Lessons from cosmic history

1. Lessons from cosmic history • Star formation laws and their role in galaxy evolution R. Feldmann UC Berkeley see Feldmann 2013, arXiv:1212.2223 1

3. M31

4. 30 Doradus • SF and Galaxy evolution strongly linked • How to move forward without solving SF?

5. Essential ingredient in theoretical models of galaxy evolution! Main applications: • use as “effective model of SF” on super-GMC scales • constrain small scale physics Abstracts from details of small scale SF physics & feedback Star formation “law” = empirical relation between SF and ISM

6. H2 - SF relation: 0 -1 -2 -3 -4 In the local Universe Bigiel+11 • 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 A simple “effective” model of SF in the local Universe !

7. H2 - SF relation: At high redshift (out to z~2) Genzel+2010 • galaxies in the “main sequence” of SF follow a ~linear relation with a ~Gyr depletion time • interacting/merging galaxies are offset • potentially observational systematics • SF tracers (IR cirrus) • CO/H2 conversion factor • quadratic relation? Determine H2 - SF relationship indirectly?

8. Outline Part I. Testing different star formation laws • linear vs quadratic law • cosmic SFH & evolution of global galaxy properties Part 2. Re-Evaluating Galaxy Evolution • the role of gas accretion, metal enrichment and outflows • galaxy evolution as an equilibrium process

9. Accretion Star formation Accretion rates A chosen SF law Molecular fraction gas. outflows a la Krumholz+09 Mass evolution Four components per halo DM halo (Mhalo) exponential gas disk (Mg) metals (MZ) stars (Mstar) Feldmann MNRAS subm.,see also Bouche+1, Krumholz & Dekel 2012

10. Star formation “linear” 1 observation-based, e.g. Bigiel+08,11 “quadratic” 2 theory-based, e.g., Ostriker & Shetty 2011, Faucher-Giguere+2013

11. Cosmic SFH for a linear H2 - SF relation Feldmann (MNRAS subm.) cold gas based SF model predictions (arbitrarily faint) Behroozi+12 H2 based SF Bouwens+12 cold gas based SF model predictions (limit MUV < -17.7) H2 based SF

12. Cosmic SFH for a quadratic H2 - SF relation Feldmann (MNRAS subm.)

13. The cosmic star formation rate density (SFRD) gas accretion dust corrected not dust corrected from Bouwens et al. 2012 • High z observations: SFR ≪ gas accretion rate onto halos • Models: often SFR ~ gas accretion rate even at fairly high z

14. accretion time ~ dynamical time ~ fraction of Hubble time Superlinear SF law in many models (exponent ~1.4 - 2) Linear SF law with ≳ Gyr depletion time • 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 • depletion time long compared with accretion time at high z • SF cannot catch up with gas accretion rate at high z z~10: tacc~2x108 yr z~5: tacc~5x108 yr Why do models often overpredict SFR? • gas depletion time - depends on SF law!

15. Gas fractions z=0: Saintonge+11 z~0.5-2.5: Magdis+12 • linear law in good agreement with observations at all z • quadratic law underpredicts gas-to-stellar fractions at high z

16. Metallicity z~0: Tremonti+04, z~2-4: Maiolino+08 • 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

17. 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

18. ! IGM metallicity stellar yield recycling fraction ratio SFR / gas accretion rate gas ejection fraction Under which circumstances does Z remain constant? • inflow of low Z gas from IGM • outflows of enriched gas from ISM • enrichment of the ISM following SF Metallicity:

19. Let , be small, and • , i.e., • galaxies should approach equilibrium metallicity Linear Stability Analysis

20. ( Z, fg, fs ) Baryonic state of a galaxy MZ/Mg Mg/Mhalo Ms/Mhalo Given then there is a (linearly) stable equilibrium that corresponds to a particular metallicity, gas fraction and stellar fraction of the galaxy. Feldmann (MNRAS subm.)

21. high z: tacc ≪ tdep fg r~0.1 r~0 r~1 low z: tacc ~ tdep Z, fs • 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

22. However: • no need for galaxies to have to be in equilibrium • expect at high z: • implies fg ~ 0 ! • galaxies are in “equilibrium” at low z • out of “equilibrium” at high z e.g., Finlator & Dave 2008, Dutton et al. 2010, Bouche et al. 2010, Dave et al. 2012 In this picture: “Equilibrium condition” better: steady state inflow rate of gas = outflow rate of gas + star formation rate ~1 Differs from “equilibrium” a la Dave et al.

23. 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 ) gravity baryonic physics The fundamental role of the star formation law 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.

24. Conclusions • Galaxy evolution studies rely on SF relations as an “effective theory of SF” • Functional form debated (observational systematics) • Predictions based on a linear relation in agreement with observations • Evolution of many global galaxy properties determined by • functional form of the SF relation (baryonic physics) • matter accretion rate (gravity) • Galaxy evolution ~ a succession of (quasi-)equilibria driven by changes in the cosmic accretion rate

25. Thank you