The Secret Lives ofMolecular Clouds

Mark Krumholz

Princeton University

Hubble Fellows Symposium

March 10 - 12, 2008

Collaborators:

Tom Gardiner (Cray Research)

Mordecai Mac Low (AMNH)

Chris Matzner (U. Toronto)

Chris McKee (UC Berkeley)

Jim Stone (Princeton)

Jonathan Tan (U. Florida)

Todd Thompson (Ohio State)

Jason Tumlinson (Yale)

Outline: Secrets of the Clouds

• GMC Basics and Mysteries

• How Much Molecular Gas?: GMCs and Atomic Gas

• Why So Slow?: GMCs and the Star Formation Rate

• Why So Long?: GMC Lifetime and the GMC “Main Sequence”

• Conclusions and future work

Giant Molecular Cloud Basics• GMCs are the basic units of star formation• Typical mass ~104 - 107 M, size ~100 pc,

density ~100 cm-3, temperature ~10 K• In MW, GMCs make up ~1/4 of ISM mass• Difficult to study in MW due to distance

uncertainty, confusion• Only in the last few years have we been

able to see molecules in other galaxies at high resolution, or at high z

• Goal: understand this new data set

Cloud Secret 1: How Much?

NGC 0628 in HI (THINGS), CO (BIMA SONG + IRAM HERA), obscured SF (SINGS), revealed SF (GALEX NGS). Resolution is ~1 kpc. (Leroy et al. 2008)

GMCs and HI

• HI appears to saturate at 10 M pc-2; higher columns are all in molecular clouds

• Threshold constant across spirals; no obvious dependence on SFR, which is surprising

SFR surface density versus HI and H2 surface density in a summed sample over many spiral galaxies (Leroy et al. 2008)

Anatomy of An Atomic-Molecular Complex

• GMCs are part of atomic-molecular complexes

• Outer parts are dissociated by interstellar Lyman-Werner photons, so H2 only in center

• Goal: understand how the molecular fraction in galaxies, and the physics that controls it

Dissociation Balance in Atomic-Molecular Complexes

(Krumholz, McKee, & Tumlinson, 2008, in preparation)

• H2 fraction determined by dissociation equilibrium and radiative transfer

• Idealized problem: spherical cloud of radius R, density n, dust opacity d, H2 formation rate R, in radiation field with LW intensity FUV, find fraction of mass in HI and H2

Calculating Molecular Fractions• Solution depends on

d = dust optical depth, = normalized radiation intensity to density ratio

• Analytic approximate fit agrees well with numerical solution

H2 fraction as a function of dimensionless parameters d,

Application to Galaxies• CNM density n WNM pressure FUV,

with weak Z dependence (Wolfire et al. 2003)

• Dust opacity d and H2 formation rate R both metallicity

dFUV/ nR ~ 10 in all galaxies!

• Hydrostatic balance in atomic-molecular complexes requires complex ~ 3-4 x galaxy

d Z galaxy

• Use model to calculate HI vs. galaxy

Model Predictions

• Explains 10 M pc-2 HI limit from microphysics

• Weak metallicity scaling testable prediction

Cloud Secret 2: Why So Slow?

Cloud depletion times are >> free-fall times

– Clouds not in collapse– Either SFE is very low or

lifetime is very long

t dep =

10

t ff

t dep =

100

0 t ff

Depletion time as a function of H2 for 2 local galaxies (left, Wong & Blitz 2002) and as a function of LHCN for a sample of local and z ~ 2 galaxies (below, Gao et al. 2007)

t dep =

10

t ff

t dep =

100

0 t ff

Slow Star Formation

Clouds convert ~few % of their mass to stars per tff, regardless of density or environment (Tan,

Krumholz, & McKee 2006; Krumholz & Tan 2007)

A Potential Solution…

Because cloud is turbulent, most mass is in low density “envelope” that is not bound, rather than in bound “cores”. The result is a low SFR.

Cores in Pipe Nebula, Alves et al. 2007 Simulation of turbulent cloud, Li et al. 2004

The SFR from Turbulence• On large scales, GMCs have 1 (i.e. PE KE)

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

• In average region, M l3 KE l4, PE l5 KE >> PE

• Hypothesis: SF only occurs in regions where PE ≥ KE and Pth ≥ Pram

• Only overdense regions meet these conditions

• Required overdensity isgiven by J ≤ s, where J = cs

[ / (G) ]1/2

l

lKE >> PE

KE ≤ PE

Calculating the SFR

• Density PDF in turbulent clouds is lognormal; width set by M

• Integrate over region where J ≤ s, to get mass in “cores”, then divide by tff to get SFR

• Result:

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

SFRff ~ 1-5% for any turbulent, virialized object

SFRff 0.073 –0.68 M –0.32

J =

s

Predicting the Kennicutt Law

• We don’t know tff, M in GMCs in other galaxies

• Estimate by assuming – GMC mass ~ Jeans mass– GMCs are virialized– GMC internal pressure

balances weight of ISM

• Result: a Kennicutt law in terms of observables

Data and dashed line: Kennicutt (1998); solid line: this model

The HCN “Kennicutt Law”(Krumholz & Thompson 2007)

• Use non-LTE molecular excitation / escape probability code to get line emission from PDF

• Find LCO , but high ncrit for HCN gives, LHCN p, p 1.5

• SFR = SFRff (M / tff) SFR 1.5

• Result: SFR LCO1.5,

but SFR LHCN1.0

Model reproduces slope and normalization of observed correlations, predicts new ones (e.g. IR-HCO+), and predicts upturn in IR-HCN at high LIR

Line Emission Model vs. Data

Circles: dataLines: model

Mystery 3: Why So Long?• Measure association of

GMCs with star clusters of known ages to get lifetime of revealed cluster phase

• Use numbers in different phases to get total lifetime of ~30 Myr

• This is ~3 crossing times, ~5 free-fall times

GMC evolutionary sequence in the LMC (Blitz et al. 2007)

GMCs Locations

M51 seen in 12CO (Koda et al.) and visible

~105 M

GMCs far from arms imply there is a tail of GMCs with lifetimes >~ 50 Myr

Constant GMC Column Density and Virial Ratio

• Individual GMCs all have about the same column density: ~100 M pc-2 ~ 1022 cm-2

• GMCs all marginally bound, virial ratio ~1

• Only exception: low metallicity GMCs in SMC

1022 c

m–2

Explaining GMC Column Density and Lifetime

(Krumholz, Matzner, & McKee 2007)

• Model GMC mass, energy, momentum budgets

• Include feedback driving turbulence, mass loss

• Use 1D model– Bad: real GMCs not spheres– Good: can solve exact equations:

non-equilibrium virial, energy equations

Follow evolution of:Mgas, M*,

R, dR/dt,

Quasi-Equilibrium Clouds

Clouds kept in approximate equilibrium, near observed values of , NH, tdep

Sample of runs for Mcl = 5 x 106 M

104

M

GMCs

= 2

= 0.5

vs. mass for GMCs, Heyer et al. 200110

22 cm

–2

GMC mass vs. radius in the Local Group, Blitz et al. 2007

Final Results of GMS SAMs

• Large clouds live 20 – 40 Myr, in agreement with observations

• Clouds destroyed by unbinding by HII regions• Lifetime SFE ~ 5 – 10%

Mass Lifetime (Crossing Times)

Lifetime (Myr)

SFE

2 x 105 M 1.6 9.9 5.3%

1 x 106 M 2.2 20 5.4%

5 x 106 M 3.2 43 8.2%

MHD Simulation of HII Expansion(Krumholz, Stone, & Gardiner 2007; Krumholz & Stone 2008, in preparation)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Preliminary Simulation Results

HII regions expand fast but then stall due to magnetic and turbulent confinement GMC survival time may be longer than estimate

Conclusions and Future Work

Where We Are Now• Observations in many galaxies are revealing

the full life cycle of GMCs:– GMC mass fraction determined by gal; HI

saturates at ~10 M pc-2

– SFR per tff in clouds roughly constant– All GMCs have ~100 M pc-2

– Lifetimes are few tdyn

• GMC fraction determined by gas column density, H2 formation-dissociation balance

• SFR set by turbulence• Lifetime, set by energy balance

The Future: Spatially-Resolved Galaxy Models

• Location of GMC formation set by gravitational instability on galactic scales

• SF rate set on sub-GMC scales

• Need both scales to get rate and location of SF

• Idea: use GMC models as subgrid physics in

Simulation of atomic gas (blue) in a galaxy forming GMCs (yellow), Li, Mac Low, & Klessen, 2006

a galaxy-scale simulation, predict intensity and spatial distribution of SF tracers (e.g. 24 µm)