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:

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

t_cool << t_ff H2-cooling

Tc ~ 200K, nc ~10⁴cm^!3 M_clump " M_J " 700 M!

Maccr " Tc3/2 m_* " (30-300)M_!

#lifc " few Myr Feedback processes:

LW photons " H2 dissociation Ionizing photons " H_IIregions

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±1Z!?#

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

Surviving stars

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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

Z_cr =10 ^!5±1Z_!#

then the most metal-poor stars, Z ~ Z_cr , 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

M_bulge " 2. 10¹⁰M_!

M_gas " 10¹⁰M_!

M_disc " 6. 10¹⁰M_!

Mhalo " 3. 10⁹M! 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

HE1327-2326

HE0107-5240 HE0557-4840

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

rvir = 258 kpc

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"10³M_! 148,285,000

mp = 4.911"10⁴M_! 2,316,893

mp = 3.143"10⁶M_!

Monte Carlo approach

MW

MMW = 10¹² M!

Time

z = 0

Redshift

Comparison with N-body Binary scheme

!

" = #_*M_g t_ff

!

dMg

dt = "#+dR dt +dM_inf

dt "dMej

dt

!

dM_Z

dt = "Z^ISM# +dY

dt + Z^virdM_inf

dt " Z^wdM_ej dt

ZwZw

Z^ISM Z^vir MW

envir onment

Z^vir

Physical prescriptions/free parameters

%_w t_inf

Model calibration

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

M_g/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 L_tot/L!

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