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