Simulating the Milky Way
… in a cosmological context …
Mo, van den Bosch & White: Galaxy Formation & Evolution Andrea Ferrara’s Saas-Fe lectures:
Intro/Chapter 2 of my Phd Thesis: http://www.astro.rug.nl/~salvadori/thesis.pdf
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
M > Msf (z) ?#
YES# Z >Zcr=10!5±1 Z!?#
YES# NO# NO#
dark halo no stars
Different evolution, photon production, metal enrichment,
Mclump $ M!
m*=(0.1-100) M! m*=(30-300) M!
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
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?
Mbulge " 2. 1010 M!
Mgas " 1010 M!
Mdisc " 6. 1010 M!
Mhalo " 3. 109 M! Stellar halo
30 kpc 8 kpc Sun
The structure of the Milky Way
thick disk open clusters
bulge thick disk globulars
young halo globulars old halo globulars thin disk
Signs of metal enrichment
Milky Way stars
N* = 2756 r < 20 kpc
Metallicity Distribution Function
Galactic halo stars
Dwarf spheroidal galaxies
dSph galaxies satellites of the MW
kpc Galactic center
Total masses M < 109 M!. Gas-free systems. Old and metal poor stars
rvir = 258 kpc
See also next Eline’
Milky Way dwarf spheroidal satellites
Kirby+2008 See also next
Via Lactea simulation
! 1,000,000,000 dark matter
particles mp= 4.100"103M!
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 = "ZISM# +dY
dt + ZvirdMinf
dt " ZwdMej dt
ZISM Zvir MW
Physical prescriptions/free parameters
Evoli&Ferrara2011 SFR ! 1.3 M!/yr M* ! 6"1010 M!
Mg/M* ! 0.1 99%
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
Imprints of radiative feedback?
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!!