Simulating the Milky Way

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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:

Intro/Chapter 2 of my Phd Thesis:

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


Subsequent generations

M > Msf (z) ?#

YES# Z >Zcr=10!5±1 Z!?#


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

Surviving stars


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


Freeman&Bland-Hawthorn 2002

Signs of metal enrichment

Milky Way stars


N* = 2756 r < 20 kpc


HE0107-5240 HE0557-4840

Metallicity Distribution Function

Galactic halo stars


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

rvir = 258 kpc

See also next Eline’

s lectures

Metallicity-Luminosity relation


Milky Way dwarf spheroidal satellites

Kirby+2008 See also next


s lectures

Via Lactea simulation


! 1,000,000,000 dark matter

particles mp= 4.100"103M!


Aquarius simulation


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


MMW = 1012 M!


z = 0


Comparison with N-body Binary scheme


" = #*Mg tff



dt = "#+dR dt +dMinf

dt "dMej




dt = "ZISM# +dY

dt + ZvirdMinf

dt " ZwdMej dt



envir onment


Physical prescriptions/free parameters

%w tinf

Model calibration

Evoli&Ferrara2011 SFR ! 1.3 M!/yr M* ! 6"1010 M!

Mg/M* ! 0.1 99%




99% 95%

Simplified case: only stars/gas no infall


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



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



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


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!



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


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!!




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