the chemical evolution of the galaxy and dwarf spheroidals of the
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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