The Astronomical Journal, 139:378–389, 2010 February doi:10.1088/0004-6256/139/2/378C© 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

A DEEP UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS IN THE GALACTICANTICENTER REGION

Sneh Lata1, Anil K. Pandey

1, Brijesh Kumar

1, Himali Bhatt

1, Giancarlo Pace

1,2, and Saurabh Sharma

1,31 ARIES, Manora Peak, Nainital-263129, Uttarakhand, India; sneh@aries.res.in

2 Centro de Astrofisica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal3 Departamento de Fısica y Astronomıa, Facultad de Ciencias, Universidad de Valparaıso, Ave. Gran Bretana 1111, Playa Ancha, Casilla 53, Valparaıso, Chile

Received 2009 April 4; accepted 2009 November 15; published 2010 January 4

ABSTRACT

We present deep UBVRI CCD photometry of six open star clusters situated in the Galactic anticenter region(l ∼ 120–200◦). The sample includes three unstudied (Be 6, Be 77, King 17) and three partly studied open clusters(Be 9, NGC 2186, and NGC 2304). The fundamental parameters have been determined by comparing color–colorand color–magnitude diagrams with the theoretical models. The structural parameters and morphology of theclusters were discussed on the basis of radial density profiles and isodensity contours, respectively. The isodensitycontours show that all the clusters have asymmetric shapes. An investigation of structural parameters indicates thatthe evolution of core and corona of the clusters is mainly controlled by internal relaxation processes.

Key words: Galaxy: structure – open clusters and associations: individual (Berkeley 6, Berkeley 9, Berkeley 77,King 17, NGC 2186, NGC 2304) – stars: luminosity function, mass function – techniques: photometric

Online-only material: color figures

1. INTRODUCTION

Star clusters are agglomerations of stars having differentmasses, presumed to be formed from the same molecular cloud.Members of a star cluster are gravitationally bound, fairlycoeval, and share the same kinematical properties and initialchemical composition. Because of these characteristics, starclusters are ideal laboratories for a number of astrophysicalstudies. Open star clusters in our Galaxy are well distributedall over the Galactic disk and have a wide range of ages andmetallicities. As a result they carry a wealth of valuable scientificinformation both as single objects and as an ensemble. Open starclusters are excellent tools to investigate the structural propertiesof the Galactic disk such as its matter distribution (Pandey &Mahra 1987; Pandey et al. 1988; Piskunov et al. 2006), itsmetallicity gradient (Friel 1995), and the spiral arm (Dias &Lepine 2005; Pandey et al. 2006).

The morphological structure or shape of open clusters canbe governed by the initial conditions in the molecular cloudsas well as internal gravitational interaction and external tidalperturbations (Chen et al. 2004). Hence the structure of openclusters provides an opportunity to understand the effects ofexternal environment as well as internal stellar encounters onthe evolution of open clusters (Sharma et al. 2006, 2008).

The stellar mass distribution, i.e., mass function (MF) isthe key parameter for constraining star formation theories andfor understanding stellar evolution. A fundamental question,whether the shape of the MF is universal in time and space ordepends upon parameters like metallicity, age, and environment,is still not well understood (cf. Scalo 1986, 1998).

In spite of continuous observational efforts by various groups,∼ 50% of the cataloged clusters by Dias et al. (2003) are stillunstudied. Therefore we carried out photometry of six openclusters (Be 6, Be 9, Be 77, King 17, NGC 2186, and NGC 2304)to improve the database of open clusters. The primary aim of thepresent study is to catalog UBVRI CCD photometric data downto V ∼ 22 mag and determine fundamental parameters (suchas radius, age, distance, and reddening) of the partly studied or

unstudied clusters. Only three of the present targets have beenpartly studied and a brief description of these clusters is givenbelow.

Be 9. Maciejewski & Niedzielski (2007) have estimated thecluster parameters such as cluster radius (7′), distance (820 pc),age (3.98×109), and reddening (E(B − V ) = 0.79) using BVCCD photometry.

NGC 2186. NGC 2186 has been studied by Moffat & Vogt(1975). The faintest star recorded in the study was ∼14 mag.They derived the distance (1.44 kpc) to the cluster and reddeningE(B − V ) = 0.31 toward the cluster region. The photometry ofthis cluster has been limited to UBV photoelectric observationsof bright to intermediate stars.

NGC 2304. UBVI CCD photometric observations for thiscluster have been published by Ann et al. (2002). They foundthat the cluster is located at a distance of ≈ 4 kpc and it hasvery little reddening E(B − V ) = 0.10 ± 0.02 mag. They alsoestimated the age (≈1 Gyr) and [Fe/H] = −0.32. The basicparameters of the target clusters are listed in Table 1.

This paper is structured as follows. In Section 2, we de-scribe observation and data reduction procedures. In Section 3,we present the structure of the clusters. We analyze color–magnitude diagrams (CMDs) of the clusters in Section 4. InSection 5, we describe fundamental parameters. Mass functionof the target clusters is studied in Section 6. We summarize theresults in Section 7.

2. OBSERVATIONS AND DATA REDUCTION

The broadband Johnson UBV and Cousins RI photometricobservations for the target clusters were carried out using theCCD camera mounted at f/f13 Cassegrain focus of the 104 cmSampurnanand Optical Telescope of the Aryabhatta ResearchInstitute of Observational Sciences,4 Nainital. The CCD detectorhas 2048 × 2048 pixel2, and each of them has a square size of24 μm on a side, resulting in a scale of 0.′′38 pixel−1 and a

4 http://www.aries.res.in

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No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 379

Figure 1. V-band CCD images of the clusters Be 6, Be 9, Be 77, King 17, NGC 2186, and NGC 2304. The circles represent the cluster radii derived in Section 3.The small circle in the Be 6 image shows an uncataloged cluster near Be 6. Right ascension (R.A.) and declination (decl.) refer to epoch J2000. The obtained centralcoordinates of the clusters are found to be (01h51m11s, 61◦03′40′′), (03h32m39s, 52◦39′14′′), (07h21m27s, −03◦14′01′′), (05h08m22s, 39◦04′08′′), (06h12m08s,05◦27′13′′), (06h55m13s, 17◦58′57′′), and (01h50m51s, 61◦05′28′′) for Be 6, Be 9, Be 77, King 17, NGC 2186, NGC 2304, and S1, respectively.

Table 1Basic Parameters of the Target Clusters

Cluster α2000 δ2000 l b Size Distance log(age)(deg) (deg) (arcmin) (kpc)

Be 6 01h51.m12s +61◦05.′0 130.09 −0.96 5 . . . . . .

Be 9 03h32.m61s +52◦39.′1 146.06 −2.83 5 0.82 9.60Be 77 07h21.m46s −03◦14.′0 219.33 5.17 6 . . . . . .

King 17 05h08.m40s +39◦05.′0 167.33 −0.73 5 . . . . . .

NGC 2186 06h12.m11s +05◦27.′5 203.55 −6.19 5 1.44 7.74NGC 2304 06h55.m18s +17◦59.′3 197.21 8.89 10 4.00 8.90

Note. Basic Parameters of the target clusters taken from the WEBDA.

≈13′×13′ field of view. To improve the signal-to-noise ratio,observations were taken in the 2 × 2 pixel2 binned mode. Theobserved CCD images of the clusters are shown in Figure 1.The log of observations is given in Table 2.

The observations consist of several twilight flat-field framesand bias frames during each night as well as long and shortexposures of the cluster regions. In order to calibrate themagnitudes of stars in the cluster field, several standard starsin the field of SA 92, SA 95, SA 98, and SA 101 (Landolt 1992)were also observed.

The data reduction was carried out using the IRAF5 andESO MIDAS6 data reduction packages. The photometry of the

5 The Image Reduction and Analysis Facility is distributed by the NationalOptical Astronomy Observatories, which are operated by the Association ofUniversities for Research in Astronomy, Inc., under cooperative agreementwith the National Science Foundation (http://iraf.noao.edu).6 The Munich Image Data Analysis System is developed and maintained byESO, the European Southern Observatory.

bias-subtracted, flat-fielded, and cosmic-removed images wasperformed using the DAOPHOT profile fitting software (Stetson1987, 1992). We used short exposures to get the photometry ofbright stars which were saturated in long-exposure observations.The Gaussian FWHMs of the star images were found to liemostly between 1.′′8 to 2.′′5 (see Table 2). The instrumentalmagnitudes were transformed to the standard Johnson UBVand Cousins RI system using the procedure outlined by Stetson(1992). The equations used for photometric calibration are givenbelow:

u = U + zu + cu(U − B) + kuX

b = B + zb + cb(B − V ) + kbX

v = V + zv + cv(V − I ) + kvX

r = R + zr + cr (V − R) + krX

i = I + zi + ci(V − I ) + kiX,

where u, b, v, r, and i are the instrumental magnitudes correctedfor time and aperture; U, B, V, R, and I are the Landolt standard

380 LATA ET AL. Vol. 139

Table 2Log of Optical Photometric CCD Observations

Date Object U B V R I Airmass FWHM in V(n×Exp.) (s) (n×Exp.) (s) (n×Exp.) (s) (n×Exp.) (s) (n×Exp.) (s) (arcsec)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

2000 Jan 4/5 NGC 2304 4 × 900 3 × 600 3 × 300 3 × 300 3 × 300 1.03–1.25 1.56–2.122000 Jan 5/6 NGC 2304 7 × 300 7 × 100 7 × 60 7 × 50 7 × 60 1.02–1.49 1.52–2.14

SA 101 3 × 600 3 × 300 2 × 120 3 × 60 3 × 60 1.15–1.40 1.93–2.062006 Jan 22/23 NGC 2186 3 × 1800 3 × 900 3 × 900 3 × 300 3 × 150 1.09–1.60 2.10–2.20Feb 28 and Mar 32006 Jan 23/24 NGC 2186 3 × 300 3 × 180 3 × 120 3 × 60 3 × 300 1.38–1.76 2.20–2.30

SA 98 7 × 300 7 × 180 7 × 120 7 × 60 7 × 60 1.15–2.40 2.20–2.312006 Mar 5/6 Be 77 2 × 1800 3 × 900 3 × 300 3 × 200 3 × 200 1.20–1.75 2.40–2.512006 Mar 4/5 Be 77 9 × 300 9 × 200 9 × 100 9 × 60 9 × 50 1.12–1.54 2.49–2.74

SA 101 5 × 500 4 × 200 3 × 150 3 × 100 3 × 100 1.20–1.65 2.52–2.722006 Nov 24/25 Be 6 3 × 1800 4 × 600 4 × 300 4 × 100 3 × 100 1.17–1.25 1.82–1.982006 Nov 23/24 Be 6 3 × 300 3 × 120 3 × 60 3 × 40 3 × 40 1.17–1.19 1.75–2.28

SA 92 3 × 300 2 × 250 3 × 200 3 × 130 3 × 130 1.14–1.22 2.31–2.50SA 95 6 × 500 6 × 300 6 × 200 6 × 100 6 × 100 1.15–1.60 2.30–2.50

2006 Nov 24/25 King 17 2 × 1800 3 × 600 3 × 300 3 × 150 3 × 150 1.02–1.20 1.80–1.902006 Nov 23/24 King 17 3 × 300 3 × 200 3 × 100 3 × 50 3 × 50 1.09–1.23 1.80–2.302007 Jan 22/23 Be 9 2 × 1800 2 × 900 2 × 600 2 × 300 2 × 300 1.10–1.46 2.60–2.802007 Jan 21/22 Be 9 3 × 500 3 × 300 3 × 100 3 × 60 3 × 50 1.11–1.21 2.19–2.42

SA 98 8 × 250 8 × 120 8 × 30 8 × 30 8 × 30 1.15–1.60 2.20-2.40

Notes. In Columns (3)–(7), we provide number of frames (n) and exposure time in seconds (s) (Exp.) for each filter. Col. (9) refersto the range of mean Gaussian FWHM seeing at the V band.

14 15

V

14 15

-0.10

0.1

V

-0.10

0.1-0.1

00.1

-0.10

0.1-0.1

00.1

V

13 14 15

V

12 14

V

12 14

Figure 2. Residuals between standard and transformed magnitudes and colorsof standard stars are plotted against V magnitude.

magnitudes; z’s are the zero-point coefficients; c’s are the colorcoefficients; k’s are the extinction coefficients in U, B, V, R,and I filters; and X is the airmass. Values of the coefficientsare listed for each observing night in Table 3. Figures 2 and3 show the difference Δ between the standard and transformedmagnitudes and colors of Landolt standards as a function ofV and (B − V ), respectively. The standard deviations of theresiduals ΔV , Δ(B −V ), Δ(U −B), Δ(V −R), and Δ(V −I ) are0.022, 0.016, 0.016, 0.009, and 0.016 mag, respectively. Theinternal errors as a function of brightness for each passbandare estimated using the artificial ADDSTAR experiment asdescribed by Stetson (1987) and the same are given in Table 4.The errors at brighter levels (V ≈ 16 mag) are � 0.01 mag,whereas for fainter stars (V � 20 mag) the errors become large(�0.05 mag). The total errors which include photometric andcalibration errors are also estimated and given in Table 4. Thesample of photometric data for cluster Be 6 along with positionsof the stars measured in the cluster is given in Table 5.

0.5 1

(B-V)

0.5 1

-0.10

0.1

(B-V)

-0.10

0.1-0.1

00.1-0.1

00.1-0.1

00.1

(B-V)

0 1

(B-V)

0 1 2

(B-V)

0 1 2

Figure 3. Residuals between standard and transformed magnitudes and colorsof standard stars are plotted against (B − V ) color.

2.1. Comparison with Earlier Photometry

Three clusters of our sample, namely Be 9, NGC 2186, andNGC 2304, were already partly studied. We plot the differencesΔV , Δ(U − B), Δ(B − V ), and Δ(V − I ) (in the sense, present-literature data) for the common stars in Figure 4 as a function ofV magnitude. The results of the comparison are given in Table 6and summarized below.

Be 9. The BV CCD photometry for 486 stars in 72′ × 48′field of view of Be 9 was reported by Maciejewski & Niedzielski(2007). The comparison of present magnitudes and colors withthose obtained by Maciejewski & Niedzielski (2007) indicatesfair agreement in V magnitudes in spite of large scatter, whereas(B −V ) colors obtained in the present study are bluer and showa systematic trend with increasing magnitudes.

NGC 2186. Moffat & Vogt (1975) reported UBV photoelectricphotometry of 23 bright stars (V � 14 mag) of NGC 2186. Thecomparison indicates that the V magnitudes and (B − V ) colorsobtained by us are in agreement with those reported by Moffat& Vogt (1975) whereas (U − B) colors obtained by Moffat &

No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 381

Table 3The Zero-point, Color, and Extinction Coefficients on Different Nights

Parameter 2000 Jan 5 2006 Jan 23 2006 Mar 4 2006 Nov 23 2007 Jan 21(SA 101) (SA 98) (SA 101) (SA 95 and SA 92) (SA 98)

No of stars 9 8 9 15 12Color range (mag) 0.51< (B − V ) <1.25 0.15< (B − V ) <2.19 0.51< (B − V ) <1.25 −0.22< (B − V ) <1.41 0.15< (B − V ) <2.19Magnitude range (mag) 13.18< V <15.60 11.95< V <14.90 13.18< V <15.60 12.52< V <16.28 11.95< V <15.67

Zero-point Coefficients

zu 6.826 ± 0.006 6.617 ± 0.008 6.908 ± 0.008 6.934 ± 0.006 6.970 ± 0.015zb 4.449 ± 0.005 4.454 ± 0.009 4.650 ± 0.005 4.765 ± 0.002 4.746 ± 0.008zv 4.092 ± 0.007 4.005 ± 0.007 4.311 ± 0.008 4.329 ± 0.009 4.363 ± 0.008zr 4.031 ± 0.005 3.944 ± 0.007 4.206 ± 0.012 4.242 ± 0.008 4.266 ± 0.011zi 4.523 ± 0.006 4.465 ± 0.007 4.666 ± 0.011 4.696 ± 0.007 4.765 ± 0.011

Color Coefficients

cu −0.064 ± 0.010 0.052 ± 0.008 −0.063 ± 0.016 −0.083 ± 0.006 0.034 ± 0.009cb −0.063 ± 0.006 −0.025 ± 0.005 −0.080 ± 0.008 −0.009 ± 0.001 −0.001 ± 0.005cv −0.149 ± 0.009 −0.017 ± 0.005 −0.119 ± 0.006 −0.011 ± 0.006 −0.016 ± 0.004cr −0.100 ± 0.011 −0.009 ± 0.007 −0.190 ± 0.009 −0.005 ± 0.014 0.009 ± 0.011ci −0.083 ± 0.005 −0.052 ± 0.002 −0.077 ± 0.005 0.004 ± 0.003 −0.039 ± 0.006

Extinction Coefficients

ku 0.423 ± 0.021 0.587 ± 0.009 0.571 ± 0.015 0.603 ± 0.016 0.655 ± 0.047kb 0.292 ± 0.008 0.332 ± 0.005 0.403 ± 0.021 0.324 ± 0.011 0.396 ± 0.024kv 0.153 ± 0.011 0.229 ± 0.009 0.264 ± 0.008 0.231 ± 0.014 0.192 ± 0.020kr 0.102 ± 0.006 0.160 ± 0.009 0.152 ± 0.016 0.163 ± 0.021 0.133 ± 0.027ki 0.051 ± 0.009 0.104 ± 0.006 0.101 ± 0.006 0.105 ± 0.018 0.087 ± 0.026

Note. Landolt fields are indicated in the respective column heads.

Be 9 NGC 2186

NGC 2304

12 14 16 18 20

V

-0.2

0

0.2

V

12 14

V

12 14 16 18

-0.2

0

0.2

-0.2

0

0.2

-0.2

0

0.2

Figure 4. Comparison of the present photometry with the photometry availablein the literature. Left panel shows a comparison of photometry with thephotometry by Maciejewski & Niedzielski (2007) in the case of Be 9. Middle andright panels compare the photometry by Moffat & Vogt (1975) for NGC 2186and Ann et al. (2002) for NGC 2304, respectively.

Vogt (1975) are redder and become even redder with increasingmagnitude.

NGC 2304. UBVI CCD photometry for NGC 2304 wasreported by Ann et al. (2002). The comparison indicates thatV magnitudes obtained by Ann et al. (2002) are systematicallyfainter by 0.045 mag at V ∼15 mag. The (U −B), (B −V ), and(V − I ) colors obtained by us are in fair agreement with thosereported by Ann et al. (2002).

3. STRUCTURE OF CLUSTERS

The stellar distribution within a cluster changes as the clusterevolves. The initial distribution of stars may be governedby the structure of parental molecular clouds and the starformation process (Chen et al. 2004; Sharma et al. 2006). As thecluster evolves, internal interactions due to encounters amongmembers may modify the distribution of stars. Moreover, stellarevaporation and external disturbance, e.g., Galactic tidal forcesand encounters with massive molecular clouds, would alterthe spatial structure and eventually dissolve the cluster. Onlymassive and compact clusters near the Galactic plane wouldhave survived against destructive forces (Chen et al. 2004).Further, the clusters away from the Galactic disk, particularly inthe case of older systems, show a tendency to have a sphericalshape, probably due to dynamical relaxation.

Isodensity contours for the target clusters have been generatedto study the effect of internal gravitational interactions andexternal tidal forces. Figure 5 shows that all the clusters haveelongated morphology. The isodensity contours for the Be 6region manifest another prominent clustering toward the north–east of Be 6 at α = 01h50m51s and δ = 61◦05′28′′. We designatethis cluster as S1.

The extent of clusters can be determined with the help of astellar surface density profile. To draw the stellar density profile,we have to first derive the center of the clusters. The center ofthe clusters was obtained iteratively following the procedureof Sagar & Griffiths (1998). We calculated the average X andY positions of stars within 100 pixels around an initially eye-estimated center, until convergence within a pixel. An errorof a few arcseconds is expected in locating the cluster center.Using the cluster center, the radial density profile was derivedby counting stars inside concentric annuli and then dividingthe number of stars by the area of the respective annulus. Theresulting radial density profile as a function of radial distance isshown in Figure 6. The point at which the cluster stellar density

382 LATA ET AL. Vol. 139

Table 4Internal Photometric Errors in Magnitude as a Function of Brightness

Magnitude σU σB σV σR σI σU T σBT σV T σRT σI T σU σB σV σR σI σU T σBT σV T σRT σI T

Be 6 Be 9

<12 0.001 0.001 0.001 0.001 0.001 0.018 0.011 0.018 0.026 0.020 0.001 0.001 0.003 0.002 0.001 0.050 0.026 0.022 0.031 0.02912–13 0.001 0.001 0.004 0.002 0.005 0.018 0.011 0.018 0.027 0.020 0.001 0.001 0.001 0.002 0.007 0.050 0.026 0.022 0.031 0.03013–14 0.001 0.003 0.006 0.002 0.002 0.018 0.012 0.019 0.027 0.020 0.001 0.002 0.002 0.003 0.003 0.050 0.026 0.022 0.031 0.02914–15 0.005 0.004 0.006 0.007 0.007 0.019 0.012 0.019 0.027 0.021 0.002 0.008 0.003 0.003 0.003 0.050 0.027 0.022 0.031 0.02915–16 0.008 0.007 0.006 0.010 0.006 0.020 0.013 0.019 0.028 0.020 0.003 0.004 0.003 0.005 0.010 0.050 0.026 0.022 0.032 0.03116–17 0.021 0.008 0.007 0.014 0.016 0.028 0.014 0.019 0.030 0.025 0.011 0.007 0.006 0.011 0.013 0.051 0.027 0.023 0.033 0.03217–18 0.016 0.009 0.042 0.022 0.029 0.024 0.014 0.046 0.034 0.035 0.021 0.012 0.009 0.019 0.017 0.054 0.028 0.024 0.036 0.03318–19 0.026 0.042 0.053 0.033 0.054 0.032 0.043 0.056 0.042 0.057 0.021 0.018 0.024 0.030 0.038 0.054 0.031 0.032 0.043 0.04819–20 0.065 0.050 0.059 0.076 0.089 0.067 0.051 0.062 0.080 0.091 0.041 0.038 0.032 0.118 0.047 0.065 0.046 0.039 0.122 0.05520–21 0.104 0.043 0.058 0.120 0.133 0.106 0.044 0.061 0.123 0.134 0.037 0.057 0.082 . . . . . . 0.062 0.063 0.085 . . . . . .

Be 77 King 17

<12 0.001 0.003 0.001 0.001 0.001 0.023 0.023 0.013 0.022 0.014 0.001 0.001 0.001 0.001 0.001 0.018 0.011 0.018 0.026 0.02012–13 0.001 0.004 0.001 0.001 0.001 0.023 0.023 0.013 0.022 0.014 0.001 0.001 0.001 0.001 0.001 0.018 0.011 0.018 0.026 0.02013–14 0.002 0.001 0.007 0.001 0.005 0.023 0.023 0.015 0.022 0.014 0.001 0.004 0.001 0.005 0.004 0.018 0.012 0.018 0.027 0.02014–15 0.003 0.001 0.001 0.002 0.006 0.024 0.023 0.013 0.022 0.015 0.003 0.004 0.001 0.005 0.004 0.018 0.012 0.018 0.027 0.02015–16 0.007 0.002 0.003 0.011 0.007 0.024 0.023 0.013 0.025 0.015 0.003 0.005 0.011 0.006 0.005 0.018 0.012 0.021 0.027 0.02016–17 0.009 0.003 0.016 0.011 0.033 0.025 0.023 0.020 0.025 0.036 0.014 0.017 0.012 0.011 0.017 0.023 0.020 0.021 0.029 0.02617–18 0.022 0.009 0.021 0.012 0.044 0.032 0.025 0.025 0.025 0.046 0.018 0.023 0.017 0.038 0.023 0.026 0.026 0.025 0.046 0.03018–19 0.048 0.027 0.022 0.055 0.083 0.053 0.035 0.025 0.059 0.084 0.035 0.027 0.018 0.039 0.027 0.039 0.029 0.025 0.047 0.03319–20 0.045 0.048 0.044 0.062 0.077 0.051 0.053 0.046 0.066 0.078 0.059 0.039 0.045 0.059 0.039 0.062 0.041 0.048 0.065 0.04420–21 0.170 0.051 0.068 0.075 0.121 0.172 0.056 0.069 0.078 0.122 0.081 0.085 0.091 0.075 0.085 0.083 0.086 0.093 0.080 0.087

NGC 2186 NGC 2304

<11 0.001 0.001 0.001 . . . 0.005 0.014 0.011 0.012 . . . 0.011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11–12 0.001 0.001 0.004 0.001 0.002 0.014 0.011 0.013 0.013 0.010 . . . . . . 0.001 0.001 0.002 . . . . . . 0.016 0.014 0.01212–13 0.002 0.001 0.005 0.001 0.004 0.015 0.011 0.013 0.013 0.010 0.001 0.002 0.002 0.002 0.002 0.024 0.011 0.016 0.014 0.01213–14 0.003 0.002 0.003 0.002 0.008 0.015 0.012 0.013 0.014 0.012 0.001 0.002 0.002 0.002 0.003 0.024 0.011 0.016 0.014 0.01214–15 0.002 0.004 0.003 0.001 0.004 0.015 0.012 0.013 0.013 0.010 0.001 0.002 0.002 0.007 0.013 0.024 0.011 0.016 0.015 0.01815–16 0.003 0.006 0.002 0.004 0.005 0.015 0.013 0.013 0.014 0.011 0.002 0.004 0.003 0.007 0.020 0.024 0.012 0.016 0.015 0.02316–17 0.008 0.008 0.012 0.008 0.016 0.017 0.014 0.017 0.016 0.019 0.005 0.007 0.008 0.007 0.025 0.025 0.013 0.018 0.015 0.02817–18 0.021 0.014 0.005 0.019 0.012 0.025 0.018 0.013 0.023 0.015 0.008 0.012 0.011 0.012 0.043 0.025 0.016 0.019 0.018 0.04518–19 0.024 0.015 0.022 0.032 0.043 0.028 0.019 0.025 0.035 0.044 0.009 0.012 0.014 0.015 0.081 0.026 0.016 0.021 0.020 0.08219–20 0.034 0.038 0.016 0.034 0.111 0.037 0.040 0.020 0.037 0.111 0.030 0.051 0.027 0.031 0.090 0.038 0.052 0.031 0.034 0.09120–21 0.100 0.094 0.049 0.096 . . . 0.101 0.095 0.051 0.097 . . . 0.036 0.062 0.075 0.070 0.131 0.043 0.063 0.077 0.071 0.13221–22 0.186 0.096 0.100 . . . . . . 0.187 0.097 0.101 . . . . . . 0.059 0.107 0.107 0.073 0.240 0.064 0.108 0.108 0.074 0.240

Note. Subscript T refers to the total error, and it is estimated as the quadratic sum of the photometric and calibration errors.

Table 5The UBVRI Photometric Data of Stars in the Cluster Field

ID R.A. Decl. X Y V U − B B − V V − R V − I σV σU σB σR σI

(d:m:s) (d:m:s) (pixel) (pixel) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag)

Be6-1 28:00:03.2 61:11:26.1 995.91 13.04 16.820 0.684 1.376 0.740 1.509 0.011 0.03 0.007 0.008 0.014Be6-2 27:59:59.5 61:08:58.8 802.77 13.27 16.880 0.664 0.950 0.600 1.286 0.009 0.081 0.025 0.010 0.010Be6-3 27:59:50.3 61:04:39.7 463.02 15.39 15.748 0.855 1.159 0.666 1.386 0.011 0.015 0.006 0.007 0.009. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

becomes equal to the field star density is considered the clusterradius. The field star density is estimated from the region welloutside the cluster extent. The estimated radii are: 4.′1 for Be 6,3.′0 for Be 9, 3.′1 for Be 77, 2.′50 for King 17, 3.′6 for NGC 2186,4.′8 for NGC 2304, and 2.′5 for S1. The radial density profile ofBe 6 was obtained by excluding the quadrant where the possiblecluster S1 is lying. Present radius values for Be 77 and King 17are in good agreement with the values given by Lyngå (1987),while for NGC 2304 the radius is found to be almost twice thatgiven by Lyngå (1987). Present radius estimates for Be 6,Be 9, and NGC 2186 are slightly larger than those given byLyngå (1987).

The observed radial density profiles of the clusters werefurther parameterized following the approach by Kaluzny &Udalski (1992), where the projected radial density ρ(r) is

described as ρ(r) = f0/(1 + (r/rc)2). The cluster’s core radiusrc is defined as the radial distance at which the value of ρ(r)becomes half of the central density f0. The best fit obtainedthrough a χ2-minimization technique is shown in Figure 6.Within the uncertainties the Kaluzny & Udalski (1992) modelreproduces well the radial density profile. The best fit gives coreradii for Be 6, Be 9, Be 77, King 17, NGC 2186, NGC 2304,and S1 as 0.′54 ± 0.′29, 0.′82 ± 0.′25, 1.′16 ± 0.′59, 0.′53 ± 0.′18,1.′00 ± 0.′19, 1.′44 ± 0.′56, and 0.′84 ± 0.′45, respectively.

Danilov & Seleznev (1994) showed that the parametersζ (= R1/R2) and μ(= N1/N2) follow the relationship ζ ∝ μ0.35,where R1 and R2 are the radii of the cluster core and corona andN1 and N2 are the number of stars in the core and corona. Danilov& Seleznev (1994) carried out a simulation of isolated clusterdynamics and found that the parameters ζ and μ obtained from

No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 383

Figure 5. Isodensity contours drawn from the sample having stars V � 18 mag. The axes are in arcminutes. The inner and outer circles represent the core and clusterradius as obtained in the present study.

Table 6Comparison of Present Photometry with the Photometry Available in the Literature

Magnitude ΔV N Δ(U − B) N Δ(B − V ) N Δ(V − I ) NRange Mean ±σ Mean ±σ Mean ±σ Mean ±σ

Be 9: comparison with Maciejewski & Niedzielski (2007)

V � 14 −0.044 ± 0.073 8 . . . . . . −0.026 ± 0.031 8 . . . . . .

14 < V � 15 −0.027 ± 0.041 9 . . . . . . −0.051 ± 0.018 9 . . . . . .

15 < V � 16 −0.033 ± 0.067 31 . . . . . . −0.076 ± 0.131 31 . . . . . .

16 < V � 17 −0.023 ± 0.081 73 . . . . . . −0.069 ± 0.084 73 . . . . . .

17 < V � 18 −0.061 ± 0.077 78 . . . . . . −0.140 ± 0.177 79 . . . . . .

18 < V � 19 −0.037 ± 0.106 15 . . . . . . −0.201 ± 0.201 15 . . . . . .

NGC 2186: comparison with Moffat & Vogt (1975)

V � 11 0.001 ± 0.075 2 0.029 ± 0.087 2 −0.012 ± 0.016 2 . . . . . .

11 < V � 13 0.022 ± 0.036 2 0.024 ± 0.026 2 −0.043 ± 0.021 2 . . . . . .

12 < V � 14 0.005 ± 0.035 6 0.040 ± 0.030 6 −0.023 ± 0.027 6 . . . . . .

13 < V � 15 0.011 ± 0.048 5 0.049 ± 0.160 5 −0.025 ± 0.035 5 . . . . . .

14 < V � 15 −0.012 ± 0.033 5 0.053 ± 0.130 6 −0.024 ± 0.038 2 . . . . . .

NGC 2304: comparison with Ann et al. (2002)

V � 14 −0.035 ± 0.064 19 0.035 ± 0.061 18 0.028 ± 0.063 20 −0.026 ± 0.061 1814 < V � 15 −0.051 ± 0.044 49 0.038 ± 0.047 49 0.042 ± 0.052 50 0.004 ± 0.069 5015 < V � 16 −0.019 ± 0.040 77 0.013 ± 0.044 75 0.024 ± 0.043 77 0.015 ± 0.054 7616 < V � 17 −0.022 ± 0.052 117 0.016 ± 0.072 109 0.008 ± 0.067 119 0.008 ± 0.061 11117 < V � 18 −0.012 ± 0.034 150 0.025 ± 0.095 112 0.015 ± 0.082 159 0.021 ± 0.060 14718 < V � 19 −0.016 ± 0.075 177 0.052 ± 0.150 38 0.019 ± 0.103 190 0.034 ± 0.060 16719 < V � 20 0.008 ± 0.081 145 . . . . . . 0.034 ± 0.165 147 0.038 ± 0.085 13020 < V � 21 0.006 ± 0.098 98 . . . . . . 0.023 ± 0.237 97 0.056 ± 0.149 9421 < V � 22 −0.071 ± 0.147 7 . . . . . . 0.103 ± 0.165 6 0.012 ± 0.283 8

Notes. The difference Δ is in mag, and it refers to the present photometry minus literature photometry. The mean and σ (standard deviation) are based onN number of stars.

384 LATA ET AL. Vol. 139

Radius (in arcmin)

20

40Be 6

0 2 4 6

10

20 S1

10

20 Be 77

102030 NGC 2304

10

20 NGC 2186

10

20 King 17

10

20 Be 9

Figure 6. Variation of stellar surface density with radius. The continuous curveshows the fit of the Kaluzny & Udalski (1992) profile to the observed datapoints. The dashed line represents the mean density level of the field stars. Theerror bars represent ±√

N errors.

simulations also follow the relation ζ ∝ μ0.35. They concludedthat the evolution of the core and corona of the clusters is mainlycontrolled by an internal relaxation process. This relationshipmay be caused by an approximate equality between the rates oftransfer of stars from the core to the corona and vice versa, asa result of stellar encounters (Danilov 1997). In order to studythe core–corona structure, we plot rc/rcn versus nc/ncn and rc/rversus nc/n diagrams for the target clusters in Figure 7, whererc, rcn(= r − rc), and r represent the core radius, size of corona,and cluster extent, respectively, and nc, ncn, and n represent thenumber of stars in the core, corona, and the cluster region (seeSection 5), respectively. We supplemented present data with thedata of Sharma et al. (2006). Figure 7 indicates that clustersunder present study follow the relation rc/rcn ∝ (nc/ncn)0.35 assuggested by Danilov & Seleznev (1994).

4. COLOR–MAGNITUDE DIAGRAMS

The CMDs of all the stars observed in the cluster regionare plotted in Figure 8 along with the visually fitted theoreticalisochrones for the cluster sequence (see Section 5). The CMDsshow a broad and contaminated main sequence (MS) extendingfrom 11 to 20 mag. The broadening of the MS may be dueto the presence of binaries, field stars, and photometric errors.The contamination due to foreground and background stars atthe fainter end is quite significant. The CMDs of all the clustersunder present study show evolutionary features. The MS of Be 6,Be 9, Be 77, King 17, NGC 2186, and NGC 2304 shows a ratherclear blue turn–off point in (V,B − V ) CMD at V magnitudesof ∼12.5, ∼16.0, ∼15.5, ∼13.5, ∼13.0, and ∼15.5 mag and(B − V ) colors of ∼0.60, ∼1.2, ∼0.20, ∼0.40, ∼0.15, and∼0.20 mag, respectively. In addition to the cluster MS, we noticeanother population in all CMDs, extending from V ∼ 14 to 20mag. This population seems to be similar to that detected inseveral other clusters located toward the anticenter direction ofthe Galaxy (Bragaglia et al. 2006; Carraro et al. 2005, 2006;Bellazzini et al. 2004, 2006; Pandey et al. 2006).

0 1 2 3 4 50

0.4

0.8

1.2 (a)

S1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

(b)

Figure 7. Diagrams of (a) rc/rcn vs. nc/ncn and (b) rc/r vs. nc/n for theclusters. The solid and open circles represent data taken from the present studyand Sharma et al. (2006), respectively. The values rc, rcn(= r − rc), and rrepresent the core radius, corona size, and cluster radius, respectively, and nc,ncn, and n represent the number of stars in the core, corona, and entire cluster,respectively. The continuous curves represent rc/rcn ∝ (nc/ncn)0.35 and rc/r ∝(nc/n)0.35 relations (see Section 3).

5. FUNDAMENTAL PARAMETERS OF THE CLUSTERS

5.1. Completeness of the CCD Data

Some stars present in the CCD frame could not be detecteddue to stellar crowding. In order to correct the data for in-completeness, the ADDSTAR routine given in the DAOPHOTsoftware package (Stetson 1987) was used. The artificial starswere added at random positions in the CCD images. The lu-minosity distribution of artificial stars is chosen in such a waythat more stars are inserted into the fainter magnitude bins. Inall, about 10%–15% of the total stars were added so that thecrowding characteristics of the original frame do not changesignificantly. The ratio of the stars recovered to those addedin each magnitude interval gives the completeness factor (CF)as a function of magnitude. The frames were re-reduced in asimilar procedure as used in the case of the original frames. Inpractice, we followed the procedure given by Sagar & Richtler(1991). We added artificial stars to both V and I images in sucha way that they have similar geometrical locations but differ inI brightness according to mean (V − I ) colors of the MS stars.The minimum value of the CF of the pair thus obtained is usedto correct the data for incompleteness (Sagar & Richtler 1991).The values of CF thus obtained are listed in Table 7 as a functionof brightness.

5.2. Cluster Members and Field Stars

In order to derive cluster parameters, it is necessary to removefield star contamination from the cluster region. In the absenceof proper motion studies, we used the statistical criterion toestimate the number of probable members in the cluster region(cf. Sagar & Griffiths 1998; Sandhu et al. 2003; Pandey et al.2007). This criterion is based on the assumption that the fieldstars within the cluster and in nearby surrounding areas aredistributed in a similar way. To estimate field star contaminationwe used the region outside the cluster region as a field region.The ratios of cluster to field region area are 0.53, 1.0, 1.0, 1.0,1.0, 0.93, and 1.0 for Be 6, Be 9, Be 77, King 17, NGC 2186,NGC 2304, and S1, respectively.

The contribution of field stars from the CMDs of the clusterregion was statistically removed using the procedure described

No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 385

21

18

15

12

21

18

15

12

21

18

15

12

-1 0 1 2

21181512

0 1 2 0 1 2 0 1 2 3

21

18

15

12

21

18

15

12

Figure 8. CMDs for all stars lying in Be 6, Be 9, Be 77, King 17, NGC 2186, and NGC 2304 regions.

(A color version of this figure is available in the online journal.)

Table 7Data Completeness Factor

Magnitude Completeness Factor (%)

Interval Be 6 Be 9 Be 77 King 17 NGC 2186 NGC 2304

Cluster Field Cluster Field Cluster Field Cluster Field Cluster Field Cluster Field

11 <V �12 . . . . . . . . . . . . . . . . . . . . . . . . 100 100 . . . . . .

12 <V �13 100 100 . . . . . . . . . . . . . . . . . . 100 100 . . . . . .

13 <V �14 100 100 100 100 100 100 100 100 100 100 100 10014 <V �15 100 100 100 100 98 100 100 100 100 100 100 10015 <V �16 98 100 100 100 97 100 100 100 100 100 100 10016 <V �17 97 100 100 99 93 100 97 100 98 98 100 10017 <V �18 96 100 89 95 93 100 93 100 99 97 100 10018 <V �19 95 98 91 94 96 98 73 100 96 97 100 10019 <V �20 93 95 70 83 86 97 57 80 76 77 99 10020 <V �21 67 74 . . . . . . 63 70 28 73 . . . . . . 99 10021 <V �22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 98

by Sandhu et al. (2003) and Pandey et al. (2007). Briefly, for astar in the (V, V − I ) CMD of the field region, the nearest starwithin V ±0.25 and (V − I ) ± 0.125 in the cluster’s (V, V − I )CMD was removed. While removing stars from the clusterCMD, the number of stars in each magnitude bin was maintainedas per the CF. The statistically cleaned color–color diagrams((V − I, B − V ) and (U − B,B − V )) and CMDs ((V,B − V ),

(V, V − I ), and (V, V − R)) for target clusters are used toestimate their fundamental parameters.

5.3. Cluster Parameters

In this section, we derive fundamental parameters of theclusters, e.g., reddenings, distance moduli, and ages of theclusters. These fundamental parameters are derived by visually

386 LATA ET AL. Vol. 139

3

2

1

0

3

2

1

0

0 1 2

(B-V)

0 1 2

(B-V)

0 1 2

3

2

1

0

(B-V)

Figure 9. Statistically cleaned (V −I ) vs. (B−V ) color–color diagrams. Dashedcurves are ZAMS by Girardi et al. (2002) for solar metallicity; see the text forfurther description.

(A color version of this figure is available in the online journal.)

fitting theoretical models given by Girardi et al. (2002) to theobserved data points.

5.3.1. Reddening

In order to find out extinction law toward the cluster region,(V − I, B − V ) color–color diagrams, as shown in Figure 9,have been used. In Figure 9, we have also plotted the reddenedzero-age main-sequence (ZAMS) assuming a normal reddeninglaw with ( E(V −I )

E(B−V ) = 1.25). The observations are fairly explainedby the theoretical ZAMS (Girardi et al. 2002), indicating anormal reddening law toward the direction of clusters. Toderive the interstellar extinction toward the clusters, we use the(U −B,B−V ) color–color diagram as shown in Figure 10. TheZAMS by Girardi et al. (2002) for solar metallicity (Z = 0.02)was used to fit the observed distribution of stars in the color–color diagram. The reddening slope E(U−B)

E(B−V ) was consideredto be normal (i.e., 0.72). The E(B − V ) values obtained aregiven in Column 5 of Table 8. The E(B − V ) values derivedhere are compared with those obtained from extinction maps bySchlegel et al. (1998). In the case of Be 6, Be 9, and King 17, theE(B − V ) values from Schlegel et al. (1998) extinction mapsare significantly higher than those obtained in the present work.The higher values of the E(B − V ) by Schlegel et al. (1998)may be due to fact that they refer to the reddening at infinity ina given direction. The color excess E(V −R) and E(V − I ) areestimated using the relation E(V − R) = 0.60×E(B − V ) andE(V − I ) = 1.25×E(B − V ), respectively.

5.3.2. Distance and Age

Using the extinction values as mentioned above, theisochrones by Girardi et al. (2002) were fitted visually to thestatistically cleaned CMDs (see Figures 11–14) to estimatethe distance and age of the clusters. The isochrone fitting tothe CMDs was done simultaneously for distance modulus and

1

0

-1

1

0

-1

0 1 2

(B-V)

0 1 2

(B-V)

0 1 2

1

0

-1

(B-V)

Figure 10. Statistically cleaned (U − B) vs. (B − V ) color–color diagrams.Solid curves are ZAMS by Girardi et al. (2002) for solar metallicity.

(A color version of this figure is available in the online journal.)

20

16

12

0 1 2

20

16

12

(B-V)

Be 6 Be 6 Be 6

Be 9 Be 9 Be 9

1 2

(V-R)

0 1 2 3

(V-I)

Figure 11. Statistically cleaned CMDs along with theoretical evolutionary mod-els by Girardi et al. (2002). The curves show the isochrones of log (age) = 7.5and 9.3 for Be 6 and Be 9, respectively. The isochrones shown by dashed linesare for the binary population.

(A color version of this figure is available in the online journal.)

age. The distance moduli, corresponding distances, and ages ofthe target clusters thus obtained are listed in Table 8. The Galac-tocentric distance RG was calculated by assuming the distanceof the Sun from the Galactic center as 8.5 kpc. Galactocentricdistances and distances of clusters above or below the Galacticplane of the target clusters are also given in Table 8. A carefulinspection of CMDs indicates the presence of blue stragglers inclusters Be 9, Be 77, King 17 and NGC 2304.

No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 387

Table 8The Estimated Parameters for the Target Clusters

Cluster (m − M) Distance log (age) E(B − V ) r rc RG |z|Name (mag) (kpc) (in yr) (mag) (pc) (pc) (kpc) (pc)

Be 6 14.80 2.52 ± 0.12 7.5 0.90 3.15 0.44 10.31 42Be 9 13.30 1.48 ± 0.07 9.3 0.79 1.36 0.38 9.76 73Be 77 13.70 4.63 ± 0.20 8.8 0.12 4.39 1.64 12.42 417King 17 15.10 4.71 ± 0.22 8.4 0.56 3.64 0.77 12.00 45NGC 2186 13.00 2.70 ± 0.12 8.3 0.27 3.20 0.82 11.02 291NGC 2304 13.55 4.44 ± 0.20 8.8 0.10 6.54 1.96 12.73 681S1 14.10 2.20 ± 0.09 7.4 0.77 1.48 0.52 9.91 33

Notes. The Galactocentric distance was calculated by assuming d = 8.5 kpc. The errors in E(B − V ) and log (age)are ±0.05 mag and 0.1 dex, respectively.

20

16

12Be 77 Be 77 Be 77

King 17 King 17 King 17

0 1 2

20

16

12

(B-V)

0 1 2

(V-R)

0 1 2 3

(V-I)

Figure 12. Same as Figure 11, but for Be 77 and King 17. The curves show theisochrones of log (age) = 8.8 and 8.4 for Be 77 and King 17, respectively.

(A color version of this figure is available in the online journal.)

5.3.3. Comparison with Previous Results

The reddening E(B − V ) derived in the present work forBe 9 agrees with that recently reported by Maciejewski &Niedzielski (2007), while the present estimate for the distance(1.48 ± 0.07 kpc) of Be 9 is higher as compared to the distance(distance = 0.82 kpc) reported by Maciejewski & Niedzielski(2007). The present determination of reddening and age forNGC 2304 agrees very well with those given by Ann et al.(2002), but the distance (4.44 ± 0.10 kpc) is slightly largerthan that derived by Ann et al. (2002) (3.98 ± 0.18 kpc). In thecase of NGC 2186 the reddening derived in the present work isin fair agreement with that given by Moffat & Vogt (1975),while the present age and distance estimates are somewhathigher.

6. LUMINOSITY AND MASS FUNCTION

We used the statistically cleaned CMDs to study the lumi-nosity function (LF). The LF of each cluster is given in Table 9.The LF was converted to MF using the theoretical evolution-

20

16

12

NGC 2186 NGC 2186 NGC 2186

NGC 2304 NGC 2304 NGC 2304

0 1 2

20

16

12

(B-V)

0 1 2

(V-R)

0 1 2 3

(V-I)

Figure 13. Same as Figure 11, but for NGC 2186 and NGC 2304. The curvesshow the isochrones of log(age) = 8.3 and 8.8 for NGC 2186 and NGC 2304,respectively.

(A color version of this figure is available in the online journal.)

0 1 2

20

16

12

(B-V)

S1 S1 S1

0 1 2

(V-R)

0 1 2 3

(V-I)

Figure 14. Same as Figure 11, but for S1. The curves show the isochrones oflog(age) = 7.4.

(A color version of this figure is available in the online journal.)

ary models given by Girardi et al. (2002). The MF generallyfollows the power law, N (log M) ∝ MΓ, and the slope of theMF is given as Γ = d log N (log M)/d log M , where N (log M)denotes the number of stars in a logarithmic mass bin and Γis the MF slope. For the mass range 0.4 < M/M < 10, the

388 LATA ET AL. Vol. 139

2

4 Be 6

2

4 Be 9

2

4 Be 77

2

4 NGC 2304

2

4 King 17

2

4 NGC 2186

0 0.5 1

2

4 S1

Figure 15. Cluster MFs for the whole cluster region. log (φ) represents log(dN/d log M). The error bars represents ±√

N errors. Continuous lines showa least-squares fit to the data.

1 2 3 4-3

-2

-1

(a)

1 2 3 4-3

-2

-1

1 2 3 4-3

-2

-1

2 4 6 8 10-3

-2

-1

2 4 6 8 10-3

-2

-1

2 4 6 8 10-3

-2

-1

(b)

r (pc)

21018-3

-2

-1

(c)

Figure 16. (a) Γ vs. rc (b) Γ vs. r (c) Γ vs. RG. Filled and open circles representdata from the present study and from Sharma et al. (2008), respectively. Theencircled data points are Be 77 and NGC 2304 (see the text).

classical value derived by Salpeter (1955) for the slope of initialmass function (IMF) in the solar neighborhood is Γ = −1.35.Figure 15 shows the plot of the MF of the clusters studied.The obtained MF slopes along with the mass range are given in

Table 9Luminosity Function of the Target Clusters

V N

Be 6 Be 9 Be 77 King 17 NGC 2186 NGC 2304 S1

10–11 1 . . . . . . . . . . . . . . . 111–12 . . . . . . . . . . . . 1 . . . . . .

12–13 3 . . . . . . . . . 7 . . . 213–14 4 . . . 2 1 5 514–15 12 2 4 7 10 19 215–16 13 8 13 14 12 26 616–17 29 23 30 12 21 37 1117–18 22 20 34 20 48 48 1118–19 43 31 13 50 43 41 1319–20 58 34 24 37 37 39 2420–21 53 . . . . . . 15 . . . 71 . . .

21–22 . . . . . . . . . . . . . . . 59 . . .

Note. N is the number of probable cluster members in various magnitude bins.

Table 10MF Slope Γ in the Given Mass Range

Cluster Mass Range ΓM

Be 6 9.05–0.90 −1.83 ± 0.21Be 9 1.64–0.80 −1.63 ± 0.41Be 77 2.40–0.95 −0.85 ± 0.38King 17 3.76–0.90 −1.90 ± 0.33NGC 2186 4.00–0.80 −2.01 ± 0.22NGC 2304 2.50–0.65 −1.00 ± 0.16S1 10.00–0.90 −1.27 ± 0.25

Table 10. Although the obtained values of Γ are within 3σ errorof the Salpeter value, the MF slope for Be 6, Be 9, King 17, andNGC 2186 seems to be steeper, whereas the Γ for Be 77 andNGC 2304 are shallower than the Salpeter value. The MF slopefor S1 matches well with that given by Salpeter (1955).

In order to see the dependence of the MF on spatial structureand location of the clusters in the Galaxy, we plot the MF slope asa function of core radius rc, cluster extent r, and Galactocentricdistance RG in Figure 16. We supplemented the present data withthe data given by Sharma et al. (2008). The Salpeter value for Γ(−1.35) is shown as a straight dashed line. Figure 16 indicatesthat clusters (barring Be 77 and NGC 2304) having core radiigreater than ∼0.5 pc and cluster radii greater than ∼ 2.5 pchave a steeper MF than the Salpeter MF. The clusters Be 77 andNGC 2304 are located at RG > 12 kpc and significantly awayfrom the Galactic plane (|z| ∼ 417 and 681 pc, respectively).Their different locations in the Galaxy may be a cause fordeviating from the general trend shown by other clusters. Theclusters located at RG ∼ 9.5–11 kpc also show a steeper MF.As these clusters are situated in the anticenter direction of theGalaxy, it can be suggested that the IMF might have been steepertoward the anticenter direction as compared to other directions.

7. DISCUSSION AND SUMMARY

The evidence of binary or double clusters are found in ourGalaxy (Subramaniam et al. 1995) as well as in the LargeMagellanic Clouds (cf. Bhatia et al. 1991). The existence ofcluster complexes can be understood in terms of star formationmodes. Although star formation is not yet well understood,there are many theories available in the literature on the starformation modes (e.g., spontaneous, sequential, and episodic

No. 2, 2010 UBVRI CCD PHOTOMETRY OF SIX OPEN STAR CLUSTERS 389

star formation). It is assumed that binary or double clusters musthave formed from the same parental molecular cloud. Molecularclouds are known to form more than one cluster in their lifetime.A cluster pair is termed as a binary cluster if the separation is lessthan 20 pc (Subramaniam et al. 1995). In the present study, wehave found a strong clustering near Be 6, which is termed as S1(see Section 3), with an angular separation of ∼2.′34 (∼ 1.5 pc).The distance (2.20 ± 0.09 kpc) and color excess E(B − V )(0.77 ± 0.05 mag) for S1 are somewhat similar to that ofBe 6 (distance = 2.52 ± 0.12 kpc and E(B − V ) = 0.90 ±0.05 mag); therefore, we conclude that there is a possibility thatthese clusters are members of a binary cluster.

7.1. Summary

This paper presents UBVRI CCD photometry of six openclusters. The cluster parameters like reddening toward thecluster region, distance, and age were calculated using color–color diagrams and CMDs. Isodensity contours show that allthe target clusters have an asymmetric shape. The structuralparameters for the target clusters were obtained using the radialdensity profile. The structural parameters rc/rcn and nc/ncnfollow the relation rc/rcn ∝ (nc/ncn)0.35. A comparison with thesimulation of isolated cluster dynamics by Danilov & Seleznev(1994) suggests that the evolution of the core and corona ofthe clusters in the anticenter direction of the Galaxy is mainlycontrolled by internal relaxation processes.

The youngest clusters of the sample, S1 and Be 6, haveMF slopes comparable to the Salpeter value. The oldest clusterBe 9 has a steeper MF slope, whereas other older clusters of thesample Be 77 and NGC 2304 (located at a larger distance fromthe Galactic plane) have shallower MF slopes. Two intermediateage clusters, King 17 and NGC 2186, have steeper MF slopes incomparison to the Salpeter value (−1.35). The clusters locatedat RG ∼ 9.5−11 kpc seem to have steeper MFs, suggesting thatthe IMF might have been steeper toward the anticenter direction.

The authors are thankful to the anonymous referee for usefulcomments that improved the scientific content of the paper. Weare also thankful to Professor Ram Sagar and Professor ElenaV. Glushkova for their valuable and useful suggestions.

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