The Initial Mass Function in Clusters

Bruce G. ElmegreenIBM T.J. Watson Research

CenterYorktown Hts., NY

bge@watson.ibm.comMay 9, 2006

Salpeter ‘55

slope=-1.35

The IMF is not well known anywhere

• Clusters: same age & distance but mass segregation, field contamination, small number statistics are problems

• OB associations : same distance, but a range of ages, extinctions and dispersals, summed IMFs of clusters

• Field: many stars but mass function/volume depends on SF history, vertical disk heating, drift from clusters, etc.

• Whole galaxies: average IMFs from abundance ratios (Fe,O), CMD, H EW, etc., but resolution, faintness, SF history are problems.

A compilation by Scalo ‘98

n(M)dlogM~M dlogM

Scatter consistent with small number statistics

LMC & MW

(Salpeter)

Stochastic model (Elmegreen ’99)

(1-10 MO range)

Clusters

R136 in 30 Dorregion of LMC

=-1.30.1 or -1.40.1 for 2 temperaturecalibrationsMassey & Hunter ‘98

Many dense clusters haveSalpeter IMFs (~-1.35)

plus: h and Persei (Slesnick, Hillenbrand & Massey ‘02) NGC 604 in M33 (Gonzalez Delgado & Perez ‘00) NGC 1960 and NGC 2194 (Sanner et al. ‘00) NGC 6611 (Belikov et al. ‘04) ......

APOD: Walborn et al. ‘01

Scalo 98: M=1-10, =-1.7 M=10-100, =-1.3

Preibisch et al. M=0.6-2, =-1.8 M=2-20, =-1.6

Kroupa 2002: M=0.08-0.5, =-0.3 M=0.5-100, =-1.3

Preibisch et al. (2002) upper Sco OB assoc.

Sco-Cen: a dispersed association, has a steep IMF.

-1.7

-1.3

-1.3-1.8

-1.6

Okumura et al. 2000

W51: small number stats at high mass end a problem, unless variations real.

=-1.8

?

?

NIR: Hodapp 05

Peretto, Andre & Belloche 05: Massive star formation in NGC

2264

NIR source density on 1.2 mm cont.

observe collapse onto core

core 3 ~ future 20 MO star

cores 2 & 4 may fall into it

Do massive stars need the cluster environment?

• Testi, Palla & Natta ’99 suggested Herbig AeBe stars have a correlation between their mass and the surrounding cluster density– Bonnell & Clarke ’99 showed this could be sampling

statistics because cluster density proportional to cluster mass

• de wit et al 05 observe 43 local “field” O stars and look for evidence of runaways: nearby clusters, high z, high v– suggest only 4% of all O stars may form isolated– consistent with cluster mass function down to single star

with slope of =1.7 (see also Oey, King & Parker 2004)

• O stars don’t need massive and dense clusters to form

Distribution of massive stars in and near R136 in 30 Dor.

Massive star formation around the periphery is common.

30 Dor in the LMC (triggering all over)

Walborn et al. 2002

Hunter et al. 96: IMF independent of densityAn example of a cluster-free “SOBA” in Maíz-Apellániz ‘01

549 stars (608 with completeness corr.)

=-1.60.7

NGC 604 in M33(APOD, Yang & Hester 96)

IMF a superposition of several processes

Elmegreen 04

Some massive stars could form by thesame process as solar-mass stars, forminga log-normal IMF with a steep slope at high M (Mark Krumholz’s mechanism?)

In dense clusters, other massive stars could form by additional processes (enhanced accretion, coalescence, etc.)(Ian Bonnell’s mechanisms?)

The upper mass slope would then be flatter in ultradense or more active SFR

Mark

Ian

Applications to Starbursts and Young Elliptical Galaxies?

• Some starburst regions may have clusters with top-heavy or bottom-light IMFs

• Massive elliptical galaxies have slightly flatter IMFs – Pipino & Matteucci 2004; Nagashima et al. 2005

• Clusters of galaxies suggest a history of top-heavy IMFs in elliptical galaxy bursts– Renzini et al. 1993; Loewenstein & Mushotsky 1996; Chiosi

2000; Moretti, Portinari, & Chiosi 2003; Tornatore et al. 2004; Romeo et al. 2004; Portinari et al. 2004; Nagashima et al. 2005

• Low Surface Brightness gal. may have steep IMF (Lee et al. 04)

• Perhaps dense cluster processes form a higher proportion of high-mass stars

Some SSC appear "top heavy" or

"bottom light" • Sternberg (1998): high L/M : ||<1 or inner cutoff in NGC 1705-1• Smith & Gallagher (2001): M82F: inner cutoff = 2-3 MO for =-

1.3• Alonso-Herrero et al. (2001): high L/M in starburst NGC 1614• McCrady et al. (2003): M82: MGG-11 deficit in low mass stars• Mengel et al. (2003): NGC 4038/9

Other Super Star Cluster have Normal IMFs

• NGC 1569-A (Ho & Filippenko 1996; Sternberg 1998)

• NGC 6946 (Larsen et al. 2001)• M82: MGG-9 (McGrady et al. 2003)

• Difficult problem: measure v, R (to get M) and measure L

• v varies inside a cluster (not isothermal) – e.g. NGC 6946 (v[r] decreases)

• which R to take is uncertain (cluster is evaporating, non-equilibrium, non-isothermal, multi-component or non-centralized, & core is poorly resolved)

• choice of aperture difficult and field star corrections are necessary

Are top-heavy SSC out of equilibrium?

• Bastian et al. suggest top heavy IMFs in SSC can be the result of dis-equilibrium.– only young clusters

appear to have top-heavy IMFs

– unbound expansion adds to v and R

– and makes shoulders in (R)

– result: overestimate R, underestimate mass

Other Variations from Mass Segregation

NGC 3603 has shallower IMF slope in core and steeper IMF slope at edge (Sung & Bessell 04)

Possible high mass drop-off:=-1.9 overall for M>40 MO

Arches cluster in Galactic Center

Yang et al. ‘02

Stolte et al. 05

Flat MFs from tidal stripping, not enhanced massive SF

• de Marchi, Pulone, & Paresce 06 show a flat mass function in the galactic cluster NGC 6218.

• At 4 radii, MF slopes are +1.4, 1.3, 0.6, & 0.1 (Salpeter = - -2.3)

• Flat MF also in NGC 6218 (de Marchi et al. ’99) and Pal 5 (Koch et al. ’04), which are expected to have undergone tidal stripping.

• suggest tidal stripping here too.– cluster mass is 1/5 original

• models by Baumgardt confirm

Luhman et al. ‘00

Briceno et al. 02,Luhman et al. 03,Muench et al. 03

Orion: Lucas et al. 05

Low mass IMFs in clusters: variations too

Theory of IMF

• Turbulent fragmentation in intersecting shocks

• Protostars form in collapsing cores• Protostars move around and accrete

gas• Protostars also coalesce, or get

ejected from dense clusters• the IMF follows ….

Bate and Bonnell 05:

SPH, no B, resolves MJ

Two 50 MJ simulations with different MJ

Mean mass of fragments follows MJ

same MJ dependence if Mmin varies -Bate 05

low MJ

3x higher MJ

Jappsen et al. 05

Variations in the eq. of state:<1 at low n and > 1 at high n

Mean mass depends on transition n

higher transition n lower MJ, more cores

Salpeter IMF results

Martel et al. 05:

SPH with particle splitting

no B, isothermal

Finds that mean mass depends on resolution(number of levels in splitting hierarchy)

Tilly and Pudritz 05

ZEUS-MP, 2563, different ratios of Grav/Mag energy.bound cores

preferred model

Padoan et al. 05

AMR effective 10243 cellsMach = 6, MHD

Forms brown dwarfs byturbulent fragmentation

Nakamura & Li 05

2D MHD-B diffusion enhanced by turbulence compression-diffusion-regulated collapse in compressed regions-low SF efficiency

(=flux/mass normalized to critical)thick lines= strong outflow

solid, dash: 0=1.2,1

What is missing from these models?

• Feedback (erosion of disks and pre-collapse objects)– Li & Nakamura 06 considers wind-driven turbulence in 3D MHD

• Long-term turbulence before SF begins & turbulent environment

• Realistic heating/cooling• Large number statistics for stars that form• SPH: Magnetic forces missing• MHD on single GRID: limited dynamic range• MHD on multi-grid: number of stars low• MHD: physics of detachment of stars from background

B field• ….

It is only a matter of time before simulations make the IMF in a realistic way

e.g., Importance of magnetism for clump confinement

• If clump field is critical (or clump formed with constant mass to flux ratio in cloud where the field was critical),

– Bclump ~ G1/2 clump

• Magnetic force/volume in clump – ~ Bclump

2/Rclump ~ Gclump2/Rclump

• Gravitational force/volume in clump – ~ Gcloud

* Mclump/Rclump3 = Gcloudclump/Rclump

• force ratio is FB/FG ~ clump/cloud >>1• clumps do not free fall in the cloud until either

– their field lines are detached or their field diffuses out

e.g., Importance of magnetism for clump accretion

• Magnetic force/volume on ambient gas:• ~ Bcloud

2/Rcloud ~ Gcloud2 / Rcloud

• Gravitational force/volume on ambient gas from clump

• ~ (GMclump/Rcloud2) * Mcloud/Rcloud

3

• force ratio FB/FG ~ Mcloud/Mclump >>1 • ambient cloud gas cannot free fall onto

single clump or any cloud core where Mcore/M<1

other Magnetic effects

• Communication with surrounding ISM– magnetic fields connect the cloud, cloud

cores, and all pre-detached clumps to the external ISM

– magnetic stresses transfer linear and angular momentum from inside cloud to outside cloud

– source of damping of clump and cloud turbulent motions

– possible source of energy to these motions too• internal feedback and external perturbations

Reflections

• Simulations make the IMF, but for the right reasons?

• The universality of the real IMF suggests an insensitivity to detailed processes:– inside and outside clusters– starbursts and slow SF galaxies– independent of metallicity, galaxy mass, epoch

(with some exceptions), …

• With similar insensitivity, the simulations would also get the right result even if the physics were oversimplified

For example,• Hierarchical fragmention alone gives n(M)dM~M-

2dM– very close to Salpeter, which is ~M-2.35

• What if the modelled IMF came mostly from fragmentation? The IMF would be mostly from geometry

• And the universal processes make it slightly more likely to form intermediate mass stars (MJ)

– i.e., steepens M-2 to M-2.4 for M>0.5 MO

– and flattens M-2 to M-1.5 for M<0.5 MO

• Additional processes act in dense clusters to make an excess of massive stars, or an excess of Brown dwarfs– ablation of LM stars, heightened accretion, coalescence,

multiple star interactions…

Conclusions• IMF observations suggest a more or less constant

IMF in many diverse environments– possible variations at high and low mass end (tri-modal

IMF)• coalescence, accretions, ejections, etc.

– possible false variations from unknown SFH’s, M-L relations, field star contamination, small number statistics, etc.

• Theory of gravo-turbulent fragmentation typically gets observed IMF but many uncertainties remain– Magnetic fields, feedback, boundary/initial conditions,

…– yet the diverse models can all get about the right IMF– what do the simulations and reality have in common?

• fragmentation? accretion? enough tunable parameters?

THE END