An upper limit to the masses of stars

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

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

7. Upper mass limit: theoretical predictions

8. Upper mass limit: observation

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

24. Arches stars: O stars 68 HI 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 -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: s=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.

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

32. Results of Monte Carlo simulation

33. 4. Violators?

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

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

36. 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

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

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

39. 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. • 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. Weidner & Kroupa 2004, MNRAS, 348, 187

40. 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.

41. 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)

42. 130 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