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Simulating the Milky Way … in a cosmological context …

Useful books/notes:

Mo, van den Bosch & White: Galaxy Formation & Evolution

Andrea Ferrara’s Saas-Fe lectures: http://www.sns.it/en/scienze/menunews/docentiscienze/ferraraandrea/lectures/

Intro/Chapter 2 of my Phd Thesis: http://www.astro.rug.nl/~salvadori/thesis.pdf

Stefania Salvadori

First stars/galaxies: simple sketch

M ~ 106M! @ z ~ 25 Tvir < 104K " H2-cooling

tcool << tff

H2-cooling Tc ~ 200K, nc ~104cm!3

Mclump " MJ " 700 M!

Maccr " Tc3/2

m* " (30-300)M!

#lifc " few Myr

Feedback processes:

LW photons " H2 dissociation Ionizing photons " HII regions

Metal production/dispersion driven by SN explosions

Low binding energy: gas/metals ejection

The minimum halo mass able to form stars increases " Msf(z)

The metallicity Z of the ISM and IGM

increases

Subsequent generations

M > Msf (z) ? #

YES# Z >Zcr=10!5±1 Z!?#

YES#NO #NO #

dark halo no stars

Different evolution, photon production, metal enrichment,

SN energy

Mclump $ M!

m*=(0.1-100) M! m*=(30-300) M!

Mclump" 700M!

Stellar lifetimes

z = 25

Age = 0.13 Gyr

# = 13.5 Gyr

z = 10

Age ~ 0.5 Gyr

# = 13.2 Gyr

z = 6

Age ~ 1 Gyr

# = 12.7 Gyr

Surv

ivin

g st

ars

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Initial Mass Function

!(m*) ~ m*!1+x exp(!mcut/m*)

x = !1.35

mcut = 0.35 M!

Looking for metal-poor stars

If the formation of low mass “normal” popII stars is triggered by the presence of metals and dust exceeding

Zcr =10 !5±1Z!#

then the most metal-poor stars, Z ~ Zcr , that survive until today may represent the oldest stellar relics of the early Universe.

Where can we observe the most metal-poor stars?

thick disk

Mbulge " 2. 1010 M!

Mgas " 1010 M!

Mdisc " 6. 1010 M!

Mhalo " 3. 109 M! Stellar halo

thin disk

30 kpc

8 kpc Sun

The structure of the Milky Way

4 kpc

thick disk open clusters

bulge thick disk globulars

young halo globulars

old halo globulars

thin disk thick disk

halo

Freeman&Bland-Hawthorn 2002

Signs of metal enrichment Milky Way stars

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N* = 2756 r < 20 kpc

HE1

327-

2326

HE0

107-

5240

HE0

557-

4840

Metallicity Distribution Function Galactic halo stars

Beers&Christlieb2005

Dwarf spheroidal galaxies

dSph galaxies satellites of the MW

kpc kpc

kpc Galactic center

Total masses M < 109 M!. Gas-free systems. Old and metal poor stars

Outer halo

r vir = 25

8 kpc

See also next Eline’s

lectures

Metallicity-Luminosity relation

Kirby+08

Milky Way dwarf spheroidal satellites

Kirby+2008

See also next Eline’s

lectures

Via Lactea simulation

Diemand+2007/2008

! 1,000,000,000 dark matter

particles mp= 4.100"103M!

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Aquarius simulation Springel+2008

Increasing resolution

4,252,607,000 mp = 1.712"103 M!

148,285,000 mp = 4.911"104 M!

2,316,893 mp = 3.143"106 M!

Monte Carlo approach

MW

MMW = 1012 M!

Tim

e

z = 0 R

edsh

ift

Comparison with N-body Binary scheme

!

" = #*Mg

t ff

!

dMg

dt= "# +

dRdt

+dM inf

dt"dMej

dt

!

dMZ

dt= "ZISM# +

dYdt

+ Zvir dM inf

dt" Zw dMej

dt

Zw

Zw

ZISM Zvir

MW en

viron

ment

Zvir

Physical prescriptions/free parameters

%w tinf

Model calibration

Evoli&Ferrara2011

SFR ! 1.3 M!/yr M* ! 6"1010 M!

Mg/M* ! 0.1

99%

95%

68%

99%

99%

95

%

Simplified case: only stars/gas no infall

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The free parameters

General rule for semi-analytical models: the higher is the number of equations (physics) involved

the higher is the number of free parameters the higher is the number of observational constraints needed

Example: if we also want to follow the evolution of metals along the build-up of the Milky Way we have to reproduce

the final metallicity of the gas/stars (~ Z!) along with the observed Z-range of Galactic halo stars

Constraining high-z properties

Once fixed the main free parameters (SF/wind efficiency) we can investigate (and then constrain?) the properties of the first stars/galaxies

and/or the efficiency of feedback processes acting at high-redshifts

•  What is the efficiency of star formation in H2-cooling haloes? •  Are H2-cooling haloes a “suicide” population?

•  What is the evolution of the minimum halo mass to form stars? •  What is the value of the critical metallicity?

•  What is the efficiency of mechanical feedback at high-z?

Questions we can try to address:

The impact of feedback processes

Number of DM haloes

Madau+08

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Missing satellites problem

If all the haloes are able to form stars with a fixed efficiency "  The number of predicted luminous satellites exceeds

by several orders of magnitude the one observed.

The higher is the resolution of the simulation the higher is the expected number of luminous satellites at z = 0

Radiative feedback processes are expected to gradually reduce the SF in minihaloes and increase the minimum mass of haloes that are able to form stars. Can we solve the problem?

The SF efficiency of minihaloes

105 104 103

Ltot/L!

Observations

Simulations: different SF efficiencies

Madau+08

The SF efficiency of mini-haloes has to decrease at decreasing mass in order to reproduce the observed

luminosity function of dwarf satellites

Imprints of radiative feedback?

Munoz+09

105 104 103 106 107 108

Ltot/L!

The number of luminous satellite galaxies predicted at z = 0 strongly depends on the

evolution of Msf(z)

Imprints of chemical feedback?

Varying the critical metallicity

The predicted Metallicity Distribution Function of Galactic halo stars strongly depends on the assumed critical metallicity. We can constrain Zcr " 10!4Z!

Salvadori+07

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The most iron-poor stars Oldest stellar relics?

1.  If the total metallicity reflects that of the ISM from which these stars form " ZISM > 10 !3Z!

>Zcr. What kind of stars are responsible for such a chemical enrichment?

2. If the iron abundance reflects the metallicity of the ISM from which they form " ZISM " 10 !5Z! " Zcr . " dust is needed.

But CNO have to be accreted from a companion star

Caveat: for these stars [Fe/H] is not a good metallicity indicator! Even if [Fe/H] < !4.8 the total metallicity is Z > 10 !3Z!

Observed chemical abundances

Iwamoto+05

We don’t see the imprint of pair instability supernovae m*=(140-260)M!

What we learnt? •  Semi-analytical models are “cosmological bridges” that connect the

physical processes acting at high-z with the Local observations.

•  They are used to investigate the feedback imprints left in the Local Universe and to constrain the properties of the first stars/galaxies.

•  If you want to build up a good semi-analytical model you have to compare your results with most of the available observations

•  The have several free parameters (physical unknowns) that are fixed in order to reproduce the observed properties of the analyzed system.

•  Because of the amount of unknown physical processes (assumption made) different studies may provide different results.

•  There are still many puzzling questions about the first cosmic objects that can be solved using these methods and the new observations!!