An upper limit to the masses of stars

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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
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Outline

• Introduction to the problem
• Observations
• Analysis
• Violators?
• Conclusions

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• 1. Introduction

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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 M150 M
• most known clusters are not massive enough

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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.

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Radial pulsations and an upper limit
Also see Eddington (1927, MNRAS, 87, 539)
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Upper mass limit theoretical predictions
Stothers Simon (1970)
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Upper mass limit theoretical predictions
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Upper mass limit observation
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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 M150 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.

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The initial mass function observations
G-1.35
G-1.35
1-120 M
Salpeter 1955
Kroupa 2002
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• 2. Observations

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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.

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Lick 3-m (1995)
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Keck 10-m (1998)
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HST (1999)
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VLT (2003)
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Galactic Center Clusters
too old (4 Myr)
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• 3. Analysis

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Arches Cluster CMD
Figer et al. 1999, ApJ, 525, 750
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Luminosity function
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Stellar evolution models
WNL
O
WNE
WCL
WCE
WO
SN
Meynet, Maeder et al. 1994, AAS, 103, 97
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NICMOS 1.87 mm image of Arches Cluster
No WNE or WC!
Figer et al. 2002, ApJ, 581, 258
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Arches stars WN9 stars
NIII
HeI
HeI
NIII
NIII
HeII
HeI/HI
Figer et al. 2002, ApJ, 581, 258
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Arches stars O stars
68
HI
HeI
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Figer et al. 2002, ApJ, 581, 258
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Arches stars quantitative spectroscopy
NIII
NIII
NIII
Najarro et al. 2004
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Age through nitrogen abundances
Najarro, Figer, Hillier, Kudritzki 2004, ApJ,
611, L105
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Mass vs. magnitude for t2 Myr
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Initial mass function
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Arches Cluster mass function confirmation
HSTNICMOS
VLTNAOSCONICA
Flat Mass Function in the Arches Cluster
Stolte et al. 2003
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Mass-loss
ZAMS
0.5 Myr
1 Myr
1.5 Myr
2 Myr
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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 s0.2.
• Transform "observed" magnitudes into initial
  masses assuming random cluster age (2.0-2.5 Myr)
  and AK3.1.
• Estimate N(NM130 M0).

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Simulated effects of errors
true initial mass function
inferred initial mass function
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Results of Monte Carlo simulation
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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 M150 M for Mc50,000
  M.
• deficit of 4 stars with M150 M for Mc20,000
  M.
• Oey Clark (2005) claim a cutoff of 120-200 M.
• Metallicity in LMC is less than in Arches
  ZLMCZ/3.
• Upper mass cutoff to IMF is roughly the same over
  a factor of three in metallicity.

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• 4. Violators?

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Figer et al. 1999, ApJ, 525, 759
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Is the Pistol Star "too" massive?
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Two Violators in the Quintuplet Cluster?
Pistol Star and 362 have same mass.
Star 362
Pistol Star
Figer et al. 1999, ApJ, 525, 759
Geballe et al. 2000, ApJ, 530, 97
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LBV 1806-20

• Claim
• 1-7 LPistol
• 150-1000 M?
• Primary uncertainties
• distance
• temperature
• singularity

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

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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)

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128 New Galactic Clusters from 2MASS
Candidate 2MASS Clusters
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Massive Young Clusters in X-rays
Arches and Quintuplet Clusters in X-rays Chandra
Law Yusef-Zadeh 2003
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Massive Young Clusters in Radio
Arches and Quintuplet Clusters in Radio VLA
Lang et al. 2001
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