An upper limit to the masses of stars
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An upper limit to the masses
of stars
Donald F. FigerSTScI
Collaborators:Sungsoo Kim (KHU)Paco Najarro (CSIC)Rolf Kudritzki (UH)
Mark Morris (UCLA)Mike Rich (UCLA)
Arches Cluster Illustration
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Outline
1. Introduction to the problem 2. Observations3. Analysis4. Violators?5. 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 M~150 M
– most known clusters are not massive enough
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Radial pulsations and an upper limit
1941, ApJ, 94, 537
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
Ledoux (1941)radial pulsation, e- opacity,H
100 M
Schwarzchild & Härm (1959)radial pulsation, e- opacity,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 opacityLos Alamos
80-100 M
Klapp et al. (1987)e- and atomic opacityLos Alamos
440 M
Stothers (1992)e- and atomic opacityRogers-Iglesias
120-150 M
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Upper mass limit: observation
R136 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
Eta Car Damineli et al. (2000) ~70+? M
LBV 1806-20 Eikenberry et al. (2004) 150-1000 M
LBV 1806-20 Figer et al. (2004) 130 (binary?) M
HDE 269810 Walborn et al. (2004) 150 M
WR20aBonanos et al. (2004)
Rauw et al. (2004) 82+83 M
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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 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.
m) N)/d(d( loglog
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The initial mass function: observations
Salpeter 1955 Kroupa 2002
=1.35
=1.35
1-120 M
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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
Meynet, Maeder et al. 1994, A&AS, 103, 97
O WNL WNE WCL WCE WO SN
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NICMOS 1.87 m image of Arches Cluster
Figer et al. 2002, ApJ, 581, 258
No WNEor WC!
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Arches stars: WN9 stars
He
I
He
I
He
I/H
I
NII
I
He
II
NII
I
NII
I
Figer et al. 2002, ApJ, 581, 258
enhanced Nitrogen
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Arches stars: O stars
68
27
HI
HeI
Figer et al. 2002, ApJ, 581, 258
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Arches stars: quantitative spectroscopy
Najarro et al. 2004
NII
IN
III
NII
I
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Age through nitrogen abundances
Najarro, Figer, Hillier, & Kudritzki 2004, ApJ, 611, L105
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Mass vs. magnitude for t=2 Myr
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Initial mass function
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Arches Cluster mass function: confirmation
Flat Mass Function in the Arches Cluster
HST•NICMOS VLT•NAOS•CONICA
Stolte et al. 2003
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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: =-1.35 and -0.90.
• Repeat for IMF cutoffs: 130, 150, 175, 200 M.
• Assign ages: = tCL± = (2.0-2.5) ± 0.3 Myr.
• Apply evolution models to determine apparent magnitudes.
• Assign extinction: = AK,CL± = 3.1 ± 0.3.
• Assign photometric error: =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).
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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 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.
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4. Violators?
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Figer et al. 1999, ApJ, 525, 759
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tracks by Langer
Figer et al. 1998, ApJ, 506, 384
Is the Pistol Star "too" massive?
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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
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• Claim•1-7 LPistol*
•150-1000 M⊙
• Primary uncertainties•distance•temperature•singularity
LBV 1806-20
SGRLBV
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Figer, Najarro, Kudritzki 2004, ApJ, 610, L109
LBV 1806-20 is a binary?
double lines
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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-raysChandra Law & Yusef-Zadeh 2003
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Arches and Quintuplet Clusters in RadioVLA Lang et al. 2001
Massive Young Clusters in Radio
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