1. 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 Myers Harvard-Smithsonian Center for Astrophysics From Stars to Planets April 2007 University of Florida, Gainesville

2. The Question ImportanceMost 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?

3. 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

4. Embedded Clusters are Special Parts of MCs Green: IR-excess sources Grey: all IRAC detections Orion A - Megeath et al 07a Orion B - Megeath et al 07b Muzerolle et al 07 Oph - Allen et al 07 Image - R. Gutermuth Embedded cluster mass < 1-10% of MC mass Very high gas column density, N >10 22 cm -2 (McKee & Tan 03)

5. Nearby Clusters Have Hubs and Filaments OphiuchusCorona AustralisOrion 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 Johnstone & Bally 1999

6. Cluster Star Properties 1.Number of stars > 100 (Lada & Lada 03; Adams & Myers 01) 2. Size ~ 1 pc (LL 03) 3.Peak surface density ~ 10 3 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

7. 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)

8. Stars Form in Cluster Cores NGC 1333 IRAC+MIPSsubmm + Class II YSOs submm + Class 0/I YSOs BIMA N 2 H + 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

9. 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

10. Cluster Cores are Self-Gravitating 93 N 2 H + 1-0 cores have M vir ~ M LTE independent of core mass or stellar content-Walsh et al 07 N 2 H + 1-0 BIMA+FCRAO NGC 1333 in Perseus virial and LTE core masses MF (core masses  4)

11. 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? “dynamic” cores play lesser role, stars form by moving accretion, competition for gas (Bonnell et al 06) this talk: Initial conditions model, layer geometry, IMF “built in”, predicts cloud & cluster properties

12. Model Scenario 1 pc 0.1 pc GMC clump compressed layercompressed 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.

13. Model Outline cloud  vertically self-gravitating isothermal layer every star follows the IMF  ~ µ 2/3 /(1+µ 2 ) µ  M star /M star,m every star comes from a core M core = M star /  ~  cld 3 /  core 2 every core comes from a Jeans mass M J ~      ~  core -2/3 M core -1/3 cloud mass is sum of Jeans massesM cld ~  dµ µ -4/3  cloud area is sum of Jeans areasR cld 2 ~  dµ µ -2/3  if perfect tiling adjustable parameters ,  core, T min,  model predicts many properties of cloud and stars core  BE sphere Cloud surface density, Core surface density, and Core mass decrease outward

14. Scaling Relations Myers 07 Scaling relations have coefficient and slope similar to those of Larson (1981). Coefficients are set by properties of “modal core.” due to layer geometry and is ~independent of , N stars. Velocity dispersions > thermal as observed. Mean cloud column density Velocity Dispersions

15. Property“group” (N stars =10) “cluster” (N stars =100) R cld (pc)0.100.99 M cld (10 3 M O )0.0181.7 SFE0.270.029  cld (km s -1 )0.250.45  core (km s -1 )0.16 - 0.380.16 - 0.67 M  (M O )0.054 - 0.720.054 - 4.1 N cld (10 22 cm -2 )2.2 - 5.32.2 - 9.5 N  s (pc -2 )96 - 54017 - 300 Assumed parameter values:  =0.7, n core =2  10 6 cm -3, T min =7 K, and  =1. SFE is computed assuming a mean stellar mass of 0.5 M O. Model Hits and Misses Model matches molecular cloud scaling relations, properties of groups 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.

16. 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).

17. Summary The questionHow do molecular clouds... make >100 IMF stars over 1 pc over 1 Myr, with spatial clustering, concentration of massive stars, and IMF dense cores? ObservationsClouds, 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