Chemical Evolution of the
Galaxy and its Satellites
Francesca Matteucci
Cristina Chiappini
Francesco Calura
Antonio Pipino
Gabriele Cescutti
Universita’ di Trieste e OATS

How to model galactic chemical evolution
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Initial conditions (open or closed-box; chemical composition of the gas)
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Birthrate function (SFRxIMF)
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Stellar yields (how elements are produced and restored into the ISM)
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Gas flows (infall, outflow, radial flow)
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Equations containing all of of this...

The Stellar Birthrate
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We define the stellar birthrate function as:
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B(m,t) =SFRxIMF
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The SFR is the star formation rate (how many solar masses go into stars per unit time)
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The IMF is the initial stellar mass function describing the distribution of stars as a function of stellar mass

The parametrization of the SFR
• The most common parametrization is the Schmidt
(1959) law where the SFR is proportional to some power (k=2) of the gas density
•
Kennicutt (1998) suggested k=1.4 from studying star forming galaxies, but also a law depending on the rotation angular speed of gas and the first power of the gas density

The accretion history of the
Galaxy
 The gas infall rate can simply be constant in space and time
 Or described by an exponential law:

Stellar Yields
• Low and intermediate mass stars (0.8-8 Msun): produce He, N, C and heavy s-process elements.
They die as C-O white dwarfs, when single, and can die as Type Ia SNe when binaries
•
Massive stars (M>8-10 Msun, core-collapse SNe): they produce mainly alpha-elements (O, Mg..), some Fe, light s-process elements and r-process elements and explode as core-collapse SNe
• Type Ia SNe produce mainly Fe (0.6-0.7M_sun per SN)

Type Ia SN progenitors: SD model
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Single-degenerate scenario (e.g. Whelan &
Iben 1974; Han & Podsiadlowsky 2004): a binary system with a C-O white dwarf plus a MS star. When the star becomes RG it starts accreting mass onto the WD
•
When the WD reaches 1.44 Msun
(Chandrasekhar mass), it explodes by Cdeflagration as Type Ia supernova

Type Ia SN progenitors: DD model
• Double-Degenerate scenario (Iben & Tutukov,
1984): two C-O WDs merge after loosing angular momentum due to gravitational wave radiation
• When the two WDs of 0.7
Msun merge, the
Chandrasekhar mass is reached and Cdeflagration occurs

The clock for the explosion
• Single-Degenerate model: the clock to the explosion is given by the lifetime of the secondary star, m2. The minimum time for the appearence of the first Type Ia SN is 30-35 Myr (the lifetime of a 8 Msun star)
•
Double-Degenerate model: the clock is given by the lifetime of the secondary plus the gravitational time-delay: 35 Myr + Delta_grav
• Minimum delay time 1 Myr (Greggio 2005), maximum delay a Hubble time and more

The two-infall model of
Chiappini, FM & Gratton 1997
• The two-infall model of
Chiappini, FM & Gratton
(1997) predicts two main episodes of gas accretion
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During the first one the halo, bulge and part of thick disk formed, the second gave rise to the disk
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Exponential infall law with different timescales

The star formation rate in the solar vicinity
• The predicted SFR
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The effect of a threshold gas density
(7 Msun pc^(-2)) for the SF is evident
• The IMF is that of
Scalo (1986)
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A gap in the SFR is predicted

The SN rates in the solar vicinity

G-dwarf metallicity distribution in the Solar Vicinity

[alpha/Fe] vs.[Fe/H] in the Solar
Vicinity: Francois et al. 04

Results of Francois, FM et al.
2004

Last data and models on C and N

How do the gradients form?
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If one assumes the disk to form inside-out, namely that first collapses the gas which forms the inner parts and then the gas which forms the outer parts
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Namely, if one assumes a timescale for the formation of the disk increasing with galactocentric distance, the gradients are well reproduced if

Predicted and Observed
Abundance Gradients
• Predicted and observed abundance gradients from
Chiappini et al. (2001)
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Data from HII regions,
PNe and B stars, red dot is the Sun
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The gradients slightly steepen with time
(from blue to red)

The Galactic Bulge
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Ballero, FM, Origlia & Rich (2007) proposed a model where the Bulge forms very quickly from gas shed by the halo
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The star formation efficiency was quite high
(starburst) and the IMF flatter than in the disk
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In this situation a long plateau for
[alpha/Fe] ratios is predicted

Predictions and Observations for the Bulge

[alpha/Fe] in galaxies with different SFRs

Dwarf Speroidals vs. Milky Way

Do do the Dwarf Spheroidals form?
• CDM models for galaxy formation predict dSph systems (10^7 Msun) to be the first to form stars
(all stars should form < 1Gyr)
•
Then heating and gas loss due to reionization must have halted soon SF
• Observationally, all dSph satellites of the MW contain old stars indistinguishable from those of
Galactic globular clusters and they have experienced SF for long periods (>2 Gyr, Grebel
& Gallagher, 04)

Modelling the dSphs
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Lanfranchi & FM (03,04) computed the evolution of 6 dSphs: Carina, Sextan,
Draco, Sculptor, Sagittarius and Ursa Minor
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They assumed the SF histories as measured by the Color-Magnitude diagrams (Mateo,
1998;Dolphin 2002; Hernandez et al. 2000;
Rizzi et al. 2003)

Results: Carina galaxy
• Model Lanfranchi &
Matteucci (2004)
• SF history from Rizzi et al. 03. Four bursts of 2 Gyr, SF eff. =
0.15 Gyr^(-1) wind=7xSFR
• Salpeter IMF

The metallicity distribution of
Carina
• Data from Koch et al.
(2005)
• Best model from
Lanfranchi & al.
(2006)
•
This model well reproduces also the
[alpha/Fe] ratios in
Carina

Chemical evolution of Sculptor
• Model and data for
Sculptor
• SF efficiency 0.05-0.5
Gyr^(-1), wind 7
XSFR
•
One long SF episide lasting 7 Gyr
• Salpeter IMF

Heavy elements in Sculptor
• Predicted and observed s- and rprocess elements in
Draco
•
The effect of the timedelay between Type II and Ia SNe coupled with slow SF produces higher [s/Fe] than in the Milky Way

Comparison Sculptor –Milky Way
• Blue line and blue data refer to Sculptor
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Red line and red data refer to the Milky Way
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The effect of the timedelay model is to shift towards left the model for Sculptor with a lower SF efficiency than in the MW

Conclusions on the Milky Way
• The Disk at the solar ring formed on a time scale not shorter than 7 Gyr
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The whole Disk formed inside-out with timescales of the order of 2 Gyr in the inner regions and 10
Gyr in the outer regions
• The inner halo formed on a timescale not longer than 2 Gyr
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Time- delay model well explains abundance ratios.
Nature of N still unknown (probably primary N from massive stars)

Conclusions on the Milky Way
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The best model for the Bulge suggests that it formed by means of a strong starburst
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The efficiency of SF was 20 times higher than in the rest of the Galaxy
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The IMF was very flat, as it is suggested for starbursts
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The timescale for the Bulge formation was
0.1 Gyr and not longer than 0.5 Gyr

Conclusions on dSphs
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By comparing the [alpha/Fe] ratios in the
MW and dSphs one concludes that they had different SF histories
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The [alpha/Fe] ratios in dSphs are always lower than in the MW at the same [Fe/H], as a consequence of the time delay model and strong galactic wind

Conclusions on dSphs
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Good agreement both for [s/Fe] and [r/Fe] ratios is obtained . These ratios are generally higher, for a given [Fe/H], than the corresponding ratios in S.N.
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This is again a consequence of the timedelay model
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It is unlikely that the dSphs are the building blocks of the MW