Turbulence, Feedback, and Slow Star Formation

1. Turbulence, Feedback, and Slow Star Formation Mark Krumholz Princeton University Hubble Fellows Symposium, April 21, 2006 Collaborators: Rob Crockett (Princeton), Tom Gardiner (Princeton), Chris Matzner (U. Toronto), Chris McKee (UC Berkeley), Jim Stone (Princeton), and Jonathan Tan (U. Florida)

2. Observations

3. Star Formation is Slow (Zuckerman & Evans 1974; Zuckerman & Palmer 1974; Rownd & Young 1999; Wong & Blitz 2002) • The Milky Way contains Mmol ~ 109M of gas in GMCs (Bronfman et al. 2000), with n ~ 100 H cm–3(Solomon et al. 1987), free-fall time tff ~ 4 Myr • This suggests a star formation rate ~ Mmol / tff ~ 250 M / yr • Observed SFR is ~ 3 M / yr(McKee & Williams 1997) • Numbers similar in nearby disks

4. …even in starbursts • Example: Arp 220 • Measured properties: n ~ 104 H cm–3, tff ~ 0.4 Myr, Mmol ~ 2  109 M(Downes & Solomon 1998) • Suggested SFR ~ Mmol / tff ~ 5000 M / yr • Observed SFR is ~ 50 M / yr(Downes & Solomon 1998): still too small by a factor of ~100 HST/NICMOS image of Arp 220, Thompson et al. 1997

5. Possible Explanations(Li, Mac Low, & Klessen 2005, Tassis & Mouschovias 2004, Clark et al. 2005) • Disk gravitational instability • Explains SF edges • Fails for dense gas • Magnetic fields • Definitely present • Fields may not be strong enough • Unbound GMCs Simulation from Li, Mac Low & Klessen (2005) • Works if GMCs unbound, but observed vir~1 • Fails for dense gas

6. (Yet Another) Idea: Turbulence Driven by Feedback

7. Step 1: Turbulence Regulates the SFR(Krumholz & McKee, 2005, ApJ, 630, 250) • Star-forming clouds turbulent, M ~ 25 – 250 • Only ~1% of GMC mass is in “cores” (Motte, André, & Neri 1998) • Simulations show strong turbulence inhibits collapse (e.g. Vazquez-Semadeni, Ballesteros-Paredes, & Klessen 2003, 2005) Collapsed mass vs. time in simulations of driven hydrodynamic turbulence, VBK (2003)

8. A Simple Model of Turbulent Regulation • Whole cloud: PE(L) ~ KE(L), (i.e. vir ~ 1) • Linewidth-size relation:  = cs (l/s)1/2 • Overdense regions can have PE(l ) ~ KE(l ) • PE = KE implies J ≈ s, where • In average region, PE(l)  l5, KE(l)  l4  most regions have KE(l) » PE(l) l l L

9. The Turbulent SFR • J ≈ s gives instability condition on density • Turbulent gas has lognormal density PDF • Gas above critical density collapses on time scale tff • Feedback efficiency  ≈ 0.5 (Matzner & McKee 2000) • Result: an estimate

10. Comparison to Milky Way • For MW GMCs, observations give constant column density, linewidth-size relation, virial parameter(Solomon et al. 1987; Williams & McKee 1997) • Integrate over GMC distribution to get SFR: • Observed SFR ~ 3 M / yr: good agreement! • Direct test: repeat calculation for M33, M64, LMC using PdBI, CARMA, SMA, ALMA

11. SFR in Dense Gas(Krumholz & Tan, 2006, submitted) • Turbulence model prediction: SFRff ~ few % in turbulent, virialized objects at any density • Direct test: use surveys of IRDCs, HCN emission, etc. to compute Model correctly predicts slow SF in dense gas! Explains IR-HCN correlation (Gao & Solomon 2005)!

12. Age Spread in Rich Clusters(Tan, Krumholz, & McKee, 2006, ApJL, 641, 121) • Compute SFRff in cluster-forming molecular clumps, M ~ 103 – 104 M • Bound cluster requires SFE > ~30% (Kroupa, Aarseth, & Hurley 2001) • Predict age spread is ~4 tcross, ~8 tff • Model agrees with observed age spreads tcross ≈ 0.4 Myr Stellar age distribution in IC 348, Palla & Stahler (2000)

13. SF Law in Other Galaxies Theory (solid line, KM05), empirical fit (dashed line, Kennicutt 1998), and data (K1998) on galactic SFRs • For other galaxies, GMCs not directly observable • Estimate GMC properties based on (1) Toomre stability of disk, (2) virial balance in GMCs • Result is SF law in terms of observables:

14. Step 2: Star Formation Regulates Turbulence(Krumholz, Matzner, & McKee 2006, in prep) • Observed GMCs have vir ~ 1 • Simulations show turbulence decays in ~1 crossing time (Stone, Ostriker, & Gammie 1998; Mac Low et al. 1998) • Need driving to maintain vir ~ 1 • Hypothesis: driving is SF feedback HII region in 30 Doradus, MCELS team

15. A Semi-Analytic GMC Model Mg, M*, R, dR/dt, • Goal: model GMCs on large scales, including evolution of radius, velocity dispersion, and gas and stellar mass • Evolution eqns: non-equilibrium virial theorem and energy conservation

16. Sources and Sinks • Sink: radiation from isothermal shocks (Stone, Ostriker, & Gammie 1998) • Dominant source is HII regions (Matzner 2002), which drive expanding shells • Use self-similar HII region model Simulation of MHD turbulence, Stone, Ostriker, & Gammie (1998) • When expansion velocity < , shell breaks up, energy goes into turbulent motions

17. Global Results • Large clouds quasi-stable, live 20-40 Myr: agrees with observed 27 Myr lifetime of LMC GMCs! (Blitz et al. 2006) • HII regions unbind most clouds • Lifetime SFE ~5 – 10%

18. Driving Keeps Clouds Virial • Lifetime-averaged vir = 1.5 - 2.2; agrees with observations • Virialization lasts for several crossing times, many free-fall times • Constant vir  roughly constant star formation rate vir and deplation time vs. time for 5  106 M clouds, Krumholz, Matzner, & McKee 2005

19. Effect of Column Density • Varying NH: only NH ≈ 1022 cm–2 stable • Lower NH  disruption; higher NH  collapse Observed GMC column density vs. radius in LG galaxies, Blitz et al. (2006) GMC column density vs. time, Krumholz, Matzner, & McKee 2005 NH=1022 cm–2 Explains observation that LG GMCs all have same column density!

20. In Progress: Radiation MHD Simulations

21. Conclusions • Turbulent regulation can explain the low rate of star formation, and SF feedback can explain the turbulence: feedback-driven turbulence regulates star formation • This model explains / predicts: • Low SFR even in very dense gas • Star cluster age spreads • GMC lifetimes and column densities • Rate of star formation in MW • Kennicutt Law • Extragalactic IR-HCN correlation

22. Final caveat:The larger our ignorance, the stronger the magnetic field… turbulence!