas restored into the ISM by an entire stellar
generation.
1.1.9 Analytical models
The Simple Model for the chemical evolution of the solar neighbourhood
is the simplest approach to model chemical evolution. The solar neigh-
bourhood is assumed to be a cylinder of 1 Kpc radius centered around
the Sun.
The basic assumptions of the Simple Model are:
- the system is one-zone and closed, no inflows or outflows with the
total mass present since the beginning,
- the initial gas is primordial (no metals),
- instantaneous recycling approximation holds,
- the IMF, ϕ(m), is assumed to be constant in time,
- the gas is well mixed at any time (IMA)
The Simple Model fails in describing the evolution of the Milky Way
(G-dwarf metallicity distribution, elements produced on long timescales
and abundance ratios) and the reason is that at least two of the above
assumptions are manifestly wrong, epecially if one intends to model the
evolution of the abundance of elements produced on long timescales,
such as Fe. In particular the assumptions of the closed boxiness and the
However, it is interesting to know the solution of the Simple Model
and its implications. Be Xi the abundance by mass of an element i.
If Xi << 1, which is generally true for metals, we obtain the solution
of the Simple Model. This solution is obtained analytically by ignoring
the stellar lifetimes:
Xi = yiln(
) (1.17)
where µ =Mgas/Mtot and yi is the yield per stellar generation, as defined
above, otherwise called effective yield. In particular, the effective yield
is defined as:
yieff =
ln(1/G)
(1.18)
namely the yield that the system would have if behaving as the simple
closed-box model. This means that if yieff > yi, then the actual system
has attained a higher abundance for the element i at a given gas fraction
G. Generally, in the IRA, we can assume:
1.1 Lecture I: basic assumptions and equations of chemical evolution9
(1.19)
which means that the ratio of two element abundances are always
equal to the ratio of their yields. This is no more true when IRA is
relaxed. In fact, relaxing IRA is necessary to study in detail the evolution
of the abundances of single elements.
One can obtain analytical solutions also in presence of infall and/or
outflow but the necessary condition is to assume IRA. Matteucci &
Chiosi (1983) found solutions for models with outflow and infall and
Matteucci (2001) found it for a model with infall and outflow acting at
the same time. The main assumption in the model with outflow but no
infall is that the outflow rate is:
W (t) = λ(1−R)ψ(t) (1.20)
where λ ≥ 0 is the wind parameter.
The solution of this model is:
(1 + λ)
ln[(1 + λ)G−1 − λ] (1.21)
for λ = 0 the equation becomes the one of the Simple Model (1.17).
The solution of the equation of metals for a model without wind but
with a primordial infalling material (XAi = 0) at a rate:
A(t) = Λ(1−R)ψ(t) (1.22)
and Λ 6= 1 is :
[1− (Λ − (Λ− 1)G−1)−Λ/(1−Λ)] (1.23)
For Λ = 1 one obtains the well known case of extreme infall studied by
Larson (1972) whose solution is:
Xi = yi[1− e
−(G−1−1)] (1.24)
This extreme infall solution shows that when G→ 0 then Xi → yi.
1.1.10 Numerical Models
Numerical models relax IRA and close boxiness but generally retain the
constancy of ϕ(m) and the IMA.
10 Chemical Evolution
If Gi is the mass fraction of gas in the form of an element i, we can
write:
Ġi(t) = −ψ(t)Xi(t)
∫ MBm
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
∫ MBM
∫ 0.5
f(γ)ψ(t− τm2)Qmi(t− τm2)dγ]dm
∫ MBM
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
+XAiA(t)−Xi(t)W (t) (1.25)
where B=1-A, A=0.05-0.09. The meaning of the A parameter is the
fraction in the IMF of binary systems with those specific features re-
quired to give rise to Type Ia SNe, whereas B is the fraction of all the
single stars and binary systems in the same mass range of definition of
the progenitors of Type Ia SNe. The values of A indicated above are cor-
rect for the evolution of the solar vicinity where an IMF of Scalo (1986,
1989) or Kroupa et al.(1993) is adopted. If one adopts a flatter IMF such
as the Salpeter (1955) one then A is different. In the above equations
the contribution of Type Ia SNe is contained in the third term on the
right hand side. The integral is made over a range of masses going from
3 to 16 M⊙ which represents the total masses of binary systems able to
produce Type Ia SNe in the framework of the SDS. There is also an inte-
gration over the mass distribution of binary systems; in particular, one
considers the function f(γ) where γ = M2
M1+M2
, with M1 and M2 being
the primary and secondary mass of the binary system, respectively (for
more details see Matteucci & Greggio 1986 and Matteucci 2001).The
functions A(t) and W(t) are the infall and wind rate, respectively. Fi-
nally, the quantity Qmi represents the stellar yields (both processed and
unprocessed material).
1.2 Lecture II: the Milky Way and other spirals 11
1.2 Lecture II: the Milky Way and other spirals
The Milky Way galaxy has four main stellar populations: 1) the halo
stars with low metallicities (the most common metallicity indicator in
stars is [Fe/H]= log(Fe/H)∗− log(Fe/H)⊙) and eccentric orbits, 2) the
bulge population with a large range of metallicities and is dominated
by random motions, 3) the thin disk stars with an average metallicity
< [Fe/H ] >=-0.5 dex and circular orbits, and finally 4) the thick stars
which possess chemical and kinematical properties intermediate between
those of the halo and those of the thin disk. The halo stars have average
metallicities of < [Fe/H ] >=-1.5 dex and a maximum metallicity of
∼ −1.0 dex although stars with [Fe/H] as high as -0.6 dex and halo
kinematics are observed. The average metallicity of thin disk stars is
∼ −0.6 dex, whereas the one of Bulge stars is ∼ −0.2 dex.
1.2.1 The Galactic formation timescales
The kinematical and chemical properties of the different Galactic stel-
lar populations can be interpreted in terms of the Galaxy formation
mechanism. Eggen et al. (1962) in a cornerstone paper suggested a
rapid collapse for the formation of the Galaxy lasting ∼ 3 · 108 years.
This suggestion was based on a kinematical and chemical study of so-
lar neighbourhood stars. Later on, Searle & Zinn (1979) proposed a
central collapse like the one proposed by Eggen et al. but also that the
outer halo formed by merging of large fragments taking place over a con-
siderable timescale > 1 Gyr. More recently, Berman & Suchov (1991)
proposed the so-called hot Galaxy picture, with an initial strong burst
of SF which inhibited further SF for few Gyr while a strong Galactic
wind was created.
From an historical point of view, the modelization of the Galactic
chemical evolution has passed through different phases that I summarize
in the following.
• SERIAL FORMATION
The Galaxy is modeled by means of one accretion episode lasting
for the entire Galactic lifetime, where halo, thick and thin disk form in
sequence as a continuous process. The obvious limit of this approach
is that it does not allow us to predict the observed overlapping in
metallicity between halo and thick disk stars and between thick and
thin disk stars, but it gives a fair representation of our Galaxy (e.g.
Matteucci & François 1989).
12 Chemical Evolution
• PARALLEL FORMATION
In this formulation, the various Galactic components start 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 implies that the thick disk formed out of gas
shed by the halo and that the thin disk formed out of gas shed by the
thick disk, and this is at variance with the distribution of the stellar
angular momentum per unit mass (Wyse & Gilmore 1992), which
indicates that the disk did not form out of gas shed by the halo.
• TWO-INFALL FORMATION
In this scenario, halo and disk formed out of two separate infall
episodes (overlapping in metallicity is also predicted) (e.g. Chiappini
et al. 1997; Chang et al. 1999). The first infall episode lasted no more
than 1-2 Gyr whereas the second, where the thin disk formed, lasted
much longer with a timescale for the formation of the solar vicinity of
6-8 Gyr (Chiappini et al. 1997; Boissier& Prantzos 1999).
• STOCHASTIC APPROACH
Here the hypothesis is that in the early halo phases ([Fe/H] < −3.0
dex), mixing was not efficient and, as a consequence, one should ob-
serve in low metallicity halo stars the effects of pollution from single
SNe (e.g. Tsujimoto et al. 1999; Argast et al. 2000; Oey 2000). These
models predict a large spread for [Fe/H] < −3.0dex which is not ob-
served, as shown by recent data with metallicities down to -4.0 dex
(Cayrel et al. 2004; see later).
1.2.2 The two-infall model
The adopted SFR (see Figure 2.1) is eq.(1.6) with different SF efficiencies
for the halo and disk, in particular νH = 2.0Gyr
−1, νD = 1.0Gyr
respectively. A threshold density (σth = 7M⊙pc
−2) for the SFR is also
assumed in agreement with results from Kennicutt (1989; 1998).
In Figure 2.2 we show the predicted SN (II and Ia) rates by the two-
infall model. Note that the Type Ia SN rate is calculated according to
the SDS (Greggio & Renzini, 1983; Matteucci & Recchi, 2001). There
is a delay between the Type II SN rate and the Type Ia SN rate, and
while the Type II SN rate strictly follows the SFR, the Type Ia SN rate
is smoothly increasing.
François et al. (2004) compared the predictions of the two-infall model
for the abundance ratios versus metallicity relations ([X/Fe] vs. [Fe/H]),
with the very recent and very accurate data of the project “First Stars”
1.2 Lecture II: the Milky Way and other spirals 13
Fig. 1.1. The predicted SFR in the solar vicinity with the two-infall model.
Figure from Chiappini et al. (1997). The oscillating behaviour at late times
is due to the assumed threshold density for SF. The threshold gas density is
also responsible for the gap in the SFR seen at around 1 Gyr.
by Cayrel et al. (2004). They adopted yields from the literature both for
Type II and Type Ia SNe and noticed that while for some elements (O,
Fe, Si, Ca) the yields of Woosley & Weaver (1995) (hereafter WW95)
reproduce the data fairly well, for the Fe-peak elements and heaviers
none of the available yields give a good agreement. Therefore, they
varied empirically the yields of these elements in order to best fit the
data. In Figures 2.3 and 2.4 we show the predictions for α-elements (O,
Mg, Si, Ca, Ti, K) plus some Fe-peak elements and Zn.
In Figure 2.4 we show also the ratios between the yields derived em-
pirically by François et al. (2004) in order to obtain the excellent fits
shown in the figures, and those of WW95 for massive stars. For some
elements it was necessary to change also the yields from Type Ia SNe
relative to the reference ones which are those of Iwamoto et al. (1999)
(hereafter I99).
In Figure 2.5 we show the predictions of chemical evolution models for
12C and 14N compared with abundance data. The behaviour of C shows
a roughly constant [C/Fe] as a function of [Fe/H], although C seems to
14 Chemical Evolution
Fig. 1.2. The predicted Type II and Ia SN rate in the solar vicinity with the
two-infall model. Figure from Chiappini et al. (1997)
slightly increase at very low metallicities, indicating that the bulk of
these two elements comes from stars with the same lifetimes. The data
in these figures, especially those for N are old and do not contain very
metal poor stars. Newer data containing stars with [Fe/H] down to ∼
-4.0 dex (Spite et al. 2005; Israelian et al. 2004) indicate that the [N/Fe]
ratio continues to be high also at low metallicities, indicating a primary
origin for N produced in massive stars. We recall here that we define
primary a chemical elements which is produced in the stars starting
from the H and He, whereas we define secondary a chemical element
which is formed from heavy elements already present in the star at its
birth and not produced in situ. The model predictions shown in Figure
2.5 for C and N assume that the bulk of these elements is produced
by low and intermediate mass stars (yields from van den Hoeck and
Groenewegen, 1997) and that N is produced as a partly secondary and
partly primary element. The N production from massive stars has only
a secondary origin (yields from WW95). In Figure 2.5 we show also a
model prediction where N is considered as a primary element in massive
stars with the yields artificially increased. Recently, Chiappini et al.
1.2 Lecture II: the Milky Way and other spirals 15
Fig. 1.3. Predicted and observed [X/Fe] vs. [Fe/H] for several α- and Fe-peak-
elements plus Zn compared with a compilation of data. In particular the black
dots are the recent high resolution data from Cayrel et al. (2004). For the
other data see references in François et al. (2004). The solar value indicated in
the upper right part of each figure represents the predicted solar value for the
ratio [X/Fe]. The assumed solar abundances are those of Grevesse & Sauval
(1998) except that for oxygen for which we take the value of Holweger (2001).
16 Chemical Evolution
Fig. 1.4. Upper panel: predicted and observed [X/Fe] vs. [Fe/H] for several
elements as in Figure 2.3. In the bottom part of this Figure are shown the
ratios between the empirical yields and the yields by WW95 for massive stars.
Such empirical yields have been suggested by François et al. (2004) in order
to fit at best all the [X/Fe] vs. [Fe/H] relations. In the small panel at the
bottom right side are shown also the ratios between the empirical yields for
Type Ia SNe and the yields by I99.
1.2 Lecture II: the Milky Way and other spirals 17
Fig. 1.5. Upper panel: predicted and observed [C/Fe] vs. [Fe/H]. Models
from Chiappini et al. (2003a). Lower panel, predicted and observed [N/Fe]
vs. [Fe/H]. For references to the data see original paper.The thin and thick
continuous lines in both panels represent models with standard nucleosynthe-
sis, as described in the text, whereas the dashed line represents the predictions
of a model where N in massive stars has been considered as a primary element
with “ad hoc” stellar yields.
(2006) have shown that primary N produced by very metal poor fastly
rotating massive stars can well reproduce the observations.
In summary, the comparison between model predictions and abun-
dance data indicate the following scenario for the formation of heavy
elements:
• 12C and 14N are mainly produced in low and intermediate mass stars
(0.8 ≤ M/M⊙ ≤ 8). The amounts of primary and secondary N is
still uncertain and also the fraction of C produced in massive stars.
Primary N from massive stars seems to be required to reproduce the
N abundance in low metallicity halo stars.
• α-elements originate in massive stars: the nucleosynthesis of O is
rather well understood (there is agreement between different authors),
the yields from WW95 as functions of metallicity produce an excellent
agreement with the observations for this particular element.
18 Chemical Evolution
• Magnesium is generally underproduced by nucleosynthesis models.
Taking the yields of WW95 as a reference, the Mg yields should be
increased in stars with masses M ≤ 20M⊙ and decreased in stars
with M > 20M⊙ to fit the data. Silicon should be slightly increased
in stars with masses M > 40M⊙.
• Fe originates mostly in Type Ia SNe. The Fe yields in massive stars
are still uncertain, WW95 metallicity dependent yields overestimate
Fe in stars < 30M⊙. For this element, it is better to adopt the yields
of WW95 for solar metallicity.
• Fe-peak elements: the yields of Cr, Mn should be increased in stars
of 10-20 M⊙ relative to the yields of WW95, whereas the yield of
Co should be increased in Type Ia SNe, relative to the yields of I99,
and decreased in stars in the range 10-20M⊙, 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).
1.2.3 Common Conclusions from MW Models
Most of the chemical evolution models for the Milky Way existing in the
literature conclude that:
• The G-dwarf metallicity distribution can be reproduced only by as-
suming a slow formation of the local disk by infall. In particular, the
time-scale for the formation of the local disk should be in the range
τd ∼ 6 − 8 Gyr (Chiappini et al. 1997; Boissier and Prantzos 1999;
Chang et al. 1999; Chiappini et al. 2001; Alibès et al. 2001).
• The relative abundance ratios [X/Fe] vs. [Fe/H], interpreted as time-
delay between Type Ia and II SNe, suggest a timescale for the halo-
thick disk formation of τh ∼ 1.5-2.0 Gyr (Matteucci and Greggio 1986;
Matteucci and François, 1989; Chiappini et al. 1997). The external
halo and thick disk probably formed more slowly or have been accreted
(Chiappini et al. 2001).
• To fit abundance gradients, SFR and gas distribution along the Galac-
tic thin disk we must assume that the disk formed inside-out (Mat-
teucci & François, 1989; Chiappini et al. 2001; Boissier & Prantzos
1999; Alibés et al. 2001). Radial flows can help in forming the gra-
dients (Portinari & Chiosi 2000) but they are probably not the main
cause for them. A variable IMF along the Disk can in principle ex-
plain abundance gradients but it creates unrealistic situations: in fact,
1.2 Lecture II: the Milky Way and other spirals 19
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 & François 1989; Chiappini et al, 1997,2001; Goswami &
Prantzos 2000; Alibés et al. 2001).
1.2.4 Abundance Gradients from Emission Lines
There are two types of abundance determinations in HII regions: one is
based on recombination lines which should have a weak temperature de-
pendence of the nebula (He, C, N, O), the other is based on collisionally
excited lines where a strong dependence is intrinsic to the method (C, N,
O, Ne, Si, S, Cl, Ar, Fe and Ni). This second method has predominated
until now. A direct determination of the abundance gradients from HII
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 only information on the internal nucleosynthesis of the
star. So, to derive gradients one should look at the abundances of O, S
and Ne, unaffected by stellar processes. In Figure 2.6 we show theoretical
predictions of abundance gradients along the disk of the Milky Way
compared with data from HII regions and B stars. The adopted model
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 τ(R) = 0.875R − 0.75 Gyr. Note that to
obtain a better fit for 12C, the yields of this element have been increased
artificially relative to those of WW95.
As already said, 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; Alibès 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. is included 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
20 Chemical Evolution
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
Fig. 1.6. Upper panel: abundance gradients along the Disk of the MW. The
lines are the models from Chiappini et al. (2003a): these models differ by the
nucleosynthesis prescriptions. In particular, the dash-dotted line represents
a model with van den Hoeck & Groenewegen (1997, hereafter HG97) yields
for low-intermediate mass stars with η (mass loss parameter) constant and
Thielemann et al.’s (1996) yields for massive stars, the long- dashed thick line
has HG97 yields with variable η and Thielemann et al. yields, the long-dashed
thin line has HG97 yields with variable η but WW95 yields for massive stars.
It is interesting to note that in all of these models the yields of 12C in stars
> 40M⊙ have been artificially increased by a factor of 3 relative to the yields
of WW95. Lower panel: the temporal behaviour 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 time gradient, whereas the lower ones
represent the gradient a few Gyr ago. It is clear that the gradients tend to
stepeen in time, a still controversial result.
1.2 Lecture II: the Milky Way and other spirals 21
therefore to a steepening of the gradients with time, as shown in Figure
2.6, bottom panel.
1.2.5 Abundance Gradients in External Galaxies
Abundance gradients expressed in dex/Kpc 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
(ref). The gradients are generally flatter in galaxies with central bars
(ref). The SFR is measured mainly from Hα emission (Kennicutt, 1998)
and show a correlation with the total surface gas density (HI+H2), in
particular the suggested law is that of eq. (1.5).
In the observed gas distributions differences between field and clus-
ter spirals are found in the sense that cluster spirals have less gas,
probably as a consequence of stronger interactions with the environ-
ment.Integrated colors of spiral galaxies (Josey & Arimoto 1992; Jimenez
et al. 1998; Prantzos & Boissier 2000) indicate inside-out formation, as
also found for the milky Way.
As an example of abundance gradients in a spiral galaxy we show
in Figure 2.7 the observed and predicted gas distribution and abun-
dance gradients for the disk of M101. In this case the gas distribu-
tion and the abundance gradients are reproduced with systematically
smaller timescales for the disk formation relative to the MW (M101
formed faster), and the difference between the timescales of formation
of the internal and external regions is smaller (τM101 = 0.75R−0.5 Gyr,
Chiappini et al. 2003a)
To conclude this section we 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, more metal rich and
more gas-poor than smaller ones. On the other hand their estimated SF
efficiency (defined as the SFR per unit mass of gas) seem to be similar
among different spirals: this leads them to conclude that more massive
disks are older than less massive ones.
1.2.6 How to model the Hubble Sequence
The Hubble Sequence can be simply thought as a sequence of objects
where the SFR 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
22 Chemical Evolution
Fig. 1.7. Upper panel: predicted and observed gas distribution along the disk
of M101. The observed HI, H2 and total gas are indicated in the Figure. 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
1000M⊙pc
−2, while the dotted line refers to a model with 800M⊙pc
−2 and the
dashed to a model with 600M⊙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).
1.2 Lecture II: the Milky Way and other spirals 23
reference galaxy and we change the SFR relatively to the Galactic one,
for which we adopt eq. (1.6). The quantity ν in eq. (1.6) 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 νhalo = 2.0Gyr
−1 and
νdisk = 1.0Gyr
−1 (see Figure 2.1). 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 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 like in a
burst with very high star formation efficiency, namely:
SFR = νσk (1.26)
with k = 1.0 for the sake of simplicity; ν = 10 − 20Gyr−1 (see Mat-
teucci, 1994; Pipino & Matteucci 2004).
For irregular galaxies, on the other hand, we assume that the SFR
proceeds more slowly and less efficiently that in the Milky Way disk,
in particular we assume the same SF law as for spheroids but with
0.01 ≤ ν(Gyr−1) ≤ 0.1. Among irregular galaxies, a special position
is taken by the Blue Compact Galaxies (BCG) namely galaxies which
have blue colors as a consequence of the fact that they are forming stars
at the present time, have small masses, large amounts of gas and low
metallicities. For these galaxies, we assume that they suffered on average
from 1 to 7 short bursts, with the SF efficiency mentioned above (see
Bradamante et al. 1998 and next Lecture).
Finally, dwarf spheroidals are also a special cathegory, characterized
by old stars, no gas and low metallicities. For these galaxies we assume
that they suffered one long starburst lasting 7-8 Gyr or at maximum a
couple of extended SF periods, in agreement with their measued Color-
Magnitude diagram. It is worth noting that both ellipticals and dwarf
spheroidals should loose most of their gas and therefore one may con-
clude that galactic winds should play an important role in their evolu-
tion, although ram pressure stripping cannot be excluded as a mecha-
nism for gas removal. Also for these galaxies we assume the previous
SF law with k = 1 and ν = 0.01− 1.0Gyr−1. Lanfranchi & Matteucci,
(2003, 2004) developed more detailed models for dwarf spheroidals by
adopting the SF history suggested by the Color-Magnitude diagrams of
24 Chemical Evolution
Fig. 1.8. Predicted SFRs in galaxies of different morphological type. Figure
from Calura (2004). Note that for the elliptical galaxy the SF stops abruptly
as a consequence of the galactic wind.
single galaxies and with the same efficiency of SF as above. In Figure
2.8 we show the adopted SFRs in different galaxies and in Figure 2.9
the corresponding predicted Type Ia SN rates. For the irregular galaxy,
the predicted Type Ia SN rate refers to a specific galaxy, LMC, with a
SFR taken from observations (see Calura et al. 2003) with an early ans
a late burts of SF and low SF in between.
1.2.7 Type Ia SN rates in different galaxies
Following Matteucci & Recchi (2001) we define the typical timescale
for Type Ia SN enrichment as the time when the SN rate reaches the
maximum. In the following we will always adopt the SDS for the pro-
genitors 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, whereas
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 spiral with a high SFR the timescale for Type Ia SN enrichment
1.2 Lecture II: the Milky Way and other spirals 25
Fig. 1.9. Predicted Type Ia SN rates for the SFRs of Figure 2.8. Figure from
Calura (2004). Note that for the irregular galaxy here the predictions are for
the LMC, where a recent SF burst is assumed.
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 SNeIa become important as Fe producers
(Matteucci and Greggio 1986) while a second less important peak occurs
at tSNIa = 4 − 5 Gyr. For an irregular galaxy with a continuous but
very low SFR the timescale is tSNIa > 5 Gyr.
1.2.8 Time-delay model for different galaxies
As we have already seen, the time-delay between the production of oxy-
gen by Type II SNe and that of Fe by Type Ia SNe allows us to explain
the [X/Fe] vs. [Fe/H] relations in an elegant way. However, the [X/Fe]
vs. [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 a different behaviour
in galaxies with different SF histories. In Figure 2.10 we show the pre-
dictions 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 this Figure, we predict a long plateau, well above
the solar value, for the [α/Fe] ratios in the Bulge (and ellipticals), owing
26 Chemical Evolution
LMC (Hill et al. 2000)
DLA (Vladilo 2002)
Fig. 1.10. Predicted [α/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 (∼ 1010M⊙), the median line represents the prediction for
the solar vicinity and the lower line the prediction for an irregular magellanic
galaxy. The differences among the various models are in the efficiency of star
formation, being quite high for spheroids (ν = 20Gyr−1), moderate for the
Milky Way (ν = 1 − 2Gyr−1) and low for irregular galaxies (ν = 0.1Gyr−1).
The nucleosynthesis prescriptions are the same in all objects. The time-delay
between the production of α-elements and Fe, coupled with the different SF
histories produces the differences in the plots. Data for Damped-Lyman-α
systems, LMC and Bulge are shown for comparison.
to the fast Fe enrichment reached in these systems by means of Type II
SNe: when the Type Ia SNe start enriching substantially the ISM, 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
in the gas is still well below solar. Therefore, here we observe a steeper
1.3 Lecture III: interpretation of abundances in dwarf irregulars 27
slope for the [α/Fe] ratio. In other words, we have below solar [α/Fe]
ratios at below solar [Fe/H] ratios. This diagram is very important since
it allows us to recognize a galaxy type only by means of its abundances,
and therefore it can be used to understand the nature of high redshift
objects.
1.3 Lecture III: interpretation of abundances in dwarf
irregulars
They are rather simple objects with low metallicity and large gas con-
tent, suggesting that they are either young or have undergone discon-
tinuous star formation activity (bursts) or a continuous but not efficient
star formation. 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 they could also be
important contributors to the population of systems giving rise to QSO-
absorption lines at high redshift (see Matteucci et al. 1997 and Calura
et al. 2002).
1.3.1 Properties of Dwarf Irregular Galaxies
Among local star forming galaxies, sometimes referred to as HII galax-
ies, most are dwarfs. Dwarf irregular galaxies can be divided into two
categories: Dwarf Irregular (DIG) and Blue Compact galaxies (BCG).
These latter have very blue colors due to active star formation at the
present time.
Chemical abundances in these galaxies are derived from optical emis-
sion lines in HII regions. Both DIG and BCG show a distinctive spread
in their chemical properties, altough this spread is decreasing with 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 DIG and BCG by means of ana-
lytical 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 the metallicity for a
given G ratio, and this means that the effective yield is lower than that
of the Simple Model and vary from galaxy to galaxy.
The possible solutions suggested to lower the effective yield were:
28 Chemical Evolution
• a. different IMF’s
• b. different amounts of galactic wind
• c. different amounts of infall
In Figure 3.1 we show graphically the solutions a), b) and c). Concerning
the solution a), one simply varies the IMF, whereas solutions b) and c)
have been already descibed (eqs. 1.21 ans 1.23).
Later on, Pilyugin (1993) forwarded the idea that the spread observed
also in other chemical properties properties of these galaxies such as
in the He/H vs. O/H and N/O vs. O/H relations, can be due to
self-pollution of the HII regions, which do not mix efficiently with the
surrounding medium, coupled with “enriched” or “differential” galac-
tic 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 type (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
BCG 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:
MT = (8.5± 0.4) + (190± 60)Z (1.27)
with Z being the global metal content. Recently, Tremonti et al. (2004)
analyzed 53000 local star-forming galaxies in the SDSS (irregulars and
spirals). 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
([OIII], Hβ , [OII], Hα, [NII], [SII]). Tremonti et al. (2004) derived a re-
lation indicating that 12+log(O/H) is increasing steeply from M∗ going
from 108.5 to 1010.5 but flattening for M∗ > 10
10.5.
In particular, the Tremonti et al. relation is:
12 + log(O/H) = −1.492 + 1.847(logM∗)− 0.08026(logM∗)
2. (1.28)
This relation extends to higher masses the mass-metallicity relation
1.3 Lecture III: interpretation of abundances in dwarf irregulars 29
Fig. 1.11. The Z-logG diagram.Solutions a), b) and c) from top to bottom,
to lower the effective yield in DIG and BCG by Matteucci & Chiosi (1983).
Solution a) consists in varying the yield per stellar generation, here indicated
by pZ , just by changing the IMF. The solution b) and c) correspond to eqs.
(1.21) and (1.23), respectively.
30 Chemical Evolution
Fig. 1.12. Figure 3 from Erb et al. (2006) showing the mass-metallicity rela-
tion for star forming galaxies at high redshift. The data from Tremonti et al.
(2004) are also shown.
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 ∼ 0.3
dex. They used Hα and [NII] spectra. In Figure 3.2 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 most simple 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 Fig. 3.1.: either by changing the IMF or the
stellar yields as a function of galactic mass, or by assuming that the
1.3 Lecture III: interpretation of abundances in dwarf irregulars 31
galactic wind is less efficient in more massive systems, or that the infall
rate is less efficient in more massive systems. One of the most common
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. Evidences for galactic winds exist for
dwarf irregular galaxies, as we will see next.
1.3.2 Galactic Winds
Papaderos et al. (1994) estimated a galactic wind flowing at a velocity of
1320 Km/sec for the irregular dwarf VIIZw403. The escape velocity es-
timated for this galaxy is ≃ 50 Km/sec. Lequeux et al. (1995) suggested
a galactic wind in Haro2=MKn33 flowing at a velocity of ≃ 200Km/sec,
also larger that the escape velocity of this object. More recently, Martin
(1996;1998) found also supershells 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)
represents a clear indication of the fact that galaxies lose their metals.
However, we cannot exclude 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:
(Eth)ISM ≥ EBgas (1.29)
namely, that the thermal energy of the gas is larger or equal to its binding
energy. The thermal energy of gas due to SN and stellar wind heating
(Eth)ISM = EthSN + Ethw (1.30)
with the contribution of SNe being:
EthSN =
ǫSNRSN (t
‘)dt‘, (1.31)
while the contribution of stellar winds is:
Ethw =
∫ 100
ϕ(m)ψ(t‘)ǫwdmdt
‘ (1.32)
with ǫSN = ηSN ǫo and ǫo = 10
51erg (typical SN energy), and ǫw =
32 Chemical Evolution
ηwEw with Ew = 10
49erg (typical energy injected by a 20M⊙ star taken
as representative). ηw and ηSN are two free parameters and indicate
the efficiency of energy transfer from stellar winds and SNe into the
ISM, respectively, quantities still largely unknown. The total mass of
the galaxy is expressed as Mtot(t) = M∗(t) +Mgas(t) +Mdark(t) with
ML(t) =M∗(t) +Mgas(t) and the binding energy of gas is:
EBgas(t) =WL(t) +WLD(t) (1.33)
with:
WL(t) = −0.5G
Mgas(t)ML(t)
(1.34)
which is the potential well due to the luminous matter and with:
WLD(t) = −GwLD
Mgas(t)Mdark
(1.35)
which represents the potential well due to the interaction between dark
and luminous matter, where wLD ∼
S(1 + 1.37S), with S = rL/rD,
being the ratio between the galaxy effective radius and the radius of the
dark matter core. The typical model for a BCG has a luminous mass
of 108 − 109M⊙, a dark matter halo ten times larger than the luminous
mass and various values for the parameter S. The galactic wind in these
galaxies develops easily but it carries out mainly metals so that the total
mass lost in the wind is small.
1.3.3 Results on DIG and BCG from purely chemical models
Purely chemical models (Bradamante et al. 1998, Marconi et al. 1994)
for DIG and BCG have been computed in the last years by varying the
number of bursts, the time of occurrence of bursts tburst, the star forma-
tion efficiency, the type of galactic wind (differential or normal), the IMF
and the nucleosynthesis prescriptions. The best model of Bradamante
et al. (1998) suggests that the number of bursts should be Nbursts ≤ 10,
the SF efficiency should vary from 0.1 to 0.7 Gyr−1 for either Salpeter or
Scalo (1986) IMF (Salpeter IMF is favored). Metal enriched winds are
favored. The results of these models also suggest that SNe of Type
II dominate the chemical evolution and energetics of these galaxies,
whereas stellar winds are negligible. The predicted [O/Fe] ratios tend to
be overabundant relative to the solar ratios, owing to the predominance
of Type II SNe during the bursts, in agreement with observational data
1.3 Lecture III: interpretation of abundances in dwarf irregulars 33
(see Figure 3.5 upper panel). Models with strong differential winds and
Nburst=10 - 15 can however give rise to negative [O/Fe] ratios. The
main difference between DIGs and BCGs, in these models, is that the
BCGs suffer a present time burst, whereas the DIGs are in a quiescent
phase.
In Figure 3.3 we show some of the results of Bradamante et al. (1998)
compared with data on BCGs: it is evident from the Figure that the
spread in the chemical properties can be simply reproduced by different
SF efficiencies, which translate into different wind efficiencies.
In Fig 3.4 we show the results of the chemical evolution models of
Henry et al. (2000). These models take into account exponential infall
but not outflow. They suggested that the SF efficiency in extragalactic
HII regions must have been low and that this effect coupled with the
primary N production from intermediate mass stars can explain the
plateau in log(N/O) observed at low 12+log(O/H). Henry et al. (2000)
also concluded that 12C is mainly produced in massive stars (yields by
Maeder 1992) whereas 14N is mainly produced in intermediate mass
stars (yields by HG97). This conclusion, however, should be tested also
on the abundances of stars in the Milky Way, where the flat behaviour
of [C/Fe] vs. [Fe/H] from [Fe/H] =-2.2 up to [Fe/H]=0 suggest a similar
origin for the two elements, namely partly from massive stars and mainly
from low and intermediate mass ones (Chiappini et al. 2003b).
Concerning the [O/Fe] ratios we show results from Thuan et al. (1995)
in Figure 3.5, where it is evident that generally BCGs have overabundant
[O/Fe] ratios.
Very recently, an extensive study from SDSS of chemical abundances
from emission lines in a sample of 310 metal poor emission line galaxies
appeared (Izotov et al. 2006). The global metallicity in these galax-
ies ranges from ∼ 7.1(Z⊙/30) to ∼ 8.5(0.7Z⊙). The SDSS sample is
merged with 109 BCGs containing extremely low metallicity objects.
These data, shown in Figure 3.5 lower panel, substantially confirm pre-
vious ones, showing how α-elements do not depend on the O abundance
suggesting a common origin for these elements in stars withM > 10M⊙,
except for a slight increase of Ne/O with metallicity which is inter-
preted as due to a moderate dust depletion of O in metal rich galaxies.
An important finding is that all the studied galaxies are found to have
log(N/O) > −1.6, which indicates that none of these galaxies is a truly
young object, unlike the DLA systems at high redshift which show a
log(N/O) ∼ −2.3.
34 Chemical Evolution
Fig. 1.13. Upper panel : predicted Log(N/O) vs. 12 + log(O/H) for a model
with 3 bursts of SF separated by quiescent periods and different SF efficien-
cies here indicated with γ = ν. Lower panel: predicted log(C/O) vs. 12 +
log(O/H). The data in both panels are from Kobulnicky and Skillman (1996).
The models assume a dark matter halo ten times larger than the luminous
mass and S=0.3 ( Bradamante et al. 1998, see text).
1.3.4 Results from Chemo-Dynamical models: IZw18
IZw18 is the most metal poor local galaxy, thus resembling to a pri-
mordial object. Probably it did not experience more than two bursts
of star formation including the present one. The age of the oldest stars
1.3 Lecture III: interpretation of abundances in dwarf irregulars 35
Fig. 1.14. Figure from Henry et al. (2000): a comparison between numerical
models and data for extragalactic HII regions and stars (filled circles, filled
boxes and filled diamonds); M and S mark the position of the Galactic HII re-
gions and the Sun, respectively. Their best model is model B with an efficiency
of SF of ν = 0.03.
in this galaxy is still uncertain, although recently Tosi et al. (2006)
suggested an age possibly > 2 Gyr. The oxygen abundance in IZW18
is 12+log(O/H)= 7.17-7.26, ∼ 15-20 times lower than the solar oxygen
(12+ log(O/H)= 8.39, Asplund et al. 2005) and log N/O= -1.54/ -1.60
(Garnett et al. 1997).
Recently, FUSE provided abundances also for HI in IZw18: the evi-
dence is that the abundances in the HI are lower than in the HII (Aloisi
et al. 2003; Lecavelier des Etangs et al. 2003). In particular, Aloisi et
al. (2003) found the largest difference relative to the HII data.
Chemo-dynamical (2-D) models (Recchi et al. 2001) studied first the
case of IZw18 with only one burst at the present time and concluded
that the starburst triggers a galactic outflow. In particular, the metals
leave the galaxy more easily than the unprocessed gas and among the
enriched material the SN Ia ejecta leave the galaxy more easily than
other ejecta. In fact, Recchi et al. (2001) had reasonably assumed that
Type Ia SNe can transfer almost all of their energy to the gas, since
36 Chemical Evolution
Fig. 1.15. Upper panel: [O/Fe] vs. [Fe/H] observed in a sample of BCGs
by Thuan et al. (1995) (filled circles), open triangles and asterisks are disk
and halo stars shown for comparison.Figure from Thuan et al. (1995). Lower
panel: new data from Izotov et al. (2006). The large filled circles represent the
BCGs whereas the dots are the SDSS galaxies. Abundances in the left panel
are calculated as in Thuan et al. (1995) whereas those in the right panel are
calculated as in Izotov et al. (2006) (see original papers for details). Figure
from Izotov et al. (2006).
1.3 Lecture III: interpretation of abundances in dwarf irregulars 37
Fig. 1.16. Figure from Recchi et al. (2004): predicted abundances for the HII
region in IZw18 (dashed lines represent a model adopting the yields of Meynet
& Maeder (2002) for Z = 10−5, whereas the continuous line refers to a higher
metallicity (Z=0.004).Observational data are represented by the shaded areas.
they explode in an already hot and rarified medium after the SN II
explosions. As a consequence of this, they predicted that the [α/Fe]
ratios in the gas inside the galaxy should be larger than the [α/Fe]
ratios in the gas outside the galaxy. At variance with previous studies,
they found that most of the metals are already in the cold gas phase
after 8-10 Myr since the superbubble does not break immediately and
thermal conduction can act efficiently. In the following, Recchi et al.
(2004) extended the model to a two-burst case, always with the aim of
reproducing the characteristics of IZw18. The model well reproduces the
chemical properties of IZw18 with a relatively long episode of SF lasting
270 Myr plus a recent burst of SF still going on. In Figure 3.6 we show
the predictions of Recchi et al. (2004) for the abundances in the HII
regions of IZW18 and in Figure 3.7 those for the HI region, showing a
little difference between the HII and HI abundances, more in agreement
with the data of Lecavelier des Etangs et al. (2004).
38 Chemical Evolution
Fig. 1.17. Figure from Recchi et al. (2004): predicted abundances for the
HI region. The models are the same as in Figure 3.6. Observational data
are represented by the shaded areas. The upper shaded area in the panel for
oxygen and the lower shaded area in the panel for N/O represent the data of
Lecavelier des Etangs et al. (2003).
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment
1.4.1 Ellipticals
We recall here some of the most important properties of ellipticals or
early type galaxies (ETG) which are systems made of old stars with no
gas and no ongoing SF. The metallicity of ellipticals is measured only
by means of metallicity indeces obtained from their integrated spectra
which are very similar to those of K giants. In order to pass from metal-
licity indices to [Fe/H] one needs then to adopt a suitable calibration
often based on population synthesis models (Worthey, 1994). We also
summarize the most common scenarios for the formation of ellipticals.
1.4.2 Chemical Properties
The main properties of the stellar populations in ellipticals are:
• There exist the well-known Color-Magnitude and Color - σo (veloc-
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 39
ity dispersion) relations indicating that the integrated colors become
redder with increasing luminosity and mass (Faber 1977; Bower et al.
1992). These relations are interpreted as a metallicity effect, although
a well known degeneracy exists between metallicity and age of the
stellar populations in the integrated colors (Worthey 1994).
• The indexMg2 is normally used as a metallicity indicator since it does
not depend much upon the age of stellar populations. There exists for
ellipticals a well defined Mg2–σo relation, equivalent to the already
discussed mass-metallicity relation for star forming galaxies (Bender
et al. 1993; Bernardi et al. 1998; Colless et al. 1999).
• Abundance gradients in the stellar populations inside ellipticals are
found (Carollo et al. 1993; Davies et al. 1993). Kobayashi & Arimoto
(1999) derived the average gradient for ETGs from a large compilation
of data and this is: ∆[Fe/H ]/∆r ∼ −0.3, with the average metallicity
in ETGs of < [Fe/H ] >∗∼ −0.3dex (from -0.8 to +0.3 dex).
• A very important characteristic of ellipticals is that their central dom-
inant stellar population (dominant in the visual light) shows an over-
abundance, relative to the Sun, of the Mg/Fe ratio, < [Mg/Fe] >∗> 0
(from 0.05 to + 0.3 dex) (Peletier 1989; Worthey et al. 1992; Weiss
et al. 1995; Kuntschner et al. 2001).
• In addition, the overabundance increases with increasing galactic mass
and luminosity, < [Mg/Fe] >∗ vs. σo, (Worthey et al. 1992; Mat-
teucci 1994; Jorgensen 1999; Kuntschner et al. 2001).
1.4.3 Scenarios for galaxy formation
The most common ideas on the formation and evolution of ellipticals
can be summarized as:
• they formed by an early monolithic collapse of a gas cloud or early
merging of lumps of gas where dissipation plays a fundamental role
(Larson 1974; Arimoto & Yoshii 1987; Matteucci & Tornambè 1987).
In this model SF proceeds very intensively until a galactic wind is
developed and SF stops after that. The galactic wind is devoiding the
galaxy from all its residual gas.
• They formed by means of intense bursts of star formation in merging
subsystems made of gas (Tinsley & Larson 1979). In this picture SF
stops after the last burst and gas is lost via ram pressure stripping or
galactic wind.
40 Chemical Evolution
Fig. 1.18. The relation [α/Fe] vs. velocity dispersion (mass) for ETGs. Figure
adapted from Thomas et al. (2002).The continuous line represents the predic-
tion of the model by Pipino & Matteucci (2004). The shaded area represents
the prediction of hierarchical models for the formation of ellipticals.The sym-
bols are the observational data.
• They formed by early merging of lumps containing gas and stars in
which some dissipation is present (Bender et al. 1993).
• They formed and continue to form in a wide redshift range and prefer-
entially at late epochs by merging of early formed stellar (e.g. Kauff-
mann et al. 1993;1996).
Pipino & Matteucci (2004), by means of recent revised monolithic
models taking into account the development of a galactic wind (see Lec-
ture III), computed the relation [Mg/Fe] versus mass (velocity disper-
sion) and compared it with the data by Thomas et al. (2002). Thomas
(1990) already showed how hierarchical semi-analitycal models cannot
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 41
reproduce the observed [Mg/Fe] vs. mass trend, since in this scenario
massive ellipticals have longer periods of star formation than smaller
ones. In Figure 4.1, the original figure from Thomas et al. (2002) is
shown, where we have plotted also our predictions. In the Pipino &
Matteucci (2004) model it is assumed that the most massive galaxies as-
semble faster and form stars faster than less massive ones. The adopted
IMF is the Salpeter one. In other words, more massive ellipticals seem to
be older than less massive ones, in agreement with what found for spirals
(Boissier et al. 2001). In particular, in order to explain the observed
< [Mg/Fe] >∗> 0 in giant ellipticals the dominant stellar population
should have formed on a time scale no longer than 3-5 ·108 yr (Weiss et
al. 1995; Pipino & Matteucci 2004).
1.4.4 Ellipticals-Quasars connection
We know now that most if not all massive ETGs are hosting an AGN
for sometime during their life. Therefore, there is a strict link between
the quasar activity and the evolution of ellipticals.
1.4.5 The chemical evolution of QSOs
It is very interesting to study the chemical evolution of QSOs by means
of the broad emission lines in the QSO region. The first studies by Wills
et al. (1985) and Collin-Souffrin et al. (1986) found that the abundance
of Fe in QSOs, as measured from broad emission lines, turned out to be
∼ a factor of 10 more than the solar one and this represented a challenge
for chemical evolution model makers. Hamman & Ferland (1992) from
N V/C IV line ratios in QSOs derived the N/C abundance ratios and
inferred the QSO metallicities. They suggested that N is overabundant
by factors of 2-9 in the high redshift sources (z > 2). Metallicities 3-14
times the solar one were also suggested in order to produce such a high
N abundance, under the assumption of a mainly secondary N. To inter-
pret their data they built a chemical evolution model, a Milky Way- like
model, and suggested that these high metallicities are reached in only
0.5 Gyr, implying that QSOs are associated with vigourous star forma-
tion. At the same time, Padovani & Matteucci (1993) and Matteucci &
Padovani (1993) proposed a model for QSOs in which QSOs are hosted
by massive ellipticals. They assumed that after the occurrence of a galac-
tic wind the galaxy evolves passively and that for massess > 1011M⊙
the gas restored by the dying stars is not lost but it feeds the central
42 Chemical Evolution
black hole. They showed that in this context the stellar mass loss rate
can explain the observed AGN luminosities. They also found that solar
abundances in the gas are reached in no more than 108 years explaining
in a natural way the standard emission lines observed in high-z QSOs.
The predicted abundances could explain the data available at that time
and solve the problem of the quasi-similarity of QSO spectra at differ-
ent redshifts. Finally, they suggested also a criterium for establishing
the ages of QSOs on the basis of the [α/Fe] ratios observed from broad
emission lines (see also Hamman & Ferland 1993).
Much more recently, Maiolino et al. (2005, 2006) used more than
5000 QSO spectra from SDSS data to investigate the metallicity of the
broad emission line region in the redshift range 2 < z < 4.5 and over
the luminosity range −24.5 < MB < −29.5. They found substantial
chemical enrichment in QSOs already at z = 6. Models for ellipticals
by Pipino & Matteucci (2004) were used as a comparison with the data
and they well reproduce the data, as one can see in Figure 4.2. In this
Figure the evolution of the abundances of several chemical elements in
the gas of a typical elliptical are shown. The elliptical suffers a galactic
wind at around 0.4 Gyr since the beginning of star formation. This wind
devoids the galaxy of all the gas present at that time. After this time,
the SF stops and the galaxy evolves passively. All the gas restored after
the galactic wind event by dying stars can in principle feed the central
black hole, thus the abundances shown in Figure 4.2, after the time of
the wind, can be compared with the abundances measured in the broad
emission line region. As one can see, the predicted Fe abundance after
the galactic wind is always higher than the O one, owing to the Type Ia
SNe which continue to produce Fe even after the stop in the SF. On the
other hand, O and α-elements stop to be produced when the SF halts.
The comparison between the predicted abundances and those derived
from the QSO spectra, are in very good agreement and indicates ages
for these objects between 0.5 and 1 Gyr.
Finally, in the context of the joint formation of QSOs and ellipticals
we recall the work of Granato et al. (2001) who includes the energy
feedback from the central AGN in ellipticals. This feedback produces
outflows and stops the SF in a down-sizing fashion, in agreement with
the chemical properties of ETGs indicating a shorter period of SF for
the more massive objects.
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 43
Fig. 1.19. The temporal evolution of the abundances of several chemical ele-
ments in the gas of an elliptical galaxy with luminous mass of 1011M⊙. Feed-
back effects are taken into account in the model (Pipino & Matteucci 2004), as
described in Lecture III. The downarrow indicates the time for the occurrence
of the galactic wind. After this time, the SF stops and the elliptical evolves
passively. All the abundances after the time for the occurrence of the wind are
those that we observe in the broad emission line region region. The shaded
area indicates the abundance sets which best fit the line ratios observed in the
QSO spectra. Figure from Maiolino et al. 2006.
1.4.6 The chemical enrichment of the ICM
The X-ray emission from galay clusters is generally interpreted as ther-
mal bremsstrahlung in a hot gas (107-108 K). There are several emission
lines (O, Mg, Si, S) including the strong Fe K-line at around 7keV which
was discovered by Mitchell et al. (1976). The iron is the best studied
element in clusters. For kT ≥ 3 keV the intracluster medium (ICM)
Fe abundance is constant and ∼ 0.3Fe⊙ in the central cluster regions;
44 Chemical Evolution
the existence of metallicity gradients seems evident only in some clusters
(see Renzini 2004). At lower temperatures, the situation is not so simple
and the Fe abundance seems to increase. The first works on chemical
enrichment of the ICM even preceeded the discovery of the Fe line (Gunn
& Gott 1972, Larson & Dinerstein 1975). In the following years other
works appeared such as those of Vigroux (1977), Himmes & Biermann
(1988) and Matteucci & Vettolani (1988). In particular, Matteucci &
Vettolani (1988) started a more detailed approach to the problem fol-
lowed by David et al. (1991), Arnaud (1992), Renzini et al. (1993),
Elbaz et al. (1995), Matteucci & Gibson (1995), Gibson & Matteucci
(1997), Lowenstein & Mushotzky (1996), Martinelli et al. (2000), Chiosi
(2000), Moretti et al. (2003). The majority of these papers assumed that
galactic winds (mainly from ellipticals and S0 galaxies) are responsible
for the ICM chemical enrichment. In fact, ETGs are the dominant type
of galaxy in clusters and Arnaud (1992) found a clear correlation be-
tween the mass of Fe in clusters and the total luminosity of ellipticals.
No such correlation was found for spirals in clusters. Alternatively, the
abundances in the ICM are due to ram pressure stripping (Himmes &
Biermann 1988) or derive from a chemical enrichment from pre-galactic
Pop III stars (White & Rees 1978).
In Matteucci & Vettolani (1988) the Fe abundance in the ICM rel-
ative to the Sun, XFe/XFe⊙ , was calculated as (MFe)pred/(Mgas)obs
to be compared with the observed ratio (XFe/XFe⊙)obs = 0.3 − 0.5
(Rothenflug & Arnaud 1985). They found a good agreement with the
observed Fe abundance in clusters if all the Fe produced by ellipticals
and S0, after SF has stopped, is eventually restored into the ICM and
if the majority of gas in clusters has a primordial origin. Low values for
[Mg/Fe] and [Si/Fe] were predicted at the present time, due to the short
period of SF in ETGs and to the Fe produced by Type Ia SNe. With
Salpeter IMF they found that the Type Ia SNe contribute ≥ 50% of the
total Fe in clusters. This leads to a bimodality in the [α/Fe] ratios in
the stars and in the gas in the ICM, since the stars have overabundances
of [α/Fe]> 0 whereas the ICM should have [α/Fe]≤ 0. The same con-
clusion was reached and more highlighted later by Renzini et al. (1993).
More recently, Pipino et al. (2002) computed the chemical enrichment
of the ICM as a function of redshift by considering the evolution of the
cluster luminosity function and an updated treatment of the SN feed-
back. They adopted Woosley & Weaver (1995) yields for Type II SNe
and Nomoto et al. (1997) W7 model for Type Ia SNe and a Salpeter
IMF. They also predicted solar or undersolar [α/Fe] ratios in the ICM.
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 45
Fig. 1.20. Observed Fe abundance and predicted Fe abundance in the ICM as
a function of redshift: data from Tozzi et al. (2003), model (continuous line)
from Pipino et al. (2002), where the formation of ETGs was assumed to occur
at z=8.
The observational data on abundance ratios in clusters are still uncertain
and vary from cluster centers where they tend to be solar or undersolar
to the outer regions where they tend to be oversolar (e.g. Tamura et al.
2004). So, no firm conclusions can be drawn on this point. Concerning
the evolution of the Fe abundance in the ICM as a function of redshift,
most of the above mentioned models predict very little or no evolution of
the Fe abundance from z=1 to z=0 (Pipino et al. 2002). This prediction
seemed to be in good agreement with data from Tozzi et al. (2003) as
shown Figure. However, more recently, more data of Fe abundance for
high redshift clusters appeared showing a different behaviour.
In Figure 4.4 we show the data of Balestra et al. (2006) who claim
an increase, by at least a factor of two, of the Fe abundance in the
ICM from z=1 to z=0. Clearly, if we assume that only ellipticals have
contributed to the Fe abundance in the ICM, this effect is difficult to
explain unless we assume recent star formation in ellipticals. Another
possible explanation could be that spiral galaxies contribute to Fe when
46 Chemical Evolution
Fig. 1.21. New data (always relative to Fe) from Balestra et al. (2006) showing
an increase of the Fe abundance in the ICM from z=1 to z=0. Error bars refer
to 1σ confidence level. The big shaded area represents the rms dispersion.
Figure from Balestra et al. (2006).
they become S0 as a consequence of ram pressure stripping, and this
morphological transformation might have started just at z=1.
1.4.7 Conclusions on the enrichment of the ICM
From what said before we can conclude that:
• Elliptical galaxies are the dominant contributors to the abundances
and energetic content of the ICM. A constant Fe abundance of ∼
0.3Fe⊙ is found in the central regions of clusters hotter than 3keV
(Renzini 2004).
• Good models for the chemical enrichment of the ICM should repro-
duce the iron mass measured in clusters plus the [α/Fe] ratios in-
side galaxies and in the ICM as well as the Fe mass to light ratio
(IMLR= MFeICM /LB, with LB being the total blue luminosity of
member galaxies, as defined by Renzini et al. (1993). Abundance
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 47
ratios are very powerful tools to impose constraints on the evolution
of ellipticals and of the ICM.
• Models which do not assume a top-heavy IMF for the galaxies in
clusters (a Salpeter IMF can reproduce at best the properties of local
ellipticals) predict [α/Fe]> 0 inside ellipticals and [α/Fe] ≤ 0 in the
ICM. Observed values are still too uncertain to draw firm conclusions
on this point.
Acknowledgements
This research has been supported by INAF (Italian National Institute
for Astrophysics), Project PRIN-INAF-2005-1.06.08.16
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	Chemical Evolution
	Lecture I: basic assumptions and equations of chemical evolution
	The basic ingredients
	The Star Formation Rate
	The Initial Mass Function
	The Infall Rate
	The Outflow Rate
	Stellar evolution and nucleosynthesis: the stellar yields
	Type Ia SN Progenitors
	Yields per Stellar Generation
	Analytical models
	Numerical Models
	Lecture II: the Milky Way and other spirals
	The Galactic formation timescales
	The two-infall model
	Common Conclusions from MW Models
	Abundance Gradients from Emission Lines
	Abundance Gradients in External Galaxies
	How to model the Hubble Sequence
	Type Ia SN rates in different galaxies
	Time-delay model for different galaxies
	Lecture III: interpretation of abundances in dwarf irregulars
	Properties of Dwarf Irregular Galaxies
	Galactic Winds
	Results on DIG and BCG from purely chemical models
	Results from Chemo-Dynamical models: IZw18
	Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment
	Ellipticals
	Chemical Properties
	Scenarios for galaxy formation
	Ellipticals-Quasars connection
	The chemical evolution of QSOs
	The chemical enrichment of the ICM
	Conclusions on the enrichment of the ICM
	References

  In this series of lectures we first describe the basic ingredients of
galactic chemical evolution and discuss both analytical and numerical models.
Then we compare model results for the Milky Way, Dwarf Irregulars, Quasars and
the Intra-Cluster- Medium with abundances derived from emission lines. These
comparisons allow us to put strong constraints on the stellar nucleosynthesis
and the mechanisms of galaxy formation.

Chemical Evolution
Francesca Matteucci
Department of Astronomy
University of Trieste
and Osservatorio Astronomico di Trieste (INAF)
Via G.B. Tiepolo, 11, 34124 Trieste
Italy
(matteucci@ts.astro.it)
http://arxiv.org/abs/0704.0770v1
Contents
1 Chemical Evolution page 1
1.1 Lecture I: basic assumptions and equations of chem-
ical evolution 1
1.1.1 The basic ingredients 1
1.1.2 The Star Formation Rate 2
1.1.3 The Initial Mass Function 3
1.1.4 The Infall Rate 4
1.1.5 The Outflow Rate 4
1.1.6 Stellar evolution and nucleosynthesis: the
stellar yields 5
1.1.7 Type Ia SN Progenitors 6
1.1.8 Yields per Stellar Generation 7
1.1.9 Analytical models 8
1.1.10 Numerical Models 9
1.2 Lecture II: the Milky Way and other spirals 11
1.2.1 The Galactic formation timescales 11
1.2.2 The two-infall model 12
1.2.3 Common Conclusions from MW Models 18
1.2.4 Abundance Gradients from Emission Lines 19
1.2.5 Abundance Gradients in External Galaxies 21
1.2.6 How to model the Hubble Sequence 21
1.2.7 Type Ia SN rates in different galaxies 24
1.2.8 Time-delay model for different galaxies 25
1.3 Lecture III: interpretation of abundances in dwarf
irregulars 27
1.3.1 Properties of Dwarf Irregular Galaxies 27
1.3.2 Galactic Winds 31
iv Contents
1.3.3 Results on DIG and BCG from purely
chemical models 32
1.3.4 Results from Chemo-Dynamical models: IZw18 34
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrich-
ment 38
1.4.1 Ellipticals 38
1.4.2 Chemical Properties 38
1.4.3 Scenarios for galaxy formation 39
1.4.4 Ellipticals-Quasars connection 41
1.4.5 The chemical evolution of QSOs 41
1.4.6 The chemical enrichment of the ICM 43
1.4.7 Conclusions on the enrichment of the ICM 46
References 48
Chemical Evolution
1.1 Lecture I: basic assumptions and equations of chemical
evolution
To build galaxy chemical evolution models one needs to elucidate a num-
ber of hypotheses and make assumptions on the basic ingredients.
1.1.1 The basic ingredients
• INITIAL CONDITIONS: whether the mass of gas out of which stars
will form is all present initially or it will be accreted later on. The
chemical composition of the initial gas (primordial or already enriched
by a pregalactic stellar generation).
• THE BIRTHRATE FUNCTION:
B(M, t) = ψ(t)ϕ(M) (1.1)
where:
ψ(t) = SFR (1.2)
is the star formation rate (SFR) and:
ϕ(M) = IMF (1.3)
is the initial mass function (IMF).
• STELLAR EVOLUTION AND NUCLEOSYNTHESIS: stellar yields,
yields per stellar generation
• SUPPLEMENTARY PARAMETERS : infall, outflow, radial flows.
2 Chemical Evolution
1.1.2 The Star Formation Rate
Here we will summarize the most common parametrizations for the SFR
in galaxies, as adopted by chemical evolution models:
• Constant in space and time and equal to the estimated present time
SFR. For example, for the local disk, the present time SFR is SFR=2-
5M⊙pc
−2Gyr−1 (Boissier& Prantzos, 1999).
• Exponentially decreasing:
SFR = νe−t/τ∗ (1.4)
with τ∗ = 5− 15 Gyr (Tosi, 1988). The quantity νis a parameter that
we call efficiency of SF since it represents the SFR per unit mass of
gas and is expressed in Gyr−1.
• The most used SFR is the Schmidt (1959) law, which assumes a de-
pendence on the gas density, in particular:
SFR = νσkgas (1.5)
where k = 1.4± 0.15, as suggested by a study of Kennicutt (1998)
of local star forming galaxies.
• Some variations of the Schmidt law with a dependence also on the
total mass have been suggested for example by Dopita & Ryder (1994).
This formulation takes into account the feedback mechanism acting
between supernovae ( SNe) and stellar winds injecting energy into the
interstellar medium (ISM) and the galactic potential well. In other
words, the SF process is regulated by the fact that in a region of
recent star formation the gas is too hot to form stars and it is easily
removed from that region. Before new stars could form the gas needs
to cool and collapse back into the star forming region and this process
depends on the potential well and therefore on the total mass density:
SFR = νσk1totσ
gas (1.6)
with k1 = 0.5 and k2 = 1.5.
• Kennicutt (1998) also suggested, as an alternative to the Schmidt law
to fit the data, the following relation:
SFR = 0.017Ωgasσgas ∝ R
−1σgas (1.7)
with Ωgas being the angular rotation speed of gas.
1.1 Lecture I: basic assumptions and equations of chemical evolution3
• Finally a SFR induced by spiral density waves was suggested by Wyse
& Silk (1989):
SFR = νV (R)R−1σ1.5gas (1.8)
with R being the galactocentric distance and V (R) the gas rotation
velocity.
1.1.3 The Initial Mass Function
The IMF is a probability function describing the distribution of stars
as a function of mass. The present day mass function is derived for
the stars in the solar vicinity by counting the Main Sequence stars as a
function of magnitude and then applying the mass-luminosty relation,
holding for Main Sequence stars, to derive the distribution of stars as
a function of mass. In order to derive the IMF one has then to make
assumptions on the past history of SF.
The derived IMF is normally approximated by a power law:
ϕ(M)dM = aM−(1+x)dM (1.9)
where ϕ(M) is the number of stars with masses in the interval M,
M+dM.
Salpeter (1955) proposed a one-slope IMF (x = 1.35) valid for stars
with M > 10M⊙. Multi-slope (x1, x2, ..) IMFs have been suggested
later on always for the solar vicinity (Scalo 1986,1998; Kroupa et al.
1993; Chabrier 2003). The IMF is generally normalized as:
∫ 100
Mϕ(M)dM = 1 (1.10)
where a is the normalization constant and the assumed interval of inte-
gration is 0.1− 100M⊙.
The IMF is generally considered constant in space and time with some
exceptions such as the IMF suggested by Larson (1998) with:
x = 1.35(1 +m/m1)
−1 (1.11)
where m1 is variable typical mass and is associated to the Jeans mass.
This IMF predicts then that m1 is a decreasing function of time.
4 Chemical Evolution
1.1.4 The Infall Rate
For the rate of gas accretion there are in the literature several parametriza-
tions:
• The infall rate is constant in space and time and equal to the present
time infall rate as measured in the Galaxy (∼ 1.0M⊙yr
• The infall rate is variable in space and time, and the most common
assumption is an exponential law (Chiosi 1980; Lacey & Fall 1985):
IR = A(R)e−t/τ(R) (1.12)
with τ(R) constant or varying with the galactocentric distance. The
parameter A(R) is derived by fitting the present day total surface
mass density, σtot(tG), at any specific galactocentric radius R.
• For the formation of the Milky Way two episodes of infall have been
suggested (Chiappini et al. 1997), where during the first infall episode
the stellar halo forms whereas during the second infall episode the
disk forms. This particular infall law gives a good representation of
the formation of the Milky Way. The proposed two-infall law is:
IR = A(R)e−t/τH(R) +B(R)e−(t−tmax)/τD(R) (1.13)
where τH(R) is the timescale for the formation of the halo which
can be costant or vary with galactocentric distance. The quantity
τD(R) is the timescale for the formation of the disk and is a function
of the galactocentric distance; in most of the models it is assumed to
increase with R (e.g. Matteucci & François, 1989).
• More recently, Prantzos (2003) suggested a gaussian law with a peak
at 0.1 Gyr and a FWHM of 0.04 Gyr for the formation of the stellar
halo.
1.1.5 The Outflow Rate
The so-called galactic winds occur when the thermal energy of the gas
in galaxies exceeds its potential energy. Generally, gas outflows are
called winds when the gas is lost forever from the galaxy. Only detailed
dynamical simulations can suggest whether there is a wind or just an
outflow of gas which will soon or later fall back again into the galaxy. In
chemical evolution models galactic winds can be sudden or continuous. If
they are sudden, the mass is assumed to be lost in a very short interval of
1.1 Lecture I: basic assumptions and equations of chemical evolution5
time and the galaxy is devoided from all the gas; if they are continuous,
one has to assume the rate of gas loss. Generally, in chemical evolution
models (Bradamante et al. 1998) and also in cosmological simulations
(Springel & Hernquist, 2003) it is assumed that the rate of gas loss is
several times the SFR:
W = −λSFR (1.14)
where λ is a free parameter with the meaning of wind efficiency. This
particular formulation for the galactic wind rate is confirmed by obser-
vational findings (see Martin, 1999).
1.1.6 Stellar evolution and nucleosynthesis: the stellar yields
Here we summarize the various contribution to the element production
by stars of all masses.
• Brown Dwarfs (M < ML, ML = 0.08 − 0.09M⊙) are objects which
never ignite H and their lifetimes are larger than the age of the Uni-
verse. They are contributing to lock up mass.
• Low mass stars (0.5 ≤ M/M⊙ ≤ MHeF ) (1.85-2.2M⊙) ignite He ex-
plosively but without destroying themselves and then become C-O
white dwarfs (WD). If M < 0.5M⊙ they become He WDs. Their
lifetimes range from several 109 years up to several Hubble times!
• Intermediate mass stars (MHeF ≤ M/M⊙ ≤ Mup) ignite He quies-
cently. The mass Mup is the limiting mass for the formation of a C-O
degenerate core and is in the range 5-9M⊙, depending on stellar evo-
lution calculations. Lifetimes are from several 107 to 109 years. They
die as C-O WDs if not in binary systems. If in binary systems they
can give rise to cataclysmic variables such as novae and Type Ia SNe.
• Massive stars (M > Mup). We distinguish here several cases:
-Mup ≤ M/M⊙ ≤ 10 − 12. Stars with Main Sequence masses in
this range end up as electron-capture SNe leaving neutron stars as
remnants. These SNe will appear as Type II SNe which show H in
their spectra.
-10 − 12 ≤ M/M⊙ ≤ MWR, (with MWR ∼ 20 − 40M⊙ being the
limiting mass for the formation of a Wolf-Rayet (WR) star). Stars in
this mass range end their life as core-collapse SNe (Type II) leaving a
neutron star or a black hole as remnants.
-MWR ≤ M/M⊙ ≤ 100. Stars in this mass range are probably
6 Chemical Evolution
exploding as Type Ib/c SNe which do not show H in their spectra.
Their lifetimes are of the order of ∼ 106 years.
• Very Massive Stars (M > 100M⊙), they should explode by means
of instability due to “pair creation” and they are called pair-creation
SNe. In fact, at T ∼ 2 · 109 K a large portion of the gravitational
energy goes into creation of pairs (e+, e−), the star becomes unstable
and explodes. They leave no remnants and their lifetimes are < 106
years. Probably these very massive stars formed only when the metal
content was almost zero (Population III stars, Schneider et al. 2004).
All the elements with mass number A from 12 to 60 have been formed
in stars during the quiescent burnings. Stars transform H into He and
then He into heaviers until the Fe-peak elements, where the binding
energy per nucleon reaches a maximum and the nuclear fusion reactions
stop.
H is transformed into He through the proton-proton chain or the CNO-
cycle, then 4He is transformed into 12C through the triple- α reaction.
Elements heavier than 12C are then produced by synthesis of α-
particles. They are called α-elements (O, Ne, Mg, Si and others).
The last main burning in stars is the 28Si -burning which produces
56Ni which then decays into 56Co and 56Fe. Si-burning can be quiescent
or explosive (depending on the temperature).
Explosive nucleosynthesis occurring during SN explosions mainly pro-
duces Fe-peak elements. Elements originating from s- and r-processes
(with A> 60 up to Th and U) are formed by means of slow or rapid (rel-
ative to the β- decay) neutron capture by Fe seed nuclei; s-processing
occurs during quiescent He-burning whereas r-processing occurs during
SN explosions.
1.1.7 Type Ia SN Progenitors
The Type Ia SNe, which do not show H in their spectra, are believed to
originate from WDs in binary systems and to be the major producers of
Fe in the Universe. The model proposed are basically two:
• Single Degenerate Scenario (SDS), with a WD plus a Main Se-
quence or Red Giant star, as originally suggested by Whelan and Iben
(1973). The explosion (C-deflagration) occurs when the C-O WD
reaches the Chandrasekhar mass, MCh =∼ 1.44M⊙, after accreting
material from thecompanion. In this model the clock to the explosion
is given by the lifetime of the companion of the WD (namely the less
1.1 Lecture I: basic assumptions and equations of chemical evolution7
massive star in the system). It is interesting to define the minimum
timescale for the explosion which is given by the lifetime of a 8M⊙
star, namely tSNIamin=0.03 Gyr (Greggio and Renzini 1983). Recent
observations in radio-galaxies by Mannucci et al. (2005;2006) seem to
confirm the existence of such prompt Type Ia SNe.
• Double Degenerate Scenario (DDS), where the merging of two C-
OWDs of mass∼ 0.7M⊙, due to loss of angular momentum as a conse-
quence of gravitational wave radiation, produces C-deflagration (Iben
and Tutukov 1984). In this case the clock to the explosion is given
by the lifetime of the secondary star, as above, plus the gravitational
time delay, namely the time necessary for the two WDs to merge. The
minimum time for the explosion is tSNIamin = 0.03+∆tgrav=0.04 Gyr
(see Tornambè 1989).
Some variations of the above scenarios have been proposed such as
the model by Hachisu et al. (1996; 1999), which is based on the sin-
gle degenerate scenario where a wind from the WD is considered. Such
a wind stabilizes the accretion from the companion and introduces a
metallicity effect. In particular, the wind, necessary to this model, oc-
curs only if the systems have metallicity ([Fe/H]< −1.0). This implies
that the minimum time for the explosion is larger than in the previous
cases. In particular, tSNIamin = 0.33 Gyr, which is the lifetime of the
more massive secondary considered (2.3M⊙) plus the metallicity delay
which depends on the assumed chemical evolution model.
1.1.8 Yields per Stellar Generation
Under the assumption of Instantaneous Recycling Approximation (IRA)
which states that all stars more massive than 1M⊙ die immediately,
whereas all stars with masses lower than 1M⊙ live forever, one can
define the yield per stellar generation (Tinsley, 1980);
mpimϕ(m)dm (1.15)
where pim is the stellar yield of the element i, namely the newly formed
and ejected element i by a star of mass m.
The quantity R is the so-called Returned Fraction:
(m−Mrem)ϕ(m)dm (1.16)
8 Chemical Evolution
and is the total mass of gas restored into the ISM by an entire stellar
generation.
1.1.9 Analytical models
The Simple Model for the chemical evolution of the solar neighbourhood
is the simplest approach to model chemical evolution. The solar neigh-
bourhood is assumed to be a cylinder of 1 Kpc radius centered around
the Sun.
The basic assumptions of the Simple Model are:
- the system is one-zone and closed, no inflows or outflows with the
total mass present since the beginning,
- the initial gas is primordial (no metals),
- instantaneous recycling approximation holds,
- the IMF, ϕ(m), is assumed to be constant in time,
- the gas is well mixed at any time (IMA)
The Simple Model fails in describing the evolution of the Milky Way
(G-dwarf metallicity distribution, elements produced on long timescales
and abundance ratios) and the reason is that at least two of the above
assumptions are manifestly wrong, epecially if one intends to model the
evolution of the abundance of elements produced on long timescales,
such as Fe. In particular the assumptions of the closed boxiness and the
However, it is interesting to know the solution of the Simple Model
and its implications. Be Xi the abundance by mass of an element i.
If Xi << 1, which is generally true for metals, we obtain the solution
of the Simple Model. This solution is obtained analytically by ignoring
the stellar lifetimes:
Xi = yiln(
) (1.17)
where µ =Mgas/Mtot and yi is the yield per stellar generation, as defined
above, otherwise called effective yield. In particular, the effective yield
is defined as:
yieff =
ln(1/G)
(1.18)
namely the yield that the system would have if behaving as the simple
closed-box model. This means that if yieff > yi, then the actual system
has attained a higher abundance for the element i at a given gas fraction
G. Generally, in the IRA, we can assume:
1.1 Lecture I: basic assumptions and equations of chemical evolution9
(1.19)
which means that the ratio of two element abundances are always
equal to the ratio of their yields. This is no more true when IRA is
relaxed. In fact, relaxing IRA is necessary to study in detail the evolution
of the abundances of single elements.
One can obtain analytical solutions also in presence of infall and/or
outflow but the necessary condition is to assume IRA. Matteucci &
Chiosi (1983) found solutions for models with outflow and infall and
Matteucci (2001) found it for a model with infall and outflow acting at
the same time. The main assumption in the model with outflow but no
infall is that the outflow rate is:
W (t) = λ(1−R)ψ(t) (1.20)
where λ ≥ 0 is the wind parameter.
The solution of this model is:
(1 + λ)
ln[(1 + λ)G−1 − λ] (1.21)
for λ = 0 the equation becomes the one of the Simple Model (1.17).
The solution of the equation of metals for a model without wind but
with a primordial infalling material (XAi = 0) at a rate:
A(t) = Λ(1−R)ψ(t) (1.22)
and Λ 6= 1 is :
[1− (Λ − (Λ− 1)G−1)−Λ/(1−Λ)] (1.23)
For Λ = 1 one obtains the well known case of extreme infall studied by
Larson (1972) whose solution is:
Xi = yi[1− e
−(G−1−1)] (1.24)
This extreme infall solution shows that when G→ 0 then Xi → yi.
1.1.10 Numerical Models
Numerical models relax IRA and close boxiness but generally retain the
constancy of ϕ(m) and the IMA.
10 Chemical Evolution
If Gi is the mass fraction of gas in the form of an element i, we can
write:
Ġi(t) = −ψ(t)Xi(t)
∫ MBm
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
∫ MBM
∫ 0.5
f(γ)ψ(t− τm2)Qmi(t− τm2)dγ]dm
∫ MBM
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
ψ(t− τm)Qmi(t− τm)ϕ(m)dm
+XAiA(t)−Xi(t)W (t) (1.25)
where B=1-A, A=0.05-0.09. The meaning of the A parameter is the
fraction in the IMF of binary systems with those specific features re-
quired to give rise to Type Ia SNe, whereas B is the fraction of all the
single stars and binary systems in the same mass range of definition of
the progenitors of Type Ia SNe. The values of A indicated above are cor-
rect for the evolution of the solar vicinity where an IMF of Scalo (1986,
1989) or Kroupa et al.(1993) is adopted. If one adopts a flatter IMF such
as the Salpeter (1955) one then A is different. In the above equations
the contribution of Type Ia SNe is contained in the third term on the
right hand side. The integral is made over a range of masses going from
3 to 16 M⊙ which represents the total masses of binary systems able to
produce Type Ia SNe in the framework of the SDS. There is also an inte-
gration over the mass distribution of binary systems; in particular, one
considers the function f(γ) where γ = M2
M1+M2
, with M1 and M2 being
the primary and secondary mass of the binary system, respectively (for
more details see Matteucci & Greggio 1986 and Matteucci 2001).The
functions A(t) and W(t) are the infall and wind rate, respectively. Fi-
nally, the quantity Qmi represents the stellar yields (both processed and
unprocessed material).
1.2 Lecture II: the Milky Way and other spirals 11
1.2 Lecture II: the Milky Way and other spirals
The Milky Way galaxy has four main stellar populations: 1) the halo
stars with low metallicities (the most common metallicity indicator in
stars is [Fe/H]= log(Fe/H)∗− log(Fe/H)⊙) and eccentric orbits, 2) the
bulge population with a large range of metallicities and is dominated
by random motions, 3) the thin disk stars with an average metallicity
< [Fe/H ] >=-0.5 dex and circular orbits, and finally 4) the thick stars
which possess chemical and kinematical properties intermediate between
those of the halo and those of the thin disk. The halo stars have average
metallicities of < [Fe/H ] >=-1.5 dex and a maximum metallicity of
∼ −1.0 dex although stars with [Fe/H] as high as -0.6 dex and halo
kinematics are observed. The average metallicity of thin disk stars is
∼ −0.6 dex, whereas the one of Bulge stars is ∼ −0.2 dex.
1.2.1 The Galactic formation timescales
The kinematical and chemical properties of the different Galactic stel-
lar populations can be interpreted in terms of the Galaxy formation
mechanism. Eggen et al. (1962) in a cornerstone paper suggested a
rapid collapse for the formation of the Galaxy lasting ∼ 3 · 108 years.
This suggestion was based on a kinematical and chemical study of so-
lar neighbourhood stars. Later on, Searle & Zinn (1979) proposed a
central collapse like the one proposed by Eggen et al. but also that the
outer halo formed by merging of large fragments taking place over a con-
siderable timescale > 1 Gyr. More recently, Berman & Suchov (1991)
proposed the so-called hot Galaxy picture, with an initial strong burst
of SF which inhibited further SF for few Gyr while a strong Galactic
wind was created.
From an historical point of view, the modelization of the Galactic
chemical evolution has passed through different phases that I summarize
in the following.
• SERIAL FORMATION
The Galaxy is modeled by means of one accretion episode lasting
for the entire Galactic lifetime, where halo, thick and thin disk form in
sequence as a continuous process. The obvious limit of this approach
is that it does not allow us to predict the observed overlapping in
metallicity between halo and thick disk stars and between thick and
thin disk stars, but it gives a fair representation of our Galaxy (e.g.
Matteucci & François 1989).
12 Chemical Evolution
• PARALLEL FORMATION
In this formulation, the various Galactic components start 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 implies that the thick disk formed out of gas
shed by the halo and that the thin disk formed out of gas shed by the
thick disk, and this is at variance with the distribution of the stellar
angular momentum per unit mass (Wyse & Gilmore 1992), which
indicates that the disk did not form out of gas shed by the halo.
• TWO-INFALL FORMATION
In this scenario, halo and disk formed out of two separate infall
episodes (overlapping in metallicity is also predicted) (e.g. Chiappini
et al. 1997; Chang et al. 1999). The first infall episode lasted no more
than 1-2 Gyr whereas the second, where the thin disk formed, lasted
much longer with a timescale for the formation of the solar vicinity of
6-8 Gyr (Chiappini et al. 1997; Boissier& Prantzos 1999).
• STOCHASTIC APPROACH
Here the hypothesis is that in the early halo phases ([Fe/H] < −3.0
dex), mixing was not efficient and, as a consequence, one should ob-
serve in low metallicity halo stars the effects of pollution from single
SNe (e.g. Tsujimoto et al. 1999; Argast et al. 2000; Oey 2000). These
models predict a large spread for [Fe/H] < −3.0dex which is not ob-
served, as shown by recent data with metallicities down to -4.0 dex
(Cayrel et al. 2004; see later).
1.2.2 The two-infall model
The adopted SFR (see Figure 2.1) is eq.(1.6) with different SF efficiencies
for the halo and disk, in particular νH = 2.0Gyr
−1, νD = 1.0Gyr
respectively. A threshold density (σth = 7M⊙pc
−2) for the SFR is also
assumed in agreement with results from Kennicutt (1989; 1998).
In Figure 2.2 we show the predicted SN (II and Ia) rates by the two-
infall model. Note that the Type Ia SN rate is calculated according to
the SDS (Greggio & Renzini, 1983; Matteucci & Recchi, 2001). There
is a delay between the Type II SN rate and the Type Ia SN rate, and
while the Type II SN rate strictly follows the SFR, the Type Ia SN rate
is smoothly increasing.
François et al. (2004) compared the predictions of the two-infall model
for the abundance ratios versus metallicity relations ([X/Fe] vs. [Fe/H]),
with the very recent and very accurate data of the project “First Stars”
1.2 Lecture II: the Milky Way and other spirals 13
Fig. 1.1. The predicted SFR in the solar vicinity with the two-infall model.
Figure from Chiappini et al. (1997). The oscillating behaviour at late times
is due to the assumed threshold density for SF. The threshold gas density is
also responsible for the gap in the SFR seen at around 1 Gyr.
by Cayrel et al. (2004). They adopted yields from the literature both for
Type II and Type Ia SNe and noticed that while for some elements (O,
Fe, Si, Ca) the yields of Woosley & Weaver (1995) (hereafter WW95)
reproduce the data fairly well, for the Fe-peak elements and heaviers
none of the available yields give a good agreement. Therefore, they
varied empirically the yields of these elements in order to best fit the
data. In Figures 2.3 and 2.4 we show the predictions for α-elements (O,
Mg, Si, Ca, Ti, K) plus some Fe-peak elements and Zn.
In Figure 2.4 we show also the ratios between the yields derived em-
pirically by François et al. (2004) in order to obtain the excellent fits
shown in the figures, and those of WW95 for massive stars. For some
elements it was necessary to change also the yields from Type Ia SNe
relative to the reference ones which are those of Iwamoto et al. (1999)
(hereafter I99).
In Figure 2.5 we show the predictions of chemical evolution models for
12C and 14N compared with abundance data. The behaviour of C shows
a roughly constant [C/Fe] as a function of [Fe/H], although C seems to
14 Chemical Evolution
Fig. 1.2. The predicted Type II and Ia SN rate in the solar vicinity with the
two-infall model. Figure from Chiappini et al. (1997)
slightly increase at very low metallicities, indicating that the bulk of
these two elements comes from stars with the same lifetimes. The data
in these figures, especially those for N are old and do not contain very
metal poor stars. Newer data containing stars with [Fe/H] down to ∼
-4.0 dex (Spite et al. 2005; Israelian et al. 2004) indicate that the [N/Fe]
ratio continues to be high also at low metallicities, indicating a primary
origin for N produced in massive stars. We recall here that we define
primary a chemical elements which is produced in the stars starting
from the H and He, whereas we define secondary a chemical element
which is formed from heavy elements already present in the star at its
birth and not produced in situ. The model predictions shown in Figure
2.5 for C and N assume that the bulk of these elements is produced
by low and intermediate mass stars (yields from van den Hoeck and
Groenewegen, 1997) and that N is produced as a partly secondary and
partly primary element. The N production from massive stars has only
a secondary origin (yields from WW95). In Figure 2.5 we show also a
model prediction where N is considered as a primary element in massive
stars with the yields artificially increased. Recently, Chiappini et al.
1.2 Lecture II: the Milky Way and other spirals 15
Fig. 1.3. Predicted and observed [X/Fe] vs. [Fe/H] for several α- and Fe-peak-
elements plus Zn compared with a compilation of data. In particular the black
dots are the recent high resolution data from Cayrel et al. (2004). For the
other data see references in François et al. (2004). The solar value indicated in
the upper right part of each figure represents the predicted solar value for the
ratio [X/Fe]. The assumed solar abundances are those of Grevesse & Sauval
(1998) except that for oxygen for which we take the value of Holweger (2001).
16 Chemical Evolution
Fig. 1.4. Upper panel: predicted and observed [X/Fe] vs. [Fe/H] for several
elements as in Figure 2.3. In the bottom part of this Figure are shown the
ratios between the empirical yields and the yields by WW95 for massive stars.
Such empirical yields have been suggested by François et al. (2004) in order
to fit at best all the [X/Fe] vs. [Fe/H] relations. In the small panel at the
bottom right side are shown also the ratios between the empirical yields for
Type Ia SNe and the yields by I99.
1.2 Lecture II: the Milky Way and other spirals 17
Fig. 1.5. Upper panel: predicted and observed [C/Fe] vs. [Fe/H]. Models
from Chiappini et al. (2003a). Lower panel, predicted and observed [N/Fe]
vs. [Fe/H]. For references to the data see original paper.The thin and thick
continuous lines in both panels represent models with standard nucleosynthe-
sis, as described in the text, whereas the dashed line represents the predictions
of a model where N in massive stars has been considered as a primary element
with “ad hoc” stellar yields.
(2006) have shown that primary N produced by very metal poor fastly
rotating massive stars can well reproduce the observations.
In summary, the comparison between model predictions and abun-
dance data indicate the following scenario for the formation of heavy
elements:
• 12C and 14N are mainly produced in low and intermediate mass stars
(0.8 ≤ M/M⊙ ≤ 8). The amounts of primary and secondary N is
still uncertain and also the fraction of C produced in massive stars.
Primary N from massive stars seems to be required to reproduce the
N abundance in low metallicity halo stars.
• α-elements originate in massive stars: the nucleosynthesis of O is
rather well understood (there is agreement between different authors),
the yields from WW95 as functions of metallicity produce an excellent
agreement with the observations for this particular element.
18 Chemical Evolution
• Magnesium is generally underproduced by nucleosynthesis models.
Taking the yields of WW95 as a reference, the Mg yields should be
increased in stars with masses M ≤ 20M⊙ and decreased in stars
with M > 20M⊙ to fit the data. Silicon should be slightly increased
in stars with masses M > 40M⊙.
• Fe originates mostly in Type Ia SNe. The Fe yields in massive stars
are still uncertain, WW95 metallicity dependent yields overestimate
Fe in stars < 30M⊙. For this element, it is better to adopt the yields
of WW95 for solar metallicity.
• Fe-peak elements: the yields of Cr, Mn should be increased in stars
of 10-20 M⊙ relative to the yields of WW95, whereas the yield of
Co should be increased in Type Ia SNe, relative to the yields of I99,
and decreased in stars in the range 10-20M⊙, 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).
1.2.3 Common Conclusions from MW Models
Most of the chemical evolution models for the Milky Way existing in the
literature conclude that:
• The G-dwarf metallicity distribution can be reproduced only by as-
suming a slow formation of the local disk by infall. In particular, the
time-scale for the formation of the local disk should be in the range
τd ∼ 6 − 8 Gyr (Chiappini et al. 1997; Boissier and Prantzos 1999;
Chang et al. 1999; Chiappini et al. 2001; Alibès et al. 2001).
• The relative abundance ratios [X/Fe] vs. [Fe/H], interpreted as time-
delay between Type Ia and II SNe, suggest a timescale for the halo-
thick disk formation of τh ∼ 1.5-2.0 Gyr (Matteucci and Greggio 1986;
Matteucci and François, 1989; Chiappini et al. 1997). The external
halo and thick disk probably formed more slowly or have been accreted
(Chiappini et al. 2001).
• To fit abundance gradients, SFR and gas distribution along the Galac-
tic thin disk we must assume that the disk formed inside-out (Mat-
teucci & François, 1989; Chiappini et al. 2001; Boissier & Prantzos
1999; Alibés et al. 2001). Radial flows can help in forming the gra-
dients (Portinari & Chiosi 2000) but they are probably not the main
cause for them. A variable IMF along the Disk can in principle ex-
plain abundance gradients but it creates unrealistic situations: in fact,
1.2 Lecture II: the Milky Way and other spirals 19
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 & François 1989; Chiappini et al, 1997,2001; Goswami &
Prantzos 2000; Alibés et al. 2001).
1.2.4 Abundance Gradients from Emission Lines
There are two types of abundance determinations in HII regions: one is
based on recombination lines which should have a weak temperature de-
pendence of the nebula (He, C, N, O), the other is based on collisionally
excited lines where a strong dependence is intrinsic to the method (C, N,
O, Ne, Si, S, Cl, Ar, Fe and Ni). This second method has predominated
until now. A direct determination of the abundance gradients from HII
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 only information on the internal nucleosynthesis of the
star. So, to derive gradients one should look at the abundances of O, S
and Ne, unaffected by stellar processes. In Figure 2.6 we show theoretical
predictions of abundance gradients along the disk of the Milky Way
compared with data from HII regions and B stars. The adopted model
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 τ(R) = 0.875R − 0.75 Gyr. Note that to
obtain a better fit for 12C, the yields of this element have been increased
artificially relative to those of WW95.
As already said, 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; Alibès 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. is included 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
20 Chemical Evolution
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
Fig. 1.6. Upper panel: abundance gradients along the Disk of the MW. The
lines are the models from Chiappini et al. (2003a): these models differ by the
nucleosynthesis prescriptions. In particular, the dash-dotted line represents
a model with van den Hoeck & Groenewegen (1997, hereafter HG97) yields
for low-intermediate mass stars with η (mass loss parameter) constant and
Thielemann et al.’s (1996) yields for massive stars, the long- dashed thick line
has HG97 yields with variable η and Thielemann et al. yields, the long-dashed
thin line has HG97 yields with variable η but WW95 yields for massive stars.
It is interesting to note that in all of these models the yields of 12C in stars
> 40M⊙ have been artificially increased by a factor of 3 relative to the yields
of WW95. Lower panel: the temporal behaviour 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 time gradient, whereas the lower ones
represent the gradient a few Gyr ago. It is clear that the gradients tend to
stepeen in time, a still controversial result.
1.2 Lecture II: the Milky Way and other spirals 21
therefore to a steepening of the gradients with time, as shown in Figure
2.6, bottom panel.
1.2.5 Abundance Gradients in External Galaxies
Abundance gradients expressed in dex/Kpc 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
(ref). The gradients are generally flatter in galaxies with central bars
(ref). The SFR is measured mainly from Hα emission (Kennicutt, 1998)
and show a correlation with the total surface gas density (HI+H2), in
particular the suggested law is that of eq. (1.5).
In the observed gas distributions differences between field and clus-
ter spirals are found in the sense that cluster spirals have less gas,
probably as a consequence of stronger interactions with the environ-
ment.Integrated colors of spiral galaxies (Josey & Arimoto 1992; Jimenez
et al. 1998; Prantzos & Boissier 2000) indicate inside-out formation, as
also found for the milky Way.
As an example of abundance gradients in a spiral galaxy we show
in Figure 2.7 the observed and predicted gas distribution and abun-
dance gradients for the disk of M101. In this case the gas distribu-
tion and the abundance gradients are reproduced with systematically
smaller timescales for the disk formation relative to the MW (M101
formed faster), and the difference between the timescales of formation
of the internal and external regions is smaller (τM101 = 0.75R−0.5 Gyr,
Chiappini et al. 2003a)
To conclude this section we 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, more metal rich and
more gas-poor than smaller ones. On the other hand their estimated SF
efficiency (defined as the SFR per unit mass of gas) seem to be similar
among different spirals: this leads them to conclude that more massive
disks are older than less massive ones.
1.2.6 How to model the Hubble Sequence
The Hubble Sequence can be simply thought as a sequence of objects
where the SFR 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
22 Chemical Evolution
Fig. 1.7. Upper panel: predicted and observed gas distribution along the disk
of M101. The observed HI, H2 and total gas are indicated in the Figure. 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
1000M⊙pc
−2, while the dotted line refers to a model with 800M⊙pc
−2 and the
dashed to a model with 600M⊙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).
1.2 Lecture II: the Milky Way and other spirals 23
reference galaxy and we change the SFR relatively to the Galactic one,
for which we adopt eq. (1.6). The quantity ν in eq. (1.6) 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 νhalo = 2.0Gyr
−1 and
νdisk = 1.0Gyr
−1 (see Figure 2.1). 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 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 like in a
burst with very high star formation efficiency, namely:
SFR = νσk (1.26)
with k = 1.0 for the sake of simplicity; ν = 10 − 20Gyr−1 (see Mat-
teucci, 1994; Pipino & Matteucci 2004).
For irregular galaxies, on the other hand, we assume that the SFR
proceeds more slowly and less efficiently that in the Milky Way disk,
in particular we assume the same SF law as for spheroids but with
0.01 ≤ ν(Gyr−1) ≤ 0.1. Among irregular galaxies, a special position
is taken by the Blue Compact Galaxies (BCG) namely galaxies which
have blue colors as a consequence of the fact that they are forming stars
at the present time, have small masses, large amounts of gas and low
metallicities. For these galaxies, we assume that they suffered on average
from 1 to 7 short bursts, with the SF efficiency mentioned above (see
Bradamante et al. 1998 and next Lecture).
Finally, dwarf spheroidals are also a special cathegory, characterized
by old stars, no gas and low metallicities. For these galaxies we assume
that they suffered one long starburst lasting 7-8 Gyr or at maximum a
couple of extended SF periods, in agreement with their measued Color-
Magnitude diagram. It is worth noting that both ellipticals and dwarf
spheroidals should loose most of their gas and therefore one may con-
clude that galactic winds should play an important role in their evolu-
tion, although ram pressure stripping cannot be excluded as a mecha-
nism for gas removal. Also for these galaxies we assume the previous
SF law with k = 1 and ν = 0.01− 1.0Gyr−1. Lanfranchi & Matteucci,
(2003, 2004) developed more detailed models for dwarf spheroidals by
adopting the SF history suggested by the Color-Magnitude diagrams of
24 Chemical Evolution
Fig. 1.8. Predicted SFRs in galaxies of different morphological type. Figure
from Calura (2004). Note that for the elliptical galaxy the SF stops abruptly
as a consequence of the galactic wind.
single galaxies and with the same efficiency of SF as above. In Figure
2.8 we show the adopted SFRs in different galaxies and in Figure 2.9
the corresponding predicted Type Ia SN rates. For the irregular galaxy,
the predicted Type Ia SN rate refers to a specific galaxy, LMC, with a
SFR taken from observations (see Calura et al. 2003) with an early ans
a late burts of SF and low SF in between.
1.2.7 Type Ia SN rates in different galaxies
Following Matteucci & Recchi (2001) we define the typical timescale
for Type Ia SN enrichment as the time when the SN rate reaches the
maximum. In the following we will always adopt the SDS for the pro-
genitors 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, whereas
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 spiral with a high SFR the timescale for Type Ia SN enrichment
1.2 Lecture II: the Milky Way and other spirals 25
Fig. 1.9. Predicted Type Ia SN rates for the SFRs of Figure 2.8. Figure from
Calura (2004). Note that for the irregular galaxy here the predictions are for
the LMC, where a recent SF burst is assumed.
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 SNeIa become important as Fe producers
(Matteucci and Greggio 1986) while a second less important peak occurs
at tSNIa = 4 − 5 Gyr. For an irregular galaxy with a continuous but
very low SFR the timescale is tSNIa > 5 Gyr.
1.2.8 Time-delay model for different galaxies
As we have already seen, the time-delay between the production of oxy-
gen by Type II SNe and that of Fe by Type Ia SNe allows us to explain
the [X/Fe] vs. [Fe/H] relations in an elegant way. However, the [X/Fe]
vs. [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 a different behaviour
in galaxies with different SF histories. In Figure 2.10 we show the pre-
dictions 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 this Figure, we predict a long plateau, well above
the solar value, for the [α/Fe] ratios in the Bulge (and ellipticals), owing
26 Chemical Evolution
LMC (Hill et al. 2000)
DLA (Vladilo 2002)
Fig. 1.10. Predicted [α/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 (∼ 1010M⊙), the median line represents the prediction for
the solar vicinity and the lower line the prediction for an irregular magellanic
galaxy. The differences among the various models are in the efficiency of star
formation, being quite high for spheroids (ν = 20Gyr−1), moderate for the
Milky Way (ν = 1 − 2Gyr−1) and low for irregular galaxies (ν = 0.1Gyr−1).
The nucleosynthesis prescriptions are the same in all objects. The time-delay
between the production of α-elements and Fe, coupled with the different SF
histories produces the differences in the plots. Data for Damped-Lyman-α
systems, LMC and Bulge are shown for comparison.
to the fast Fe enrichment reached in these systems by means of Type II
SNe: when the Type Ia SNe start enriching substantially the ISM, 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
in the gas is still well below solar. Therefore, here we observe a steeper
1.3 Lecture III: interpretation of abundances in dwarf irregulars 27
slope for the [α/Fe] ratio. In other words, we have below solar [α/Fe]
ratios at below solar [Fe/H] ratios. This diagram is very important since
it allows us to recognize a galaxy type only by means of its abundances,
and therefore it can be used to understand the nature of high redshift
objects.
1.3 Lecture III: interpretation of abundances in dwarf
irregulars
They are rather simple objects with low metallicity and large gas con-
tent, suggesting that they are either young or have undergone discon-
tinuous star formation activity (bursts) or a continuous but not efficient
star formation. 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 they could also be
important contributors to the population of systems giving rise to QSO-
absorption lines at high redshift (see Matteucci et al. 1997 and Calura
et al. 2002).
1.3.1 Properties of Dwarf Irregular Galaxies
Among local star forming galaxies, sometimes referred to as HII galax-
ies, most are dwarfs. Dwarf irregular galaxies can be divided into two
categories: Dwarf Irregular (DIG) and Blue Compact galaxies (BCG).
These latter have very blue colors due to active star formation at the
present time.
Chemical abundances in these galaxies are derived from optical emis-
sion lines in HII regions. Both DIG and BCG show a distinctive spread
in their chemical properties, altough this spread is decreasing with 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 DIG and BCG by means of ana-
lytical 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 the metallicity for a
given G ratio, and this means that the effective yield is lower than that
of the Simple Model and vary from galaxy to galaxy.
The possible solutions suggested to lower the effective yield were:
28 Chemical Evolution
• a. different IMF’s
• b. different amounts of galactic wind
• c. different amounts of infall
In Figure 3.1 we show graphically the solutions a), b) and c). Concerning
the solution a), one simply varies the IMF, whereas solutions b) and c)
have been already descibed (eqs. 1.21 ans 1.23).
Later on, Pilyugin (1993) forwarded the idea that the spread observed
also in other chemical properties properties of these galaxies such as
in the He/H vs. O/H and N/O vs. O/H relations, can be due to
self-pollution of the HII regions, which do not mix efficiently with the
surrounding medium, coupled with “enriched” or “differential” galac-
tic 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 type (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
BCG 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:
MT = (8.5± 0.4) + (190± 60)Z (1.27)
with Z being the global metal content. Recently, Tremonti et al. (2004)
analyzed 53000 local star-forming galaxies in the SDSS (irregulars and
spirals). 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
([OIII], Hβ , [OII], Hα, [NII], [SII]). Tremonti et al. (2004) derived a re-
lation indicating that 12+log(O/H) is increasing steeply from M∗ going
from 108.5 to 1010.5 but flattening for M∗ > 10
10.5.
In particular, the Tremonti et al. relation is:
12 + log(O/H) = −1.492 + 1.847(logM∗)− 0.08026(logM∗)
2. (1.28)
This relation extends to higher masses the mass-metallicity relation
1.3 Lecture III: interpretation of abundances in dwarf irregulars 29
Fig. 1.11. The Z-logG diagram.Solutions a), b) and c) from top to bottom,
to lower the effective yield in DIG and BCG by Matteucci & Chiosi (1983).
Solution a) consists in varying the yield per stellar generation, here indicated
by pZ , just by changing the IMF. The solution b) and c) correspond to eqs.
(1.21) and (1.23), respectively.
30 Chemical Evolution
Fig. 1.12. Figure 3 from Erb et al. (2006) showing the mass-metallicity rela-
tion for star forming galaxies at high redshift. The data from Tremonti et al.
(2004) are also shown.
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 ∼ 0.3
dex. They used Hα and [NII] spectra. In Figure 3.2 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 most simple 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 Fig. 3.1.: either by changing the IMF or the
stellar yields as a function of galactic mass, or by assuming that the
1.3 Lecture III: interpretation of abundances in dwarf irregulars 31
galactic wind is less efficient in more massive systems, or that the infall
rate is less efficient in more massive systems. One of the most common
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. Evidences for galactic winds exist for
dwarf irregular galaxies, as we will see next.
1.3.2 Galactic Winds
Papaderos et al. (1994) estimated a galactic wind flowing at a velocity of
1320 Km/sec for the irregular dwarf VIIZw403. The escape velocity es-
timated for this galaxy is ≃ 50 Km/sec. Lequeux et al. (1995) suggested
a galactic wind in Haro2=MKn33 flowing at a velocity of ≃ 200Km/sec,
also larger that the escape velocity of this object. More recently, Martin
(1996;1998) found also supershells 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)
represents a clear indication of the fact that galaxies lose their metals.
However, we cannot exclude 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:
(Eth)ISM ≥ EBgas (1.29)
namely, that the thermal energy of the gas is larger or equal to its binding
energy. The thermal energy of gas due to SN and stellar wind heating
(Eth)ISM = EthSN + Ethw (1.30)
with the contribution of SNe being:
EthSN =
ǫSNRSN (t
‘)dt‘, (1.31)
while the contribution of stellar winds is:
Ethw =
∫ 100
ϕ(m)ψ(t‘)ǫwdmdt
‘ (1.32)
with ǫSN = ηSN ǫo and ǫo = 10
51erg (typical SN energy), and ǫw =
32 Chemical Evolution
ηwEw with Ew = 10
49erg (typical energy injected by a 20M⊙ star taken
as representative). ηw and ηSN are two free parameters and indicate
the efficiency of energy transfer from stellar winds and SNe into the
ISM, respectively, quantities still largely unknown. The total mass of
the galaxy is expressed as Mtot(t) = M∗(t) +Mgas(t) +Mdark(t) with
ML(t) =M∗(t) +Mgas(t) and the binding energy of gas is:
EBgas(t) =WL(t) +WLD(t) (1.33)
with:
WL(t) = −0.5G
Mgas(t)ML(t)
(1.34)
which is the potential well due to the luminous matter and with:
WLD(t) = −GwLD
Mgas(t)Mdark
(1.35)
which represents the potential well due to the interaction between dark
and luminous matter, where wLD ∼
S(1 + 1.37S), with S = rL/rD,
being the ratio between the galaxy effective radius and the radius of the
dark matter core. The typical model for a BCG has a luminous mass
of 108 − 109M⊙, a dark matter halo ten times larger than the luminous
mass and various values for the parameter S. The galactic wind in these
galaxies develops easily but it carries out mainly metals so that the total
mass lost in the wind is small.
1.3.3 Results on DIG and BCG from purely chemical models
Purely chemical models (Bradamante et al. 1998, Marconi et al. 1994)
for DIG and BCG have been computed in the last years by varying the
number of bursts, the time of occurrence of bursts tburst, the star forma-
tion efficiency, the type of galactic wind (differential or normal), the IMF
and the nucleosynthesis prescriptions. The best model of Bradamante
et al. (1998) suggests that the number of bursts should be Nbursts ≤ 10,
the SF efficiency should vary from 0.1 to 0.7 Gyr−1 for either Salpeter or
Scalo (1986) IMF (Salpeter IMF is favored). Metal enriched winds are
favored. The results of these models also suggest that SNe of Type
II dominate the chemical evolution and energetics of these galaxies,
whereas stellar winds are negligible. The predicted [O/Fe] ratios tend to
be overabundant relative to the solar ratios, owing to the predominance
of Type II SNe during the bursts, in agreement with observational data
1.3 Lecture III: interpretation of abundances in dwarf irregulars 33
(see Figure 3.5 upper panel). Models with strong differential winds and
Nburst=10 - 15 can however give rise to negative [O/Fe] ratios. The
main difference between DIGs and BCGs, in these models, is that the
BCGs suffer a present time burst, whereas the DIGs are in a quiescent
phase.
In Figure 3.3 we show some of the results of Bradamante et al. (1998)
compared with data on BCGs: it is evident from the Figure that the
spread in the chemical properties can be simply reproduced by different
SF efficiencies, which translate into different wind efficiencies.
In Fig 3.4 we show the results of the chemical evolution models of
Henry et al. (2000). These models take into account exponential infall
but not outflow. They suggested that the SF efficiency in extragalactic
HII regions must have been low and that this effect coupled with the
primary N production from intermediate mass stars can explain the
plateau in log(N/O) observed at low 12+log(O/H). Henry et al. (2000)
also concluded that 12C is mainly produced in massive stars (yields by
Maeder 1992) whereas 14N is mainly produced in intermediate mass
stars (yields by HG97). This conclusion, however, should be tested also
on the abundances of stars in the Milky Way, where the flat behaviour
of [C/Fe] vs. [Fe/H] from [Fe/H] =-2.2 up to [Fe/H]=0 suggest a similar
origin for the two elements, namely partly from massive stars and mainly
from low and intermediate mass ones (Chiappini et al. 2003b).
Concerning the [O/Fe] ratios we show results from Thuan et al. (1995)
in Figure 3.5, where it is evident that generally BCGs have overabundant
[O/Fe] ratios.
Very recently, an extensive study from SDSS of chemical abundances
from emission lines in a sample of 310 metal poor emission line galaxies
appeared (Izotov et al. 2006). The global metallicity in these galax-
ies ranges from ∼ 7.1(Z⊙/30) to ∼ 8.5(0.7Z⊙). The SDSS sample is
merged with 109 BCGs containing extremely low metallicity objects.
These data, shown in Figure 3.5 lower panel, substantially confirm pre-
vious ones, showing how α-elements do not depend on the O abundance
suggesting a common origin for these elements in stars withM > 10M⊙,
except for a slight increase of Ne/O with metallicity which is inter-
preted as due to a moderate dust depletion of O in metal rich galaxies.
An important finding is that all the studied galaxies are found to have
log(N/O) > −1.6, which indicates that none of these galaxies is a truly
young object, unlike the DLA systems at high redshift which show a
log(N/O) ∼ −2.3.
34 Chemical Evolution
Fig. 1.13. Upper panel : predicted Log(N/O) vs. 12 + log(O/H) for a model
with 3 bursts of SF separated by quiescent periods and different SF efficien-
cies here indicated with γ = ν. Lower panel: predicted log(C/O) vs. 12 +
log(O/H). The data in both panels are from Kobulnicky and Skillman (1996).
The models assume a dark matter halo ten times larger than the luminous
mass and S=0.3 ( Bradamante et al. 1998, see text).
1.3.4 Results from Chemo-Dynamical models: IZw18
IZw18 is the most metal poor local galaxy, thus resembling to a pri-
mordial object. Probably it did not experience more than two bursts
of star formation including the present one. The age of the oldest stars
1.3 Lecture III: interpretation of abundances in dwarf irregulars 35
Fig. 1.14. Figure from Henry et al. (2000): a comparison between numerical
models and data for extragalactic HII regions and stars (filled circles, filled
boxes and filled diamonds); M and S mark the position of the Galactic HII re-
gions and the Sun, respectively. Their best model is model B with an efficiency
of SF of ν = 0.03.
in this galaxy is still uncertain, although recently Tosi et al. (2006)
suggested an age possibly > 2 Gyr. The oxygen abundance in IZW18
is 12+log(O/H)= 7.17-7.26, ∼ 15-20 times lower than the solar oxygen
(12+ log(O/H)= 8.39, Asplund et al. 2005) and log N/O= -1.54/ -1.60
(Garnett et al. 1997).
Recently, FUSE provided abundances also for HI in IZw18: the evi-
dence is that the abundances in the HI are lower than in the HII (Aloisi
et al. 2003; Lecavelier des Etangs et al. 2003). In particular, Aloisi et
al. (2003) found the largest difference relative to the HII data.
Chemo-dynamical (2-D) models (Recchi et al. 2001) studied first the
case of IZw18 with only one burst at the present time and concluded
that the starburst triggers a galactic outflow. In particular, the metals
leave the galaxy more easily than the unprocessed gas and among the
enriched material the SN Ia ejecta leave the galaxy more easily than
other ejecta. In fact, Recchi et al. (2001) had reasonably assumed that
Type Ia SNe can transfer almost all of their energy to the gas, since
36 Chemical Evolution
Fig. 1.15. Upper panel: [O/Fe] vs. [Fe/H] observed in a sample of BCGs
by Thuan et al. (1995) (filled circles), open triangles and asterisks are disk
and halo stars shown for comparison.Figure from Thuan et al. (1995). Lower
panel: new data from Izotov et al. (2006). The large filled circles represent the
BCGs whereas the dots are the SDSS galaxies. Abundances in the left panel
are calculated as in Thuan et al. (1995) whereas those in the right panel are
calculated as in Izotov et al. (2006) (see original papers for details). Figure
from Izotov et al. (2006).
1.3 Lecture III: interpretation of abundances in dwarf irregulars 37
Fig. 1.16. Figure from Recchi et al. (2004): predicted abundances for the HII
region in IZw18 (dashed lines represent a model adopting the yields of Meynet
& Maeder (2002) for Z = 10−5, whereas the continuous line refers to a higher
metallicity (Z=0.004).Observational data are represented by the shaded areas.
they explode in an already hot and rarified medium after the SN II
explosions. As a consequence of this, they predicted that the [α/Fe]
ratios in the gas inside the galaxy should be larger than the [α/Fe]
ratios in the gas outside the galaxy. At variance with previous studies,
they found that most of the metals are already in the cold gas phase
after 8-10 Myr since the superbubble does not break immediately and
thermal conduction can act efficiently. In the following, Recchi et al.
(2004) extended the model to a two-burst case, always with the aim of
reproducing the characteristics of IZw18. The model well reproduces the
chemical properties of IZw18 with a relatively long episode of SF lasting
270 Myr plus a recent burst of SF still going on. In Figure 3.6 we show
the predictions of Recchi et al. (2004) for the abundances in the HII
regions of IZW18 and in Figure 3.7 those for the HI region, showing a
little difference between the HII and HI abundances, more in agreement
with the data of Lecavelier des Etangs et al. (2004).
38 Chemical Evolution
Fig. 1.17. Figure from Recchi et al. (2004): predicted abundances for the
HI region. The models are the same as in Figure 3.6. Observational data
are represented by the shaded areas. The upper shaded area in the panel for
oxygen and the lower shaded area in the panel for N/O represent the data of
Lecavelier des Etangs et al. (2003).
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment
1.4.1 Ellipticals
We recall here some of the most important properties of ellipticals or
early type galaxies (ETG) which are systems made of old stars with no
gas and no ongoing SF. The metallicity of ellipticals is measured only
by means of metallicity indeces obtained from their integrated spectra
which are very similar to those of K giants. In order to pass from metal-
licity indices to [Fe/H] one needs then to adopt a suitable calibration
often based on population synthesis models (Worthey, 1994). We also
summarize the most common scenarios for the formation of ellipticals.
1.4.2 Chemical Properties
The main properties of the stellar populations in ellipticals are:
• There exist the well-known Color-Magnitude and Color - σo (veloc-
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 39
ity dispersion) relations indicating that the integrated colors become
redder with increasing luminosity and mass (Faber 1977; Bower et al.
1992). These relations are interpreted as a metallicity effect, although
a well known degeneracy exists between metallicity and age of the
stellar populations in the integrated colors (Worthey 1994).
• The indexMg2 is normally used as a metallicity indicator since it does
not depend much upon the age of stellar populations. There exists for
ellipticals a well defined Mg2–σo relation, equivalent to the already
discussed mass-metallicity relation for star forming galaxies (Bender
et al. 1993; Bernardi et al. 1998; Colless et al. 1999).
• Abundance gradients in the stellar populations inside ellipticals are
found (Carollo et al. 1993; Davies et al. 1993). Kobayashi & Arimoto
(1999) derived the average gradient for ETGs from a large compilation
of data and this is: ∆[Fe/H ]/∆r ∼ −0.3, with the average metallicity
in ETGs of < [Fe/H ] >∗∼ −0.3dex (from -0.8 to +0.3 dex).
• A very important characteristic of ellipticals is that their central dom-
inant stellar population (dominant in the visual light) shows an over-
abundance, relative to the Sun, of the Mg/Fe ratio, < [Mg/Fe] >∗> 0
(from 0.05 to + 0.3 dex) (Peletier 1989; Worthey et al. 1992; Weiss
et al. 1995; Kuntschner et al. 2001).
• In addition, the overabundance increases with increasing galactic mass
and luminosity, < [Mg/Fe] >∗ vs. σo, (Worthey et al. 1992; Mat-
teucci 1994; Jorgensen 1999; Kuntschner et al. 2001).
1.4.3 Scenarios for galaxy formation
The most common ideas on the formation and evolution of ellipticals
can be summarized as:
• they formed by an early monolithic collapse of a gas cloud or early
merging of lumps of gas where dissipation plays a fundamental role
(Larson 1974; Arimoto & Yoshii 1987; Matteucci & Tornambè 1987).
In this model SF proceeds very intensively until a galactic wind is
developed and SF stops after that. The galactic wind is devoiding the
galaxy from all its residual gas.
• They formed by means of intense bursts of star formation in merging
subsystems made of gas (Tinsley & Larson 1979). In this picture SF
stops after the last burst and gas is lost via ram pressure stripping or
galactic wind.
40 Chemical Evolution
Fig. 1.18. The relation [α/Fe] vs. velocity dispersion (mass) for ETGs. Figure
adapted from Thomas et al. (2002).The continuous line represents the predic-
tion of the model by Pipino & Matteucci (2004). The shaded area represents
the prediction of hierarchical models for the formation of ellipticals.The sym-
bols are the observational data.
• They formed by early merging of lumps containing gas and stars in
which some dissipation is present (Bender et al. 1993).
• They formed and continue to form in a wide redshift range and prefer-
entially at late epochs by merging of early formed stellar (e.g. Kauff-
mann et al. 1993;1996).
Pipino & Matteucci (2004), by means of recent revised monolithic
models taking into account the development of a galactic wind (see Lec-
ture III), computed the relation [Mg/Fe] versus mass (velocity disper-
sion) and compared it with the data by Thomas et al. (2002). Thomas
(1990) already showed how hierarchical semi-analitycal models cannot
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 41
reproduce the observed [Mg/Fe] vs. mass trend, since in this scenario
massive ellipticals have longer periods of star formation than smaller
ones. In Figure 4.1, the original figure from Thomas et al. (2002) is
shown, where we have plotted also our predictions. In the Pipino &
Matteucci (2004) model it is assumed that the most massive galaxies as-
semble faster and form stars faster than less massive ones. The adopted
IMF is the Salpeter one. In other words, more massive ellipticals seem to
be older than less massive ones, in agreement with what found for spirals
(Boissier et al. 2001). In particular, in order to explain the observed
< [Mg/Fe] >∗> 0 in giant ellipticals the dominant stellar population
should have formed on a time scale no longer than 3-5 ·108 yr (Weiss et
al. 1995; Pipino & Matteucci 2004).
1.4.4 Ellipticals-Quasars connection
We know now that most if not all massive ETGs are hosting an AGN
for sometime during their life. Therefore, there is a strict link between
the quasar activity and the evolution of ellipticals.
1.4.5 The chemical evolution of QSOs
It is very interesting to study the chemical evolution of QSOs by means
of the broad emission lines in the QSO region. The first studies by Wills
et al. (1985) and Collin-Souffrin et al. (1986) found that the abundance
of Fe in QSOs, as measured from broad emission lines, turned out to be
∼ a factor of 10 more than the solar one and this represented a challenge
for chemical evolution model makers. Hamman & Ferland (1992) from
N V/C IV line ratios in QSOs derived the N/C abundance ratios and
inferred the QSO metallicities. They suggested that N is overabundant
by factors of 2-9 in the high redshift sources (z > 2). Metallicities 3-14
times the solar one were also suggested in order to produce such a high
N abundance, under the assumption of a mainly secondary N. To inter-
pret their data they built a chemical evolution model, a Milky Way- like
model, and suggested that these high metallicities are reached in only
0.5 Gyr, implying that QSOs are associated with vigourous star forma-
tion. At the same time, Padovani & Matteucci (1993) and Matteucci &
Padovani (1993) proposed a model for QSOs in which QSOs are hosted
by massive ellipticals. They assumed that after the occurrence of a galac-
tic wind the galaxy evolves passively and that for massess > 1011M⊙
the gas restored by the dying stars is not lost but it feeds the central
42 Chemical Evolution
black hole. They showed that in this context the stellar mass loss rate
can explain the observed AGN luminosities. They also found that solar
abundances in the gas are reached in no more than 108 years explaining
in a natural way the standard emission lines observed in high-z QSOs.
The predicted abundances could explain the data available at that time
and solve the problem of the quasi-similarity of QSO spectra at differ-
ent redshifts. Finally, they suggested also a criterium for establishing
the ages of QSOs on the basis of the [α/Fe] ratios observed from broad
emission lines (see also Hamman & Ferland 1993).
Much more recently, Maiolino et al. (2005, 2006) used more than
5000 QSO spectra from SDSS data to investigate the metallicity of the
broad emission line region in the redshift range 2 < z < 4.5 and over
the luminosity range −24.5 < MB < −29.5. They found substantial
chemical enrichment in QSOs already at z = 6. Models for ellipticals
by Pipino & Matteucci (2004) were used as a comparison with the data
and they well reproduce the data, as one can see in Figure 4.2. In this
Figure the evolution of the abundances of several chemical elements in
the gas of a typical elliptical are shown. The elliptical suffers a galactic
wind at around 0.4 Gyr since the beginning of star formation. This wind
devoids the galaxy of all the gas present at that time. After this time,
the SF stops and the galaxy evolves passively. All the gas restored after
the galactic wind event by dying stars can in principle feed the central
black hole, thus the abundances shown in Figure 4.2, after the time of
the wind, can be compared with the abundances measured in the broad
emission line region. As one can see, the predicted Fe abundance after
the galactic wind is always higher than the O one, owing to the Type Ia
SNe which continue to produce Fe even after the stop in the SF. On the
other hand, O and α-elements stop to be produced when the SF halts.
The comparison between the predicted abundances and those derived
from the QSO spectra, are in very good agreement and indicates ages
for these objects between 0.5 and 1 Gyr.
Finally, in the context of the joint formation of QSOs and ellipticals
we recall the work of Granato et al. (2001) who includes the energy
feedback from the central AGN in ellipticals. This feedback produces
outflows and stops the SF in a down-sizing fashion, in agreement with
the chemical properties of ETGs indicating a shorter period of SF for
the more massive objects.
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 43
Fig. 1.19. The temporal evolution of the abundances of several chemical ele-
ments in the gas of an elliptical galaxy with luminous mass of 1011M⊙. Feed-
back effects are taken into account in the model (Pipino & Matteucci 2004), as
described in Lecture III. The downarrow indicates the time for the occurrence
of the galactic wind. After this time, the SF stops and the elliptical evolves
passively. All the abundances after the time for the occurrence of the wind are
those that we observe in the broad emission line region region. The shaded
area indicates the abundance sets which best fit the line ratios observed in the
QSO spectra. Figure from Maiolino et al. 2006.
1.4.6 The chemical enrichment of the ICM
The X-ray emission from galay clusters is generally interpreted as ther-
mal bremsstrahlung in a hot gas (107-108 K). There are several emission
lines (O, Mg, Si, S) including the strong Fe K-line at around 7keV which
was discovered by Mitchell et al. (1976). The iron is the best studied
element in clusters. For kT ≥ 3 keV the intracluster medium (ICM)
Fe abundance is constant and ∼ 0.3Fe⊙ in the central cluster regions;
44 Chemical Evolution
the existence of metallicity gradients seems evident only in some clusters
(see Renzini 2004). At lower temperatures, the situation is not so simple
and the Fe abundance seems to increase. The first works on chemical
enrichment of the ICM even preceeded the discovery of the Fe line (Gunn
& Gott 1972, Larson & Dinerstein 1975). In the following years other
works appeared such as those of Vigroux (1977), Himmes & Biermann
(1988) and Matteucci & Vettolani (1988). In particular, Matteucci &
Vettolani (1988) started a more detailed approach to the problem fol-
lowed by David et al. (1991), Arnaud (1992), Renzini et al. (1993),
Elbaz et al. (1995), Matteucci & Gibson (1995), Gibson & Matteucci
(1997), Lowenstein & Mushotzky (1996), Martinelli et al. (2000), Chiosi
(2000), Moretti et al. (2003). The majority of these papers assumed that
galactic winds (mainly from ellipticals and S0 galaxies) are responsible
for the ICM chemical enrichment. In fact, ETGs are the dominant type
of galaxy in clusters and Arnaud (1992) found a clear correlation be-
tween the mass of Fe in clusters and the total luminosity of ellipticals.
No such correlation was found for spirals in clusters. Alternatively, the
abundances in the ICM are due to ram pressure stripping (Himmes &
Biermann 1988) or derive from a chemical enrichment from pre-galactic
Pop III stars (White & Rees 1978).
In Matteucci & Vettolani (1988) the Fe abundance in the ICM rel-
ative to the Sun, XFe/XFe⊙ , was calculated as (MFe)pred/(Mgas)obs
to be compared with the observed ratio (XFe/XFe⊙)obs = 0.3 − 0.5
(Rothenflug & Arnaud 1985). They found a good agreement with the
observed Fe abundance in clusters if all the Fe produced by ellipticals
and S0, after SF has stopped, is eventually restored into the ICM and
if the majority of gas in clusters has a primordial origin. Low values for
[Mg/Fe] and [Si/Fe] were predicted at the present time, due to the short
period of SF in ETGs and to the Fe produced by Type Ia SNe. With
Salpeter IMF they found that the Type Ia SNe contribute ≥ 50% of the
total Fe in clusters. This leads to a bimodality in the [α/Fe] ratios in
the stars and in the gas in the ICM, since the stars have overabundances
of [α/Fe]> 0 whereas the ICM should have [α/Fe]≤ 0. The same con-
clusion was reached and more highlighted later by Renzini et al. (1993).
More recently, Pipino et al. (2002) computed the chemical enrichment
of the ICM as a function of redshift by considering the evolution of the
cluster luminosity function and an updated treatment of the SN feed-
back. They adopted Woosley & Weaver (1995) yields for Type II SNe
and Nomoto et al. (1997) W7 model for Type Ia SNe and a Salpeter
IMF. They also predicted solar or undersolar [α/Fe] ratios in the ICM.
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 45
Fig. 1.20. Observed Fe abundance and predicted Fe abundance in the ICM as
a function of redshift: data from Tozzi et al. (2003), model (continuous line)
from Pipino et al. (2002), where the formation of ETGs was assumed to occur
at z=8.
The observational data on abundance ratios in clusters are still uncertain
and vary from cluster centers where they tend to be solar or undersolar
to the outer regions where they tend to be oversolar (e.g. Tamura et al.
2004). So, no firm conclusions can be drawn on this point. Concerning
the evolution of the Fe abundance in the ICM as a function of redshift,
most of the above mentioned models predict very little or no evolution of
the Fe abundance from z=1 to z=0 (Pipino et al. 2002). This prediction
seemed to be in good agreement with data from Tozzi et al. (2003) as
shown Figure. However, more recently, more data of Fe abundance for
high redshift clusters appeared showing a different behaviour.
In Figure 4.4 we show the data of Balestra et al. (2006) who claim
an increase, by at least a factor of two, of the Fe abundance in the
ICM from z=1 to z=0. Clearly, if we assume that only ellipticals have
contributed to the Fe abundance in the ICM, this effect is difficult to
explain unless we assume recent star formation in ellipticals. Another
possible explanation could be that spiral galaxies contribute to Fe when
46 Chemical Evolution
Fig. 1.21. New data (always relative to Fe) from Balestra et al. (2006) showing
an increase of the Fe abundance in the ICM from z=1 to z=0. Error bars refer
to 1σ confidence level. The big shaded area represents the rms dispersion.
Figure from Balestra et al. (2006).
they become S0 as a consequence of ram pressure stripping, and this
morphological transformation might have started just at z=1.
1.4.7 Conclusions on the enrichment of the ICM
From what said before we can conclude that:
• Elliptical galaxies are the dominant contributors to the abundances
and energetic content of the ICM. A constant Fe abundance of ∼
0.3Fe⊙ is found in the central regions of clusters hotter than 3keV
(Renzini 2004).
• Good models for the chemical enrichment of the ICM should repro-
duce the iron mass measured in clusters plus the [α/Fe] ratios in-
side galaxies and in the ICM as well as the Fe mass to light ratio
(IMLR= MFeICM /LB, with LB being the total blue luminosity of
member galaxies, as defined by Renzini et al. (1993). Abundance
1.4 Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment 47
ratios are very powerful tools to impose constraints on the evolution
of ellipticals and of the ICM.
• Models which do not assume a top-heavy IMF for the galaxies in
clusters (a Salpeter IMF can reproduce at best the properties of local
ellipticals) predict [α/Fe]> 0 inside ellipticals and [α/Fe] ≤ 0 in the
ICM. Observed values are still too uncertain to draw firm conclusions
on this point.
Acknowledgements
This research has been supported by INAF (Italian National Institute
for Astrophysics), Project PRIN-INAF-2005-1.06.08.16
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	Chemical Evolution
	Lecture I: basic assumptions and equations of chemical evolution
	The basic ingredients
	The Star Formation Rate
	The Initial Mass Function
	The Infall Rate
	The Outflow Rate
	Stellar evolution and nucleosynthesis: the stellar yields
	Type Ia SN Progenitors
	Yields per Stellar Generation
	Analytical models
	Numerical Models
	Lecture II: the Milky Way and other spirals
	The Galactic formation timescales
	The two-infall model
	Common Conclusions from MW Models
	Abundance Gradients from Emission Lines
	Abundance Gradients in External Galaxies
	How to model the Hubble Sequence
	Type Ia SN rates in different galaxies
	Time-delay model for different galaxies
	Lecture III: interpretation of abundances in dwarf irregulars
	Properties of Dwarf Irregular Galaxies
	Galactic Winds
	Results on DIG and BCG from purely chemical models
	Results from Chemo-Dynamical models: IZw18
	Lecture IV: Elliptical galaxies-Quasars- ICM Enrichment
	Ellipticals
	Chemical Properties
	Scenarios for galaxy formation
	Ellipticals-Quasars connection
	The chemical evolution of QSOs
	The chemical enrichment of the ICM
	Conclusions on the enrichment of the ICM
	References
