The Central Problem of Star Formation: Why So Slow?

Neal J. Evans II University of Texas at Austin

Korea Astronomy and Space Science Institute

The Basic Problem of Star Formation

§  It is slower than expected §  For Milky Way, Mmol = 1 x 109 Msun §  Typical tff = 3 x 106 yr (n ~ 100 cm–3) §  Simple estimate: SFR = 300 Msun/yr §  100 times average over last Gyr

§  Zuckerman & Palmer 1974, ARAA, 12, 279 §  Zuckerman & Evans 1974, ApJL, 192, L149

§  εff = SFR tff/Mcloud = tff/tdep ~ 0.01 §  Nearby clouds εff = 0.04

And Less Efficient ε = Μ*/(Μ*+Μcl)

§  Distribution of cloud masses §  dN/dlogM~ M–0.6 and Mu ~ 6 x 106 Msun

§  Distribution of young cluster masses §  dN/dlogM ~ M–1.0 and Mu ~ 6 x 104 Msun § Williams and McKee 97, Portegies Zwart

2010,…

§  Suggests ε = 0.01 at high end §  Nearby clouds ε = 0.05

Galaxy Scale: Extreme Diversity

log SFR

log Σ

(SFR

)

Kennicutt & Evans 2012

4

3

2

1

0

–1

–2

–3

–4

–4 –3 –2

0.1 kpc

1 kpc

10 kpc

–1 0 1 2 3–5

log

[ΣSF

R (M

Ī y

ear–1

kpc

–2)]

log [SFR (MĪ year–1)]

Galaxy typeSt

arbu

rst Normal/irregular

Blue compactInfrared-selected

Circumnuclear

MW

KennicuttFig09.pdf 1 5/2/12 12:01 PM

(R = 13.5 kpc)

Collapses to KS Relation Solid circles are disk-averaged normal spirals Open circles are central regions of normal disks Squares are circumnuclear starbursts ΣSFR = A Σgas

N N = 1.4±0.15

Kennicutt 1998, ARAA 36, 189

blue open: Low metals (<~1/3 solar), mostly dwarfs Blue line: slope of 1.4, not a fit Assumes one value of α(CO) for all.

Kennicutt & Evans 2012

The 2012 Version

log

[ΣSF

R (M

Ī y

ear–1

kpc

–2)]

log [Σgas (MĪ pc –2)]

3

10 3

LIGs/ULIGs LIR > 1011 LĪNormal spirals

Linear fit

N = 1.

4

10 2

10 1

10 0

10 –1107 108 109 1010 1011

2

1

0

–1

–2

–3

–40 1 2 3 4 5

SFR

(MĪ

yea

r–1)

Mdense (MĪ)

a

b

MW

Normal/irregularGalaxy type

Low surface brightness

Circumnuclear Infrared-selected

Metal-poorStar

burs

t

KennicuttFig11.pdf 1 5/2/12 12:03 PM

Inefficiency within galaxies

Bigiel et al. 2008

Threshold around 10 Msunpc–2 in total gas: transition from HI to H2 Linear above threshold Typical depletion time 1-2 Gyr Factor of 1000 slower than naïve prediction.

Log Σ (HI + H2)

Log Σ

(SFR

)

SFR in Starburst Galaxies

§  LIR correlates better with L(HCN)

§  “Efficiency” for dense gas constant and higher

Gao & Solomon (2004) ApJ 606, 271

Amount of dense molecular gas

Sta

r fo

rmat

ion

rate

Seems Universal

From talk by Yu Gao in 2017 (see Shimajiri et al. 2017)

Extends from MW dense clumps to high-z starbursts: Linear with standard deviation about half that for CO

Dense clumps In MW

M31/M33 clumps

M51 GMAs

Whole galaxies

High-z galaxies

Testing Star Formation Prescriptions

§  Use Star Formation “Efficiency” §  SFE = SFR/X §  Units of 1/Myr, inverse of depletion time §  A linear SFR law becomes flat in SFE §  Better measure of scatter §  What is the best predictor?

§  Mass of molecular gas §  Mass of molecular gas divided by free-fall time §  Mass of dense gas

Combine Studies

§  Nearby dark clouds (c2d, Gould Belt) § Dunham (29 clouds)

§  Galactic Plane Clouds § Vutisalchavakul (44 clouds)

§  Other galaxies §  Leroy (30 galaxies, CO) (~ 1 kpc res) § Chen (M51, CO, HCN) (~ 1 kpc res) §  Liu (115 spirals, 66 (U)LIRGS, CO, HCN)

Averages

§  Big picture §  Take mean and std deviation (in log) of all

the nearby clouds, all the GP clouds, and various galaxy studies

§  Plot SFE versus X

Star Formation Efficiency

N. Vutisalchavakul et al.

Nearby

GP Resolved galaxies

Galaxies

(U)LIRGS

αCO = 0.8

Efficiency per molecular gas varies by a factor of 40.

M/tff

<Log[εff]> = –1.80 +/– 0.50

SFE for Dense Gas

N. Vutisalchavakul et al.

Note: plotted on the same scale. Scatter is a factor of 4.

Independent of Scale

N. Vutisalchavakul et al.

pc

10 pc kpc 10 kpc

SFE for dense gas is remarkably constant from scales of pc to 10 kpc.

What is the Best Predictor?

§  Grand average of log(SFE) §  For Mcloud, std dev = 0.42

§  0.59 if use (U)LIRG α(CO) § Total range, factor of 40

§  For Mcloud/tff, std dev = 0.5 §  For Mdense, std dev = 0.19

§ Total range, factor of 4 §  Including center of M51

SFE for Dense Gas

N. Vutisalchavakul et al.

Center of M51

Similar effect seen in central molecular zone of MW. Kruijssen et al. (2014) suggest that threshold density there is >107 cm–3, rather than about 104 cm–3, as in other regions.

What about the other efficiency?

§  Mass spectrum of dense clumps §  dN/dlogM ~ M–1, like MF of clusters

§ Shirley et al. 2003 § <exp> = –1.05 +/–0.08 (Elia17, ~104 SF clumps)

§ Mu about 1 x 105 Msun § Shirley03, Svoboda16, Urquart18, Merello18, …

§  Ratios of stars/dense gas closer to unity §  Dense Clumps more plausible precursors

What do we mean by “dense”?

§  AV > 8 mag (nearby clouds) §  Clumps defined by mm/smm continuum

emission (Galactic Plane) §  Regions emitting HCN J = 1-0 line (exgal) §  Need cross-calibration! §  Look for second parameters

Summary So Far

§  Among empirical relations, SFR-Mdense works best

§  Centers of galaxies, other special regions need more parameters

§  Probably gas has to be still denser in regions of high turbulence

§  Need to calibrate tracers of dense gas

Let’s Re-examine Assumptions

§  The Fundamental Problem of Slow Star Formation arises from two assumptions: § Molecular clouds are gravitationally bound §  The relevant timescale is the free-fall time

Assumption 1

§  Molecular clouds are gravitationally bound § Assumed by most observers §  Theorists less devoted to this one

§  What is the actual evidence? §  Some Definitions

§ Molecular cloud defined by CO 1-0 emission §  Bound if αvir < 2 (Ekin < |Egrav|)

Does this look bound?

The Taurus Cloud : three colors for velocity components (Heyer & Dame, ARAA)

More like which of these?

Cirrus No precip.

Cumulonimbus Precipitates

A Proposal

Molecular “clouds” are unbound structures.

Observational Support

Galactic Radius

Median αvir

αvir

Miville-Deschenes et al. 2017; new catalog of 8107 clouds from decomposition of CO maps; recover 98% of CO emission

Theoretical Support “Low SFE requires initially unbound clouds even with radiative feedback.” R. Pudritz Based on simulations by Howard et al. (2016)

“MCs are continuously being formed and dispersed by the SN-driven turbulence… ... so they can hardly be considered as well-defined and long-lived isolated entities” Padoan et al. 2017

“Why are most molecular clouds not gravitationally bound?” Title of paper by Dobbs, Burkert, Pringle 2011

“The cloud must be unbound to get low εff” E. Ostriker

Model of ISM with SN-driven Turbulence

From Padoan et al. 2017 Models SN-driven turbulence and identifies “MC” by density threshold at 200 cm–3 (open blue) or 400 cm–3 (closed red).

The role of feedback is to keep most of the ISM, even “clouds” unbound.

Gets εff Close to Observations

Padoan et al. 2017

Red empty circles are model “MCs” defined by n > 400 cm–3 Blue closed are nearby clouds (corrected from figure in paper) Green shaded are CMZ clouds

= ε f

f

Dense Clumps are Clearly Bound

Clumps defined by smm continuum, HIGAL plus ATLASgal. Linewidths from NH3 Merello (2018)

Assumption 2

§  The free-fall time is the characteristic timescale for molecular cloud evolution §  If clouds are not bound, this is clearly not

true §  What is the actual evidence?

§  If true, Mcloud/tff should predict SFR § Requires factor of 50-100 fudge factor (εff) § Does not decrease dispersion

Is tff Predictive at cloud level?

§  Does SFR of a cloud depend on free-fall time of the cloud (tff based on mean ρ)?

No, correlation is not statistically significant (r = 0.34)

A Modest Suggestion

§  Suppose molecular clouds are not bound §  Just part of the ISM that becomes molecular for

a while §  Turbulence causes a small fraction (few percent)

to become bound dense clumps §  Virial Parameter may be the best predictor

§  The rest of the molecular gas rejoins the ISM flow

§  Galactic feedback keeps ISM stirred up, unbound (Padoan, Ostriker)

Benefits

§  The basic problem of slow star formation goes away (mostly…)

§  Low efficiency (M*/Mcloud) because §  Mdense/Mcloud is low §  0.21 for local (AV > 8/AV > 2) §  0.06-0.12 for Gal plane (SMM/13CO) §  And factor of two more mass below 13CO

detection threshold (Taurus, Pineda10) §  So say Mdense/Mcloud = 0.05

Mass-weighted virial parameters for 15 galaxies (J. Sun et al. 2018) on 120 pc scales. Most have distributions peaked between 1 and 3 (borderline) Antennae are low, M31, M33 are high.

1 10 100

Galaxy “GMC”Universe DenseCore

DenseGas Star

Galaxy

Universe

GMC

Galaxy

Dense Gas

GMC

Dense Core

Dense Gas

Star

Dense Core

time dependent

mass fractions

Gal

GMC

GMC

dense

dense

core

core

star

Galdense

GMC

core

dense

star

Gal

core

GMC

star

KS, all gas

Gal

star

KS “CO”

e.g. BGPS, ATLASGal

KS“HCN”

CMF-IMF

debate

column density

PDF

column density

PDF

column density

PDF

CO census

ALMA

effic

iency

Star Formation Efficiency Pyramid Scheme

Alyssa Goodman, Ringberg, RSF13

Galaxy “GMC”Universe DenseCore

DenseGas Star

Galaxy

Universe

GMC

Galaxy

Dense Gas

GMC

Dense Core

Dense Gas

Star

Dense Core

time dependent

mass fractions

Gal

GMC

GMC

dense

dense

core

core

star

Galdense

GMC

core

dense

star

Gal

core

GMC

star

KS, all gas

Gal

star

KS “CO”

e.g. BGPS, ATLASGal

KS“HCN”

CMF-IMF

debate

column density

PDF

column density

PDF

column density

PDF

CO census

ALMA

effic

iency

Star Formation Efficiency Pyramid Scheme

Alyssa Goodman, Ringberg, RSF13

0.3 0.05 0.1? Efficiency

Summary

§  Dense gas is the site of star formation §  Really gravitationally dominated (αvir small)

§  Most MCs in many galaxies are unbound §  Free-fall time is meaningless when nothing

is falling §  Feedback: stops SF before it starts, not after §  MW and exgal star formation are unifying

Complementary

§  Exgal studies § MC formation and evolution § Connection to other ISM phases §  Effects of metals, interactions, outflows, …

§  MW studies §  Structure within a cloud, clumps, cores, ... § Where stars form within clouds § What tracers actually measure (HCN vs...)

Back-up slides