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 1.Introduction to the problem 2.Observations 3.Analysis 4.Violators? 5.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. 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.

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

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

8. 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 atomic80-120 M  Larson & Starrfield (1971)pressure in HII region50-60 M  Cox & Tabor (1976) e- and atomic opacity Los Alamos 80-100 M  Klapp et al. (1987) e- and atomic opacity Los Alamos 440 M  Stothers (1992) e- and atomic opacity Rogers-Iglesias 120-150 M 

9. Upper mass limit: observation R136Feitzinger et al. (1980)250-1000 M  Eta Carvarious120-150 M  R136a1Massey & Hunter (1998)136-155 M  Pistol StarFiger et al. (1998)140-180 M  Eta CarDamineli et al. (2000)~70+? M  LBV 1806-20Eikenberry et al. (2004)150-1000 M  LBV 1806-20Figer et al. (2004)130 (binary?) M  HDE 269810Walborn et al. (2004)150 M  WR20a Bonanos et al. (2004) Rauw et al. (2004) 82+83 M 

10. 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 >10 4 M . This requirement limits the potential sample of stellar clusters that can constrain the upper mass limit to only a few in the Galaxy.

11. The initial mass function: observations Salpeter 1955Kroupa 2002  =  1.35 1-120 M 

12. 2. Observations

13. 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.

14. Lick 3-m (1995)

15. Keck 10-m (1998)

16. HST (1999)

17. VLT (2003)

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

19. 3. Analysis

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

21. Luminosity function

22. Stellar evolution models Meynet, Maeder et al. 1994, A&AS, 103, 97 O WNL WNE WCL WCEWO SN

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

24. Arches stars: WN9 stars HeI HeI/HI NIII HeII NIII Figer et al. 2002, ApJ, 581, 258 enhanced Nitrogen

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

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

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

28. Mass vs. magnitude for t=2 Myr

29. Initial mass function

30. Arches Cluster mass function: confirmation Flat Mass Function in the Arches Cluster HSTNICMOS VLTNAOSCONICA Stolte et al. 2003

31. Mass-loss ZAMS 0.5 Myr 1 Myr 1.5 Myr 2 Myr

32. 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: = t CL ±  = (2.0-2.5) ± 0.3 Myr. Apply evolution models to determine apparent magnitudes. Assign extinction: = A K,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 A K =3.1. Estimate N(N M>130 M  )=0.

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

34. Results of Monte Carlo simulation

35. 4. Violators?

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

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

38. 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

39. Claim 1-7 L Pistol* 150-1000 M ⊙ Primary uncertainties distance temperature singularity LBV 1806-20 SGR LBV

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

41. Does R136 have a cutoff? Weidner & Kroupa 2004, MNRAS, 348, 187 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 M c ~50,000 M . –deficit of 4 stars with M>150 M  for M c ~20,000 M . Metallicity in LMC is less than in Arches: Z LMC ~Z  /3. Upper mass cutoff to IMF is roughly the same over a factor of three in metallicity.

42. 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.

43. 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)

44. 130 New Galactic Clusters from 2MASS Candidate 2MASS Clusters

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

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