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 1.Introduction to the problem 2.Observations 3.Analysis 4.Violators? 5.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

Upper mass limit: theory Theory provides little guide in determining the most massive star that can form. Radial pulsations were once thought to limit envelope mass, but they may be damped. Radiation/wind pressure, and/or ionizing flux, inhibit accretion but direct collisions of protostellar clumps may overcome these effects. Stellar evolution models have been computed up to 1000 M , but no such stars have ever been observed.

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) radial pulsation, e- opacity, H and He, evolution M  Stothers & Simon (1970)radial pulsation, e- and atomic M  Larson & Starrfield (1971)pressure in HII region50-60 M  Cox & Tabor (1976) e- and atomic opacity Los Alamos M  Klapp et al. (1987) e- and atomic opacity Los Alamos 440 M  Stothers (1992) e- and atomic opacity Rogers-Iglesias M 

Upper mass limit: observation R136Feitzinger et al. (1980) M  Eta Carvarious M  R136a1Massey & Hunter (1998) M  Pistol StarFiger et al. (1998) M  Eta CarDamineli et al. (2000)~70+? M  LBV Eikenberry et al. (2004) M  LBV Figer et al. (2004)130 (binary?) M  HDE Walborn et al. (2004)150 M  WR20a Bonanos et al. (2004) Rauw et al. (2004) 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 >10 4 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 Salpeter 1955Kroupa 2002  =  M 

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 Meynet, Maeder et al. 1994, A&AS, 103, 97 O WNL WNE WCL WCEWO SN

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

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

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

Arches stars: quantitative spectroscopy Najarro et al NIII

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 Flat Mass Function in the Arches Cluster HSTNICMOS VLTNAOSCONICA Stolte et al. 2003

Mass-loss ZAMS 0.5 Myr 1 Myr 1.5 Myr 2 Myr

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

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

Results of Monte Carlo simulation

4. Violators?

Figer et al. 1999, ApJ, 525, 759

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

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

Claim 1-7 L Pistol* M ⊙ Primary uncertainties distance temperature singularity LBV SGR LBV

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

Does R136 have a cutoff? Weidner & Kroupa 2004, MNRAS, 348, 187 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 M c ~50,000 M . –deficit of 4 stars with M>150 M  for M c ~20,000 M . Metallicity in LMC is less than in Arches: Z LMC ~Z  /3. Upper mass cutoff to IMF is roughly the same over a factor of three in metallicity.

Conclusions The Arches Cluster is the only known cluster in the Galaxy that can be used to test for an upper mass cutoff to the stellar initial mass function. The upper mass cutoff in the Arches Cluster 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 –Chandra –NIRSPEC/Keck –Phoenix/Gemini (30 hours) –IRMOS/KPNO 4-m –EMIR/GTC –VLA (~100 hours)

130 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

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