Simulating the Milky Way formation

Simulating the Milky Way formation

- comparing models with real data -

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/

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 T_vir < 10⁴K  H₂-cooling

t_cool << t_ff H₂-cooling

T_c ~ 200K, n_c ~10⁴cm⁻³ M_clump ≈ M_J ≈ 700 M_

M_accr ≈ T_c^3/2

m_* > 10 M_

τ_lifc ≈ few Myr Feedback processes:

LW photons  H₂ dissociation Ionizing photons  H_II regions

Metal production/dispersion driven by SN explosions

Low binding energy:

gas/metals ejection

The minimum halo mass able to form stars increases  M_sf(z)

The metallicity Z of the ISM and IGM

increases

Subsequent generations

M > M_sf (z) ?_# ^YES# Z >Z_cr=10^−5±1 Z_?_#

YES_# NO_#

NO_#

dark halo no stars

Different evolution, photon production, metal enrichment,

SN energy

M_clump ≤ M_

m_*=(0.1-100) M_ m_* > 10 M_

M_clump≈ 700M_

PopIII vs PopII star-formation

Tornatore+2007

PopIII stars (Z < Z_cr) are very rare and they disappear at z ~ 2

Stellar lifetimes

z = 25 Age = 0.13 Gyr

τ = 13.5 Gyr

z = 6 Age ~ 1 Gyr τ = 12.7 Gyr

z = 2 Age ~ 3.3 Gyr

τ = 10.3 Gyr

Surviving stars

Initial Mass Function

ϕ(m_*) ~ m_*^−1+x exp(−m_cut/m_*) x = −1.35

m_cut = 0.35 M_

Looking for metal-poor stars

If the formation of “normal” low mass 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. 10¹⁰ M_

M_gas ≈ 10¹⁰ M_

M_disc ≈ 6. 10¹⁰ M_

M_halo ≈ 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

N_* = 2756 r < 20 kpc

HE1327-2326

HE0107-5240 HE0557-4840

Metallicity Distribution Function

Galactic halo stars

Beers&Christlieb2005

Caffau+11

N_* = 2756 r < 20 kpc

HE1327-2326 HE0107-5240 HE0557-4840

Metallicity Distribution Function

Galactic halo stars

Beers&Christlieb2005

Caffau+11

Log Z/Z_ Z_cr =10 ^−5±1Z_

Dwarf spheroidal galaxies

dSph galaxies satellites of the MW

kpc

kpc Galactic center

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

Outer halo

Metallicity-Luminosity relation

Kirby+08

Milky Way dwarf spheroidal satellites

Kirby+2008

Via Lactea simulation

Diemand+2007/2008

≈ 1,000,000,000 dark matter

particles

m_p= 4.100×10³M_

Aquarius simulation

Springel+2008

Increasing resolution

4,252,607,000 m_p = 1.712×10³ M_ 148,285,000

m_p = 4.911×10⁴ M_ 2,316,893

m_p = 3.143×10⁶ M_

Monte Carlo approach

MW

M_MW = 10¹² M_

Time

z = 0

Redshift

Comparison with N-body Binary scheme

€

ψ = ε

^M

t

€

dM_g

dt = −

ψ

dt + dM_inf

dt − dM_ej dt

€

dM

dt = − Z

ψ + dY

dt + Z

dM

dt − Z

dM

dt

Z wZ w

Z^ISM

Z^vir Z^vir

Physical prescriptions/free parameters

ε_w t_inf

Model calibration

Evoli&Ferrara2011

SFR ≈ 1.3 M_/yr M_* ≈ 6×10¹⁰ M_

M_g/M_* ≈ 0.1

68%

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:

Number of DM haloes

Madau+08

The 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. This is really a problem?

The SF efficiency of minihaloes

10⁵ 10⁴

10³

L_tot/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. The existence of the Caffau star implies Z_cr < 10 ⁻⁴ Z_

Salvadori+07

Second generation stars

Second generation stars are extremely rare. The expected number of second generation stars in the currently limited Galactic halo sample is < 1-2.

Salvadori+07

Z_cr = 10 ^{– 4} Z_ Z_cr = 10 ^{– 6} Z_ Z_cr = 0

2nd generation vs all generations

The most metal-deficient star

M ~ 0.7 M_ SDSS J102915+172927

Z = 5 × 10⁻⁵ Z_

Can we finally see the imprint of the first stars?

Caffau+11

Just a “common” metal-poor star

The chemical abundance patter of SDSS J102915+172927 is consistent with that of stars with − 4 ≤ [Fe/H] ≤ − 3  no characteristic features produced by massive first stars !

Not surprising: second generation stars are extremely rare !

This observation does not implies that the first stars were not massive

Cayrel+04 Mean [X/Mg] value for 35 stars with [Mg/H] < − 3

The most iron-poor stars

Second generation stars ?

1.  If the total metallicity reflects that of the ISM from which these stars form  Z_ISM > 10 ⁻³Z_ >Z_cr. 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  Z_ISM ≈ 10 ⁻⁵Z_ ≈ Z_cr .  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_

What we learnt?

•  Semi-analytical models are “cosmological bridges” that connect the physical processes acting at high-z with the Local observations.

•  They are powerful tools to investigate the feedback imprints left in the Local Universe and 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

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

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