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Lessons from cosmic Lessons from cosmic historyhistory
Star formation laws and their role in galaxy Star formation laws and their role in galaxy evolutionevolution
R. FeldmannUC Berkeleysee Feldmann 2013,
arXiv:1212.2223 1
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M31
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30 Doradus•SF and Galaxy evolution strongly
linked•How to move forward without
solving SF?
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Star formation “law” = empirical relation between SF and ISM
Abstracts from details of small scale SF physics & feedback
Essential ingredient in theoretical models of galaxy evolution!
Main applications:•use as “effective model of SF” on super-
GMC scales
•constrain small scale physics
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0
-1
-2
-3
-4
•strong correlation over orders of magnitude of ISM surface densities
• reasonably tight
•slope ~1, tdep ~ 2.3 Gyr
•deceptively simple: the more H2 the more SF
H2 - SF relation:
A simple “effective” model of SF in the local Universe !
Bigiel+11In the local Universe
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At high redshift (out to z~2)
•galaxies in the “main sequence” of SF follow a ~linear relation with a ~Gyr depletion time
• interacting/merging galaxies are offset
•potentially observational systematics
Genzel+2010
•SF tracers (IR cirrus)
•CO/H2 conversion factor
•quadratic relation?Determine H2 - SF relationship
indirectly?
H2 - SF relation:
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Part I. Testing different star formation laws
•linear vs quadratic law•cosmic SFH & evolution of global galaxy properties
Outline
Part 2. Re-Evaluating Galaxy Evolution
•the role of gas accretion, metal enrichment and outflows
•galaxy evolution as an equilibrium process
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Krumholz & Dekel 2012
Accretion
gas. outflows
Four components per halo
DM halo (Mhalo)exponential gas disk (Mg)
stars (Mstar)
metals (MZ)
Molecular fraction
a la Krumholz+09
Star formationA chosen SF
law
Feldmann MNRAS subm.,see also Bouche+1,
Accretion rates
Mass evolution
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Star formation
11 observation-based, e.g. Bigiel+08,11
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theory-based, e.g., Ostriker & Shetty 2011, Faucher-Giguere+2013
“linear”
“quadratic”
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Cosmic SFH for a linear H2 - SF relation
Behroozi+12
Bouwens+12
model predictions (limit MUV < -17.7)
model predictions (arbitrarily faint)
H2 based SF
cold gas based SF
H2 based SF
cold gas based SF
Feldmann (MNRAS subm.)
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Feldmann (MNRAS subm.)
Cosmic SFH for a quadratic H2 - SF relation
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from Bouwens et al. 2012
not dust corrected
The cosmic star formation rate density (SFRD)
•High z observations: SFR ≪ gas accretion rate onto halos
•Models: often SFR ~ gas accretion rate even at fairly high z
dust corrected
gas accretion
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Superlinear SF law in many models (exponent ~1.4 - 2)
•more SF in high density gas => short depletion time
•overall SFR of a galaxy dominated by high density regions
•SF can catch up with the gas accretion rate
Why do models often overpredict SFR?
Linear SF law with ≳ Gyr depletion time
•depletion time long compared with accretion time at high z
•SF cannot catch up with gas accretion rate at high z
•accretion time ~ dynamical time ~ fraction of Hubble time
z~10: tacc~2x108 yr z~5: tacc~5x108 yr
•gas depletion time - depends on SF law!
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• linear law in good agreement with observations at all z
•quadratic law underpredicts gas-to-stellar fractions at high z
Gas fractions
z=0: Saintonge+11z~0.5-2.5: Magdis+12
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• linear law in good agreement with observations at all z, except in low mass galaxies at low z
•“frozen” mass-metallicity relation above z~2 in the quadratic case
Metallicity
z~0: Tremonti+04, z~2-4: Maiolino+08
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•Linear H2 - SF relation in good agreement with observations
•cosmic SFH
•mass-metallicity relation
•gas-to-stellar mass ratios
•high z UV luminosity function, ...
•Quadratic H2 - SF relation in disagreement
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• inflow of low Z gas from IGM
•outflows of enriched gas from ISM
•enrichment of the ISM following SF
Under which circumstances does Z remain constant?
!
stellar yieldrecycling fraction
gas ejection fraction
IGM metallicityratio SFR / gas accretion rate
Metallicity:
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Let , be small, and
Linear Stability Analysis
• , i.e.,
•galaxies should approach equilibrium metallicity
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Baryonic state of a galaxy ( Z, fg, fs )
then there is a (linearly) stable equilibrium that corresponds to a particular metallicity, gas fraction and stellar fraction of the galaxy.
Mg/Mhalo Ms/MhaloMZ/Mg
Given
Feldmann (MNRAS subm.)
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fg
Z, fs
r~0r~0.1r~1
•Ratio r determines the fundamental galaxy properties at any given time
•predicts strong correlations between Z, fg, and fs, and between Z, SFR, Ms, i.e., fundamental mass-metallicity relation
•Evolution of a galaxy along 1-d ``world line’’ in the baryonic state space
high z: tacc ≪ tdep
low z: tacc ~ tdep
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Differs from “equilibrium” a la Dave et al.
•galaxies are in “equilibrium” at low z
•out of “equilibrium” at high zIn this picture:
However:•no need for galaxies to have to be in equilibrium
•expect at high z:
• implies fg ~ 0
e.g., Finlator & Dave 2008, Dutton et al. 2010, Bouche et al. 2010, Dave et al. 2012
inflow rate of gas = outflow rate of gas + star formation rate
“Equilibrium condition”better: steady state
!
~1
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Zeq, fg,eq, fs,eq depend on r
Galaxy evolution is a sequence of (quasi-)equilibria in the baryonic state space driven by the (gradually) changing cosmic accretion rate.
The fundamental role of the star formation law
• functional form of SF law => equilibrium properties of galaxies
•evolution caused by the modulation of the accretion rate
Zeq, fg,eq, fs,eq ( accretion rate, adopted SF - gas relation ) baryonic physicsgravity
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Conclusions
1.Galaxy evolution studies rely on SF relations as an “effective theory of SF”
2.Functional form debated (observational systematics)
3.Predictions based on a linear relation in agreement with observations
4.Evolution of many global galaxy properties determined by • functional form of the SF relation (baryonic physics)
• matter accretion rate (gravity)
1.Galaxy evolution ~ a succession of (quasi-)equilibria driven by changes in the cosmic accretion rate
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Thank you