An upper limit to the masses of stars Donald F. Figer STScI Collaborators: Sungsoo Kim (KHU) Paco Najarro (CSIC) Rolf Kudritzki (UH) Mark Morris (UCLA) Mike Rich (UCLA) Arches Cluster Illustration

Outline Introduction to the problem Observations Analysis Violators? Conclusions

1. Introduction

An upper mass limit has been elusive There is no accepted upper mass limit for stars. Theory: incomplete understanding of star formation/destruction. accretion may be inhibited by opacity to radiation pressure/winds formation may be aided by collisions of protostellar clumps destruction may be due to pulsational instability Observation: incompleteness in surveying massive stars in the Galaxy. the most massive stars known have M~150 M most known clusters are not massive enough

Radial pulsations and an upper limit 1941, ApJ, 94, 537 Also see Eddington (1927, MNRAS, 87, 539)

Upper mass limit: theoretical predictions Stothers & Simon (1970)

Upper mass limit: theoretical predictions Ledoux (1941) radial pulsation, e- opacity, H 100 M Schwarzchild & Härm (1959) H and He, evolution 65-95 M Stothers & Simon (1970) radial pulsation, e- and atomic 80-120 M Larson & Starrfield (1971) pressure in HII region 50-60 M Cox & Tabor (1976) e- and atomic opacity Los Alamos 80-100 M Klapp et al. (1987) 440 M Stothers (1992) Rogers-Iglesias 120-150 M

Upper mass limit: observation Feitzinger et al. (1980) 250-1000 M Eta Car various 120-150 M R136a1 Massey & Hunter (1998) 136-155 M Pistol Star Figer et al. (1998) 140-180 M Damineli et al. (2000) ~70+? M LBV 1806-20 Eikenberry et al. (2004) 150-1000 M Figer et al. (2004) 130 (binary?) M HDE 269810 Walborn et al. (2004) 150 M WR20a Bonanos et al. (2004) Rauw et al. (2004) 82+83 M

The initial mass function: a tutorial Stars generally form with a frequency that decreases with increasing mass for masses greater than ~1 M: Stars with M>150 M can only be observed in clusters with total stellar mass >104 M. This requirement limits the potential sample of stellar clusters that can constrain the upper mass limit to only a few in the Galaxy.

The initial mass function: observations G=-1.35 G=-1.35 1-120 M Salpeter 1955 Kroupa 2002

2. Observations

Upper mass limit: an observational test Target sample must satisfy many criteria. massive enough to populate massive bins young enough to be pre-supernova phase old enough to be free of natal molecular material close enough to discern individual stars at known distance coeval enough to constitute a single event of a known age Number of "expected" massive stars given by extrapolating observed initial mass function.

Lick 3-m (1995)

Keck 10-m (1998)

HST (1999)

VLT (2003)

Galactic Center Clusters too old (~4 Myr)

3. Analysis

Arches Cluster CMD Figer et al. 1999, ApJ, 525, 750

Luminosity function

Stellar evolution models WNL WNE WCL WCE WO SN Meynet, Maeder et al. 1994, A&AS, 103, 97

NICMOS 1.87 mm image of Arches Cluster No WNE or WC! Figer et al. 2002, ApJ, 581, 258

Arches stars: WN9 stars Figer et al. 2002, ApJ, 581, 258 enhanced Nitrogen HeI NIII HeI HeII NIII NIII HeI/HI Figer et al. 2002, ApJ, 581, 258

Arches stars: O stars HI 68 HeI 27 Figer et al. 2002, ApJ, 581, 258

Arches stars: quantitative spectroscopy NIII NIII NIII Najarro et al. 2004

Age through nitrogen abundances Najarro, Figer, Hillier, & Kudritzki 2004, ApJ, 611, L105

Mass vs. magnitude for t=2 Myr

Initial mass function

Arches Cluster mass function: confirmation HST•NICMOS VLT•NAOS•CONICA Flat Mass Function in the Arches Cluster Stolte et al. 2003

Monte Carlo simulation Simulate 100,000 model clusters, each with 39 stars in four highest mass bins. Repeat for two IMF slopes: G=-1.35 and -0.90. Repeat for IMF cutoffs: 130, 150, 175, 200 M. Assign ages: = tCL± s = (2.0-2.5) ± 0.3 Myr. Apply evolution models to determine apparent magnitudes. Assign extinction: = AK,CL± s = 3.1 ± 0.3. Assign photometric error: s=0.2. Transform "observed" magnitudes into initial masses assuming random cluster age (2.0-2.5 Myr) and AK=3.1. Estimate N(NM>130 M=0).

Simulated effects of errors true initial mass function inferred initial mass function

Results of Monte Carlo simulation

Does R136 have a cutoff? Massey & Hunter (1998) claim no upper mass cutoff. Weidner & Kroupa (2004) claim a cutoff of 150 M. deficit of 10 stars with M>150 M for Mc~50,000 M. deficit of 4 stars with M>150 M for Mc~20,000 M. Oey & Clark (2005) claim a cutoff of 120-200 M. Metallicity in LMC is less than in Arches: ZLMC~Z/3. Upper mass cutoff to IMF is roughly the same over a factor of three in metallicity.

4. Violators?

Figer et al. 1999, ApJ, 525, 759

Is the Pistol Star "too" massive? tracks by Langer Figer et al. 1998, ApJ, 506, 384

Two Violators in the Quintuplet Cluster? Pistol Star and #362 have ~ same mass. Pistol Star Star #362 Figer et al. 1999, ApJ, 525, 759 Geballe et al. 2000, ApJ, 530, 97

LBV 1806-20 Claim 1-7 LPistol* 150-1000 M⊙ Primary uncertainties distance temperature singularity SGR LBV

LBV 1806-20 is a binary? double lines Figer, Najarro, Kudritzki 2004, ApJ, 610, L109

Conclusions The Arches Cluster has an upper mass cutoff to the stellar initial mass function. The upper mass cutoff is ~150 M. The upper mass cutoff may be invariant over a range of a factor of three in metallicity.

The next step: search the Galaxy! Find massive stellar cluster candidates 2MASS Spitzer (GLIMPSE) Target for intensive observation NICMOS/HST (128 orbits proposed) Chandra (50 ks approved, 50 ks proposed) NIRSPEC/Keck (2 half nights appoved) Phoenix/Gemini (30 hours approved) IRMOS/KPNO 4-m (10 nights contingent on HST) EMIR/GTC (10 nights approved) VLA (~100 hours approved)

128 New Galactic Clusters from 2MASS Candidate 2MASS Clusters

Massive Young Clusters in X-rays Arches and Quintuplet Clusters in X-rays Chandra Law & Yusef-Zadeh 2003

Massive Young Clusters in Radio Arches and Quintuplet Clusters in Radio VLA Lang et al. 2001