CCD BV survey of 42 open clusters
Astronomy & Astrophysics manuscript no. 6588 c© ESO 2018
October 23, 2018
CCD BV survey of 42 open clusters
G. Maciejewski and A. Niedzielski
Centrum Astronomii Uniwersytetu Mikołaja Kopernika, ul. Gagarina 11, Pl-87100 Toruń, Poland
e-mail: gm@astri.uni.torun.pl
Received 10 January 2006 / Accepted 10 January 2006
ABSTRACT
Aims. We present results of a photometric survey whose aim was to derive structural and astrophysical parameters for 42 open clusters. While
our sample is definitively not representative of the total open cluster sample in the Galaxy, it does cover a wide range of cluster parameters and
is uniform enough to allow for simple statistical considerations.
Methods. BV wide-field CCD photometry was obtained for open clusters for which photometric, structural, and dynamical evolution
parameters were determined. The limiting and core radii were determined by analyzing radial density profiles. The ages, reddenings, and
distances were obtained from the solar metallicity isochrone fitting. The mass function was used to study the dynamical state of the systems,
mass segregation effect and to estimate the total mass and number of cluster members.
Results. This study reports on the first determination of basic parameters for 11 out of 42 observed open clusters. The angular sizes for
the majority of the observed clusters appear to be several times larger than the catalogue data indicate. The core and limiting cluster
radii are correlated and the latter parameter is 3.2 times larger on average. The limiting radius increases with the cluster’s mass, and
both the limiting and core radii decrease in the course of dynamical evolution. For dynamically not advanced clusters, the mass function
slope is similar to the universal IMF slope. For more evolved systems, the effect of evaporation of low-mass members is clearly visible.
The initial mass segregation is present in all the observed young clusters, whereas the dynamical mass segregation appears in clusters older
than about log(age) = 8. Low-mass stars are deficient in the cores of clusters older than log(age) = 8.5 and not younger than one relaxation time.
Key words. open clusters and associations: general; stars: evolution
1. Introduction
Open clusters are not trivial stellar systems, and their dynami-
cal evolution is not yet fully understood. Most of them are not
very populous assemblages of a few hundred stars. The least
massive clusters do not last longer than a few hundred Myr
(Bergond et al. 2001). The dynamics of more massive and pop-
ulous clusters is driven by internal forces to considerable de-
gree, which leads to evaporation of low-mass members and to
a mass segregation effect. Moreover, cluster member stars in-
cessantly evolve along stellar evolution paths, which makes an
open cluster a vivid system evolving in time; hence, star clus-
ters are considered excellent laboratories of stellar evolution
and stellar-system dynamics (Bonatto & Bica 2005).
To obtain a complete picture of a cluster, it is necessary to
study not only its most dense region (center) but also the ex-
panded and sparse coronal region (halo). As wide-field CCD
imaging of open clusters is usually difficult, the majority of
studies published so far are based on observations of the cen-
tral, most populous, and relatively dense core region. Nilakshi
et al. (2002) have presented the first, to our knowledge, results
of an extensive study of spatial structure of 38 rich open clus-
Send offprint requests to: G. Maciejewski
ters based on star counts performed on images taken from the
Digital Sky Survey (DSS). Bonatto & Bica (2005) and Bica &
Bonatto (2005) analyzed over a dozen open clusters in detail
using 2MASS photometry. In the former paper, the possible
existence of a fundamental plane of several open clusters pa-
rameters was suggested. More recently, Sharma et al. (2006)
published results of studies concerning cores and coronae evo-
lution of nine open clusters based on projected radial profiles
analysis.
In this paper a sample of 42 northern open clusters of linear
diameters, distances, ages, and number of potential members
from a wide range is investigated in detail based on wide-field
BV CCD photometry. The basic parameters and CCD photom-
etry of 11 clusters were obtained for the first time.
This paper is organized as follows. In Sect. 2 the sample
selection, observations, and data reduction are described. In
Sect. 3 the radial structure of clusters under investigation is
presented based on star counts. Results of color-magnitude-
diagram fitting are given in Sect. 4. The mass functions of tar-
get clusters are analyzed in Sect. 5. The obtained photometric
parameters for individual clusters under investigation and the
reliability of the results are discussed in Sect. 6, while in Sect. 7
http://arxiv.org/abs/0704.1364v1
2 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
Table 1. List of observed open clusters with redetermined
equatorial and Galactic coordinates.
Name Coordinates J2000.0 l b
(hhmmss±ddmmss) (◦) (◦)
King 13 001004+611215 117.9695 −1.2683
King 1 002204+642250 119.7626 1.6897
King 14 003205+630903 120.7486 0.3612
NGC 146 003258+632003 120.8612 0.5367
Dias 1 004235+640405 121.9639 1.2130
King 16 004345+641108 122.0949 1.3263
Berkeley 4 004501+642305 122.2377 1.5216
Skiff J0058+68.4 005829+682808 123.5814 5.6060
NGC 559 012935+631814 127.2008 0.7487
NGC 884 022223+570733 135.0659 −3.5878
Tombaugh 4 022910+614742 134.2071 1.0815
Czernik 9 023332+595312 135.4172 −0.4869
NGC 1027 024243+613801 135.7473 1.5623
King 5 031445+524112 143.7757 −4.2866
King 6 032750+562359 143.3584 −0.1389
Berkeley 9 033237+523904 146.0621 −2.8275
Berkeley 10 033932+662909 138.6158 8.8785
Tombaugh 5 034752+590407 143.9374 3.5924
NGC 1513 040946+492828 152.5955 −1.6243
Berkeley 67 043749+504647 154.8255 2.4896
Berkeley 13 045552+524800 155.0851 5.9244
Czernik 19 045709+284647 174.0986 −8.8321
Berkeley 15 050206+443043 162.2580 1.6187
NGC 1798 051138+474124 160.7028 4.8463
Berkeley 71 054055+321640 176.6249 0.8942
NGC 2126 060229+495304 163.2169 13.1294
NGC 2168 060904+241743 186.6426 2.2061
NGC 2192 061517+395019 173.4298 10.6469
NGC 2266 064319+265906 187.7759 10.3003
King 25 192432+134132 48.8615 −0.9454
Czernik 40 194236+210914 57.4762 −1.1003
Czernik 41 195101+251607 62.0054 −0.7010
NGC 6885 201140+263213 65.5359 −3.9766
IC 4996 201631+373919 75.3734 1.3158
Berkeley 85 201855+374533 75.7257 0.9812
Collinder 421 202310+414135 79.4299 2.5418
NGC 6939 203130+603922 95.8982 12.3012
NGC 6996 205631+443549 85.4401 −0.5039
Berkeley 55 211658+514532 93.0267 1.7978
Berkeley 98 224238+522316 103.8561 −5.6477
NGC 7654 232440+613451 112.7998 0.4279
NGC 7762 234956+680203 117.2100 5.8483
the relations between structural and dynamical parameters are
presented and discussed. Sect. 8 contains the final conclusions.
2. Observations and reduction
In this survey the cluster diameter and location on the sky were
the main criteria of target selection. In the first step we need
the New catalog of optically visible open clusters and candi-
dates by Dias et al. (2002) to select Galactic clusters with ap-
parent diameters ranging from 5 to 20 arcmin and a declina-
tion larger than +10◦. The former limitation guaranteed that
the entire cluster with its possible extended halo would fit in
the instrument’s field of view. The latter one comes from the
observatory location and eliminates potential targets that can-
not be observed at elevations higher than 45◦. We found 295
open clusters fulfilling these criteria.
In the second step, all small and relatively populous clusters
were rejected from the sample. In these clusters stellar images
are blended, making some portion of stars undetectable due to a
considerable seeing of about 5′′(FWHM) at the observing loca-
tion. To avoid poorly populated objects, hardly distinguishable
from the stellar background, the minimal number of potential
cluster members was set for 20. Moreover, to obtain at least 2
mag of the main sequence coverage, only clusters for which the
brightest stars were brighter than 16 mag in V were selected,
since the limiting magnitude was estimated as 18.5–19.5 mag.
All of the selected clusters were also visually inspected on DSS
images.
Finally, the sample of 62 open clusters was adopted. We
preferred previously unstudied open clusters, for which no ba-
sic parameters were available in the literature, and these clus-
ters were observed with higher priority. In this paper we present
results for 42 open clusters, which are listed in Table 1.
The collected photometric data for 20 unstudied clusters
deny their cluster nature, suggesting that they constitute only an
accidental aggregation of stars on the sky. These objects will be
discussed in a forthcoming paper (Maciejewski & Niedzielski
2007, in preparation) where extensive, detailed analysis of ev-
ery object will be presented.
2.1. Observations
Observations were performed with the 90/180 cm Schmidt-
Cassegrain Telescope located at the Astronomical Observatory
of the Nicolaus Copernicus University in Piwnice near Toruń,
Poland. A recently upgraded telescope was used in Schmidt
imaging mode with a correction plate with a 60 cm diameter
and a field-flattening lens mounted near the focal plane to com-
pensate for the curvature typical of Schmidt cameras.
The telescope was equipped with an SBIG STL-11000
CCD camera with a KAI-11000M CCD detector (4008 × 2672
pixels × 9 µm). The field of view of the instrument was 72 ar-
cmin in declination and 48 arcmin in right ascension with the
scale of 1.08 arcsec per pixel. The camera was equipped with a
filter wheel with standard UBVR Johnson-Cousins filters. The
2 × 2 binning was used to increase the signal-to-noise ratio.
Observations were carried out between September 2005
and February 2006 (see Table 2 for details). A set of 4 expo-
sures in B and V filters was acquired for each program field:
2 long (600 s) and 2 short (60 s) exposures in every filter. For
open clusters containing very bright stars, 2 extra very short
(10 s) exposures in each filter were obtained. One of Landolt’s
(1992) calibration fields was observed several times during
each night, at wide range of airmasses. The field was observed
between succeeding program exposures, in practice every hour.
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 3
Table 2. Calibration (aV , aB, bV , bB, a(V−B), and b(V−B)) and
atmospheric extinction (kV and kB) coefficients for individual
nights.
Date kV aV aB a(B−V)
kB bV bB b(B−V)
05.09.2005 0.3072 -0.0922 0.1876 1.2799
0.4648 20.4407 20.5982 0.1573
06.09.2005 0.4614 -0.0886 0.1825 1.2694
0.6387 20.4518 20.5750 0.1230
07.09.2005 0.5689 -0.0782 0.1775 1.2579
0.6790 20.5841 20.5501 -0.0349
08.09.2005 0.5346 -0.0997 0.1752 1.2749
0.7134 20.5139 20.6531 0.1394
04.10.2005 0.1804 -0.1030 0.1754 1.2784
0.3136 20.1073 20.2526 0.1452
05.10.2005 0.2448 -0.0990 0.1946 1.2935
0.3767 20.2757 20.3897 0.1140
06.10.2005 0.3447 -0.0911 0.1682 1.2593
0.4640 20.4129 20.4985 0.0855
07.10.2005 0.3621 -0.0975 0.2251 1.3227
0.4879 20.4133 20.3996 -0.0137
08.10.2005 0.1810 -0.0830 0.1906 1.2736
0.3014 20.1319 20.2151 0.0832
23.02.2006 0.3968 -0.1023 0.1458 1.2642
0.7820 20.9667 20.7216 0.5354
26.02.2006 0.1911 -0.1281 0.1142 1.2512
0.3658 21.0104 21.2547 0.2419
2.2. Data reduction and calibration
The collected observations were reduced with the software
pipeline developed for the Semi-Automatic Variability Search1
sky survey (Niedzielski et al. 2003, Maciejewski & Niedzielski
2005). CCD frames were processed with a standard proce-
dure including debiasing, subtraction of dark frames, and flat-
fielding.
The instrumental coordinates of stars were transformed into
equatorial ones based on positions of stars brighter than 16 mag
extracted from the Guide Star Catalog (Lasker et al. 1990). The
instrumental magnitudes in B and V bands were corrected for
atmospheric extinction and then transformed into the standard
system.
The preliminary analysis, including determining the width
of stellar profiles, calculating of the atmospheric extinction co-
efficients in both filters, and determining the transformation
equations between instrumental magnitudes and the standard
ones, was performed based on observations of Landolt fields.
The mean FWHM of the stellar profiles was calculated for each
Landolt field frame acquired during one night. The aperture ra-
dius used for photometric measurements was calculated as 3σ
of the maximum mean FWHM obtained from the Landolt field
observed during a night, and in practice it was between 6 and 8
arcsec.
The atmospheric extinction coefficients kV and kB were de-
termined for each night from 6–8 observations of the adopted
Landolt field at airmasses X between 1.6 and 3.2. Typically
more than 1000 stars in V and 750 in B were detected in ev-
1 http://www.astri.uni.torun.pl/˜gm/SAVS
ery Landolt field frame and the extinction coefficient in a given
filter was determined for each star from changes in its raw in-
strumental magnitudes with X. The median value was taken as
the one best representing a night. The values of the atmospheric
extinction coefficients for individual nights are listed in Table 2.
The raw instrumental magnitudes braw, vraw of stars in the
Landolt field were corrected for the atmospheric extinction, and
instrumental magnitudes outside the atmosphere b, v were cal-
culated as
b = braw − kbX , (1)
v = vraw − kvX . (2)
Next, the mean values of instrumental magnitudes outside the
atmosphere were calculated for every star. In every Landolt
field there were about 30 standard stars that were used to deter-
mine coefficients in the calibration equations of the form:
V − v = aV(b − v) + bV , (3)
B − b = aB(b − v) + bB , (4)
B − V = a(V−B)(b − v) + b(V−B) , (5)
where B, V are standard magnitudes and b, v are the mean in-
strumental ones corrected for the atmospheric extinction. The
detailed list of transformation coefficients for each night is pre-
sented in Table 2.
The final list of stars observed in all fields contains equa-
torial coordinates (J2000.0), V magnitude, and (B–V) color in-
dex. The files with data for individual open clusters are avail-
able on the survey’s web site2.
3. Radial structure
Analysis of the radial density profiles (RDP) is a commonly
used method for investigating cluster structure. It loses infor-
mation on 2-dimensional cluster morphology but it provides a
uniform description of its structure with a few basic parameters
instead. Defining the cluster’s center is essential for the RDP
analysis. Since the coordinates of clusters as given in Dias et
al. (2002) were found in several cases to be different from the
actual ones, we started with redetermination of the centers for
all the open clusters in our sample.
3.1. Redetermination of central coordinates
Our algorithm for redetermining the central coordinates started
with the approximated coordinates taken from the compilation
by Dias et al. (2002) or from a tentative approximate position
when the catalogue data were found to be inconsistent with the
cluster position as seen on DSS charts.
To determine the center position more accurately, two per-
pendicular stripes (20 arcmin long and 3–6 arcmin wide, de-
pending on cluster size) were cut along declination and right as-
cension starting from the approximate cluster center, and stars
were counted within every stripe. The histogram of star counts
2 http://www.astri.uni.torun.pl/˜gm/OCS
4 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
Table 3. Structural parameters obtained from the King profile
Name rlim rcore f0 fbg
(′) (′)
stars
arcmin2
stars
arcmin2
(1) (2) (3) (4) (5)
King 13 11.8 3.3±0.3 5.02±0.27 3.09±0.11
King 1 12.3 2.1±0.1 5.16±1.92 1.76±0.05
King 14 9.0 2.3±0.4 2.84±0.31 4.97±0.09
NGC 146 2.7 1.2±0.3 5.61±0.80 4.87±0.16
Dias 1 2.3 0.3±0.1 13.29±6.33 2.96±0.07
King 16 8.8 1.9±0.2 4.70±0.27 3.25±0.06
Berkeley 4 3.1 1.3±0.3 2.84±0.40 3.57±0.09
Skiff J0058+68.4 10.9 3.8±0.4 3.66±0.20 2.04±0.09
NGC 559 14.5 2.3±0.2 6.72±0.32 2.38±0.09
NGC 884 10.1 5.8±1.3 1.08±0.11 0.94±0.09
Tombaugh 4 5.6 1.1±0.1 12.91±0.53 1.62±0.07
Czernik 9 3.3 0.8±0.1 6.36±0.59 1.43±0.08
NGC 1027 10.3 3.3±0.5 1.63±0.13 0.81±0.05
King 5 10.9 2.4±0.2 5.81±0.29 1.96±0.09
King 6 10.9 3.6±0.4 1.55±0.09 0.62±0.04
Berkeley 9 7.3 1.2±0.1 3.88±0.18 1.16±0.03
Berkeley 10 8.3 1.3±0.1 6.36±0.39 1.28±0.07
Tombaugh 5 11.8 2.2±0.4 3.75±0.35 2.41±0.10
NGC 1513 9.2 3.7±0.6 2.47±0.20 1.04±0.09
Berkeley 67 5.2 1.9±0.1 3.53±0.16 0.92±0.04
Berkeley 13 6.1 1.4±0.1 5.20±0.32 2.13±0.06
Czernik 19 5.5 1.4±0.2 4.12±0.30 1.41±0.07
Berkeley 15 7.6 1.4±0.1 5.74±0.28 1.53±0.05
NGC 1798 9.0 1.3±0.1 9.55±0.28 3.14±0.05
Berkeley 71 3.3 1.2±0.2 6.04±0.58 1.99±0.09
NGC 2126 10.0 1.9±0.3 1.78±0.15 0.93±0.04
NGC 2168 9.8 4.8±0.5 2.27±0.16 1.03±0.08
NGC 2192 4.6 1.4±0.2 2.19±0.18 0.57±0.04
NGC 2266 5.9 1.2±0.1 7.69±0.50 2.32±0.08
King 25 6.3 2.3±0.3 4.93±0.34 1.36±0.13
Czernik 40 8.5 2.3±0.3 8.44±0.53 3.40±0.18
Czernik 41 5.6 1.7±0.2 3.96±0.28 1.65±0.09
NGC 6885 8.6 2.4±0.3 2.74±0.21 2.66±0.08
IC 4996 2.2 1.2±0.4 3.27±0.58 4.61±0.14
Berkeley 85 5.0 1.5±0.2 4.84±0.43 2.94±0.09
Collinder 421 6.1 1.1±0.3 2.67±0.46 0.93±0.07
NGC 6939 15.2 2.2±0.1 6.92±0.22 2.62±0.06
NGC 6996 2.1 0.9±0.3 3.58±0.78 3.66±0.10
Berkeley 55 6.0 0.7±0.1 7.63±0.67 1.45±0.04
Berkeley 98 4.6 2.1±0.3 4.00±0.30 5.40±0.08
NGC 7654 11.2 5.0±0.5 4.39±0.21 3.36±0.20
NGC 7762 9.5 2.4±0.2 5.06±0.29 1.45±0.08
was built along each stripe with a bin size of 1.0 arcmin for the
cluster with a diameter larger than 10 arcmin and 0.5 arcmin
for the smaller ones. The bin with the maximum value in both
coordinates was taken as the new cluster center. This proce-
dure was repeated until the new center position became stable,
usually a few times. The accuracy of the new coordinates was
determined by the histogram’s bin size and was assumed to be 1
arc min typically. The new equatorial and Galactic coordinates
are listed in Table 1.
3.2. Analysis of radial density profiles
The RDPs were built by calculating the mean stellar surface
density in concentric rings, 1 arcmin wide, centered on the re-
determined cluster center. If Ni denotes the number of stars
counted in the ith ring of the inner radius Ri and outer Ri+1
the stellar surface density ρi can be expressed as
π(R2i+1 − R
. (6)
The density uncertainty in each ring was estimated assuming
the Poisson statistics. The basic structural parameters were de-
rived by least-square fitting the two-parameter King (1966) sur-
face density profile
ρ(r) = fbg +
rcore
, (7)
where f0 is the central density, fbg the density of the stellar
background in a field, and rcore the core radius defined as the
distance between the center and the point where ρ(r) becomes
half of the central density.
The RDPs and the fitted King profiles are shown in Fig. 1
where the densities were normalized (after background density
subtraction) to the central value. As one can note, all clusters
can be described by the King profile reasonably well, and even
for relatively small objects, no significant systematic deviation
is noticeable. The RDP of Berkeley 67 indicates the presence
of a strong background gradient, so the background level was
artificially straightened for the profile fitting procedure. In sev-
eral cases (NGC 146, Dias 1, Berkeley 4, and NGC 7654), the
RDPs were cut off at r smaller than expected. That is because
these clusters were located in a field centered on another open
cluster and were observed serendipitously.
The RDPs were also used to determine the limiting radius
rlim, the radius where cluster’s outskirts merge with the stellar
background. This is not a trivial task and properly determin-
ing rlim is important for further investigations. Therefore a uni-
form algorithm was developed and applied to all clusters. In its
first step the boundary density level ρb was calculated for every
RDP as
ρb = fbg + 3σbg , (8)
where σbg denotes the background density error derived from
the King profile fit. Next, moving from the cluster center (r = 0
arcmin) outwards, the first point below ρb was sought. When
this ith point was encountered, the algorithm was checked to
see if farther-out points were also located below ρb. If this con-
dition was fulfilled, the limiting radius was interpolated as the
crossing point between the boundary density level ρb and the
line passing through the (i–1)th and ith points. When farther-
out (at least two) points following the ith point were located
above the boundary density level ρb, the algorithm skipped the
ith point and continued seeking the next point located below
ρb, and the procedure was repeated. As the formal error of rlim
determination, one half of RDP bin size was taken, i.e. 0.5 arc
min. Due to the limited field of view for several clusters (for
instance King 13, King 16, NGC 884, NGC 1027, King 6,
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 5
1 King 13
r (arcmin)
King 1
r (arcmin)
King 14
r (arcmin)
NGC 146
r (arcmin)
Dias 1
r (arcmin)
King 16
r (arcmin)
1 Berkeley 4
r (arcmin)
Skiff J0058+68.4
r (arcmin)
NGC 559
r (arcmin)
NGC 884
r (arcmin)
Tombaugh 4
r (arcmin)
Czernik 9
r (arcmin)
1 NGC 1027
r (arcmin)
King 5
r (arcmin)
King 6
r (arcmin)
Berkeley 9
r (arcmin)
Berkeley 10
r (arcmin)
Tombaugh 5
r (arcmin)
1 NGC 1513
r (arcmin)
Berkeley 67
r (arcmin)
Berkeley 13
r (arcmin)
Czernik 19
r (arcmin)
Berkeley 15
r (arcmin)
NGC 1798
r (arcmin)
1 Berkeley 71
r (arcmin)
NGC 2126
r (arcmin)
NGC 2168
r (arcmin)
NGC 2192
r (arcmin)
NGC 2266
r (arcmin)
King 25
r (arcmin)
1 Czernik 40
r (arcmin)
Czernik 41
r (arcmin)
NGC 6885
r (arcmin)
IC 4996
r (arcmin)
Berkeley 85
r (arcmin)
Collinder 421
r (arcmin)
0 10 20
NGC 6939
r (arcmin)
0 10 20
NGC 6996
r (arcmin)
0 10 20
Berkeley 55
r (arcmin)
0 10 20
Berkeley 98
r (arcmin)
0 10 20
NGC 7654
r (arcmin)
0 10 20
NGC 7762
r (arcmin)
Fig. 1. Radial density profiles normalized to the central value after background level subtraction.
NGC 1513, NGC 2168, NGC 6885, NGC 6939, NGC 7654,
and NGC 7762) our determination of rlim may in fact represent
a lower limit. The results of the RDP analysis (limiting radius
rlim, core radius rcore, central density f0, and background level
fbg) are listed in Table 3 in Cols. 2, 3, 4, and 5, respectively.
4. The color–magnitude diagrams
The collected V and (B−V) data allowed us to construct color–
magnitude diagrams (CMDs) for all observed clusters. Since
the field of view was wide and the majority of clusters oc-
curred relatively small, the CMD for the cluster region could
be decontaminated for the field stars’ contribution. While in
general it is impossible to point out individual cluster members
based only on photometry, the contribution from field stars can
be removed from the cluster CMD in a statistical manner. The
algorithm applied to our data was based on ideas presented in
Mighell et al. (1996) and discussed in Bica & Bonato (2005).
Two separate CMDs were built: one for the cluster and one
for an offset field. The offset field was defined as a ring of the
inner radius rlim+1 arcmin and the outer radius was set as large
as possible to fit within the observed CCD frame but avoiding
contribution from other clusters, typically 15–19 arcmin. Both
CMDs were divided into 2-dimensional bins of ∆V = 0.4 mag
and ∆(B − V) = 0.1 mag size (both values being fixed after
a series of tests, as a compromise between resolution and the
star numbers in individual boxes). The number of stars within
each box was counted. Then the cleaned cluster CMD was built
by subtracting the number of stars from the corresponding off-
set box from the number of stars in a cluster box. The latter
number was weighted with the cluster to offset field surface ra-
tio. Knowing the number of cluster stars occupying any given
box on clean CMD, the algorithm randomly chose the required
number of stars with adequate V magnitude and B − V color
index from the cluster field. Finally, the list of stars in aech
6 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
Table 4. Astrophysical parameters obtained from isochrone fitting.
Name log(age) E(B − V) (M − m) d Rlim Rcore
(mag) (mag) (kpc) (pc) (pc)
(1) (2) (3) (4) (5) (6) (7)
King 13 8.4 0.86+0.14
−0.12 15.49
+0.55
−0.58 3.67
+1.37
−1.30 12.6
−4.5 3.54
+1.32
−1.26
King 1 9.6 0.76+0.09
−0.09 12.53
+0.32
−0.51 1.08
+0.23
−0.33 3.9
−1.2 0.67
+0.14
−0.20
King 14 7.0 0.58+0.10
−0.10 13.75
+0.85
−0.73 2.46
+1.35
−0.94 6.5
−2.5 1.62
+0.89
−0.62
NGC 146 7.6 0.56+0.07
−0.07 13.97
+0.50
−0.61 2.80
+0.84
−0.89 2.2
−0.7 0.94
+0.28
−0.30
Dias 1 7.1 1.08+0.13
−0.11 14.49
+1.04
−0.57 1.69
+1.21
−0.58 1.2
−0.4 0.17
+0.12
−0.06
King 16 7.0 0.89+0.10
−0.13 14.18
+0.72
−0.87 1.92
+0.88
−0.85 4.9
−2.2 1.09
+0.50
−0.48
Berkeley 4 7.1 0.83+0.08
−0.08 14.53
+1.14
−0.69 2.46
+1.86
−0.86 2.2
−0.8 0.94
+0.71
−0.33
Skiff J0058+68.4 9.1 0.85+0.12
−0.13 13.48
+0.57
−0.49 1.48
+0.55
−0.50 4.7
−1.6 1.63
+0.61
−0.55
NGC 559 8.8 0.68+0.11
−0.12 13.79
+0.39
−0.66 2.17
+0.56
−0.82 9.2
−3.5 1.48
+0.38
−0.56
NGC 884 7.1 0.56+0.06
−0.06 14.08
+0.43
−0.57 2.94
+0.75
−0.87 8.6
−2.5 5.00
+1.27
−1.47
Tombaugh 4 9.0 1.01+0.08
−0.10 14.81
+0.59
−0.37 2.17
+0.78
−0.58 3.5
−1.0 0.67
+0.24
−0.18
Czernik 9 8.8 1.05+0.12
−0.14 14.35
+0.36
−0.76 1.66
+0.41
−0.70 1.6
−0.7 0.39
+0.10
−0.17
NGC 1027 8.4 0.41+0.12
−0.11 11.34
+0.35
−0.53 1.03
+0.25
−0.34 3.1
−1.0 1.00
+0.24
−0.33
King 5 9.1 0.67+0.09
−0.10 13.82
+0.32
−0.61 2.23
+0.46
−0.77 7.1
−2.4 1.56
+0.32
−0.54
King 6 8.4 0.53+0.12
−0.11 11.17
+0.55
−0.47 0.80
+0.29
−0.25 2.6
−0.8 0.85
+0.31
−0.27
Berkeley 9 9.6 0.79+0.08
−0.08 12.03
+0.34
−0.52 0.82
+0.18
−0.25 1.7
−0.5 0.29
+0.06
−0.09
Berkeley 10 9.0 0.71+0.10
−0.08 13.46
+0.70
−0.40 1.79
+0.80
−0.46 4.3
−1.1 0.70
+0.31
−0.18
Tombaugh 5 8.4 0.80+0.08
−0.10 13.10
+0.38
−0.40 1.33
+0.31
−0.37 4.6
−1.3 0.85
+0.20
−0.24
NGC 1513 7.4 0.76+0.13
−0.18 12.96
+0.76
−1.16 1.32
+0.67
−0.72 3.5
−1.9 1.41
+0.71
−0.77
Berkeley 67 9.0 0.90+0.09
−0.08 13.86
+0.60
−0.37 1.64
+0.61
−0.41 2.5
−0.6 0.90
+0.34
−0.22
Berkeley 13 9.0 0.66+0.15
−0.14 14.01
+1.05
−0.80 2.47
+1.82
−1.07 4.4
−1.9 1.02
+0.75
−0.44
Czernik 19 7.4 0.67+0.08
−0.08 14.07
+0.73
−0.56 2.50
+1.13
−0.78 4.0
−1.2 1.05
+0.47
−0.32
Berkeley 15 8.7 1.01+0.15
−0.16 15.28
+0.36
−0.46 2.69
+0.71
−0.96 6.0
−2.1 1.12
+0.30
−0.40
NGC 1798 9.2 0.37+0.10
−0.09 13.90
+0.26
−0.63 3.55
+0.64
−1.22 9.3
−3.2 1.36
+0.25
−0.47
Berkeley 71 9.0 0.81+0.08
−0.08 15.08
+0.65
−0.30 3.26
+1.30
−0.73 3.1
−0.7 1.11
+0.44
−0.25
NGC 2126 9.1 0.27+0.11
−0.12 11.02
+0.64
−1.03 1.09
+0.45
−0.52 3.2
−1.5 0.61
+0.25
−0.29
NGC 2168 7.9 0.28+0.15
−0.16 10.49
+1.14
−1.00 0.84
+0.68
−0.42 2.4
−1.2 1.12
+0.91
−0.56
NGC 2192 9.3 0.04+0.11
−0.14 12.11
+0.53
−0.42 2.50
+0.86
−0.81 3.3
−1.1 1.02
+0.35
−0.33
NGC 2266 9.0 0.00+0.09
−0.09 12.24
+0.50
−0.30 2.81
+0.88
−0.66 4.8
−1.1 0.95
+0.30
−0.22
King 25 8.8 1.36+0.11
−0.13 15.03
+0.46
−0.93 1.45
+0.44
−0.67 2.7
−1.2 0.99
+0.30
−0.45
Czernik 40 8.9 0.99+0.13
−0.14 15.52
+0.42
−0.38 3.09
+0.89
−0.97 7.7
−2.4 2.03
+0.59
−0.64
Czernik 41 8.7 1.28+0.14
−0.17 14.64
+0.42
−0.87 1.36
+0.40
−0.65 2.2
−1.1 0.69
+0.20
−0.33
NGC 6885 7.1 0.66+0.14
−0.25 12.06
+1.03
−1.48 1.01
+0.72
−0.65 2.5
−1.6 0.69
+0.50
−0.45
IC 4996 7.0 0.58+0.05
−0.07 12.86
+0.53
−0.64 1.63
+0.50
−0.53 1.1
−0.3 0.57
+0.18
−0.19
Berkeley 85 9.0 0.77+0.14
−0.15 13.61
+0.47
−0.85 1.76
+0.57
−0.80 2.5
−1.2 0.76
+0.25
−0.35
Collinder 421 8.4 0.64+0.11
−0.12 12.08
+0.48
−0.48 1.05
+0.33
−0.34 1.8
−0.6 0.33
+0.10
−0.11
NGC 6939 9.1 0.38+0.18
−0.10 12.15
+0.56
−0.72 1.56
+0.64
−0.59 6.9
−2.6 0.98
+0.40
−0.37
NGC 6996 8.3 0.84+0.10
−0.12 13.49
+0.41
−0.66 1.50
+0.40
−0.57 0.9
−0.4 0.40
+0.10
−0.15
Berkeley 55 8.5 1.74+0.10
−0.11 15.81
+0.40
−0.51 1.21
+0.31
−0.39 2.1
−0.7 0.26
+0.07
−0.08
Berkeley 98 9.4 0.13+0.11
−0.11 13.26
+0.25
−0.38 3.73
+0.67
−1.05 5.0
−1.4 2.29
+0.41
−0.65
NGC 7654 7.0 0.73+0.14
−0.16 13.11
+1.18
−1.12 1.48
+1.24
−0.78 4.8
−2.5 2.13
+1.78
−1.12
NGC 7762 9.3 0.66+0.08
−0.09 11.52
+0.42
−0.75 0.78
+0.20
−0.30 2.2
−0.8 0.54
+0.14
−0.20
cleaned cluster box was saved and used for constructing the
decontaminated CMD.
The photometric parameters, such as distance modulus,
reddening, and age of the target clusters, were derived by fit-
ting a set of theoretical isochrones of sollar metallicity (Bertelli
at al. 1994) to the decontaminated CMDs. For every isochrone
of a given age, a grid of χ2 was calculated for a number of ob-
served distance moduli and reddenings in steps of 0.01 mag.
The isochrone with the lowest χ2 value was chosen as the final
result.
The resolution of the isochrone set was assumed to be the
cluster age uncertainty, i.e. 0.1 in log(age). A map of scaled
chi-square statistics ∆χ2 for the best-fit isochrone was prepared
to estimate the uncertainties of E(B − V) and (M − m). Here,
∆χ2 was defined as
χ2 − χ2min
χ2min/ν
, (9)
where χ2min is the minimum χ
2 and ν the number of degrees of
freedom (equal 2 in this case, Burke at al. 2004). The projection
of the ∆χ2 = 1.0 contour on the parameter axes was taken as
the 1-σ error.
The decontaminated CMDs for individual clusters are pre-
sented in Fig. 2 where the best-fit isochrones are also shown.
The parameters such as log(age), reddening, and distance mod-
ulus obtained for investigated clusters are listed in Table 4 in
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 7
King 13
B-V (mag)
King 1
B-V (mag)
King 14
B-V (mag)
NGC 146
B-V (mag)
Dias 1
B-V (mag)
King 16
B-V (mag)
Berkeley 4
B-V (mag)
Skiff J0058+68.4
B-V (mag)
NGC 559
B-V (mag)
NGC 884
B-V (mag)
Tombaugh 4
B-V (mag)
Czernik 9
B-V (mag)
NGC 1027
B-V (mag)
King 5
B-V (mag)
King 6
B-V (mag)
Berkeley 9
B-V (mag)
Berkeley 10
B-V (mag)
Tombaugh 5
B-V (mag)
NGC 1513
B-V (mag)
Berkeley 67
B-V (mag)
Berkeley 13
B-V (mag)
Czernik 19
B-V (mag)
Berkeley 15
B-V (mag)
NGC 1798
B-V (mag)
Berkeley 71
B-V (mag)
NGC 2126
B-V (mag)
NGC 2168
B-V (mag)
NGC 2192
B-V (mag)
NGC 2266
B-V (mag)
King 25
B-V (mag)
Czernik 40
B-V (mag)
Czernik 41
B-V (mag)
NGC 6885
B-V (mag)
IC 4996
B-V (mag)
Berkeley 85
B-V (mag)
Collinder 421
B-V (mag)
0 1 2
NGC 6939
B-V (mag)
0 1 2
NGC 6996
B-V (mag)
0 1 2
Berkeley 55
B-V (mag)
0 1 2
Berkeley 98
B-V (mag)
0 1 2
NGC 7654
B-V (mag)
0 1 2
NGC 7762
B-V (mag)
Fig. 2. Decontaminated CMDs for individual clusters. The best-fitted isochrones are drawn with solid lines.
Cols. 2, 3, and 4, respectively. The distances were calculated
under the assumption of the total-to-selective absorption ratio
of R = 3.1 and are listed in Col. 5. The linear sizes of limiting
radii Rlim and core radii Rcore are also listed in Cols. 6 and 7,
respectively.
5. Mass functions
The first step towards deriving the cluster mass function (MF)
was to build the cluster’s luminosity functions (LF) for the core,
halo, and overall regions separately. We used 0.5 mag bins.
Another LF was built for an offset field starting at r = rlim + 1
arcmin and extending to the edge of the clean field on a frame.
The LF of the offset field was subtracted, bin by bin, from every
region LF, taking the area proportion into account, and this way
the decontaminated LF was derived. The resulting LFs were
converted into MFs using the respective isochrone. The derived
mass functions φ(m) for the overall cluster region, defined as
the number of stars N per mass unit, are plotted as functions
8 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
Table 5. Astrophysical parameters obtained from the mass function analysis.
Name χ χcore χhalo Nevolved Mturno f f Ntot Mtot Ncore Mcore
(stars) (M⊙) (stars) (M⊙) (stars) (M⊙)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
King 13 2.23 ± 1.23 0.63 ± 1.62 2.57 ± 1.02 14 3.36 44538 15598 1178 757
King 1 2.43 ± 1.56 −3.46 ± 0.44 3.58 ± 1.81 45 1.16 10520 3305 188 177
King 14 1.16 ± 0.38 0.63 ± 0.17 1.35 ± 0.63 0 14.77 1436 906 316 244
NGC 146 1.16 ± 0.66 − − 0 7.71 1066 624 − −
Dias 1 1.07 ± 0.38 − − 0 5.27 426 248 − −
King 16 1.12 ± 0.37 0.66 ± 0.27 1.26 ± 0.39 0 11.90 1084 709 244 261
Berkeley 4 0.75 ± 0.54 − − 0 12.81 479 467 − −
Skiff J0058+68.4 −0.38 ± 0.66 −0.85 ± 1.54 0.36 ± 0.86 76 1.79 1053 851 232 214
NGC 559 1.31 ± 0.43 0.02 ± 0.33 2.09 ± 0.66 28 1.97 7286 3170 585 395
NGC 884 −0.05 ± 0.28 −0.81 ± 0.23 0.49 ± 0.22 1 15.24 341 1103 104 732
Tombaugh 4 0.53 ± 2.51 −6.03 ± 2.95 2.42 ± 0.47 6 1.75 3407 1744 102 164
Czernik 9 1.71 ± 1.58 − − 7 2.38 1424 559 − −
NGC 1027 1.51 ± 0.36 0.47 ± 0.80 1.83 ± 0.39 0 3.34 1946 833 127 89
King 5 1.52 ± 0.30 0.06 ± 0.09 1.77 ± 0.42 22 1.88 5933 2313 417 227
King 6 1.74 ± 0.39 1.44 ± 0.32 1.58 ± 0.47 0 3.35 1172 465 321 141
Berkeley 9 1.94 ± 1.27 −5.58 ± 1.85 3.40 ± 2.05 4 1.24 2097 697 10 14
Berkeley 10 1.27 ± 0.55 −0.66 ± 0.75 2.45 ± 0.69 12 1.97 2641 1121 67 61
Tombaugh 5 1.31 ± 0.38 0.65 ± 0.27 1.82 ± 0.22 7 3.33 2750 1287 257 163
NGC 1513 1.55 ± 0.20 0.54 ± 0.36 1.27 ± 0.20 0 9.16 2813 1317 365 295
Berkeley 67 −1.66 ± 1.43 −2.61 ± 0.86 −1.02 ± 3.31 6 1.86 112 140 31 43
Berkeley 13 1.87 ± 0.96 1.67 ± 2.72 2.84 ± 1.29 7 1.92 1960 717 983 370
Czernik 19 1.14 ± 0.18 0.48 ± 0.18 0.87 ± 0.22 0 9.76 811 502 186 171
Berkeley 15 1.10 ± 1.09 0.00 ± 1.67 1.43 ± 1.30 12 2.21 2574 1230 170 124
NGC 1798 3.13 ± 0.57 −1.13 ± 1.43 4.69 ± 1.29 28 1.74 23209 6932 202 229
Berkeley 71 −1.06 ± 1.83 − − 9 1.92 232 256 − −
NGC 2126 1.14 ± 0.41 0.73 ± 0.86 1.20 ± 0.57 10 1.82 901 395 223 106
NGC 2168 0.93 ± 0.20 0.82 ± 0.51 0.89 ± 0.16 0 4.25 1421 849 339 216
NGC 2192 −4.59 ± 2.12 −9.50 ± 3.35 −3.12 ± 1.14 23 1.54 78 107 5 8
NGC 2266 1.58 ± 0.91 0.15 ± 0.52 2.28 ± 0.96 12 1.93 3570 1392 312 167
King 25 1.73 ± 1.00 0.43 ± 1.38 2.62 ± 1.84 9 2.31 6075 2336 467 278
Czernik 40 2.41 ± 0.62 0.49 ± 1.28 3.37 ± 1.13 71 2.13 47503 15790 1066 597
Czernik 41 0.77 ± 0.70 −2.22 ± 2.83 2.72 ± 0.54 5 2.56 1161 635 24 44
NGC 6885 1.68 ± 0.27 0.70 ± 0.38 1.66 ± 0.42 0 6.78 711 1641 250 141
IC 4996 0.87 ± 0.45 − − 0 14.47 347 304 − −
Berkeley 85 1.50 ± 0.73 −1.86 ± 0.99 1.99 ± 0.79 10 1.94 4082 1618 40 54
Collinder 421 1.04 ± 0.37 0.97 ± 0.42 1.32 ± 0.36 6 3.14 424 233 153 81
NGC 6939 0.96 ± 0.46 0.19 ± 0.48 1.56 ± 0.44 48 1.80 5154 2363 786 391
NGC 6996 1.73 ± 0.57 − − 3 3.72 664 277 − −
Berkeley 55 0.91 ± 1.54 −1.53 ± 0.81 2.34 ± 2.00 4 3.00 1466 795 45 85
Berkeley 98 2.52 ± 1.18 0.94 ± 2.60 3.22 ± 1.35 29 1.41 6158 1967 1024 421
NGC 7654 1.42 ± 0.15 1.11 ± 0.13 1.89 ± 0.37 0 9.23 6163 3133 2351 1491
NGC 7762 −0.12 ± 0.33 −0.35 ± 0.78 0.24 ± 0.36 28 1.47 1106 616 186 113
of stellar mass m in Fig. 3, where the standard relations of the
logφ(m) = log
= −(1 + χ) log m + b0 , (10)
fitted to the data for each cluster, are also shown. The error bars
were calculated assuming the Poisson statistics. The values of
the MF slope parameters χ for overall clusters regions are listed
in Col. 2 of Table 5.
This procedure was applied to objects with rlim > 4
′. For
smaller ones, core and halo regions were not separated to avoid
small number statistics. The resulting fit parameters χcore and
χhalo are collected in Table 5 in Cols. 3 and 4, respectively.
The completeness of our photometry was estimated by
adding a set of artificial stars to the data. It was defined as a
ratio of the number of artificial stars recovered by our code and
the number of artificial stars added. To preserve the original
region crowding, the number of artificial stars was limited to
10% of the number of actually detected stars found in the orig-
inal images within a given magnitude bin. The completeness
factor was calculated for every magnitude bin. The obtained
completeness factor was close to 100% for stars brighter than
17 mag in all clusters and decreased for fainter stars more or
less rapidly depending on the stellar density in a given field.
The faint limit of the LM was set individually for each field af-
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 9
King 13
log (m)
King 1
log (m)
King 14
log (m)
NGC 146
log (m)
Dias 1
log (m)
King 16
log (m)
Berkeley 4
log (m)
Skiff J0058+68.4
log (m)
NGC 559
log (m)
NGC 884
log (m)
Tombaugh 4
log (m)
Czernik 9
log (m)
NGC 1027
log (m)
King 5
log (m)
King 6
log (m)
Berkeley 9
log (m)
Berkeley 10
log (m)
Tombaugh 5
log (m)
NGC 1513
log (m)
) Berkeley 67
log (m)
) Berkeley 13
log (m)
) Czernik 19
log (m)
) Berkeley 15
log (m)
) NGC 1798
log (m)
Berkeley 71
log (m)
NGC 2126
log (m)
NGC 2168
log (m)
NGC 2192
log (m)
NGC 2266
log (m)
King 25
log (m)
Czernik 40
log (m)
Czernik 41
log (m)
NGC 6885
log (m)
IC 4996
log (m)
Berkeley 85
log (m)
Collinder 421
log (m)
0 0.5 1
NGC 6939
log (m)
0 0.5 1
NGC 6996
log (m)
0 0.5 1
Berkeley 55
log (m)
0 0.5 1
Berkeley 98
log (m)
0 0.5 1
NGC 7654
log (m)
0 0.5 1
NGC 7762
log (m)
Fig. 3. The mass functions for individual clusters with the standard relation (Eq. 10) fitted (solid lines).
ter careful inspection of the observed faint-end range (typically
18–19 mag) with the completeness factor lower than 50%.
The derived cluster parameters allowed us to estimate the
total mass Mtot, total number of stars Ntot, core mass Mcore,
and the number of stars within the core Ncore for each cluster.
These quantities were calculated by extrapolating the MF from
the turnoff down to the H-burning mass limit of 0.08 M⊙ using
the method described in Bica & Bonatto (2005). If the value of
χ was similar or greater than that of the universal initial mass
function (IMF), χIMF = 1.3±0.3 (Kroupa 2001), the mass func-
tion was extrapolated with given χ to the mass of 0.5 M⊙ and
then with χ = 0.3 down to 0.08 M⊙. For the lower actual values
of χ, the MFs were extrapolated with the actual value within
the entire range from the turnoff mass down to 0.08 M⊙. The
contribution of the evolved stars was included in the cluster’s
total mass by multiplying their actual number Nevolved (Col. 5
in Table 5) by the turnoffmass Mturno f f (Col. 6 in Table 5). The
total number of cluster’s stars Ntot, total cluster’s mass Mtot,
number of stars in the core Ncore, and the core mass Mcore are
given in Cols. 7, 8, 9, and 10 of Table 5, respectively.
To describe the dynamical state of a cluster under investi-
gation, the relaxation time was calculated in the form
trelax =
8 ln N
tcross , (11)
where tcross = D/σV denotes the crossing time, N is the total
number of stars in the investigated region of diameter D, and
σV is the velocity dispersion (Binney & Tremaine 1987) with
a typical value of 3 km s−1 (Binney & Merrifield 1998). The
calculations were performed separately for the overall cluster
and core region.
The cluster dynamic evolution was described by the
dynamical-evolution parameter τ, defined as
trelax
, (12)
which was calculated for the core and the overall cluster sep-
arately. The difference between MF slopes of the core and
corona ∆χ = χhalo−χcore can be treated as the mass segregation
measure. These quantities were used for a statistical description
of the cluster’s sample properties.
10 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
7 8 9
log (age)
0 0.5 1
E(B-V) (mag)
10 12 14 16
(M-m) (mag)
0 5 10 15
r (arcmin)
Fig. 4. Reliability of the obtained results. The data obtained in
this paper (vertical axes) are plotted versus the literature ones
(horizontal axes).
6. Reliability of results and comparison with
previous studies
To test the reliability of the results of age, reddening, distance
modulus, and apparent diameter determination presented in this
paper, we compared them with the available catalogue data
taken from the WEBDA3 open cluster data base (Mermilliod
1996). Our determinations of basic cluster parameters are plot-
ted against the results of the previous studies of 30 clusters in
Fig. 4. The ages of clusters show excellent agreement with the
literature data. The least-square-fitted linear relation for the 30
clusters is
log(ageour) = (0.993 ± 0.009) log(age) (13)
with a correlation coefficient of 0.90 and fits the perfect match
line within the error.
As shown in Fig. 4b, satisfactory reliability of our E(B−V)
determination was also achieved. Only two clusters come sig-
nificantly off the line of perfect match. The least-square-fitted
linear relation for the 28 clusters is
E(B − V)our = (0.99 ± 0.04)E(B− V) (14)
with a correlation coefficient of 0.88. The distance moduli de-
termined in this study, Fig. 4c, are very similar to the literature
data as well. The best-fit linear relation for the 27 clusters is
(M − m)our = (0.99 ± 0.01)(M − m) (15)
with the correlation coefficient of 0.90. All three relations prove
that our results are reliable.
As displayed in Fig. 4d, the literature values of apparent
radii of open clusters are considerably (4–5 times) lower for
the majority of the clusters under investigation.
3 http:///www.univie.ac.at/webda
0 1 2 3 4 5
Rcore (pc)
0 1 2 3 4 5
Rcore (pc)
Fig. 5. Relation between limiting and core radii. See text for
description.
7. Statistical considerations
The sample of 42 open clusters studied in detail within this sur-
vey is by no means complete. Since it was defined by celestial
coordinates, estimated sizes, and richness of potential objects,
as well as non-availability of previous CCD studies, it is defini-
tively not representative of the total open cluster sample in the
Galaxy. However the sample covers quite a wide range of clus-
ters parameters and is uniform enough to perform simple sta-
tistical analysis.
Even though 20 clusters out of 62 covered by this sur-
vey were found not to be real does not necessarily mean that
∼30% of clusters in Dias et al. (2002) are doubtful. Such a
high frequency of accidental star density fluctuations is defi-
nitely caused by our selection criteria.
7.1. Limiting and core radii
From their analysis based on DSS images of 38 open clus-
ters Nilakshi et al. (2002) concluded that the angular size of
the coronal region is about 5 times the core radius, hence
Rlim ≈ 6Rcore. Bonatto & Bica (2005) reported a similar re-
lation between the core and limiting radii based on their study
of 11 open clusters. Bica & Bonatto (2005) used data for 16
clusters to find that Rlim = (1.05 ± 0.45) + (7.73 ± 0.66)Rcore.
More recently, Sharma et al. (2006) determined core and limit-
ing radii of 9 open clusters using optical data and presented the
relation Rlim = (3.1 ± 0.5)Rcore with the correlation coefficient
of 0.72. The best fit obtained using the data reported in this
study gives Rlim = (3.1 ± 0.2)Rcore with the correlation coeffi-
cient of 0.74 (Fig. 5 a). Although the correlation is quite strong,
Rlim may vary for individual clusters between about 2Rcore and
7Rcore (Fig. 5a).
The obtained relation is quite different from the one ob-
tained in the papers mentioned above, except for Sharma et
al. (2006) who used observations gathered with a wide-field
Schmidt telescope similar to ours. The field of view in sur-
veys by Nilakshi et al. (2002), Bonatto & Bica (2005), and Bica
& Bonatto (2005) was wider with a radius of 1–2◦. That sug-
gests that our determinations of the limiting radius for some
extensive clusters are underestimated due to a limited field of
view (see Sect. 3.2). However, it has to be pointed out that the
methods of determining the cluster limiting radius differ con-
siderably, and sometimes the adopted definition is not clear.
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 11
We also note that our open clusters’ size determinations differ
from many in the literature at the level of angular diameters
(Fig. 4d). One of the reasons for such an inconsistency may
be the difference in the content of the cluster samples used by
different authors who frequently use non uniform photometric
data. Finally, as Sharma et al. (2006) notes, open clusters ap-
pear to be larger in the near-infrared than in the optical data.
To illustrate the difference between results, we again plot
our data in Fig. 5b as in Fig. 5a, together with the literature
determinations taken from the following papers: open squares
denote results from Bica & Bonatto (2005) and Bonatto & Bica
(2005), open circles those of Nilakshi et al. (2002), and open
triangles Sharma et al. (2006). It is clear that data coming from
optical investigations fit each other. We also note that the litera-
ture data contain no determination of sizes for clusters smaller
than 2 pc.
7.2. Structural parameters
The data gathered within this survey show that the limiting ra-
dius correlates with the cluster’s total mass (Fig. 6a). We ob-
tained the relation log Rlim = (0.39±0.07) log Mtot − (0.6±0.2)
with a moderate correlation coefficient of 0.70. This result indi-
cates that clusters with large diameters and small total masses
do not form bound systems. On the other hand, small massive
clusters are dissolved by the internal dynamics (Bonatto & Bica
2005). As one could expect, the core radius is also related to the
cluster’s total mass (Fig. 6b). The obtained least-square linear
relation is log Rcore = (0.32±0.08) log Mtot − (0.99±0.25) with
a weak correlation coefficient of 0.53.
As shown in Figs. 6c and d, both radii tend to decrease
in the course of the dynamical evolution. For the limiting ra-
dius, the obtained relation is log Rlim = (−0.13 ± 0.04) logτ +
(0.66 ± 0.05) with a weak correlation coefficient of 0.47. This
suggests that dynamical evolution makes a cluster smaller due
to dissolving coronae. The dynamical evolution of the core ra-
dius is more visible. The least-square fitted linear relation is
log Rcore = (−0.16 ± 0.04) logτ + (0.10 ± 0.05) with a corre-
lation coefficient of 0.51. Moreover, the core radius is mod-
erately correlated with the dynamical-evolution parameter of
the core τcore. The obtained relation, plotted in Fig. 6e, is
log Rcore = (−0.15 ± 0.03) logτcore + (0.36 ± 0.08) with a cor-
relation coefficient of 0.66. The last two relations indicate that
the dynamical evolution of both, overall cluster and core, tends
to reduce the core radius. No relation of Rlim and Rcore with
cluster age or mass segregation was noted in the investigated
sample.
To investigate the relative size of halos, the concentration
parameter c, defined as c = (Rlim/Rcore), was plotted against
other parameters. The concentration parameter seems to be re-
lated to cluster age, as shown in Fig. 6f. For clusters younger
than about log(age) = 9, it tends to increase with cluster age
(log c = (0.11 ± 0.03) log(age) − (0.38 ± 0.23) with a correla-
tion coefficient of 0.56). Nilakshi et al. (2002) notes a decrease
in the size of halos for older systems.
In Fig. 6g the concentration parameter is plotted against
mass segregation parameter ∆χ. As no relation is seen, one can
2 3 4
log Mtot
2 3 4
log Mtot
-1 0 1 2 3
log τ
-1 0 1 2 3
log τ
0 1 2 3 4 5
log τcore
7 8 9
log (age)
0 2 4 6 8
Fig. 6. Relations between structural parameters with each other.
See text for details.
conclude that there is no low concentrated clusters with log c <
0.5 with a high value of ∆χ > 3.
7.3. Mass function slopes
The mass function slopes of the overall cluster, core, and halo
were sought for relations with other parameters. As displayed
in Fig. 7a, the mass function slope of the overall cluster re-
gion and the cluster age are not strictly related. However,
a deficit in low-mass members occurs in clusters older than
log(age) = 9.0. We also investigated relations between the
mass function slopes and the dynamical-evolution parameter τ
– Fig. 7b. Bonatto & Bica (2005) report a relation between the
overall χ and τ in the form of χ(τ) = χ0 − χ1 exp(−τ0/τ), sug-
gesting that the MF slopes decrease exponentially with τ. Our
results confirm this relation, and the least-square fit was ob-
12 G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters
7 8 9
log (age)
-1 0 1 2 3
log τ
7 8 9
log (age)
-1 0 1 2 3
log τ
0 1 2 3 4 5
log τcore
0 2 4 6 8
7 8 9
log (age)
-1 0 1 2 3
log τ
Fig. 7. Relations between mass function slopes and other clus-
ters parameters. See text for details.
tained with χ0 = 1.34±0.13, χ1 = 9.9±2.3, and τ0 = 450±130
(a correlation coefficient was 0.81). It is worth noting that the
obtained value of χ0 is almost identical to χIMF .
In Fig. 7c the relation between χcore and the log(age) is
presented. It is clear that χcore decreases rapidly with cluster
age for clusters older than log(age) = 8.5. This suggests that
evaporation of the low-mass members from cluster cores does
not occur in clusters younger than log(age) = 8.5. The cores of
clusters older than log(age) = 8.5 are dynamically evolved and
deprived of low-mass stars.
As one can see in Fig. 7d, χcore does not correlate with τ.
However, χcore tends to decrease with τ, which indicates that
low-mass-star depleted cores appear in dynamically evolved
clusters with log τ > 1.
In Fig. 7e we show that χcore and τcore are related, and the
relation is similar to the one for χ and τ – χcore = (0.44 ±
0.27) − (8.1 ± 1.1) exp(− 2790±630
τcore
). Such an evolution of χcore
was also reported by Bica & Bonatto (2005). Our fit indicates,
however, that the initial χcore(0) = 0.44 ± 0.27 is much lower
than the value of 1.17 ± 0.23 obtained by these authors. This
suggests that χcore is significantly lower than χIMF for dynami-
cally young systems.
As displayed in Fig. 7f, χcore is correlated with the
mass segregation parameter ∆χ. The least-square-fitted relation
χcore = (−0.83 ± 0.10)∆χ + (1.33 ± 0.33) with the correlation
coefficient of −0.83 indicates that – as one could expect – χcore
decreases with the increase in mass segregation.
Finally, in Figs. 7g and h relations between χhalo and
log(age) or τ were plotted, respectively. The MF slopes of the
coronal regions of clusters younger than log(age) = 8.9 tend
to increase with age. That relation was marked with the least-
square-fitted dashed line for which the correlation coefficient
is 0.61. Bifurcation occurs for older clusters and χhalo becomes
either very high or low as compared to the mean value. This
suggests that the clusters were observed in different stages of
dynamical evolution. In clusters with higher values of χhalo,
the mechanism of dynamical mass segregation is more effi-
cient than the evaporation of low-mass members from halos.
Clusters with low values of χhalo are dynamical evolved sys-
tems devoid of low-mass stars in the overall volume. Then,
χhalo seems to decrease with τ for log τ > 2. That suggests that
in general the dynamical evolution of a cluster halo is driven
by the dynamical evolution of the overall system (we obtained
χhalo = (2.0±0.2)− (12.3±6.5) exp(−
700±350
) with the correla-
tion coefficient of 0.69). It is also worth noting that the average
χhalo for dynamically not evolved clusters is larger than χIMF .
7.4. Mass segregation
The mass segregation ∆χ is most prominent for clusters older
than about log(age) = 8 (Fig. 8a). The mean values of χhalo
and χcore differ significantly for clusters with log(age) < 8,
and ∆χ , 0 even for very young clusters. This suggests the
existence of the initial mass segregation within the protostellar
gas cloud.
We plotted ∆χ in Fig. 8b as a function of the dynamical-
evolution parameter τ. No relation can be seen. However,
one can note that strong mass segregation occurs in cluster
older then their relaxation time, i.e. log τ > 0. As displayed
in Fig. 8c, mass segregation seems to be related to the core
dynamical-evolution parameter τcore. Although a strict rela-
tion is not present, one can see that clusters with dynamically
evolved cores (log τcore > 3) reveal a strong mass segregation
effect.
8. Conclusions
Wide-field CCD photometry in B and V filters was collected
for 42 open clusters and the basic structural and astrophysical
parameters were obtained. Eleven cluster under investigation
were studied for the first time.
G. Maciejewski and A. Niedzielski: CCD BV survey of 42 open clusters 13
7 8 9
log (age)
-1 0 1 2 3
log τ
0 1 2 3 4 5
log τcore
Fig. 8. Evolution of the mass segregation measure in time. See
text for details.
A simple statistical analysis of our sample of open clusters
leads to the following conclusions:
– The angular sizes of most of the observed open clusters ap-
peared to be several times larger than the catalogue data
indicate.
– A correlation exists between core and limiting radii of open
clusters. The latter seem to be 2-7 times larger, with average
ratio of 3.2. The limiting radius tends to increase with the
cluster’s mass. Both limiting and core radii decrease in the
course of the dynamical evolution. Moreover, core radius
decreases with the core dynamical-evolution parameter.
– The relative size of a cluster halo (in units of the core ra-
dius) tends to increase with cluster age for systems younger
than log(age) = 9. Among clusters with a strong mass-
segregation effect, there are no systems with small halos.
– The MF slope of the overall cluster region is related to the
dynamical-evolution parameter with the relation found in
Bica & Bonatto (2005). For clusters with log τ < 2, the
MF slope is similar to the slope of the universal IMF. For
clusters with log τ > 2 (older than about log(age) = 9), the
results of evaporation of the low-mass members are seen,
and χ reaches an extremely low value for clusters with log
τ = 3.
– The MF slope of the core region is smaller than the uni-
versal value even for very young clusters, while the mass
function slope of the corona is larger. This indicates the ex-
istence of the initial mass segregation. The dynamical mass
segregation appears in clusters older than about log(age) =
– A strong deficiency of low-mass stars appears in cores of
clusters older than log(age) = 8.5 and not younger than
one relaxation time.
Acknowledgements. We thank the anonymous referee for remarks
that significantly improved the paper. This research is partially sup-
ported by UMK grant 369-A and has made use of the WEBDA data
base operated at the Institute for Astronomy of the University of
Vienna, SIMBAD data base, as well as The Guide Star Catalogue-
II, which is a joint project of the Space Telescope Science Institute
and the Osservatorio Astronomico di Torino. Space Telescope
Science Institute is operated by the Association of Universities for
Research in Astronomy, for the National Aeronautics and Space
Administration under contract NAS5-26555. The participation of
the Osservatorio Astronomico di Torino is supported by the Italian
Council for Research in Astronomy. Additional support is provided
by the European Southern Observatory, Space Telescope European
Coordinating Facility, the International GEMINI project, and the
European Space Agency Astrophysics Division.
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	Introduction
	Observations and reduction
	Observations
	Data reduction and calibration
	Radial structure
	Redetermination of central coordinates
	Analysis of radial density profiles
	The color–magnitude diagrams
	Mass functions
	Reliability of results and comparison with previous studies
	Statistical considerations
	Limiting and core radii
	Structural parameters
	Mass function slopes
	Mass segregation
	Conclusions
