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
Outline
1. Introduction to the problem 2. Observations3. Analysis4. 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
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
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
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
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
The initial mass function: observations
Salpeter 1955 Kroupa 2002
=1.35
=1.35
1-120 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 WCE WO SN
NICMOS 1.87 m image of Arches Cluster
Figer et al. 2002, ApJ, 581, 258
No WNEor WC!
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
Arches stars: O stars
68
27
HI
HeI
Figer et al. 2002, ApJ, 581, 258
Arches stars: quantitative spectroscopy
Najarro et al. 2004
NII
IN
III
NII
I
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
HST•NICMOS VLT•NAOS•CONICA
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: =-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).
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
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 LPistol*
•150-1000 M⊙
• Primary uncertainties•distance•temperature•singularity
LBV 1806-20
SGRLBV
Figer, Najarro, Kudritzki 2004, ApJ, 610, L109
LBV 1806-20 is a binary?
double lines
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-raysChandra Law & Yusef-Zadeh 2003
Arches and Quintuplet Clusters in RadioVLA Lang et al. 2001
Massive Young Clusters in Radio
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