1. 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

2. Hubble Fellowship Symposium, March 2013 2

3. 3 M31

4. Hubble Fellowship Symposium, March 2013 4 30 Doradus SF and Galaxy evolution strongly linked How to move forward without solving SF?

5. Hubble Fellowship Symposium, March 2013 5 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

6. Hubble Fellowship Symposium, March 2013 6 0 -2 -3 -4 strong correlation over orders of magnitude of ISM surface densities reasonably tight slope ~1, t dep ~ 2.3 Gyr deceptively simple: the more H 2 the more SF H 2 - SF relation: A simple “effective” model of SF in the local Universe ! Bigiel+11 In the local Universe

7. Hubble Fellowship Symposium, March 2013 7 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 H 2 - SF relationship indirectly? H 2 - SF relation:

8. Hubble Fellowship Symposium, March 2013 8 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

9. Hubble Fellowship Symposium, March 2013 9 Krumholz & Dekel 2012 Accretion gas. outflows Four components per halo DM halo (M halo ) exponential gas disk (M g ) stars (M star ) metals (M Z ) Molecular fraction a la Krumholz+09 Star formation A chosen SF law Feldmann MNRAS subm., see also Bouche+1, Accretion rates Mass evolution

10. Hubble Fellowship Symposium, March 2013 10 Star formation 1 observation-based, e.g. Bigiel+08,11 2 theory-based, e.g., Ostriker & Shetty 2011, Faucher- Giguere+2013 “linear” “quadrati c”

11. Hubble Fellowship Symposium, March 2013 11 Cosmic SFH for a linear H 2 - SF relation Behroozi+12 Bouwens+12 model predictions (limit M UV < -17.7) model predictions (arbitrarily faint) H 2 based SF cold gas based SF H 2 based SF cold gas based SF Feldmann (MNRAS subm.)

12. Hubble Fellowship Symposium, March 2013 12 Feldmann (MNRAS subm.) Cosmic SFH for a quadratic H 2 - SF relation

13. Hubble Fellowship Symposium, March 2013 13 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

14. Hubble Fellowship Symposium, March 2013 14 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: t acc ~2x10 8 yr z~5: t acc ~5x10 8 yr gas depletion time - depends on SF law!

15. Hubble Fellowship Symposium, March 2013 15 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+11 z~0.5-2.5: Magdis+12

16. Hubble Fellowship Symposium, March 2013 16 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

17. Hubble Fellowship Symposium, March 2013 17 Linear H 2 - SF relation in good agreement with observations cosmic SFH mass-metallicity relation gas-to-stellar mass ratios high z UV luminosity function,... Quadratic H 2 - SF relation in disagreement

18. Hubble Fellowship Symposium, March 2013 18 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 yield recycling fraction gas ejection fraction IGM metallicity ratio SFR / gas accretion rate Metallicity:

19. Hubble Fellowship Symposium, March 2013 19 Let, be small, and Linear Stability Analysis, i.e., galaxies should approach equilibrium metallicity

20. Hubble Fellowship Symposium, March 2013 20 Baryonic state of a galaxy ( Z, f g, f s ) then there is a (linearly) stable equilibrium that corresponds to a particular metallicity, gas fraction and stellar fraction of the galaxy. M g /M halo M s /M halo M Z /M g Given Feldmann (MNRAS subm.)

21. Hubble Fellowship Symposium, March 2013 21 fgfg Z, f s r~0r~0.1r~1 Ratio r determines the fundamental galaxy properties at any given time predicts strong correlations between Z, f g, and f s, and between Z, SFR, M s, i.e., fundamental mass-metallicity relation Evolution of a galaxy along 1-d ``world line’’ in the baryonic state space high z: t acc ≪ t dep low z: t acc ~ t dep

22. Hubble Fellowship Symposium, March 2013 22 Differs from “equilibrium” a la Dave et al. galaxies are in “equilibrium” at low z out of “equilibrium” at high z In this picture: However: no need for galaxies to have to be in equilibrium expect at high z: implies f g ~ 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

23. Hubble Fellowship Symposium, March 2013 23 Z eq, f g,eq, f s,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 Z eq, f g,eq, f s,eq ( accretion rate, adopted SF - gas relation ) baryonic physicsgravity

24. Hubble Fellowship Symposium, March 2013 24 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

25. Hubble Fellowship Symposium, March 2013 25 Thank you