The Secret Lives of Molecular Clouds Mark Krumholz Princeton University Hubble Fellows Symposium March , 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 ~ 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 H 2 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 H 2 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) H 2 fraction determined by dissociation equilibrium and radiative transfer Idealized problem: spherical cloud of radius R, density n, dust opacity  d, H 2 formation rate R, in radiation field with LW intensity  FUV, find fraction of mass in HI and H 2

Calculating Molecular Fractions Solution depends on  d = dust optical depth,  = normalized radiation intensity to density ratio Analytic approximate fit agrees well with numerical solution H 2 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 H 2 formation rate R both  metallicity     d  FUV / n R ~ 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 = 1000 t ff Depletion time as a function of  H2 for 2 local galaxies (left, Wong & Blitz 2002) and as a function of L HCN for a sample of local and z ~ 2 galaxies (below, Gao et al. 2007) t dep = 10 t ff t dep = 1000 t ff

Slow Star Formation Clouds convert ~few % of their mass to stars per t ff, 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. 2007Simulation 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  c s ( l / s ) 1/2 In average region, M  l 3  KE  l 4, PE  l 5  KE >> PE Hypothesis: SF only occurs in regions where PE ≥ KE and P th ≥ P ram Only overdense regions meet these conditions Required overdensity is given by J ≤ s, where J = c s [  / (G  ) ] 1/2 l l KE >> 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 t ff to get SFR Result: SFR ff ~ 1-5% for any turbulent, virialized object SFR ff   –0.68 M –0.32 J = s

Predicting the Kennicutt Law We don’t know t ff, 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 L CO  , but high n crit for HCN gives, L HCN   p, p  1.5 SFR = SFR ff (M / t ff )  SFR   1.5 Result: SFR  L CO 1.5, but SFR  L HCN 1.0

Model reproduces slope and normalization of observed correlations, predicts new ones (e.g. IR- HCO + ), and predicts upturn in IR-HCN at high L IR Line Emission Model vs. Data Circles: data Lines: 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 12 CO (Koda et al.) and visible ~10 5 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 ~ cm -2 GMCs all marginally bound, virial ratio ~1 Only exception: low metallicity GMCs in SMC cm –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: M gas, M *, R, dR/dt, 

Quasi-Equilibrium Clouds Clouds kept in approximate equilibrium, near observed values of , N H, t dep Sample of runs for M cl = 5 x 10 6 M  10 4 M  GMCs  = 2  = 0.5  vs. mass for GMCs, Heyer et al 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 10 5 M  % 1 x 10 6 M  % 5 x 10 6 M  %

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

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 t ff in clouds roughly constant –All GMCs have  ~100 M  pc -2 –Lifetimes are few t dyn GMC fraction determined by gas column density, H 2 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)