the low end of the initial mass function in young clusters ... - IOPscience

The Astrophysical Journal, 579:275–288, 2002 November 1 # 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE LOW END OF THE INITIAL MASS FUNCTION IN YOUNG CLUSTERS. II. EVIDENCE FOR PRIMORDIAL MASS SEGREGATION IN NGC 330 IN THE SMALL MAGELLANIC CLOUD1 Marco Sirianni,2 Antonella Nota,3,4 Guido De Marchi,3,4 Claus Leitherer,3 and Mark Clampin3 Received 2002 February 14; accepted 2002 July 9

ABSTRACT As part of a larger program aimed at investigating the universality of the initial mass function (IMF) at low masses in a number of young clusters in the LMC and SMC, we present a new study of the low end of the stellar IMF of NGC 330, the richest young star cluster in the SMC, from deep broadband V and I images obtained with HST/WFPC2. We detect stars down to a limiting magnitude of m555 ¼ 24:9, which corresponds to stellar masses of
0:8 M at the distance of the SMC. A comparison of the cluster color-magnitude diagram with theoretical evolutionary tracks indicates an age of
30 Myr for NGC 330, in agreement with previous published results. We derive the cluster luminosity function, which we correct for background contamination using an adjacent SMC field, and construct the mass function in the 1 7 M mass range. Given the young cluster age, the MF can well approximate the IMF. We find that the IMF in the central cluster regions (within 3000 ) is well reproduced by a power law with a slope consistent with Salpeter’s. In addition, the richness of the cluster allows us to investigate the IMF as a function of radial distance from the center. We find that the IMF becomes steeper at increasing distances from the cluster center (between 3000 and 9000 ), with the number of massive stars (> 5 M ) decreasing from the core to the outskirts of the cluster 5 times more rapidly than the less-massive objects (’ 1 M ). We believe the observed mass segregation to be of a primordial nature rather than dynamical since the age of NGC 330 is 10 times shorter than the expected relaxation time of the cluster. Subject headings: galaxies: star clusters — Magellanic Clouds — stars: evolution — stars: luminosity function, mass function (1988; ’ 2) to the much shallower slopes ( ’ 0; 1) derived by Elson, Fall, & Freeman (1989) and Hunter et al. (1995, 1996). The low- and intermediate-mass end of the IMF in starburst galaxies may be even more peculiar. The mass-to-light ratio of the stellar population in the prototypical starburst galaxy M82 can be understood if stars with masses below
3 5 M are absent (Rieke et al. 1993). At the smallest masses, the spread of IMF slopes determined is even larger: Are we observing true deviations from the Salpeter (1955) IMF, most likely triggered by local conditions of stellar density or star formation history? Or are we simply dominated by the observational uncertainties related to the data analysis and interpretation such as the choice of the evolutionary models or treatment of completeness? The conflicting claims of steep or shallow IMFs in LMC/ SMC clusters (see references above) could also be attributed to the limitations of the data so far. In fact, ground-based observations were typically restricted to the clusters’ periphery; and, as such, they often ignored the mass contribution from massive stars in the core: the shape of the resulting MF could then depend on the combination of the age of the cluster and the radial location at which the observations were conducted, as we discuss in x 9, without necessarily reflecting the properties of the IMF. When investigations are restricted to a limited portion of the cluster, the effects of dynamical evolution on the shape of the local MF must be taken into account (G. De Marchi, F. Paresce, & S. Portegies Zwart 2002, in preparation). In order to put the observational results on an equal footing, we have undertaken a systematic HST study of a number of young clusters in the LMC and in the SMC at different conditions of stellar density, age, and metallicity,

1. INTRODUCTION

The stellar initial mass function (IMF) and its possible universality has been the object of many studies and intense discussion since stars could be individually counted and clusters could be resolved. With the advent of the Hubble Space Telescope (HST), the commissioning of large ground-based telescopes (Keck, VLT), and the increased sophistication of the available instrumentation, new energy has infused the debate. How universal is the IMF (Kroupa 2001)? In star clusters and associations, where the distance effects are removed and the star formation history is simple, the answer should be straightforward. At high masses (10 100 M ) there is evidence for an IMF having a slope ¼ dðlog
Þ= dðlog MÞ ¼ 1:3  0:5 (Scalo 1998). Any variations, if present, would be masked by the observational uncertainties (Scalo 1998). At small and intermediate masses (1  10 M ), the situation is very different. Even in the LMC itself, where the field population shows a very steep IMF ( ’ 4; Massey et al. 1995), deep photometry of clusters has produced IMF parameters ranging from the steep IMFs found by Mateo

1 Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555. 2 Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218; [email protected]. 3 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218; [email protected], [email protected], [email protected], [email protected]. 4 Affiliated with the Research and Science Support Department of the European Space Agency.

275

276

SIRIANNI ET AL.

with the objective of studying the low end of the stellar IMF and understanding whether the IMF is constrained by local conditions at small masses. The advantage of such a study is to reduce the uncertainties associated with data analysis by establishing a homogeneous data treatment procedure, including a unique choice of models. Moreover, all the clusters have the same known distance, and they are very populous, providing good statistics to our sample. This procedure has been already applied to the R136 cluster in the LMC (Sirianni et al. 2000, hereafter S00). Very deep broadband V and I WFPC2 images of R136 from the HST archive were been used to sample the luminosity function below the detection limit of 2:8 M previously reached. In these new images, reaching a limiting magnitude of mF555W ¼ 24:7, S00 found a population of red stars evenly distributed in area surrounding the R136 cluster, most likely pre–main-sequence stars in the mass range 0:6 3 M . They constructed the IMF for the cluster in the 1:35 6:5 M range and found that, after correcting for incompleteness, the IMF shows a flattening below ’ 2 M . So far, this result is unique. Using the same methodology, HST images have been obtained for 10 additional clusters in the LMC (M. Sirianni et al. 2002, in preparation) and one in the SMC—NGC 330, for which we present the results in this paper. 2. NGC 330

NGC 330 is one of the brightest young clusters in the SMC. It is young (age less than 50 Myr) and very populous. Initial indications of a very peculiar abundance (lower than a factor of 5 with respect to the SMC field young population; Richtler, Spite, & Spite 1990) have recently been revised by Gonzalez & Wallerstein (1999) and Hill (1999). Gonzalez & Wallerstein (1999) find a mean value of ½Fe=H ¼ 0:94  0:02 dex for NGC 330, compared with the SMC field of ½Fe=H ¼ 0:69  0:10 dex (Hill 1999). Hill (1999) finds a slightly different value ½Fe=H ¼ 0:82  0:11 dex, which argues in favor of a formation of the cluster from gas that has experienced the same chemical history of the SMC, and this strengthens the suitability of NGC 330 for our comparative study. NGC 330 is known for its intrinsic abundance of Be stars (Feast 1972; Grebel, Richtler, & de Boer 1992; Keller, Wood, & Bessell 1998; Keller & Bessell 1998). Keller, Wood, & Bessell (1998) found a much higher fraction of Be stars with respect to the total number of B stars for NGC 330 than in the surrounding field. In Be stars, the emission is believed to arise from an optically thick rotating disk of material in the equatorial plane of the star (Struve 1931). Keller, Wood, & Bessell (1998) also found the Be population in NGC 330 to peak strongly at magnitudes corresponding to the main-sequence termination, whereas the Be stars in the field display a normal luminosity function. They concluded that the unusual concentration of Be stars in NGC 330 can be explained by a combination of evolutionary enhancement (due to an increase in the stellar rotational velocity during main-sequence evolution) and a distribution of intrinsically high rotational velocities within the cluster. Keller, Bessell, & Da Costa (2000) used the WFPC2 on HST to investigate the stellar population further. Their images reached a limiting magnitude of mF555W ’ 20. They obtained a color-magnitude diagram (CMD) that displays a peculiar feature: a clump of hot and luminous stars sepa-

Vol. 579

rated from the main sequence (MS), with a bluer color (F160W F555W < 3:1). In lower-mass clusters, this region of the CMD typically contains blue stragglers, and Keller et al. (2000) concluded that there might be blue stragglers even in the case of NGC 330. They also noted a finite width in the MS, larger than the photometric uncertainties, and they indicated as a possible explanation the combination of differential reddening across the cluster with residual uncertainties in the position-dependent flat field. Since our main interest lies in the characterization of the low end of the IMF, we proposed to revisit NGC 330 with the WFPC2 on HST and obtained much deeper images designed to sample the stellar IMF down to the lower limit of
1 M . We present the results of this imaging program in the following sections of this paper.

3. OBSERVATIONS AND DATA REDUCTION

Multiple images of NGC 330 were obtained in 1999 September using the WFPC2 on board the HST. Several exposures were taken through the filters F555W and F814W. These filters are described in detail by Biretta (1996) and closely resemble the Johnson V and I filters in their photometric properties. The images were dithered to allow a better removal of the detector blemishes and to improve both point-spread function (PSF) sampling and the photometric accuracy by averaging over the flat-field errors. For each filter, a dithered pair of 350 s exposures shifted by 0>5 was obtained, in addition to a single short (10 s) exposure to obtain photometry for the brighter sources. The cluster was centered in the planetary camera (PC), which has a field of view (FOV) of 3500  3500 with an effective plate scale of 0>045 pixel1. The other three wide field (WF) chips observed the outer regions of the cluster and flanking fields of the SMC with the same filter configuration but a larger FOV of 7500  7500 chip1 and a plate scale of 0>1 pixel1. All the images were taken with a gain of 7 e ADU1. The journal of all observations is provided in Table 1. The data set was processed adopting the standard STScI pipeline, which uses calibration observations and reference data such as bias, flat-field, and dark frames that are constantly updated by the STScI WFPC2 team to track any TABLE 1 Journal of HST + WFPC2 Observations

Proposal

Date

Filter

Exposure Time (s)

Image Name

NGC 330 (: 00h56m22906, :72 280 13>22; J2000.0) 8134 ......... 8134 ......... 8134 ......... 8134 ......... 8134 ......... 8134 .........

1999 Sep 4 1999 Sep 4 1999 Sep 4 1999 Sep 4 1999 Sep 4 1999 Sep 4

F555W F555W F555W F814W F814W F814W

350 350 10 350 350 10

U5AY1001R U5AY1002R U5AY1003R U5AY1004R U5AY1005R U5AY1006R

NGC 330 (: 00h56m22910, :72 280 13>51; J2000.0) 8134 ......... 8134 ......... 8134 ......... 8134 .........

1999 Sep 4 1999 Sep 4 1999 Sep 4 1999 Sep 4

F814W F814W F555W F555W

350 350 350 350

U5AY1007R U5AY1008R U5AY1009R U5AY100AR

No. 1, 2002

LOW END OF IMF IN YOUNG SMC CLUSTERS. II.

changes in the performance of the camera and its detectors. The basic steps of the calibration include the correction for the errors introduced by the analog to digital conversion, the removal of the bias level and bias pixel-to-pixel variations, the dark subtraction, the flat-field application, and, for only the short 10 s exposure, a shutter shading correction. Pixels with elevated dark current were corrected or marked as bad with the task WARMPIX in IRAF. Finally, in order to preserve the precision of our photometry across the entire FOV, two additional corrections were applied to the images after pipeline processing. First, a correction for the 3% reduction in the quantum efficiency due to a manufacturing pattern defect known as ‘‘ the 34th row error ’’ (Anderson & King 1999); and, second, the correction for the normalization of pixel area due to the geometric distortion removal caused by flat-fielding the images (Holtzman et al. 1995). The set of dithered observations was processed following the recipe of Gonzaga et al. (1998) using the STSDAS DITHER-II package in IRAF. First, the individual images were cosmic-ray rejected and stacked into a single image per

277

filter per dithered position. Then, in order to measure the shifts and rotation between these images, they were geometrically corrected and resampled using the DRIZZLE task. This method applies a cross-correlation–based technique to each of the three wide-field chips and averages the results from each chip to determine a better estimate of the overall image offset with respect to the reference image. Once the shifts were measured, the images were aligned and combined using the DRIZZLE algorithm, which corrects for geometric distortion and produces a final output image sampled on a finer grid than the input images. The final pixel scale is 7/10 the original PC pixel, which translates into 0>03185. Figure 1 shows the final combined image of NGC 330 in the F555W filter. The entire field is shown (PC + WF chips) together with an expanded view of the PC frame, to show at high resolution the inner regions of the cluster. 4. THE PHOTOMETRY

The strength of our proposed approach to the determination of the IMF in the clusters of the sample rests on the consistency of our data reduction and analysis. Therefore,

Fig. 1.—Final combined WFPC2 image of the NGC 330 cluster in the F555W filter. Insert: Portion of the FOV of the Planetary Camera (34>4  3400 ), where the cluster is centered. The orientation on the sky is indicated in the image.

278

SIRIANNI ET AL.

for NGC 330, we have followed the same methodology used for R136 (S00) and used the PSF fitting and aperture photometry routines provided within DAOPHOT. Given the different characteristics of crowding of the PC and WF fields in the long and short exposures, we have opted to perform PSF fitting photometry on the images generated by the long exposures and aperture photometry in all short exposures. First, we performed a statistical study on a sample of bona fide stars, carefully selected by eye in the F555W images, so as to define an appropriate range for the parameters that DAOFIND uses as selection criteria. The two parameters that permit one to discriminate between true stars and spurious objects are the roundness, which allows us to eliminate objects which are too elongated along rows or columns, and the sharpness, which can be used to discard objects whose profile largely differs from a Gaussian. From our sample of 215 stars in the PC frame, we found mean values of 0:63  0:08 and 0:14  0:23 for the sharpness and roundness, respectively. In the same way, from the sample of 139 stars in the WF frames, we found mean values of 0:75  0:61 and 0:04  0:30, respectively. We then ran DAOFIND on our data and conservatively set the detection threshold at 5  above the local background level. We excluded any object with sharpness and roundness parameters exceeding 3 times the standard deviations of the average bona fide values. We carefully examined the rejected objects and found that almost all of them were noise peaks associated with hot columns, diffraction spikes, or highly saturated stars, with a small number being isolated hot pixels and extended objects. The list of stars detected in the F555W image was then used to identify the stars in the F814W image: 3536 stars were found to be common to both filters in the PC and 13,191 in the three WF chips. In the case of the short exposures, we combined the two single images in each filter to remove cosmic rays and ran the DAOFIND routine on the output image: 585 stars were found to be common to both frames in the PC and 1129 in the three WF chips, respectively. We then performed core aperture photometry on the resulting images. With this technique (De Marchi, Paresce, & Ferraro 1993), the stellar flux is measured in a very small aperture 0>1 in size for the PC and 0>2 for the WF chips. The background is measured in an annulus located between 5 and 10 pixels (0>16 0>32Þ from the PSF peak in the PC frame and between 3 and 5 pixels (0>3 0>5) in the WF chips. The background annulus is deliberately chosen in close proximity to the star peak to ensure high-precision photometric measurements in the presence of crowding. The annulus itself contains a nonnegligible amount of light from the PSF wings, which is subtracted together with the background but needs to be estimated carefully and added back to the photometric measurement of the stellar source. This aperture correction is derived by assessing how the PSF encircled energy varies as a function of radial distance from the central peak. For each image, we have measured the encircled energy profile for a number of isolated stars and have used these measurements to correct the fluxes derived with aperture photometry. As previously mentioned, we used a PSF fitting technique on the images generated from the longest exposures. We constructed a sample PSF by combining seven moderately bright and isolated stars uniformly distributed over the

Vol. 579

image. We then performed PSF fitting photometry on the DRIZZLEd PC frame. As expected, the brightest stars were saturated in the longest exposures and were discarded during the detection process. However, the magnitude of these stars had been measured in the short integration frames and added to the list of unsaturated objects. The final database contains the photometry obtained from the short exposures (stars with mF555W < 18:0) and the long exposures (mF555W  18). The absolute photometric calibration was performed by converting the magnitudes of the individual stars to an aperture of radius 0>5 and by applying the transformation from the on-orbit system to the WFPC2 photometric system provided by Holtzman et al. (1995). The zero points used were 22.48 for the F555W filter and 21.60 for the F814W band. The original zero points were provided for a gain of 14 e ADU1, to which we added the correction for the different gain adopted in these observations (7 e ADU1; Holtzman et al. 1995). In Figures 2 and 3, we show the photometric errors assigned by DAOPHOT to all our measurements for the long and short exposures for the PC and for the WFs, respectively. For our study, we discarded all stars with an associated error larger than 0.2 mags in both filters. With this limitation, our final photometric list contains 3052 stars common to both filters in the PC frame, down to a limiting magnitude mF555W ¼ 24:9 and 12,674 stars in the FOV of the three WF chips, down to mF555W ¼ 25:7. We finally applied corrections for the charge transfer efficiency and the short versus long effect (see the Appendix). Although we do not include the full photometry database in this paper, the complete table is available in electronic form upon request.

5. THE COLOR-MAGNITUDE DIAGRAM

With the magnitudes obtained as described above, we have constructed a CMD where mF555W is plotted as a function of the mF555W mF814W color for all the stars with photometric errors smaller than
0.2 mag in the combined frames. Figures 4a and 4b show the CMD, referring to the PC and WF frames, respectively. The brightest portion of the CMD of NGC 330 has already been extensively studied in previous papers. The presence of two well-detached clumps of red and blue supergiants made it problematic to understand the evolutionary state of the most massive stars in the cluster (Caloi et al. 1993) and to determine its age (Chiosi et al. 1995). Grebel, Roberts, & Brandner (1996), using spectroscopic and photometric data, investigated the nature of the blue giants and suggested that they represent a mixture of rapidly rotating B/Be stars and blue straggler stars (BSSs) formed by the interaction of binary systems. The interpretation of these stars as a hot extension of the main sequence (MS) led to a systematic underestimate of the cluster age (Grebel et al. 1966). The presence of BSS is also responsible of much of the previously inferred age spread (Chiosi et al. 1995), which has been largely overestimated. The rich population of Be stars, clearly visible as a strip at mF555W mF814W
0:1 between mF555W ¼ 18 and 15.5 parallel to the MS, has recently been investigated by Hummel et al. (1998) and Keller et al. (1998, 2000). The BSSs are not, however, as easily discernible on our CMD as they are in the UV data of Keller et al. (2000) because their colors saturate in the visible and

No. 1, 2002

LOW END OF IMF IN YOUNG SMC CLUSTERS. II.

279

Fig. 2.—Photometric errors assigned by DAOPHOT to all our measurements in the PC frame in long exposures (top) and short exposures (bottom). We have discarded all stars with an associated error larger than 0.2 mag in both filters.

near-IR bands (thence the uncertainties on the age mentioned above). The MS turnoff is located at mF555W ’ 16 mag. The similarity between the CMDs plotted in the two figures indicates that NGC 330 extends well beyond the PC FOV: the rich population of Be stars and the evolved red supergiants seen in the CMD of the PC are also present in the CMD of the WF. Moreover, the red giant branch visible in the PC diagram shows that the contamination by the surrounding LMC field population in the inner regions of the cluster cannot be ignored and must be taken into account when measuring the luminosity function (LF). An interesting feature of the cluster MS is its nonnegligible broadening at all magnitude levels. Keller et al. (2000) have addressed this issue in detail and conclude that, although the broadening could be caused in part by flatfielding errors in their data (WFPC2 images in the F160W and F555W bands), it is most likely intrinsic to the cluster and/or due to differential reddening. They suggest both the presence of binary systems containing a red supergiant and an MS star as well as patchy absorption as possible explanations. Comparing Figures 4a and 4b with one another, however, reveals a marked increase of this effect with distance from the center: the spread in color around the MS ridge line in Figure 4a at 17 < mF555W < 20 is  ’ 0:06, whereas outside of the core (Fig. 4b), it grows to  ’ 0:10 over the same magnitude range. In the innermost regions, the extent of the spread is consistent with the error in the colors of the stars

of up to
0.25 mag stemming from the internal uncertainty in our photometry alone (see Figs. 2 and 3). It is also consistent with the contamination due to SMC field stars, whose color spread can easily be judged from the shape of the red giant branch shown in Figure 4b. In the WF frames, however, the effect is even larger, but the photometric error is smaller than in the innermost regions at the same magnitude level due to the lower level of crowding. The area covered by the WF fields is also larger (’4.65 arcmin2 vs. ’0.32 arcmin2 of the PC field), thus making patchy absorption resulting from gas not yet dispersed the most likely explanation of the observed MS broadening. The amount of reddening toward NGC 330 is still an unsettled matter. Estimates range from EðBV Þ ¼ 0:03 (Carney, Janes, & Flower 1985) to EðBV Þ ¼ 0:12 (Bessell 1991). Reddening estimates from the most recent spectroscopic observations seem to converge to an intermediate value (Caloi et al. 1993). In light of the possibility of patchy absorption, however, all these numbers have to be taken with care. For the purpose of measuring the MF, we adopt in the following a reddening correction of AV ¼ 0:16, which is based on the EðBV Þ ¼ 0:06 value of Gonzalez & Wallerstein (1999) and on the SMC extinction curve with R ¼ AV =EðBV Þ ¼ 2:7 presented by Bouchet at al. (1985). Because we measure our LF in magnitude bins of DV ¼ 0:5 mag, our determination of the MF is not significantly affected by the current uncertainties on the actual value of AV .

Fig. 3.—Same as in Fig. 3 but for the WFs frames

Fig. 4.—Observed color magnitude diagram of NGC 330 for all the stars with associated photometric error smaller than 0.2 in both filters. Objects 4252 and 12708 are found in the image with the PC (left) and WFs (right), respectively. A reddening vector for Av ¼ 0:5 is also shown.

LOW END OF IMF IN YOUNG SMC CLUSTERS. II. 6. THE AGE OF NGC 330

An estimate of the age of NGC 330 can be obtained by comparing the CMD of Figure 4a with the colors and magnitudes predicted by theoretical isochrones. Most models in the recent literature provide isochrones in the Johnson/ Cousin magnitude systems. In the following, we therefore make the simplifying assumption that the HST F555W and F814W filters coincide in practice with the standard V and I bands. In fact, as Holzman et al. (1995) show, the difference between F555W and F814W and their corresponding Johnson/Cousin bands never exceeds
0.03 mag for stars in the range 0:5 < V  I < 1 spanned by our CMD. These differences are smaller than our photometric errors, and, therefore, they will not significantly decrease the accuracy of our age determination. In order to derive the age of the cluster, we used (as in S00) isochrones constructed from the stellar evolutionary models provided by Siess, Fiorentini, & Dougados (1997). These tracks offer the choice of different metallicities: (Z ¼ 0:02, 0.04, 0.005). We adopted Z ¼ 0:005 for this study, which is as close as possible to the value of Z ¼ 0:003 estimated for NGC 330 (Hill 1999). However, the tracks of Seiss et al. (1997) do not consider stars more massive than 7 M , yet the CMD clearly shows the presence of evolved stars that can be more effectively used to estimate the age of the cluster with higher precision than simple isochrone fitting to the MS alone. To take advantage of red supergiant stars, and in order to assess the uncertainty affecting the age determination, we decided to also use the evolutionary tracks of Schaerer et al. (1993; published in the WFPC2 photometric system by Lejeune & Schaerer 2001). In this

281

case, the choice for the metallicity is Z ¼ 0:004, slightly different from the Z ¼ 0:005 of Siess et al. (1997). Isochrone fitting for the sole purpose of age determination has been restricted to the CMD of the innermost cluster regions (i.e., the PC field, or r < 2500 ), where the effects of background/foreground contamination are less severe. To translate absolute magnitudes into the apparent ones, we assumed a distance modulus ðm  MÞV ¼ 18:85 and reddening AV ¼ 0:16, EðBV Þ ¼ 0:06 as appropriate for NGC 330 (see x 5). Comparison with the isochrones suggests an age of 30 Myr, in excellent agreement with the logðageÞ ¼ 7:5 determined by Keller et al. (2000). This is shown graphically in Figure 5, where the isochrones that best fitted the central cluster regions (Fig. 5a) are also traced on the CMD of the stars in the outskirts (Fig. 5b). The dotted line shows the model of Siess et al. (1997), extending up to the MS turnoff. The solid line shows the model of Schaerer et al. (1993), which reaches the red giant branch. Because of the errors in our photometry, the age of NGC 330 estimated in this way can only be considered accurate to within 2 Myr. In Figure 5b, we also plot the isochrones of Schaerer et al. (1993) that seem to best fit the red giant branch of the older stellar population in the SMC. The age that we infer in this way is of the order of 1–2 Gyr. The isochrone that best fits the MS of the innermost cluster regions can also be used to derive the mass-luminosity (M-L) relation that we need to convert the LF into an MF as we explain in x 8 below. Since we are interested in the MF of MS stars, we decided to use the models of Siess et al. (1997) for compatibility with the determination of the MF in R136 (S00).

Fig. 5.—Observed color-magnitude diagram of NGC 330 (left panel: PC, right panel: WFC) with the 30 Myr isochrones from Schaerer et al. (1993; solid line) and Siess et al. (1997; dotted line). The 2 Gyr isochrone in the right panel is from Schaerer et al. (1993; dashed line). Black dots: Original positions of the Be stars, which have been relocated to the MS after correction for the excess flux due to the circumstellar envelope (see x 8).

282

SIRIANNI ET AL. 7. THE COMPLETENESS AND THE PHOTOMETRIC ERRORS

Before proceeding to the derivation of the IMF, it is also necessary to establish the completeness of our data. For both filters and for both the short and long combined images, the completeness has been assessed with the standard procedure. Artificial stars were inserted into the image for each half-magnitude bin. The number of artificial stars was less than 10% of the total number of stars in order not to severely affect the crowding in the region considered. The artificial stars have been retrieved using the same selection criteria of sharpness and roundness adopted in this work. Stars with a photometric error larger than 0.2 mag have been discarded. This test was repeated 10,000 times. The results of the test are summarized in Figures 6a and 6b, where we have plotted the completeness factor in each filter as a percentage of the stars successfully retrieved versus the total number of stars artificially added in the PC (inner region) and the three WFs (outer regions). As can be seen in Figure 6a, the completeness is worse in the brightest magnitude bin, where saturation effects prevent the detection of other very bright objects, and toward the faint end, where signal-to-noise ratio (S/N) effects start to dominate. The drop in completeness at mF555W ¼ 18:2 for the inner region of the cluster corresponds to the brightest magnitude bin from the long-exposure images, which is affected by the contamination of saturated stars. The completeness is better than 50% down to mF555W ¼ 23:5, mF814W ¼ 22:8 for the photometry in the center and down to mF555W ¼ 24:1, mF814W ¼ 23:2 for the outer regions.

8. THE LUMINOSITY AND MASS FUNCTIONS

The CMDs plotted in Figures 4a and 4b and the photometric completeness estimated as described above are the basis for deriving the LF and, from it, the MF. While, in

Vol. 579

principle, determining the LF would simply require the counting of the number of stars along the cluster MS, in practice, this task is complicated by a number of effects. First and foremost, as Figure 4b demonstrates, the contamination due to stars in the field of the SMC is rather severe. We have tackled this issue by adopting as background the most external region of our FOV. The core radius of NGC 330 is 9>5 (Vallenari, Ortolani, & Chiosi 1994) and, as such, it is completely contained within the PC FOV (3400  3400 ). Its surface brightness profile extends beyond 8000 , yet still within the three adjacent WFs FOV. We can, therefore, study the mass distribution along the entire extension of the cluster. We will assume that the LF measured in the most external region, between 9500 and 12500 from the center, represents an estimate of the LF of the background field. Second, to obtain a reliable estimate of the LF for MS stars, we must make sure that we count only the MS stars, yet all of them. This requires that we properly place the Be stars on the MS at a luminosity that would correspond to stars of their mass. Because Be stars are all clumped together in the CMD (see Fig. 4), there is no doubt that they all belong to the cluster. We thus need not apply the field star correction to them, and instead, we can directly place them onto the MS at the magnitude that corresponds to their mass. The latter translation has already been derived by Keller et al. (2000) for most Be stars in our sample. These authors have calculated a correction to apply to the effective temperature and luminosity of Be stars in order to remove the effect of the circumstellar reddening on the underlying stars. We identified in our FOV the Be stars found by Keller et al. (2000) and used their grid of colors and bolometric correction to assign to each Be star, with the corrected Teff and L=L , the appropriate photometry in the F555W and F814W bandpasses. In this way, we are able to place 99 Be stars on the MS position they would have without the excess flux due to their circumstellar envelope. Be stars that have

Fig. 6.—Completeness curves for F555W (left) and F814W (right). Horizontal lines show the 50% completeness level.

No. 1, 2002

LOW END OF IMF IN YOUNG SMC CLUSTERS. II.

been properly placed on the MS have been marked with a black dot in Figures 5a and 5b. A handful of stars that occupy the Be star locus in the CMD (4 in the PC and 10 in the WF frames) is not in the Keller et al. list due to a different FOV and, therefore, have not been corrected and were not included in the LF. Their absence has negligible influence on our conclusions. We notice here that patchy absorption (that we suspect to be at the origin of the observed MS broadening) has no systematic effects on the slope of the LF: it merely increases the photometric uncertainty and therefore smooths the LF as it allows stars of a given magnitude to spread into neighboring magnitude bins. Such an effect is also not relevant for the conclusions of this work. Due to the richness of our fields, we can study the variation of the LF with radial distance. After conversion to an MF, we will be able to analyze in detail the radial distribution of the stellar masses within the cluster to determine whether the star forming process is uniform or changes significantly in the core. We have chosen as cluster center the point of maximum stellar density in the frame, but our results are not significantly affected by a small uncertainty of its exact location. We have then traced five annuli between 000 and 2500 , each spanning 500 , and 10 more annuli 1000 wide between 2500 and 12500 from the center. We have extracted the stars whose position is defined by each annulus and constructed the LF. The artificial star experiments allow us to assess the completeness within each annulus. In Figure 7, we show the results of this analysis for several representative annuli. In the left column, we plot the CMDs derived from stars in our photometric catalog whose position is defined by each annulus. The LF after photometric completeness correction and relocation of the Be stars in the appropriate magnitude bin are shown as a solid line in Figure 7 (second column). The vertical dashed lines in those plots indicate the magnitude level for 50% completeness, whereas the dotted lines show the LF before correction for completeness. Converting the LF into an MF requires the knowledge of the ML relation to translate a given observed magnitude into a mass. To this end, we have used Siess et al.’s (1997) 30 Myr isochrone (from 0.6 to 7 M ) as plotted in Figure 5a and discussed in x 6 above. The derivative of the ML relationship is calculated by using a spline interpolation. Any other fit to the isochrone (e.g., a cubic spline) would considerably increase the uncertainty of the derivative (Silvestri et al. 1998) and, as a result, of the MF as well. The MFs determined in this way in each annulus are plotted in Figure 7 (middle column). Filled symbols mark the portion of the data with photometric completeness greater than 50%, which we use for our analysis; whereas below the mass limit set by 50% completeness (vertical dashed lines), the data can no longer be reliably interpreted. The dotted lines show the MFs derived from the LFs before correction for photometric incompleteness and prove that the latter is significant only at very low masses. Comparing the slope of the LFs and MFs in all the annuli, we noticed sharp steepening with increasing radial distance up to ’ 8000 from the center. At larger distance, the slopes of the MF appear constant,
3.5, in very good agreement with the value of 3:7  0:5 for the SMC field star population of Massey et al. (1995). This gives us some confidence that the most external annuli are populated

283

mostly by background/foreground stars. Therefore, we have constructed the LF in the region between 9500 and 12500 and subtracted the result from that measured in all other annuli. The panels in the fourth column in Figure 7 show the LF of each annulus corrected for completeness (dashed line), the background LF (dash-dotted line), and the final LF after correction for field star contamination for photometric completeness and replacement of the Be stars in the appropriate magnitude bin (solid line). The errors on the LFs reflect the Poisson statistics of the counting process (corresponding to the square root of the number of stars detected in each bin, suitably corrected for completeness) as well as the uncertainty stemming from the artificial star tests. The two errors are combined quadratically and included in the figure as 1  error bars. The progression of LFs in Figure 7 shows a noticeable steepening with increasing radial distance. The total number of objects in each annulus is, of course, not constant. If, however, all LFs were renormalized so that they have the same number of stars at m555 ’ 22, one could notice that the steepening of the LF with radial distance is due to the lack of more luminous (massive) stars in the periphery rather than to the lack of fainter stars in the core. This issue is addressed in more detail in the discussion. We finally calculated the MF from the corrected LF and plotted the results in the last column of Figure 7. The shape of the MFs measured at different radial distances is consistent in that it features a monotonic increase with decreasing mass for stars more massive than
1 M . The error bars on the MFs come directly from those on the LF, as we have assumed that the M-L relation is not affected by the statistical uncertainty. A flattening could be indicated by the data below that limit as is the case of R136 (S00). Yet, because the photometric completeness in that mass range is always less than 50%, we cannot assess the reliability of this intriguing conclusion, which would require deeper photometry. Consequently, we will concentrate on the mass range above
1 M . 9. DISCUSSION AND CONCLUSIONS

The most remarkable feature of the MFs shown in Figure 7 (right column) is the pronounced increase of the slope with increasing distance from the cluster center at r > 300 . This trend confirms the marked steepening already apparent in the LFs. The MFs are well fitted by a power-law distribution in the range 1 6 M spanned by our observations as shown by the solid lines. The slopes were obtained with a weighted least-squares 1 degree polynomial fit. Only measurements with a finite error were considered for the fit (Fig. 7, right column, solid circle). At an age of
30 Myr, NGC 330 is young enough that its present-day MF should reflect the cluster’s IMF, at least for stars that still are on their MS (i.e., for the objects less massive than
8 M ). Figure 8 shows the radial distribution of the index C of the IMF (Salpeter’s 1955 IMF, ¼ 1:35, is indicated in the upper right corner for reference). In the core (000 –3000 ), with ’ 1:5, the MF shows little variation, and it is very similar to Salpeter’s IMF but becomes considerably steeper than the latter in the periphery r > 3000 . A careful inspection of Figure 7 reveals that the steepening of the MF with distance is due to the lack of massive stars in the periphery rather than to the excess of low-mass

284

Fig. 7.—In this composite diagram (Figs. 7a and 7b), each row corresponds to a specific annulus around the center of the NGC 330 cluster. From left to right: (a) Observed CMD. (b) Observed LF (dotted line) and completeness corrected LF (solid line). Vertical long-dashed line: Magnitude level for 50% completeness. (c) Mass function. Filled symbols: Portion of the data with photometric completeness greater than 50% on which we base our analysis, whereas below the mass limit set by 50% completeness (vertical dashed line), the data can no longer be considered reliable. Dotted lines: MF derived from the LF before correction for photometric incompleteness. (d ) Luminosity function before (dashed line) and after (solid line) the subtraction of the field LF (dash-dotted line). (e) MF derived from the completeness corrected LF before (dashed line) and after ( filled circles) the background subtraction. Filled circles: Measurements used for the fit of the MF slope. Open circles: Points with photometric completeness less than 50% or with a nonfinite error.

285 Fig. 7.—Continued

286

SIRIANNI ET AL.

Fig. 8.—Slope of the IMFs constructed in equally spaced annuli are plotted as a function of distance from the cluster center. Dashed lines: Values corrected only for completeness, to be compared with the values corrected for completeness and field star contamination (solid line).

objects there: the projected density (stars=D log m=pc2 ) of the latter decreases by a factor of
4 between the core and the outskirts, whereas the former are depleted by a factor of 20 (measured at
1.5 and
5:0 M , respectively). Concerning the actual slope of the MF, however, we recall that the presence of binaries has been ignored as is often the case in studies of this kind. Obviously, we know that most stars in young clusters are binaries and when the latter are included, the MF becomes steeper as a whole (Kroupa 2000). This does not modify any of the conclusions that follow, but the index of the MF (C) must be scaled accordingly: it is thus well possible the MF is never as flat as indicated at the top of Figure 7. The observed mass segregation (i.e., the preponderance of massive stars in the core) can be understood the result of two mechanisms: (1) internal dynamical evolution and (2) local variations in star formation. In the following, we discuss both effects. Through repeated stellar encounters the stars in a cluster approach energy equipartition, inducing more massive stars to give part of their kinetic energy to lighter objects and to sink deeper into the cluster’s potential well. Light stars, on the other hand, can diffuse outward, passing onto larger, more energetic orbits (see, e.g., Spitzer 1987). The net result of these effects is a flattening of the MF in the central regions and a steepening in the periphery, a phenomenon called mass segregation. In order for two- and three-body encounters to allow enough objects to exchange energy and, thus, to impart a noticeable modification of the MF, a time of the order of the half-mass relaxation time is required. For NGC 330, the latter is about an order of magnitude longer than the cluster’s age, namely,
5  108 yr (Kontizas 1984) versus an estimated cluster age of
3  107 yr. Although it is possible that dynamical evolution has played some role in reshaping the MF in the innermost cluster regions where the

Vol. 579

density is high and the relaxation time is short, it is nevertheless quite unlikely that internal dynamical evolution might have had enough time to act on the stars throughout the whole cluster and produce the effects that we see in Figure 7, particularly the shortage of massive stars in the outer regions. In the scenario recently proposed by Bonnell et al. (2001b), however, mass segregation is a natural consequence of the mechanism of star formation itself, in such a way that forming clusters are already segregated at birth. A similar hypothesis had previously been suggested by Larson (1982) and addressed observationally by Sagar et al. (1988). As a result of the competitive accretion that occurs in stellar clusters, stars forming near the center would have a higher accretion rate, as the latter depends on the local gas density. The simulations of Bonnell et al. (2001a) show that, although low-mass stars form equally well throughout the cluster, more massive objects are almost exclusively relegated to the central regions (see their Fig. 4). As a consequence, they also predict that the MF should be considerably flatter in the core than it is in the periphery, much in the same way we see in Figure 8. The prevalence of more massive stars in young cluster cores has already been observed by Hillenbrand (1997) and Hillenbrand & Hartmann (1998), who studied the Orion Nebula Cluster (ONC) and found that the most massive stars are more concentrated than lower-mass objects. As Hillenbrand (1997) points out, however, the age distribution is also biased, with the youngest stars occupying the innermost regions. Thus, because of the young age of the ONC (of order
1 Myr) and the considerable spread of the latter (a few Myr; see Hillenbrand 1997 for a discussion), it is difficult to assess whether the observed concentration of massive stars is due to mass segregation or to age segregation and to understand which of the two processes dominates. On the other hand, with an age of 30  2 Myr and an age spread not larger than the uncertainty on the age (see x 6), NGC 330 could offer a clear-cut opportunity for investigating the nature of the segregation of massive stars in a rather young cluster. Kontizas et al. (1998) present a good case for mass segregation in the intermediate-age LMC open clusters SL 666 and, less convincingly, in NGC 2098. Although not as detailed and robust as the ones that we present in Figure 8, their LFs of SL 666 show a clear steepening with increasing radial distance. These authors discuss at length the dynamical state of SL 666 and conclude that, in spite of an age as high as
1.2 Myr, this cluster is not likely to have undergone extensive dynamical evolution and that the observed mass segregation must be primordial. A similar conclusion is reached by Fischer et al. (1998), who study NGC 2157 in the LMC and detect a modest amount of mass segregation (although, within the quoted uncertainties, all their MFs are consistent with the same ’ 1:1  0:45 index). They attribute this to the properties of the star formation process rather than to the dynamical evolution of the cluster, as the two-body relaxation timescale at the half-mass radius of NGC 2157 is large (trh ’ 1  109 yr) when compared with the cluster age (
1  108 yr). Another example of a young (3 4 Myr), segregated cluster is NGC 6231, studied by Raboud & Mermilliod (1998). These authors notice that only the most massive stars (> 25 M ) are centrally concentrated, whereas the distribution of less-massive objects is more uniform. They thus speculate that primordial mass

No. 1, 2002

LOW END OF IMF IN YOUNG SMC CLUSTERS. II.

segregation might be completely washed out when the most massive stars evolve and disappear after
10 Myr and cause a violent relaxation, which could, in principle, also disrupt the cluster. None of these prescriptions seem to apply to the case of NGC 330, where, as we show in Figure 8, mass segregation is still present at an age of
30 Myr, and the degree of central concentration decreases proportionally with mass at all levels, as one can see from the smooth steepening of the MF with increasing radial distance shown in Figure 7. A body of observational evidence is mounting that suggests that the mass distribution at birth, namely the IMF, is a sensitive function of the location in which stars form. Due to the uncertainties which have accompanied the various

287

claims of mass segregation detections in young clusters, little theoretical work has been done so far. Yet a robust and comprehensive model of star formation should now incorporate and treat primordial mass segregation as a constraint, as suggested by Bonnell et al. (2001a). We wish to thank Stefano Casertano for several helpful discussions and for making his data available for our comparison. Support for this work was provided by NASA grant G0-8134-01-97 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

APPENDIX THE CTE CORRECTION Shortly after the installation of WFPC2 on HST, it was discovered that the camera suffered from variable charge transfer efficiency (CTE). In 1994 March, a 10%–15% gradient in the photometric response of the CCDs along the column of each chip was discovered in all four of the WFPC2 CCDs. This effect is due to the partial loss of signal when charge is transferred down the chip during the readout, with the consequence that stars at higher row numbers appear fainter than they would if they were at low row numbers (Holtzman et al. 1995). The main cause of CTE degradation is the continuous radiation damage that occurs for space-borne CCDs such as the WFPC2. A significant reduction to the CTE effect was achieved by cooling down the four CCDs from 76 C to 88 C. The new temperature became operational on 1994 April 23, and the CTE stabilized at a
4% level. The first detailed characterization of the CTE degradation for WFPC2 was published by Whitmore & Heyer (1997), who made available an algorithm to calculate the CTE correction as function of position in the chip, background counts, and target counts. Later it was discovered that CTE increased with time, and an additional temporal dependence was included in the correction formulae (Whitmore 1998). By the end of the fifth year of operation, the charge loss for the faintest sources is quite dramatic: a star with 20–50 counts superposed on a low background was observed to be
40% fainter at Y ¼ 800 than at Y ¼ 1. The most updated CTE loss characterization with a longer time baseline (through 1999 February) is given in Whitmore, Heyer, & Casertano (1999), where a final set of formulae has been developed to correct for CTE loss when performing stellar aperture photometry with radii of 2 pixels. In addition to these studies from the STScI WFPC2 group, there have been three independent determinations of the CTE loss. Stetson (1998) derived a calibration that produced results similar to those of Whitmore & Heyer (1997) but without finding a significant time dependence. Later, Saha, Labheardt, & Prosser (2000) found a possible correction for their data that differs significantly from previous results and does not include an X position dependence, a time dependence, or a dependence on counts in the Y position. Finally, very recently, Dolphin (2000b) analyzed all the corrections available in the literature and concluded that the differences between the various methods might be related to the packages used to do photometry and, in particular, in the different treatments of the background. Using their new photometry package created specifically for WFPC2 data (Dolphin 2000a), they produced corrections similar to those of Whitmore et al. (1999) with a more updated temporal coverage (2000 March). Recently, Riess, Biretta, & Casertano (1999) have applied a new method to monitor CTE with a finer time sampling by measuring the counts in cosmic ray tails in dark calibration frames. Their results confirmed a steady growth of both X and Y CTE loss with time since installation of the instrument on board the HST. The CTE loss time dependence is very significant in the Y direction, causing time-independent CTE solutions (Stetson 1998; Saha et al. 2000) to be valid only for small intervals of time. The data we have collected for our program span over more than a year. We performed our photometry with DAOPHOT and eventually decided to use the correction formulae provided by Whitmore et al. (1999). In addition to the CTE effect, a position-independent charge loss was detected by P. Stetson (Kelson et al. 1993) and called the ‘‘ long versus short anomaly ’’ because it was first seen as difference in magnitude of a star in short and long exposures. This effect has been confirmed in a number of studies and finally characterized by Casertano & Mutchler (1998, hereafter CM98) as a nonlinearity defect strictly dependent on total counts in a stellar image and independent on exposure time or position on the chip. CM98 provide a general formula to correct the observed counts in a variety of conditions. The presence of such effects and the need for a correction has been recently discussed by Saha et al. (2000), who find such position-independent correction only in one filter, and by Stetson (1998), who finds no clear evidence of this anomaly. Dolphin (2000b) attempted to determine a position-independent loss in his CTE solution but found no evidence and concluded that all the detections of the long versus short error are ultimately the result of sky overestimation. We extensively examined our data in both filters to find evidence to rule out the presence of a short versus long effect. Of the entire sample of stars, 442 objects were found in both short and long exposures. After the CTE correction, we still have some discrepancy between the resulting magnitudes in the short and long exposures. Such a discrepancy is not completely removed by applying the short versus long correction. In particular, we found that the CM98 formula overcorrects the faintest sources.

288

SIRIANNI ET AL. TABLE 2 Coefficient of the Polynomial Fit Degree

Coefficient

0............................... 1............................... 2............................... 3............................... 4............................... 5............................... 6...............................

0.3537422 0.0093738 8.5775988e5 3.9170822e7 9.4029811e10 1.12550963e12 5.2748128e16

In order to assess whether this effect was due to different aperture parameters used for the photometry or was, instead, intrinsic in our data, we extracted the NGC 2419 images used by CM98 from the archive. After performing aperture photometry on the new data using the same parameters and selection rules as in our NGC 330 data, we confirmed the overcorrection for sources with signal lower than 120 counts. We therefore compared our photometry with the tables used by CM98 for their calibration, kindly provided by S. Casertano. We found perfect agreement between the two independent reductions; however, we also found that by selecting stars with photometric error less than 0.2 mag in the CM98 tables, we derive the overcorrection up to 0.25 mags for stars with only 20 counts. The correction formula provided by CM98 has been obtained by fitting all the photometric measurements in the FOV regardless of the photometric error associated with the measurements and, therefore, might not be the best solution in our study, since we are interested only in stars with solid photometric measurement. We decided to adopt the CM98 correction formula, which properly corrects the magnitude discrepancy for signal level higher than 120 counts, and to apply a further correction to remove the residuals. Given the similarities of the effect on our NGC 330 and the NGC 2419 data sets, we decided to calibrate the short versus long correction on the latter due to the higher number of sources (
1900) available for the calibration. The correction formula, to be applied to the source flux (DN) after CTE and the CM98 corrections, has been obtained with a least-squares sixth-degree polynomial fit whose coefficients are listed in Table 2. We did not find any significant color dependence and, therefore, applied the same correction to both the F555W and F814W data. REFERENCES Anderson, J., & King, I. R. 1999, PASP, 111, 1095 Keller, S. C., Wood, P. R., & Bessell, M. S. 1998, A&AS, 134, 489 Bessell, M. S. 1991, in IAU Symp. 148, The Magellanic Clouds, ed. Kelson, D. D., et al. 1993, ApJ, 463, 26 Kontizas, M. 1984, A&A, 131, 58 R. Haynes & D. Milne (Dordrecht: Kluwer), 273 Kontizas, M., Hatzidimitriou, D., Bellas-Velidis, I., Gouliermis, D., Biretta, J. 1996, WFPC2 Instrument Handbook (Baltimore: STScI) Kontizas, E., & Cannon, R. D. 1998, A&A, 336, 503 Bonnell, I. A., Bate, M. R., Clarke, C. J., & Pringle, J. E. 2001a, MNRAS, Kroupa, P. 2001, MNRAS, 322, 231 323, 758 ———. 2000, in ASP Conf. Ser. 211, Massive Stellar Clusters, ed. A. Lanc¸ Bonnell, I. A., Clarke, C. J., Bate, M. R., & Pringle, J. E. 2001b, MNRAS, on & C. Boily (San Francisco: ASP), 233 324, 573 Larson, R. B. 1982, MNRAS, 200, 159 Bouchet, P., Lequeux, J., Maurice, E., Prevot, L., & Prevot-Burnichon, Lejeune, T., & Schaerer, D. 2001, A&A, 366, 358 M. L. 1985, A&A, 149, 330 Massey, P., Lang, C. C., DeGioia-Eastwood, K., & Garmany, C. D. 1995, Caloi, V., Cassatella, A., Castellani, V., & Walker, A. 1993, A&A, 271, 109 ApJ, 438, 188 Carney, B. W., Janes, K. A., & Flower, P. J. 1985, AJ, 90, 1196 Mateo, M. 1988, ApJ, 331, 261 Casertano, S., & Mutchler, M. 1998, WFPC2 Instrument Science Report Raboud, D., & Mermilliod, J.-C. 1998, A&A, 333, 897 98-02 (Baltimore: STScI) Richtler, T., Spite, M., & Spite, F. 1990, in IAU Symp. 148, The Magellanic Chiosi, C., Vallenari, A., Bressan, A., Deng, L., & Ortolani, S. 1995, A&A, Clouds (Dordrecht: Kluwer), 374 293, 710 Rieke, G. H., Loken, K., Rieke, M. J., & Tamblyn, P. 1993, ApJ, 412, 99 De Marchi, G., Paresce, F., & Ferraro, F. R. 1993, ApJS, 85, 293 Riess, A., Biretta, J., & Casertano, S. 1999, WFPC2 Instrument Science Dolphin, A. E. 2000a, PASP, 112, 1383 Report 99-04 (Baltimore: STScI) ———. 2000b, PASP, 112, 1397 Sagar, R., Miakutin, V. I., Piskunov, A. E., & Dluzhnevskaia, O. B. 1988, Elson, R. A. W., Fall, S. M., & Freeman, K. C. 1989, ApJ, 336, 734 MNRAS, 234, 831 Feast, M. W. 1972, MNRAS, 159, 113 Saha, A., Labhardt, L., & Prosser, C. 2000, PASP, 112, 163 Fischer, P., Pryor, C., Murray, S., Mateo, M., & Richtler, T. 1998, AJ, 115, Salpeter, E. E. 1955, ApJ, 121, 161 592 Scalo, J. 1998 in ASP Conf. Ser. 142, The Stellar Initial Mass Function, ed. Gonzaga, S., et al. 1998,WFPC2 Instrument Science Report 98-04 (BaltiG. Gilmore & D. Howell (San Francisco: ASP), 201 more: STScI) Schaerer, D., Meynet, G., Maeder, A., & Schaller, G. 1993, A&AS, 98, 523 Gonzalez, G., & Wallerstein, G. 1999, AJ, 117, 2286 Siess, L., Fiorentini, M., & Dougados, C. 1997, A&A, 324, 556 Grebel, E. K., Richtler, T., & de Boer, K. S. 1992, A&A, 254, L5 Silvestri, F., Ventura, P., D’Antona, F., & Mazzitelli, I. 1998, ApJ, 509, 192 Grebel, E. K., Roberts, W. J., & Brandner, W. 1996, A&A, 311, 470 Sirianni, M., Nota, A., Leitherer, C., De Marchi, G., & Clampin, M. 2000, Hill, V. 1999, A&A, 345, 430 ApJ, 533, 203 Hillenbrand, L. A. 1997, AJ, 114, 198 Spitzer, L. 1987, Dynamical Evolution of Globular Clusters (Princeton: Hillenbrand, L. A., & Hartmann, L. W. 1998, ApJ, 492, 540 Princeton Univ. Press) Holtzman, J. A., Burrows, C. J., Casertano, S., Hester, J. J., Trauger, J. T., Stetson, P. B. 1998, PASP, 110, 1448 Watson, A. M., & Worthey, G. 1995, PASP, 107, 1065 Struve, O. 1931, ApJ, 73, 94 Hummel, W., Szeifert, T., Ga¨ssler, W., Muschielok, B., Seifert, W., Vallenari, A., Ortolani, S., & Chiosi, C. 1994, A&A, 108, 571 Appenzeller, I., & Rupprecht, G. 1998, A&A, 352, L31 Whitmore, B. 1998, WFPC2 Instrument Science Report 98-01 (Baltimore: Hunter, D. A., O’Neil, E. J. J. R., Lynds, R., Shaya, E. J., Groth, E. J., & STScI) Holtzman, J. A. 1996, ApJ, 459, L27 Whitmore, B., & Heyer, I. 1997, WFPC2 Instrument Science Report 97-08 Hunter, D. A., Shaya, E. J., Holtzman, J. A., Light, R. M., O’Neil, E. J., (Baltimore: STScI) Jr., & Lynds, R. 1995, ApJ, 448, 179 Whitmore, B., Heyer, I., & Casertano, S. 1999, PASP, 111, 1559 Keller, S. C., & Bessell, M. S. 1998, A&A, 340, 379 Keller, S. C., Bessell, M. S., & Da Costa, G. S. 2000, ApJ, 119, 1748