Turbulence, Feedback, and Slow Star

Formation

Turbulence, Feedback, and Slow Star

FormationMark Krumholz

Princeton UniversityHubble Fellows Symposium,

April 21, 2006Collaborators:

Rob Crockett (Princeton), Tom Gardiner (Princeton), Chris Matzner (U. Toronto),

Chris McKee (UC Berkeley), Jim Stone (Princeton), and Jonathan Tan (U.

Florida)

Mark KrumholzPrinceton 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)

ObservationsObservations

Star Formation is Slow

(Zuckerman & Evans 1974; Zuckerman & Palmer 1974; Rownd & Young 1999; Wong & Blitz 2002)

Star Formation is Slow

(Zuckerman & Evans 1974; Zuckerman & Palmer 1974; Rownd & Young 1999; Wong & Blitz 2002)The Milky Way contains Mmol ~ 109

M 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

The Milky Way contains Mmol ~ 109 M 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

…even in starbursts…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

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

HST/NICMOS image of Arp 220, Thompson et al. 1997

Possible Explanations(Li, Mac Low, & Klessen 2005,

Tassis & Mouschovias 2004, Clark et al. 2005)

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)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

(Yet Another) Idea: Turbulence Driven by

Feedback

(Yet Another) Idea: Turbulence Driven by

Feedback

Step 1: Turbulence Regulates the SFR(Krumholz & McKee, 2005, ApJ, 630, 250)

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)

Collapsed mass vs. time in simulations of driven hydrodynamic turbulence, VBK (2003)

A Simple Model of Turbulent Regulation

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 LL

ll

ll

Whole cloud: PE(L) ~ KE(L), (i.e. vir ~ 1)

Linewidth-size relation: = cs (l/s)1/2

Whole cloud: PE(L) ~ KE(L), (i.e. vir ~ 1)

Linewidth-size relation: = cs (l/s)1/2

In average region, PE(l) l5, KE(l) l4 most regions have KE(l) » PE(l)

In average region, PE(l) l5, KE(l) l4 most regions have KE(l) » PE(l)

The Turbulent SFRThe 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

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

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Comparison to Milky Way

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

SFR in Dense Gas(Krumholz & Tan, 2006, submitted)

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

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)!Model correctly predicts slow SF in dense gas!Explains IR-HCN correlation (Gao & Solomon 2005)!

Age Spread in Rich Clusters

(Tan, Krumholz, & McKee, 2006, ApJL, 641, 121)

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

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

Stellar age distribution in IC 348, Palla & Stahler (2000)

Stellar age distribution in IC 348, Palla & Stahler (2000)

tcross ≈ 0.4 Myr

SF Law in Other Galaxies

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

Theory (solid line, KM05), empirical fit (dashed line, Kennicutt 1998), and data (K1998) on galactic SFRs

Step 2: Star Formation Regulates Turbulence

(Krumholz, Matzner, & McKee 2006, in prep)

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 teamHII region in 30 Doradus, MCELS team

A Semi-Analytic GMC Model

A Semi-Analytic GMC Model

Goal: model GMCs on large scales, including evolution of radius, velocity dispersion, and gas and stellar mass

Goal: model GMCs on large scales, including evolution of radius, velocity dispersion, and gas and stellar mass

Mg, M*, R, dR/dt, Mg, M*,

R, dR/dt,

Evolution eqns: non-equilibrium virial theorem and energy conservation

Evolution eqns: non-equilibrium virial theorem and energy conservation

Sources and SinksSources 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)

Simulation of MHD turbulence, Stone, Ostriker, & Gammie (1998)

When expansion velocity < , shell breaks up, energy goes into turbulent motions

When expansion velocity < , shell breaks up, energy goes into turbulent motions

Global ResultsGlobal ResultsMass Lifetime SFE Destroyed By?

2 105 M 9.9 Myr

(1.6 tdyn, 3.2 tff)5.3%

Unbinding and dissociation

1 106 M20 Myr

(2.2 tdyn, 4.4 tff)5.4% Unbinding

5 106 M43 Myr

(3.2 tdyn, 6.4 tff)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%

Driving Keeps Clouds Virial

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 5 106 M clouds, Krumholz, Matzner, & McKee 2005

vir and deplation time vs. time for 5 106 M clouds, Krumholz, Matzner, & McKee 2005

Effect of Column Density

Effect of Column Density Varying NH: only NH ≈

1022 cm–2 stable Lower NH disruption; higher NH collapse

Varying NH: only NH ≈ 1022 cm–2 stable

Lower NH disruption; higher NH collapse

GMC column density vs. time, Krumholz, Matzner, & McKee 2005

GMC column density vs. time, Krumholz, Matzner, & McKee 2005

Explains observation that LG GMCs all have same column density!

Explains observation that LG GMCs all have same column density!

Observed GMC column density vs. radius in LG galaxies, Blitz et al. (2006)

Observed GMC column density vs. radius in LG galaxies, Blitz et al. (2006)

N H=1

022 c

m–2

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In Progress: Radiation MHD SimulationsIn Progress: Radiation MHD Simulations

ConclusionsConclusions 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

Final caveat:

The larger our ignorance, the stronger

the magnetic field…

Final caveat:

The larger our ignorance, the stronger

the magnetic field…turbulence!turbulence!