1. 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

2. Outline Introduction to the problem Observations Analysis Violators?
Conclusions

3. 1. Introduction

4. 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

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

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

7. 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 M
Larson & Starrfield (1971)
pressure in HII region
50-60 M
Cox & Tabor (1976)
e- and atomic opacity
Los Alamos M
Klapp et al. (1987)
440 M
Stothers (1992)
Rogers-Iglesias M

8. Upper mass limit: observation
Feitzinger et al. (1980) M
Eta Car
various M
R136a1
Massey & Hunter (1998) M
Pistol Star
Figer et al. (1998) M
Damineli et al. (2000)
~70+? M
LBV
Eikenberry et al. (2004) M
Figer et al. (2004)
130 (binary?) M
HDE
Walborn et al. (2004)
150 M
WR20a
Bonanos et al. (2004)
Rauw et al. (2004)
82+83 M

9. 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.

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

11. 2. Observations

12. 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.

13. Lick 3-m (1995)

14. Keck 10-m (1998)

15. HST (1999)

16. VLT (2003)

17. Galactic Center Clusters
too old (~4 Myr)

18. 3. Analysis

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

20. Luminosity function

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

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

23. 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

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

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

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

27. Mass vs. magnitude for t=2 Myr

28. Initial mass function

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

30. 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
Repeat for IMF cutoffs: 130, 150, 175, 200 M.
Assign ages: = tCL± s = ( ) ± 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 ( Myr) and AK=3.1.
Estimate N(NM>130 M=0).

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

32. Results of Monte Carlo simulation

33. 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 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.

34. 4. Violators?

35. Figer et al. 1999, ApJ, 525, 759

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

37. 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

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

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

40. 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.

41. 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)

42. 128 New Galactic Clusters from 2MASS
Candidate 2MASS Clusters

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

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