The Low-End MF of the Arches Cluster

Sungsoo S. KimKyung Hee Univ., Korea

with

Jihye ShinDon Figer

The Arches Cluster

• ~30 pc away from the Galactic Center (in projection)• Young, compact cluster

– Age = ~2.5 Myr old

– Mass = 3-4x104 M⊙

– Size = ~1 pc (from King-profile fit)

• One of the most massive & youngest clusters in the Milky Way

Star Formation in the GC

• Harsh environment– Strong tidal forces

– Large internal velocity dispersions within clouds

– Strong magnetic fields

• A different mode of star formation is expected in the Galactic Center

Large Fg, T, B

External Compression Required

Flatter IMF ?

Elevated IMF Lower Limit ?

The Arches Cluster as a Benchmark of Infrared Cameras

Lick 3-m Figer (1995)

Keck I 10-m Serabyn et al. (1998)

HST/NICMOS Figer et al. (1999)

Keck II NIRC2-LGSKim et al. (2006)

Luminosity & Mass Functions from the Most Recent Observation

Kim, Figer, Kudritzki, & Najarro (2007)

Keck II NIRC2-LGSMay 2006

One of the first crowded-field observations with the Keck LGS/AO

0.02”/pix, 1024x1024900s exp., H & Ks

Medium & wide cameras9-point dither pattern

0.06~0.25 Strehl ratio0.06”~0.10” FWHM

Moderate radial elongation of PSF due to a small isoplanatic patch

Less extinction in the core – winds or from massive

stars? – photo-evaporation by

intense UV radiation?

One cluster field + three control fields

Controls are needed to estimate the background population.

No NGS near the cluster Need for LGS/AO

Reduced with DAOPHOT

mag error 0.05 down to Ks19

Calibrated against HST/ NICMOS obs.

2Myr solar Z isochrone for the cluster

1Gyr solar Z isochrone for the control

Luminosity functions: Cluster & Controls

(Dereddened, completeness-corrected)

Mass Functions

(Keck: Background-subtracted, VLT: Includes background)

Γ=-0.9

Bump in the NGC 3603(Eisenhauer 1998)

Is the bump real?

• Eisenhauer et al. (1998) adopted a PMS mass-mag relation by Palla & Stahler (1993), which has a steep slope at 3-7 M⊙.

• But, PMS mass-mag relations are thought to have rather large uncertainties with

– the extinction by the dust envelope

– the assumed accretion rate during the star formation.

Evolution of the MF

• The Arches cluster has dynamically evolved:– High density short relaxation timescale– Strong tidal field, large stellar mass range makes it evolve even faster,– Thus even at the age of 2.5 Myr, the PDMF may be quite different from

the IMF.

• We performed Fokker-Planck & Nbody6 simulations:– Circular orbits assumed.

– Results are insensitive to the lower mass cutoff (0.1, 1 M⊙).

– Power-law slope decreases by 0.1–0.2 during 2–2.5 Myr.

– Thus the IMF slope is estimated to be 2.0–2.1.

1.3–50 M⊙; 5”–9” annulus

The Latest MF of the Arches

• Without the proper control field data, it was previously thought that– there may be a turnover near 6.3 M⊙,

– this indicates a global decrease of the cluster MF.

• But we find that– the 6.3 M⊙ turnover is simply a local bump in the MF,

– the MF continues to increase at least down to 1.3 M⊙,

– the present-day MF has a power-law slope 1.9 for 5”–9” annulus.

• The bump was also observed in another young cluster, NGC 3603.

• Can we get more information below 1.3 M⊙?

The Pixel Intensity Histogram Method for the Low-End Mass Function

The Pixel Intensity Histogram Method

• Conventional Photometry– Identifies resolved stars and assigns magnitudes to them.

– Unable to recover too faint stars (background-limited) stars in crowded regions (confusion-limited)

• Pixel Intensity Histogram Method– Uses the intensity histograms of pixels with low intensities, i.e., the

pixels that do not belong to the bright, resolved stars.

Pixels that belong to resolved stars

– One can find the model mass function that best fits the observed pixel histogram.

– One needs to model not only the cluster stars, but also the background and the field stars.

– For the Arches cluster, we use the HST/NICMOS data because the characteristics of the images are relatively well known.

• Other Statistical Methods– Count-Brightness Ratio (Baum & Schwarzschild 1955)

• Estimates the stellar content (population) of external galaxies.• Analyzes the ratio of the number of resolved stars to the surface brightness.

– Surface Brightness Fluctuations (Tonry & Schneider 1988)• Measures distances of distant galaxies.• Analyzes pixel-to-pixel intensity variation.• Needs to have a large number of stars falling onto each pixel.

– Two-Point Correlation Function (e.g., Peebles 1980)• Measures the clustering of galaxies.• Analyzes the distribution of resolved objects.

Components of the Pixel Intensities

• Readout Noise– Mean = 31 e-, STDEV = 5.7 e-

• Dark Currents– 0.03 e-/s → 8 e- for 256 sec.

• Zodiacal Light– ~0.2 e-/s → ~40 e- for 256 sec.

• Thermal Radiation from the Telescope– ~100 e-/s → ~25,000 e- for 256 sec.

• Background and Foreground Stars– Observed control field LF + Star count model

• Cluster Stars– Observed cluster LF + Various model MFs

• Diffuse Near-IR Background– Scattered off dust grains?– ~5,000 e- for 256 sec.

Modeling the Control Fields (1/3)

1. Create a synthetic LF– with the observed LF from the HST and Keck observations for the bright part– with a Milky Way star count model (Wainscoat et al. 1992) for the faint part

HST

Keck

Model

Combined

Modeling the Control Fields (2/3)

2. Create an artificial image– with model PSFs from TinyTim (80x80 pixel)– with a thermal background level that fits the observation

Observation

Artificial

Modeling the Control Fields (3/3)

3. Add dark clouds to match the lowest intensity pixels– by introducing a certain amount of diffuse IR radiation

ObservationArtificial Image

Bright-Pixel Masked Images

Modeling the Cluster Field(0.2−0.35 pc annulus)

• Create synthetic LFs– with the observed LF from the HST and Keck observations for the bright part– with several power-law MFs for the faint part

HST

Keck

Power-law

Combined

α = −1 ( Γ = 2 )

MF

LF

Pixel Histogram

α = 1 ( Γ = 0 )

MF

LF

Pixel Histogram

α = 2 (Γ = −1 )

MF

LF

Pixel Histogram

α = 3 (Γ = −2 )

MF

LF

Pixel Histogram

• The pixel histogram method can be used to estimate the stellar content below the completeness limit of the PSF photometry.

• The MF in the 0.2-0.35 pc annulus has = 2−3 at least down to 0.5 M⊙.

• The integrated luminosity from stars with M<0.3 M⊙ is too small that even the pixel histogram method is not applicable.

• The existence of a relatively large amount of diffuse IR radiation remains to be examined.

• One could apply this method to other star clusters with unresolved, faint stellar population.

Results from the Pixel Histograms

• From the conventional PSF photometry, we know that the PDMF of the Arches cluster rises at least down to ~1 M⊙.

• The Arches cluster is dynamically evolved, but simulations show that its IMF is not much different from the PDMF in the intermediate annulus, which is not much different the Salpeter IMF ( = 2.1 down to 1 M⊙).

• Analysis of pixel intensity histograms suggests a non-negligible fraction of stars below 1 M⊙ ( ~ 2−3 down to 0.5 M⊙).

Summary