Formation of an IMF-Cluster in a Filamentary Layer

Collaborators: F. Adams (Michigan), L. Allen (CfA), R. Gutermuth (CfA), J. Jørgensen (CfA), S. T. Megeath (Toledo)

Phil MyersHarvard-Smithsonian Center for Astrophysics

From Stars to Planets • April 2007 • University of Florida, Gainesville

The Question

Importance Most stars are born in “clusters” (Orion) rather than in “isolation” (Taurus - Lada & Lada 03)

Most stars are born in big clusters (Porras et al 03)

Data Numerous groups and clusters known within 1 kpc

Many big surveys recently available - stars: Spitzer GTO, c2d; gas: COMPLETE; dust: SCUBA,...

Confusion Many models contending - turbulence, competitive accretion, collapse of cores

Porras et al 03

How do molecular clouds make >100 IMF stars in ~1 pc in ~1 Myr, with close spacing, concentration of massive stars, and IMF dense cores?

Observations • clusters form in massive filamentary clouds • cores follow IMF, are virial, form stars in clusters

Model • GMC clump compressed into SG layer • layer fragments into filaments and Jeans masses • Jeans mass ->BE core->IMF star

Results • 100 stars follow IMF in 1 pc • scaling relations - Larson’s Laws • surface density and SFE match groups and sparse clusters--”first generation” of cluster formation

Outline

Embedded Clusters are Special Parts of MCs

Green: IR-excess sources

Grey: all IRAC detections

Orion A - Megeath et al 07aOrion B - Megeath et al 07b Muzerolle et al 07Oph - Allen et al 07Image - R. Gutermuth

Embedded cluster mass< 1-10% of MC mass

Very high gas column density,N >1022 cm-2 (McKee & Tan 03)

Nearby Clusters Have Hubs and Filaments

Ophiuchus Corona Australis Orion A

5-10 filaments radiating from pc-size hub, hosting embedded cluster.Slightly diverging filaments with remarkably regular spacing.“Head-tail” structure - Tachihara et al 02 - deeper images: more “ tails”

www.panther-observatory.com www.panther-observatory.com Johnstone & Bally 1999

Cluster Star Properties

1. Number of stars > 100 (Lada & Lada 03; Adams & Myers 01)

2. Size ~ 1 pc (LL 03)

3. Peak surface density ~ 103 stars pc-2 (Allen et al 07)

4. MF follows IMF (Meyer et al 00)

5. Most massive stars near center, low-mass stars widespread

(Hillenbrand & Hartmann 98)

6. Massive stars form only in clusters (96 ± 2 % of O stars - de Wit et al 05)

7. Spatial extent follows molecular gas

8. Cluster SFE = 20-30% (LL03), >> cloud SFE=few %

9. Duration of star formation ~ few Myr (Hartmann 01, but Stahler & Palla 02)

Red: > 100 pc-2 Blue: 10-100 pc-2 Green: 1 - 10 pc-2

Allen et al 07

Cluster Cores are Clustered

Like cluster stars, cluster cores have finer spacing than their isolated counterparts (Lada, Myers & Strom 93, Ward-Thompson et al 07)

Stars Form in Cluster Cores

NGC 1333 IRAC+MIPS submm + Class II YSOs submm + Class 0/I YSOs

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BIMA N2H+ cores

NGC 1333 Offsets YSOs - submm cores Nonclustered Perseus Offsets

Walsh et al 07

Gutermuth et al 07

Jørgensen et al 07

The reddest, youngest YSOs in the NGC 1333 cluster project on dense cores, just as they do in nearby regions of more “isolated” star formation

Cluster Cores Follow IMF

1.1 mm cores in Oph: IMF distribution with SFE = 0.3-0.5 and with “mass segregation” only for most massive cores (Stanke et al 06; Motte, André & Neri 98, Johnstone et al 00, Alves, Lombardi & Lada 07) --close relation between core and star masses

Cluster Cores are Self-Gravitating

93 N2H+ 1-0 cores have Mvir~ MLTE independent of core mass or stellar content-Walsh et al 07

N2H+ 1-0 BIMA+FCRAO

NGC 1333 in Perseus

virial and LTE core masses

MF (core masses 4)

Young Cluster Models

Klessen et al 98

“initial conditions” stars form by gravitational fragmentation of virial cores (Shu, Li & Allen 04, Larson 05; Tan, Krumholz, & McKee 06)

“turbulent”

cores form by turbulent cascade, quickly collapse to stars, or disperse (Ballesteros-Paredes et al 06)

What sets the stellar mass, density, and mass distribution in a cluster?

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“dynamic” cores play lesser role, stars form by moving accretion, competition for gas (Bonnell et al 06)

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this talk:Initial conditions model, layer geometry, IMF “built in”, predicts cloud & clusterproperties

Model Scenario

1 pc

0.1 pc

GMC clump compressed layer compressed layer Jeans fragments

Jeans fragment BE core BE core protostar

1, 2. OB winds compress GMC clump into a filamentary layer of Jeans fragments. 3. Fragments condense into BE cores, 4. BE cores collapse into protostellar star-disk systems.

Model Outline

cloud vertically self-gravitating isothermal layer

• every star follows the IMF ~ µ2/3/(1+µ2) µ Mstar/Mstar,m

• every star comes from a core Mcore = Mstar/ ~ cld3/core

2

• every core comes from a Jeans mass M J ~ ~ core-2/3Mcore

-1/3

• cloud mass is sum of Jeans masses Mcld ~ dµ µ-4/3

• cloud area is sum of Jeans areas Rcld2 ~ dµ µ-2/3 if perfect tiling

• adjustable parameters , core, Tmin, model predicts many properties of cloud and stars

core BE sphereCloud surface density, Core surface density, andCore mass decrease outward

Scaling Relations

Myers 07

Scaling relations have coefficient and slope similar to those of Larson (1981).Coefficients are set by properties of “modal core.” <Ncld> due to layer geometry and is ~independent of , Nstars. Velocity dispersions > thermal as observed.

Mean cloud column density Velocity Dispersions

Property “group” (Nstars=10) “cluster” (Nstars=100) Rcld (pc) 0.10 0.99Mcld (103 MO) 0.018 1.7SFE 0.27 0.029cld (km s-1) 0.25 0.45core (km s-1) 0.16 - 0.38 0.16 - 0.67M (MO) 0.054 - 0.72 0.054 - 4.1Ncld (1022 cm-2) 2.2 - 5.3 2.2 - 9.5Ns (pc-2) 96 - 540 17 - 300

Assumed parameter values: =0.7, ncore=2 106 cm-3, Tmin=7 K, and =1. SFE is computed assuming a mean stellar mass of 0.5 MO.

Model Hits and Misses

Model matches molecular cloud scaling relations, properties ofgroups and sparse clusters (e.g. L1495-Taurus), but not rich clusters.

Speculation--model describes properties of star-forming molecular clouds, and the “first generation” of cluster-forming regions.

From Sparse to Rich Clusters

Two ways to increase SFE and stellar surface density from their sparse-cluster values:

Generation 0 1 2

1. Stellar feedback - heating and winds from each generation of stars compress gas above and below midplane into new star-forming layers (like Elmegreen

& Lada 77).

2. Horizontal contraction - gravitational contraction concentrates more dense gas near central positions, on dynamical time < 1 Myr (Burkert & Hartmann 04).

SummaryThe question How do molecular clouds... make >100 IMF stars over 1 pc over 1 Myr, with spatial clustering, concentration of massive stars, and IMF dense cores?

Observations Clouds, clusters, and cores many new “complete” surveys

clusters form in massive filamentary clouds cores are virial, form stars, match shape of IMF

Model IMF layer model filamentary layer hosts star-forming cores scaling relations match Larson’s Laws ~100 stars in ~ 1 pc, but SFE ~ few % good match to groups and “sparse clusters” may describe first generation of stars in a “rich cluster”

Summary