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) 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 M mol ~ 10 9 M  of gas in GMCs (Bronfman et al. 2000), with n ~ 100 H cm –3 (Solomon et al. 1987), free-fall time t ff ~ 4 Myr  This suggests a star formation rate ~ M mol / t ff ~ 250 M  / yr  Observed SFR is ~ 3 M  / yr (McKee & Williams 1997)  Numbers similar in nearby disks  The Milky Way contains M mol ~ 10 9 M  of gas in GMCs (Bronfman et al. 2000), with n ~ 100 H cm –3 (Solomon et al. 1987), free-fall time t ff ~ 4 Myr  This suggests a star formation rate ~ M mol / t ff ~ 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 ~ 10 4 H cm –3, t ff ~ 0.4 Myr, M mol ~ 2  10 9 M  (Downes & Solomon 1998)  Suggested SFR ~ M mol / t ff ~ 5000 M  / yr  Observed SFR is ~ 50 M  / yr (Downes & Solomon 1998) : still too small by a factor of ~100  Example: Arp 220  Measured properties: n ~ 10 4 H cm –3, t ff ~ 0.4 Myr, M mol ~ 2  10 9 M  (Downes & Solomon 1998)  Suggested SFR ~ M mol / t ff ~ 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  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  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)  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  Overdense regions can have PE(l ) ~ KE(l )  PE = KE implies J ≈ s, where  Overdense regions can have PE(l ) ~ KE(l )  PE = KE implies J ≈ s, where L L l l l l  Whole cloud: PE(L) ~ KE(L), (i.e.  vir ~ 1)  Linewidth-size relation:  = c s (l/ s ) 1/2  Whole cloud: PE(L) ~ KE(L), (i.e.  vir ~ 1)  Linewidth-size relation:  = c s (l/ s ) 1/2  In average region, PE(l)  l 5, KE(l)  l 4  most regions have KE(l) » PE(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 t ff  Feedback efficiency  ≈ 0.5 (Matzner & McKee 2000)  Result: an estimate  J ≈ s gives instability condition on density  Turbulent gas has lognormal density PDF  Gas above critical density collapses on time scale t ff  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  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: SFR ff ~ few % in turbulent, virialized objects at any density  Direct test: use surveys of IRDCs, HCN emission, etc. to compute  Turbulence model prediction: SFR ff ~ 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) ! 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 SFR ff in cluster-forming molecular clumps, M ~ 10 3 – 10 4 M   Bound cluster requires SFE > ~30% (Kroupa, Aarseth, & Hurley 2001)  Predict age spread is ~4 t cross, ~8 t ff  Model agrees with observed age spreads  Compute SFR ff in cluster-forming molecular clumps, M ~ 10 3 – 10 4 M   Bound cluster requires SFE > ~30% (Kroupa, Aarseth, & Hurley 2001)  Predict age spread is ~4 t cross, ~8 t ff  Model agrees with observed age spreads Stellar age distribution in IC 348, Palla & Stahler (2000) t cross ≈ 0.4 Myr

13. SF Law in Other Galaxies  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:  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: Theory (solid line, KM05), empirical fit (dashed line, Kennicutt 1998), and data (K1998) on galactic SFRs

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  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  Goal: model GMCs on large scales, including evolution of radius, velocity dispersion, and gas and stellar mass M g, M *, R, dR/dt,  M g, M *, R, dR/dt,   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  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 MassLifetimeSFEDestroyed By? 2  10 5 M  9.9 Myr (1.6 t dyn, 3.2 t ff ) 5.3% Unbinding and dissociation 1  10 6 M  20 Myr (2.2 t dyn, 4.4 t ff ) 5.4%Unbinding 5  10 6 M  43 Myr (3.2 t dyn, 6.4 t ff ) 8.2%Unbinding  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%  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  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  10 6 M  clouds, Krumholz, Matzner, & McKee 2005

19. Effect of Column Density  Varying N H : only N H ≈ 10 22 cm –2 stable  Lower N H  disruption; higher N H  collapse  Varying N H : only N H ≈ 10 22 cm –2 stable  Lower N H  disruption; higher N H  collapse GMC column density vs. time, Krumholz, Matzner, & McKee 2005 Explains observation that LG GMCs all have same column density! Observed GMC column density vs. radius in LG galaxies, Blitz et al. (2006) N H =10 22 cm –2

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  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!