The Chemical Evolution of the Galaxy and Dwarf Spheroidals of the Local Group

Saas-Fee, March 4-10, 2007

Chemical Evolution of the Galaxy and dSphs of the

Local Group

Outline of the lectures

Lecture I: Basic principles of chemical evolution, main ingredients (star formation history, nucleosynthesis and gas flows)Lecture II: Supernova progenitors, basic equations, analytical and numerical solutionsLecture III: Detailed chemical evolution models for the Milky WayLecture IV: Model results for the formation and evolution of the Milky Way

Outline of the lectures

Lecture V: SFR and Hubble sequence, the effects of the time-delay model on different galaxies

Lecture VI: Chemical properties and models of chemical evolution of dSphs

Lecture VII: Comparison between the evolution of dSphs and the Milky Way. Interpretation of the alpha/Fe and s- and r- process el./Fe ratios

How to model galactic chemical evolution

Initial conditions (open or closed-box; chemical composition of the gas)

Birthrate function (SFRxIMF)

Stellar yields (how elements are produced and restored into the ISM)

Gas flows (infall, outflow, radial flow)

Equations containing all of of this...

Initial Conditions

a) Start from a gas cloud already present at t=0 (monolithic model). No flows allowed (closed-box)b) Assume that the gas accumulates either fastly or slowly and the system suffers outflows (open model)c) We assume that the gas at t=o is primordial (no metals)d) We assume that the gas at t=o is pre-enriched by Pop III stars

Star Formation History

We define the stellar birthrate function as:

B(m,t) =SFRxIMF

The SFR is the star formation rate (how many solar masses go into stars per unit time)

The IMF is the initial stellar mass function describing the distribution of stars as a function of stellar mass

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=1.5 from studying star forming galaxies, but also a law depending of the rotation angular speed of gas Other parameters such as gas temperature, viscosity and magnetic field are usually ignored

Kennicutt’s (1998) SFR

Kennicutt’s law

SF induced by spiral density waves

SFR accounting for feedback

The IMF

How to derive the IMF

The current mass distribution of local MS stars per unit area, n(m), is called Present Day Mass Function (PDMF)

For stars in the range 0.1-1 Msun, with lifetimes > the age of the Galaxy, tG, we can write:

How to derive the IMF

If the IMF is assumed to be constant in time, we can write:

How to derive the IMF

For stars with lifetimes << tG (m> 2 Msun) we can see only the stars born after

Therefore, we can write:

How to derive the IMF

If we assume the IMF is constant in time we can write:

Having assumed that the SFR did not change during the time interval corresponding to stellar lifetimes

How to derive the IMF

We cannot apply the previous approximations to stars in the range 1-2 Msun

Therefore, the IMF is this mass range will depend on b(tG):

Constraints on the SFH from the IMF

In order to obtain a good fit of the two branches of the IMF in the solar vicinity one needs to assume (Scalo 1986):

The IMF

Upper panel: different IMFs

Lower panel: normalization of the multi-slope IMFs to the Salpeter IMF

Figure from Boissier & Prantzos (1999)

How to derive the local SFR

An IMF should be assumed and then one should integrate the PDMF in time

Timmes et al. (1995), by adopting the Miller & Scalo (1979) IMF , obtained:

The Infall law

The infall rate can simply be constant in space and time

Or described by an exponential law:

The outflow law

The rate of gas loss from a galaxy through a galactic wind can be expressed as:

The Yield per stellar generation

The yield per stellar generation of a single chemical element, can be defined as (Tinsley 1980):

Where p_im is the stellar yield and the instantaneous recycling approximation has been assumed

Instantaneous Recycling Approximation

The I.R.A. states that all the stars with masses < 1 Msun live forever (and this is true) but also that the stars with masses > 1 Msun die instantaneously (and this is not true)

I.R.A. affects mainly the chemical elements produced on long timescales (e.g. N and Fe)

The returned fraction

We define returned fraction the amount of mass ejected into the ISM by an entire stellar generation

Instantaneous recycling approximation (IRA) is assumed , namely stellar lifetimes of stars with M> 1 Msun are neglected

We call stellar yield the newly produced and ejected mass of a given chemical element by a star of mass m

Stellar yields depend upon the mass and the chemical composition of the parent star

Stellar Yields

Primary and Secondary elements

We define primary element an element produced directly from H and He

A typical primary element is carbon or oxygen which originate from the 3- alpha reaction

We define secondary element an element produced starting from metals already present in the star at birth (e.g. Nitrogen produced in the CNO cycle)

Simple Model and Secondary Elements

The solution of the Simple model of chemical evolution for a secondary element Xs formed from a seed element Z

Xs is proportional to Z^(2)

Xs/Z goes like Z

Primary versus secondary

Figure from Pettini et al. (2002)Small dots are extragalactic HII regionsRed triangles are Damped Lyman-alpha systems (DLA)Dashed lines mark the solution of the simple model for a primary and a secondary element

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): they produce mainly alpha-elements, some Fe, light s-process elements and r-process elements and explode as core-collapse SNe

Stellar Yields

Yields for Fe in massive stars (Woosley & Weaver 1995; Thielemann et al. 1996; Nomoto et al. 1997; Rauscher et al. 2002, Limongi & Chieffi 2003)

Stellar Yields

Mg yields from massive stars

Big differences among different studies

Mg yields are too low to reproduce the Mg abundances in stars

Stellar Yields

Oxygen yields from massive stars

Different studies agree on O yields

Oxygen increases continuously with stellar mass from 10 to 40 Msun

Not clear what happens for M>40 Msun

Stellar Yields

New yield from Nomoto et al. (2007) for Oxygen in massive stars

They are computed for 4 different metallicities

Stellar Yields

Yields of Fe from massive stars from Nomoto et al. (2007)

The yields are computed for 4 different metallicities

HHI II

SiSi

Ia

IbIc

HeHeIIPIIL

phasephase

light curve

IIb

early

phase

late

IIn

line profile

core collapse

thermo nuclear

Hypernovae = GRBs ?energy

Supernova taxonomySupernova taxonomy

faint IIluminosity

Basic SN types

Ia

Ib

II

max. +10 months

Ia II+Ib/cProgenitor WD in binary

system (M < 8MO)

single or binary massive star (>

8MO)

Mechanism thermo-nuclear core-collapse

total energy ~1051 ergs ~1053 ergs

Remnant none neutron star (or BH)

Ejecta 1.4 MO 1 - 30 MO

composition Fe O, Mg, Si, Ne, Ca

age 0.03 – 10 Gyr < 30 Myr

realization 5% ? 100%

SN type

Kennicutt (1998)

SFR and galaxy type

Type Ia SN progenitors

Single-degenerate scenario Whelan & Iben 1974): a binary system with a C-O white dwarf plus a normal star. When the star becomes RG it starts accreting mass onto the WD

When the WD reaches the Chandrasekhar mass it explodes by C-deflagration as Type Ia supernova

Type Ia SN progenitors

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 C-deflagration occurs

The nucleosynthesis is the same in the two scenarios

Single-Degenerate scenario

DD-scenario

The clocks for the explosions of SNe Ia

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 tSNIa= 30Myr (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. tSNIa= 35 Myr + Delta_grav= 40 MyrThe maximum timescale is 10 Gyr in the SD

and several Hubble times in the DD

Type Ia SN nucleosynthesis

A Chandrasekhar mass (1.44 Msun) explodes by C-deflagration

C-deflagration produces 0.6 Msun of Fe plus traces of other elements from C to Si

Tycho SNR (type Ia)

Chandra X-ray images

color code: red .30-.95 keV, green .95-2.65 keV, blue 2.65-7.00 keV

Type II SNe

Type II SNe arise from the core collapse of massive stars (M=8-40 Msun) and produce mainly alpha-elements (O, Mg, Si, Ca...) and some Fe

Stars more massive can end up as Type Ib/c SNe

Summary of Nucleosynthesis

During the Big Bang light elements are

formed,

Spallation process in the ISM produces 6Li, Be and B

Supernovae II produce alpha-elements (O, Ne, Mg, S, S, Ca), some Fe, light s- and r-process elements

Summary of Nucleosynthesis

Type Ia SNe produce mainly Fe and Fe-peak elements plus some traces of elements from C to Si

Low and intermediate mass stars produce

Deuterium is only destroyed to produce 3He which is also mainly destroyed

The Simple model

The Simple Model of galactic chemical evolution

One-zone, closed -box model (no infall or outflow)

IMF constant in time

Instantaneous recycling approximation

Instantaneous mixing approximation

Solution of the Simple Model

If we assume that Xi is the abundance by mass of an element i, we have:

where

Simple model with outflow

Simple model with infall

Abundance ratios and Simple Models

Under the assumption of the I.R.A.

it is always true that the ratio of two abundances is equal to the ratio of the two corresponding yields:

Models with no I.R.A.

When the I.R.A. Is relaxed then is NOT more true that the ratio between the abundances of two different elements is equal to the ratio of the corresponding yield!!

Basic Equations

Definitions of variables

dGi/dt is the rate of time variation of the gas fraction in the form of an element i

Xi(t) is the abundance by mass of a given element i

Qmi is a term containing all the information about stellar evolution and nucleosynthesis

Definition of variables

A =0.05-0.09 is the fraction in the IMF of binary systems of that particular type to give rise to Type Ia SNe. B=1-A

Tau_m is the lifetime of a star of mass m

f(mu) is the distribution function of the mass ratio in binary systems

A(t) and W(t) are the accretion and outflow rate, respectively

The Milky Way

The Milky Way

The formation of the Milky Way

Eggen, Lynden-Bell & Sandage (1962) suggested a rapid collapse lasting 300 Myr for the formation of the Galaxy

Searle & Zinn (1978) proposed a central collapse but also that the outer halo formed by merging of large fragments taking place over a timescale > 1Gyr

Different approaches in modelling the MW

Serial approach: halo, thick and thin disk form as a continuous process (e.g. Matteucci & Francois 1989)

Parallel approach: the different galactic component evolve at different rates but they are inter-connected (e. G. Pardi, Ferrini & Matteucci 1995)

Different approaches in modelling the MW

Two-infall approach: halo and disk form out of two different infall episodes (e.g. Chiappini, Matteucci & Gratton 1997; Alibes, Labay & Canal 2001)

Stochastic approach: mixing not efficient especially in the early halo phases (e.g. Tsujimoto et al. 1999; Argast et al. 2000; Oey 2000)

A scenario for the formation of the Galaxy

The two-infall model of Chiappini, Matteucci & Gratton (1997) predicts two main episodes of gas accretionDuring the first one the halo and bulge formed, the second gave rise to the disk

The two-infall model

The two-infall model has been adopted also in other studies such as Chang et al.(1999) and Alibes et al. (2001)In particular, Chang et al. applied the two-infall scheme to the thick and thin diskAlibes et al. adopted the same scheme as Chiappini et al. (1997)

Gas Infall at the present time

Another scenario

The creation of the Milky way

Hera, flowed when she realized she had been giving milk to Heracles and thrust him away her breast

Recipes for the two-infall model

SFR- Kennicutt’s law with a dependence on the surface gas density (exponent k=1.5) plus a dependence on the total surface mass density (feedback). Threshold of 7 solar masses per pc squaredIMF, Scalo (1986) normalized over a mass range of 0.1-100 solar massesExponential infall law with different timescales for inner halo (1-2 Gyr) and disk (inside-out formation with 7 Gyr at the S.N.)

Recipes for the model

Type Ia SNe- Single degenerate model (WD+RG or MS star), recipe from Greggio & Renzini (1983) and Matteucci & Recchi (2001)

Minimum time for explosion 35 Myr (lifetime of a 8 solar masses star), confirmed by recent findings (Mannucci et al. 2005, 2006)

Time for restoring the bulk of Fe in the S.N. is 1 Gyr (depends on the assumed SFR)

Solar Vicinity

We study first the solar vicinity, namely the local ring at 8 kpc from the galactic center

Then we study the properties of the entire disk from 4 to 22 Kpc

Stellar Lifetimes

The star formation rate (threshold effects)

Stellar abundances

[X/Fe]= log(X/Fe)_star-log(X/Fe)_sun is the abundance of an element X relative to iron and to the SunThe most recent accurate solar abundances are from Asplund et al. (2005)Previous abundances from Anders & Grevesse (1989) and Grevesse & Sauval (1998)The main difference is in the O abundance, now lower

Predicted SN rates

Type II SN rate (blue) follows the SFR

Type Ia SN rate (red) increases smoothly (small peak at 1 Gyr)

Time-delay model

Blue line= only Type II SNe to produce FeRed line= only Type Ia SNe to produce FeBlack line: Type II SNe produce 1/3 of Fe and Type Ia SNe produce 2/3 of Fe

Specific prediction by the two-infall model

The adoption of a threshold in the gas density for the SFR creates a gap in the SFRThis gap occurs between the halo-thick disk and the thin-disk phaseIt is observed in the data

G-dwarf distribution (Chiappini et al.)

Different timescales for disk formation

G-dwarf distribution(Alibes et al.)

G-dwarf distribution

Chiappini et al. (1997) , Alibes et al. (2001) and Kotoneva et al. (2002) concluded that a good fit to the G-dwarf metallicity distribution can be obtained only with a time scale of disk formation at the solar distance of 7-8 Gyr

Evolution of the element abundances

Chiappini et al. follow the evolution in space and time of 35 chemical species (H, D, He, Li, C, N, O, Ne, Mg, Si, S, Ca, Ti, K, Fe, Mn, Cr, Ni, Co, Sc, Zn, Cu, Ba, Eu, Y, La, Sr plus other isotopes)They solve a system of 35 equations where SFR, IMF, nucleosynthesis and gas accretion are taken into accountYields from massive stars WW95, from low-intermediate stars van den Hoeck+ Groenewegen 1997, from Type Ia SNe Iwamoto et al. 1999

Results from Francois et al. 2004

Results from Francois et al. 2004

Results from Francois et al. 2004

Corrected Yields

Corrected Yields

Corrected Yields

Suggestions for the Yields

Yields from Woosley & Weaver 1995 (WW95), Iwamoto et al. (1999)

Major corrections for Fe-peak elements

O, Fe, Si and Ca are ok. Mg should be increased

Inhomogeneous Model

Argast et al. (2000) computed 3-D hydrodynamical calculations following the evolution of SN remnantsNo mixing was assumed for [Fe/H] > -3.0 dex, complete mixing for [Fe/H]> -2.0 dexThey predicted a too large spread for [Mg/Fe] and [O/Fe] vs. [Fe/H]

Results from Alibes et al.

Alibes et al. (2001) adopted the two-infall model

Metallicity-dependent yields from WW95 and Van den Hoeck & Groenewegen (1997)

Results from Chiappini et al.

Evolution of Carbon and Nitrogen as predicted by the two-infall model of Chiappini, Matteucci & Gratton (1997)

The green line in the N plot is an euristic model with primary N from massive stars

Last data on Nitrogen

From Ballero et al. (2005)It shows new data (filled circles and triangles) at low metallicity endorsing the suggestion that N should be primary in massive starStellar rotation can produce such N (Meynet & Maeder 2002)

Last data on N and C

Primary nitrogen from rotating very metal poor massive starsModels from Chiappini et al. (2006) (dashed lines)Large squares from Israelian et al. 04; asterisks from Spite et al. 05; pentagons from Nissen 04

s- and r-process elements

Data from Francois et al.(2006) with UVES on VLTModels Cescutti et al. (2006): red line, best model, with Ba_s from 1-3 solar masses (Busso et al.01) and Ba_r from 10-30 solar masses

Old Prescriptions

Travaglio et al.(1999) assumed Ba_r from 8-10 solar masses

The new data show a source of Ba_r from more massive stars is required

s- and r- process elements

Data from Francois et al. (2006)

Models from Cescutti et al. (2006): red line, best model with Eu only r-process from 10-30 solar masses

s- and r- process elements

Lanthanum- Data from: Francois et al. (2006)

(filled red squares), Cowan & al.(2005) (blue hexagons), Venn et al.(2004) (blue triangles), Pompeia et al.(2003) (green hexagons)Models from Cescutti, Matteucci, Francois & Chiappini (2006): same origin as Ba

Abundance Gradients

The abundances of heavy elements decrease with galactocentric distance

in the disk

Gradients of different elements are slightly different (depend on their nucleosynthesis and timescales of production)

Gradients are measured from HII regions, PNe, B stars, open clusters and Cepheids

How does the gradient form?

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

Namely, if one assumes a timescale for the formation of the disk increasing with galactocentric distance, the gradients are well reproduced

Abundance gradients

Predicted and observed abundance gradients from Chiappini, Matteucci & Romano (2001)Data from HII regions, PNe and B stars, red dot is the SunThe gradients steepen with time (from blue to red)

Abundance gradients

Predictions from Boissier & Prantzos (1999), no threshold density in the SFThey predict the gradient to flatten in timeThe difference is due to the effect of the threshold

Abundance Gradients

New data on Cepheids from Andrievsky & al.(02,04) (open blue circles)Red triangles-OB stars from Daflon & Cunha (2004)Blue filled hexagons, Cepheids from Yong et al.(2006), blue open triangles from Young et al. 05, cian data from Carraro et al.(2004)

Different halo densities

Only Cepheids data from AndrievskyBlue dot-dashed line: model with halo density decreasing outwardsRed continuous line (BM):model with halo constant density

Abundance Gradients

Blue filled hexagons from open Cepheids (Yong et al. 2006)Cian data from open clusters (Carraro et al. 2004), open triangles are open clusters Black data from Cepheids (Andrievsky et al., 2002,04)Dashed lines=prediction for 4.5 Gyr ago

Abundance Gradients

Blue filled hexagons from Andrievsky & al.(02,04) Red squares are the average valuesFor Barium there are not yet enough data to compare

The Galactic Bulge

A model for the Bulge (green line, Ballero et al. 2006)

Yields from Francois et al. (04), SF efficiency of 20 Gyr^(-1), timescale of accretion 0.1 Gyr

Data from Zoccali et al. 06, Fulbright et al. 06, Origlia &Rich (04, 05)

The Galactic Bulge

Model (red, Ballero et al. 2006)

Predicts large Mg to Fe for a large Fe interval

Turning point at larger than solar Fe. Mg flatter than O

Data from Zoccali et al. 06; Fulbright et al. 06, Origlia & Rich (04, 05)

The Galactic Bulge

Metallicity Distribution of Bulge stars, data from Zoccali et al. (2003) and Fulbright et al. (2006) (dot-dashed)

Models from Ballero et al. 06, with different SF eff.

The Galactic Bulge

Models with different IMF

The best IMF for the Bulge is flatter than in the S.N: and flatter than Salpeter

Best IMF: x=0.95 for M> 1 solar mass and x=0.33 below

Bulge vs. Thick and Thin Disk Stars

Zoccali et al. (2006) compared new high resolution data for the Bulge (green dots and red crosses) with data for thick disk (yellow triangles) and thin disk (blue crosses)The Bulge stars are systematically more overabundant in O

Other Bulge Models

Molla, Ferrini & Gozzi (2000): the Bulge formed by collapse but with a more prolonged star formation history

They failed in reproduding [Mg/Fe]

Other Bulge Models

Immeli et al. (2004) computed dynamical simulations for the formation of the Bulge

They studied the efficiency of energy dissipation and different SF histories

Model B assumes an early and fast SFR

Comparison with data

Comparison between the B, D and F models of Immeli et al. (2004) with data from Zoccali et al. (2006)The best model predicts a very fast Bulge formationHowever, Immeli’s models have a fixed delay for Type Ia SNe

Conclusions on the Bulge

The best model for the Bulge suggests that it formed by means of a strong starburst

The efficiency of SF was 20 times higher than in the rest of the Galaxy

The IMF was very flat, as it is suggested for starbursts

The timescale for the Bulge formation was 0.1 Gyr and not longer than 0.5 Gyr

Conclusions on the Milky Way

The Disk at the solar ring formed on a time scale not shorter than 7 GyrThe whole Disk formed inside-out with timescales of the order of 2 Gyr in the inner regions and 10 Gyr in the outer regionsThe inner halo formed on a timescale not longer than 2 Gyr Gradients from Cepheids are flatter at large Rg than gradients from other indicators

Dwarf Spheroidals of the Local Group

SF and Hubble Sequence from Sandage

SF and HS from Kennicutt

Models for the Hubble Sequence

Type Ia SN rate in galaxies

Timescales for Type Ia SNe enrichment

The typical timescale for the Type Ia SN enrichment is the maximum in the Type Ia SN rate (Matteucci & Recchi 2001)

It depends on the star formation history of a specific galaxy, IMF and stellar lifetimes

Typical timescales for SNIa

In ellipticals and bulges the timescale for the maximum enrichment from Type Ia SNe is 0.3-0.5 GyrIn the solar vicinity there is a first peak at 1 Gyr, then it decreases slightly (gap in the SF) and increases again till 3 Gyr In irregulars the peak is for a time > 4 Gyr

Time-delay model in different galaxies

Interpretation of time-delay model

Galaxies with intense SF (ellipticals and bulges) show overabundance of alpha-elements for a large [Fe/H] rangeGalaxies with slow SF (irregulars) show instead low [alpha/Fe] ratios at low [Fe/H]The SFR determines the shape of the [alpha/Fe] vs. [Fe/H] relations

Identifying high-z objects

Lyman-break galaxy cB58, data from Pettini et al. 2002

The model predictions are for an elliptical galaxy of 10^(10) Msun (Matteucci & Pipino 2002)

Dating high-z objects

The Lyman-break galaxy cB58

Predicted abundance ratios versus redshift

The estimated age is 35 Myr

Conclusions on high-z objects

Comparison between data and abundance ratios of high-z objects suggests:DLA are probably dwarf irregulars or at most external parts of disksLyman-break galaxies are probably small ellipticals in the phase of galactic wind

How do dSphs 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 SFObservationally, 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)

Chemical Evolution of Dwarf Spheroidals

Lanfranchi & Matteucci (2003, 2004) proposed a model which assumes the SF as derived by the CMDsInitial baryonic masses 5x10^(8)MsunA strong galactic wind occurs when the gas thermal energy equates the gas potential energy. DM ten times LM but diffuse (M/L today of the order of 100)The wind rate is assumed to be several times the SFR

Standard Model of LM03

LM03 computed a standard models for dwarf spheroidalsThey assumed 1 long star formation episode (8 Gyr), a low star formation efficiency <1 Gyr^(-1)They assumed that galactic winds are triggered by SN explosions at rates > 5 times the SFR . The final mass is 10^(7)MsunThe IMF is that of Salpeter (1955)

Galactic winds

LM03 included the energetics from SNe and stellar winds to study the occurrence of galactic winds, the condition for the wind being:

Dark matter halos 10 times more massive than the initial luminous mass (5x10^(8) Msun) but not very concentrated (see later)

The binding energy of gas

The binding energy of gas

Binding energy of gas

S is the ratio between the effective radius of the galaxy and the radius of the dark matter core

We assume S=0.10 in dSphs

DM in Dwarf Spheroidals

Mass to light ratios vs. Galaxy absolute V magnitude (Gilmore et al. 2006)The solid curve shows the relation expected if all the dSphs contain about 4x10^(7) Msun of DM interior to their stellar distributionsNo galaxy has a DM halo < 5x10^(7)Msun

DM in dSphs

Mass to light ratios in dSphs from Mateo et al. (1998)In the bottom panel the visual absolute magnitude has been corrected for stellar evolution effectsThe Sgr point is an upper limit

Galactic Winds

The energy feedback from SNe and stellar winds in LM03 is: SNe II inject 0.03 Eo (Eo is the initial blast wave energy of 10^(51) erg )SNe Ia inject Eo since they explode when the gas is already hot and with low density (Recchi et al. 2001)Stellar winds inject 0.03 Ew (Ew is 10^(49) erg)

Gas Infall and Galaxy Formation

LM03 assumed that each galaxy forms by infall of gas of primordial chemical composition

The formation occurs on a short timescale of 0.5 Gyr

Standard Model of LM03

Standard Model: SF lasts for 8 Gyr, strong wind removes all the gasDifferent SF eff. and wind eff. are tested, from 0.005 to 5 Gyr^(-1) for SF and from (6 to 15) xSF for the winds

Abundance patterns

It is evident that the [alpha/Fe] ratios in dSphs show a steeper decline with [Fe/H] than in the stars in the Milky Way

This is the effect of the time-delay model, namely of a low SF efficiency coupled with a strong galactic wind

After the wind SF continues for a while

Individual galaxies

Then LM03,04 computed the evolution of 6 dSphs: Carina, Sextan, Draco, Sculptor, Sagittarius and Ursa Minor

They assumed the SF histories as measured by the Color-Magnitude diagrams (Mateo, 1998;Dolphin 2002; Hernandez et al. 2000; Rizzi et al. 2003)

Star Formation Historiesin LM03

SF histories of dSphs (Mateo et al. 1998)

Individual galaxies

Dwarf Spheroidals : Carina

Model Lanfranchi & Matteucci (04,06)SF history from Rizzi et al. 03. Four bursts of 2 Gyr, SF efficiency 0.15 Gyr^(-1) < 1- 2 Gyr^(-1) (S.N.), wind=7xSFRSalpeter IMF

Predicted C and N in Carina

Predicted evolution of C and N for Carina’s best model

The continuous line is for secondary N in massive stars

The dashed line assumes primary N from massive stars

Metallicity distribution in Carina

Data from Koch et al. (2005)

Best model from Lanfranchi & al. (2006)

This model well reproduces also the [alpha/Fe] ratios in Carina

Dwarf Spheroidals: Draco

Model and data for Draco

SF history, 1 burst of 4 Gyr, SF efficiency of 0.03 Gyr^(-1)

Wind=6xSFR

Salpeter IMF

Draco’s metallicity distribution

Predicted metallicity distribution for Draco compared with the predicted metallicity distribution for the Solar Vicinity

Dwarf Spheroidals: Sextans

Best Model: 1 burst of 8 Gyr

SF efficiency 0.08 Gyr^(-1)

Wind=9xSFR

Salpeter IMF

Sextans: metallicity distribution

Predicted metallicity distribution for Sextans by LM04

The predicted G-dwarf metallicity distribution for Solar Vicinity stars is shown for comparison

Dwarf Spheroidals: Ursa Minor

Best Model: 1 burst of 3 Gyr

SF efficiency 0.2 Gyr^(-1)

Wind=10xSFR

Salpeter IMF

Ursa Minor’s metallicity distribution

Predicted metallicity distribution for Ursa Minor by LM04

The predicted G-dwarf metallicity distribution for the solar vicinity is shown for comparison

Dwarf spheroidals: Sagittarius

Best model:one long episode of SF of duration 13 Gyr (Dolphin et al 2002)

SF eff. Like the S.N., but very strong wind 9XSFR

Metallicity distribution in Sagittarius

Predicted metallicity distribution by LM04 for Sagittarius: continuous line (Salpeter IMF), dashed line (Scalo IMF)

The predicted G-dwarf metallicity distribution for the solar vicinity is shown by the dotted line

Dwarf Spheroidals: 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

Sculptor’s metallicity distribution

Predicted metallicity distribution in Sculptor (LM04)

The predicted G-dwarf metallicity distribution for the solar vicinity is shown for comparison

s- and r- process elements in dSphs

Lanfranchi et al. 2006 adopted the nucleosynthesis prescriptions for the s- and r- process elements as in the S.N.They calculated the evolution of the [s/Fe] and [r/Fe] ratios in dSphsThey predicted that s-process elements, which are produced on long timescales are higher for the same [Fe/H] in dSphs

Model and data for Carina

Model and data for Draco

Model and data for Sextans

Model and data for Sculptor

Model and data for Sagittarius

Sagittarius: more data

Best model is continuous line. Dotted lines are different SF efficienciesDashed line is the best model with no windThe strong wind compensate the high SF efficiencyData from Bonifacio et al. 02,04 & Monaco et al. 05 (open squares)

C and N in Sagittarius: predictions

Other Models for dSphs

Carigi, Hernandez & Gilmore (2002) computed models for 4 dSphs by assuming SF histories derived by Hernandez et al. (2000)

They assumed gas infall and computed the gas thermal energy to study galactic winds

They assumed a Kroupa et al.(1993) IMF

Carigi et al. (2002)

They assumed only a sudden wind which devoids the galaxy from gas instantaneously

They predicted a too high metallicity for dSphs and not the correct slope for [alpha/ Fe] ratios

Carigi et al’s predictions for Ursa Minor

Model of Ikuta & Arimoto (2002)

They adopted a closed model (no infall, no outflow)

They suggested a very low SFR such as that of LM03, 04

They had to invoke external mechanisms to stop the SF

They assumed different IMFs

Ikuta & Arimoto (2002)

Model of Fenner et al. 2006

Very similar to the model of LM03, 04 with galactic winds for Sculptor

They suggest 0.05 Gyr^(-1) as SF efficiency

Their galactic wind is not as strong as the winds of LM03, 04

They conclude that chemical evolution in dSphs is inconsistent with SF being truncated after reionization epoch (z =8)

Comparison between dSphs and MW

Blue line and blue data refer to Sculptor

Red line and red data refer to the Milky Way

The effect of the time-delay model is to shift towards left the model for Sculptor with a lower SF efficiency than in the MW

Comparison dSph and MW

Eu/Fe in Sculptor and the MW

Model and data for Sculptor are in blue

Model and data for the MW are in red

Conclusions on dSphs

By comparing the [alpha/Fe] ratios in the MW and dSphs one concludes that they had different SF histories

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

Very good agreement both for [alpha/Fe] and [s/Fe] and [r/Fe] ratios is obtained if a less efficient SF than the S.N. one and a strong wind are adopted

It is unlikely that the dSphs are the building blocks of the MW

Interactions between the MW and its satellites are not excluded but they must have occurred after the bulk of stars of dSphs was formed

Other spirals

Results for M101 (Chiappini et al. 03)

Results for M101

Properties of spirals (Boissier et al. 01)

Conclusions on Spirals

[SII] red, [OIII] green, [OI] blue N132D in LMCoxygen rich SN remnant

SN 1998dh How to search

Compare images taken at different epochs

• few days < time interval < 1-2 month

• 14 < limiting magnitude < 24

• 0.01 < target redshift < 1

• 5 arcmin < field of view < 1 deg

• B-V < band < R-I

SN search

target reference

-SN 2000fctype Ia z = 0.42 V=22.4IAUC7537

difference

=

SN distribution in galactic coordinates

Madau, Della Valle & Panagia 1998 On the evolution of the cosmic supernova rate

Sadat et al. 1998 A&A 331, L69 Cosmic star formation and Type Ia/II supernova rates at high Z

Yungelson & Livio 2000 ApJ 528, 108 Supernova Rates: A Cosmic History

Kobayashi et al. 2000 ApJ 539, 26 The History of the Cosmic Supernova Rate Derived from the Evolution of the Host Galaxies

Sullivan et al. 2000 MNRAS 319, 549 A strategy for finding gravitationally lensed distant supernovae

Dahlèn & Fransson 1999 A&A 350, 349 Rates and redshift distributions of high-z supernovae

Calura & Matteucci 2003 ApJ 596, 734

SN rate with redshift

τ =3Gy

1Gy

0.3Gy

Madau, Della Valle & Panagia 1998 MNRAS 297, L17

Zampieri et al. (2003) MNRAS 338, 711

NS BH

GRBs

Astrophysics: massive star evolution