Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 23 November 2021 (MN LATEX style file v2.2)
The old open clusters Berkeley 32 and King 11⋆
Monica Tosi1,† Angela Bragaglia1 and Michele Cignoni1,2
1 INAF–Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna (Italy)
2 Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, I-40127 Bologna (Italy)
ABSTRACT
We have obtained CCD BV I imaging of the old open clusters Berkeley 32 and King 11.
Using the synthetic colour-magnitude diagram method with three different sets of stellar evo-
lution models of various metallicities, with and without overshooting, we have determined
their age, distance, reddening, and indicative metallicity, as well as distance from the Galactic
centre and height from the Galactic plane. The best parameters derived for Berkeley 32 are:
subsolar metallicity (Z=0.008 represents the best choice, Z=0.006 or 0.01 are more marginally
acceptable), age = 5.0–5.5 Gyr (models with overshooting; without overshooting the age is
4.2–4.4 Gyr with poorer agreement), (m −M)0 = 12.4 − 12.6, E(B − V ) = 0.12 − 0.18
(with the lower value being more probable because it corresponds to the best metallicity),
RGC ∼ 10.7−11 kpc, and |Z| ∼ 231−254 pc. The best parameters for King 11 are: Z=0.01,
age=3.5–4.75 Gyr, (m−M)0 = 11.67−11.75,E(B−V ) = 1.03−1.06,RGC ∼ 9.2−10 kpc,
and |Z| ∼ 253− 387 pc.
Key words: Galaxy: disc – Hertzsprung-Russell (HR) diagram – open clusters and associa-
tions: general – open clusters and associations: individual: Berkeley 32, King 11
1 INTRODUCTION
This paper is part of the BOCCE (Bologna Open Cluster Chemical
Evolution) project, described in detail by Bragaglia & Tosi (2006).
With this project, we intend to derive homogeneous measures of
age, distance, reddening and chemical abundance for a large sample
of open clusters (OCs), to study the present day properties of the
Galactic disc and their evolution with time.
As part of this project, we present here a photometric study
of the two old OCs King 11 (α2000 = 23
h47m40s, δ2000 =
+68◦38′30′′, l = 117.◦2, b = +6.◦5) and Berkeley 32 (α2000 =
06h58m07s , δ2000 = +06
◦25′43′′, l = 208◦ , b = +4.4◦), lo-
cated in the second and third Galactic quadrants, respectively.
King 11 has been the subject of a few publications in the past.
Kaluzny (1989) obtained a rather shallow colour-magnitude dia-
gram (CMD) using the 0.9m KPNO telescope. He found it old
(about the same age of M 67) and highly reddened, with a distance
modulus (m − M)V ∼ 15.3, derived assuming MV (clump)=0.7
mag. Aparicio et al. (1991) acquired deep UBV R data at the 3.5m
telescope in Calar Alto on a small field of view (2.7×4.3 arcmin2);
⋆ Based on observations made with the Italian Telescopio Nazionale
Galileo (TNG) operated on the island of La Palma by the Fundación Galileo
Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Ob-
servatorio del Roque de los Muchachos of the Instituto de Astrofisica de
Canarias.
† E-mail: monica.tosi@oabo.inaf.it (MT), angela.bragaglia@oabo.inaf.it
(AB), michele.cignoni@unibo.it (MC)
they derived a reddening E(B − V ) =1, a distance modulus
(m − M)0 ≃ 11.7, a metallicity about solar (with some uncer-
tainty, because different methods produced contrasting answers),
and an age of 5±1 Gyr. Phelps, Janes & Montgomery (1994) ob-
tained not perfectly calibrated BV I photometry and measured a
difference in magnitude between the main sequence turn-off point
and the red clump of δV =2.3, that translates, using the so-called
MAI (Morphological Age Indicator, see Janes & Phelps 1994) into
an age of 6.3 Gyr. From their recalibration of the δV - age re-
lation, assuming [Fe/H]=−0.23, Salaris, Weiss & Percival (2004)
infer an age of 5.5 Gyr. Note that the BDA1 (Mermilliod 1995)
indicates a spurious low age for this cluster (1.1 Gyr), directly
taken from the Dias et al. (2002) catalogue, whose source is un-
clear. Finally, Scott et al. (1995) obtained low resolution spectra
of 16 bright stars, from which an average cluster radial velocity
(RV) was computed (〈RV 〉 = −35 ± 16 km s−1). These spectra
were later reanalyzed by Friel et al. (2002), finding [Fe/H]=−0.27
(rms=0.15) dex.
Be 32 has been photometrically studied by Kaluzny & Mazur
(1991), Richtler & Sagar (2001) and Hasegawa et al. (2004). Be 32
seems to be quite old (age about 6 Gyr) and moderately metal poor
([Fe/H] between -0.2 and -0.5). We have recently presented the RVs
of about 50 stars in Be 32 and a preliminary analysis of the photo-
metric data (D’Orazi et al. 2006, hereafter D06) based on isochrone
fitting and the magnitude of the red clump. In D06 we also dis-
1 http://www.univie.ac.at/webda//webda.html
c© 0000 RAS
http://arxiv.org/abs/0704.0550v1
http://www.univie.ac.at/webda//webda.html
2 Tosi et al.
cussed the literature related to Be 32 available at the time, and we
will not repeat it here. We now refine our determinations, apply-
ing the synthetic CMD method, as done for all the clusters in the
BOCCE project. Finally, Sestito et al. (2006) presented an analysis
of high resolution FLAMES@VLT spectra of 9 red clump giants
in Be 32, finding an average metallicity [Fe/H]= −0.29 dex (rms
0.04 dex), in very good agreement with that found by D06.
The paper is organized as follows: observations and reductions
are presented in Sect. 2, a description of the resulting CMDs can be
found in Sect. 3; the derivation of the cluster parameters using the
synthetic CMD technique is discussed in Sect. 4, while conclusions
and summary are given in Sect. 5.
2 OBSERVATIONS AND DATA REDUCTION
Observations in the BV I Johnson-Cousins filters of Be 32 and
King 11 were performed at the Telescopio Nazionale Galileo
(TNG) in November 2000 (plus three additional exposures in
February 2004 for Be 32). We also acquired associated control
fields to check the field stars contamination, as detailed in Table 1
and D’Orazi et al. (2006). We used DOLORES (Device Optimized
for the LOw RESolution), with scale of 0.275 arcsec/pix, and a
field of view 9.4 × 9.4 arcmin2. Of the two November nights, only
the first one resulted photometric. Fig. 1 shows the position of our
pointings for King 11 and the associated control field.
A description of the data and reduction procedure for Be 32
can be found in D’Orazi (2005) and in D06; we report here briefly
the analysis of King 11, which is absolutely equivalent to that
of Be 32. The standard IRAF 2 routines were utilized for pre-
reduction, and the IRAF version of the DAOPHOT-II package
(Stetson 1987, Davis 1994) was used with a quadratically varying
point spread function (PSF) to derive positions and magnitudes for
the stars. Output catalogues for each frame were aligned in position
and magnitude, and final (instrumental) magnitudes were computed
as weighted averages of the individual values. Even with the short-
est exposure times we did not avoid saturation of the brightest red
giants in the I filter; unfortunately, we could not obtain additional
exposures as we did for Be 32 (D06), so we will mostly concentrate
in the following on the V,B − V CMD.
The final catalogs have been created including all the objects
identified in at least two filters, after applying a moderate selection
in the shape-defining parameter sharpness (|sharpness| 6 2)
and on the goodness-of-fit estimator χ2 (χ2 6 10). To the two fi-
nal catalogs, one for the cluster and one for the comparison field,
we applied the transformation to astrometrize the α and δ coor-
dinates, using software written by P. Montegriffo at the Bologna
Observatory.
After application of a correction to the PSF magnitudes to
bring them on the same scale of the aperture magnitudes of the stan-
dard stars, we calibrated our catalogues to the standard Johnson-
Cousins BV I system. We adopted the calibration equations that
can be found in D’Orazi et al. (2006), since King 11 was observed
in the photometric night beginning on UT 2000 November 25 when
Be 32 was observed too.
Finally, we determined our completeness level using exten-
sive artificial stars experiments: we iteratively added, one at a time,
about 50000 simulated stars to the deepest frames and repeated the
2 IRAF is distributed by the National Optical Astronomical Observatory,
which are operated by the Association of Universities for Research in As-
tronomy, under contract with the National Science Foundation
Figure 1. Approximate positions of our pointings on King 11 and the con-
trol field. The map is 15 × 45 arcmin2 , has North to the top and East to the
left.
reduction procedure, determining the ratio of recovered over added
stars (see Tosi et al. 2004 for a more detailed description). The re-
sults for Be 32 are given in Table 2 and those for King 11 in Table
We checked the quality of the calibration comparing our pho-
tometry for both clusters with that presented in previous litera-
ture papers, i.e. with Kaluzny & Mazur (1991) for B, V and with
Richtler & Sagar (2001) for V I in Be 32, and with Aparicio et al.
(1991) for King 11 (only for B, V , since there are no other sources
to compare the I photometry with). Fig. 2 shows the differences
c© 0000 RAS, MNRAS 000, 000–000
Berkeley 32 and King 11 3
Table 1. Log of observations for the clusters and the control fields; exposure times are in seconds.
Field α2000 δ2000 exp.timeB exp.timeV exp.timeI UT Date
Berkeley 32 06h58m07s +06◦25′43′′ 600, 40, 5 480, 20, 2 480, 20, 1 26/11/2000, 14/02/2004
Be 32 - ext 06h57m27s +06◦08′26′′ 600, 240, 40 300, 120, 20 300, 120, 20 26/11/2000
King 11 23h47m39s +68◦38′25′′ 300, 1200, 240, 40 120, 600, 120, 20 120, 600, 120, 20 25/11/2000, 26/11/2000
King 11 - ext 23h47m40s +68◦08′18′′ 1200, 300, 40 600, 1280, 20 25/11/2000
Figure 2. Comparison between our photometry and literature data. (a) and (b) are for Be 32 by Kaluzny & Mazur (1991); (c) and (d) are for Be 32 by Richtler
& Sagar (2001); (e) and (f) for King 11 by Aparicio et al. (1991). The horizontal lines are on zero; stars used to compute the average differences are indicated
by (orange) open squares, while the ones discarded are indicated by crosses.
c© 0000 RAS, MNRAS 000, 000–000
4 Tosi et al.
Table 2. Completeness level for the central (Cols 2, 3 and 4) and external
(Cols 5, 6 and 7) fields of Be 32; mag is the calibrated B, V or I magnitude.
mag cB cV cI cB cV cI
16.00 1.00 1.00 1.00 1.00 1.00 1.00
16.50 1.00 0.95 0.92 1.00 0.99 0.95
17.00 0.92 0.94 0.88 0.99 0.98 0.94
17.50 0.91 0.93 0.85 0.97 0.97 0.92
18.00 0.89 0.92 0.78 0.97 0.94 0.87
18.50 0.88 0.91 0.68 0.96 0.93 0.84
19.00 0.86 0.87 0.54 0.93 0.93 0.73
19.50 0.82 0.85 0.37 0.91 0.90 0.52
20.00 0.77 0.80 0.21 0.89 0.86 0.29
20.50 0.66 0.74 0.09 0.85 0.78 0.11
21.00 0.51 0.60 0.03 0.69 0.58 0.04
21.50 0.32 0.39 0.01 0.42 0.32 0.01
22.00 0.16 0.19 0.00 0.22 0.15 0.00
22.50 0.06 0.09 0.00 0.07 0.05 0.00
Table 3. Completeness level for the central (Cols 2 and 3) and external
(Cols 4 and 5) fields of King 11; mag is the B or V calibrated magnitude.
mag cB cV cB cV
16.5 1.0 1.0 1.0 1.0
17.0 1.0 0.99 1.0 0.99
17.5 1.0 0.97 0.99 0.98
18.0 1.00 0.97 0.98 0.95
18.5 1.00 0.95 0.99 0.94
19.0 0.98 0.94 0.96 0.94
19.5 0.97 0.93 0.94 0.93
20.0 0.97 0.92 0.91 0.90
20.5 0.97 0.87 0.88 0.87
21.0 0.95 0.87 0.81 0.82
21.5 0.93 0.74 0.78 0.70
22.0 0.91 0.56 0.63 0.43
22.5 0.88 0.27 0.38 0.21
23.0 0.74 0.06 0.15 0.04
23.5 0.45 0.00 0.02 0.00
24.0 0.18 0.0 0.00 0.0
24.5 0.02 0.0 0.0 0.0
25.0 0.00 0.0 0.0 0.0
with these photometries for the stars in common; the comparison is
particularly favorable with the work by Kaluzny & Mazur (1991),
but is good in all cases.
3 THE COLOUR - MAGNITUDE DIAGRAMS
The CMDs for Be 32 were described in D06 and the data are al-
ready available at the BDA. Fig. 3 shows the V,B−V CMD of the
stars at various distances from the centre of Be 32 and of the con-
trol field. It is apparent that contamination is quite high, with about
half the stars likely to be foreground/background objects even in
the central regions. However, in the area with a radius of 3′ from
the cluster centre the main-sequence (MS), the turn-off (TO) and
the subgiant branch (SGB) are well defined. The MS extends more
than 5 magnitudes below the TO. With the additional help of the
available RVs (from D06 and Randich et al. in preparation, see
next section) to select the most probable cluster members, we can
Table 4. Stellar evolution models adopted for the synthetic CMDs. The FST
models actually adopted here are an updated version of the published ones
(Ventura, private communication).
Set metallicity overshooting Reference
BBC 0.008 yes Fagotto et al. 1994
BBC 0.004 yes Fagotto et al. 1994
BBC 0.02 yes Bressan et al. 1993
FRA 0.006 no Dominguez et al. 1999
FRA 0.01 no Dominguez et al. 1999
FRA 0.02 no Dominguez et al. 1999
FST 0.006 η=0.00,0.02,0,03 Ventura et al. 1998
FST 0.01 η=0.00,0.02,0,03 Ventura et al. 1998
FST 0.02 η=0.00,0.02,0,03 Ventura et al. 1998
satisfactorily identify the TO (V = 16.3, B − V = 0.52 and
V − I = 0.60), the SGB, the red giant branch (RGB), and the red
clump (V = 13.7, B − V = 1.07 and V − I = 1.10).
For King 11, the final, calibrated sample of cluster stars (which
will also be made available through the BDA) consists of 1971 ob-
jects, and the external field catalogue comprises 880 stars. The cor-
responding CMDs are shown in Fig. 4. In spite of a contamination
lower than in Be 32, the location of the foreground/background
objects in the CMD makes the definition of the evolutionary se-
quences more complicated. We can improve the definition by using
the information on membership of a few giant stars from Scott et al.
(1995), which perfectly define the red clump position. If we con-
sider the CMDs of regions with increasing distance from the cluster
centre displayed in Fig. 5, it is apparent that a safe identification of
the main evolutionary loci becomes difficult beyond a radius of 2′.
Within such radius, the cluster main sequence extends for almost 4
magnitudes and the RGB and red clump are well delineated. The
Turn-off point is at V = 18.2, B − V ≃ 1.3, while the red clump
is at V = 16.0, B − V ≃ 1.8.
In the V, V − I CMD of King 11 we lack the brightest RGB
stars, because they were saturated even in the shortest image, and
the MS is less well defined. For this reason, we refer to the V,B−V
CMD to derive the cluster distance, reddening and age and use the I
data only to discriminate in metallicity among degenerate solutions
(see next Section).
4 CLUSTER PARAMETERS
Age, distance and reddening of King 11 and Be 32 have been de-
rived with the same procedure applied to all the clusters of our
project (see Bragaglia & Tosi 2006 and references therein), namely
the synthetic CMD method originally described by Tosi et al.
(1991). The best values of the parameters are found by selecting the
cases providing synthetic CMDs with morphology, colours, num-
ber of stars in the various evolutionary phases and luminosity func-
tions (LFs) in better agreement with the observational ones. As for
the other clusters of this series, to estimate the effect on the re-
sults of different stellar evolution assumptions, we have adopted
three different sets of stellar models, with various assumptions on
the metallicity, treatment of convection, opacities and equation of
state. The adopted models are listed in Table 4.
In addition to the usual synthetic CMD method, the cluster
parameters have also been searched by means of statistical tests.
c© 0000 RAS, MNRAS 000, 000–000
Berkeley 32 and King 11 5
Figure 3. Radial CMDs for Be 32 (upper panels) and equal areas in the comparison field (lower panels); we plot stars within distances of 1, 2, 3 arcmin from
the cluster and field centres. The CMDs contain 133, 444, 903 objects in panels (a), (b), (c) respectively, and 57, 229, 524 in panels (d), (e), (f) respectively.
Figure 4. (a) V,B −V CMD for King 11; (b) the same CMD, with stars member (open circles, red in the electronic version) and non member (filled squares,
blue in the electronic version) according to the RVs in Scott et al. (1995); (c) V,B − V CMD for the comparison field; (d)V, V − I CMD for King 11
The problem of comparing colour-magnitude diagrams (and two
dimensional histograms in general) is still unsolved in astrophysics.
However, several approaches have been explored. For instance,
in Cignoni et al. (2006) the entire CMD is used: data and model
CMDs are binned and a function of residuals is minimized. In
Gallart et al. (1999), the number of stars in a few regions (repre-
sentative of the most important evolutionary phases) is controlled
through a χ2 test. The goal of those papers was to recover a com-
plex star formation history. Here, the nature of the problem is
in principle simpler (single stellar generation), thus we follow a
c© 0000 RAS, MNRAS 000, 000–000
6 Tosi et al.
Figure 5. Radial CMDs for King 11 (upper panels) and equal areas of the comparison field (lower panels); we plot stars within distances of 1, 2, 3 arcmin from
the cluster and field centres. The CMDs contains 173, 531, 941 objects in panels (a), (b), (c) respectively, and 38, 143, 317 in panels (d), (e), (f) respectively.
more classical approach: the luminosity and the colour distribution
of each model are independently compared with the data using a
Kolmogorov-Smirnov (KS) test (Press et al. 1995). One of the ad-
vantages of using also the colour distribution lies in the fact that the
major drawback of using the LF alone, i.e, the degeneracy among
parameters (distance, reddening, age and metallicity) can be miti-
gated. Moreover, the KS does not require to bin the data; therefore,
arbitrary parametrizations of the CMD (typical of the χ2) can be
avoided. In order to reduce the Poisson noise, that is the dominant
uncertainty in our luminosity functions, the model CMDs are built
with a large number of stars. Only CMDs yielding a KS probability
larger than 5% both for the LF and for the colour distribution are
accepted.
Unavoidably, poorly populated CMD regions like the core he-
lium burning region or the RGB are often under-represented by a
similar analysis (washed out by Poisson noise). However, also in
these cases, a good KS probability still indicates that the most pop-
ulous stellar phases (e.g., MS and TO) are well matched. In other
words, the adopted statistical procedure provides a quick tool to
exclude those solutions for which the synthetic CMD does not re-
produce the properties of MS and TO stars. Then, the remaining
parameter space is explored with a traditional analysis: i) exploit-
ing the difference in luminosity between the lower envelope of the
subgiants and the red clump; ii) fitting the SGB; iii) matching the
RGB colour.
4.1 King 11
As already said in Sect. 3, for King 11 we have mainly used the
V,B− V CMD because the V, V − I lacks the brighter part of the
RGB. To minimize contamination from field stars we have selected
as reference field the region within a radius of 2′ from its centre.
Since this region contains 531 stars, and the control field of the
same area contains 143 stars, we assume the cluster members to
be 388. Incompleteness and photometric errors are those inferred
from the data and described in Section 2. In order to minimize the
Poisson noise of the models, all available field stars (∼ 880) are
used: hence the synthetic CMDs are built with 3259 synthetic stars
(in order to preserve the ratio cluster members/field stars). Only
afterwards we randomly extract from the whole sample of synthetic
stars 388 objects, as attributed to the cluster central region.
Almost all models have been computed assuming a fraction of
binary stars of 20% 3 (following Bragaglia & Tosi 2006 prescrip-
tions) and a power law IMF with Salpeter’s exponent. The KS test
is applied to the stars brighter than V ≈ 20. The constraint on the
KS probability doesn’t guarantee a unique solution, mostly because
the statistics is dominated by MS stars fainter than the TO, less af-
fected than other evolutionary phases by small parameters varia-
tions. We have then decided to validate only models with accept-
able KS probabilities and with a predicted clump within 0.05 mag
3 The low number of observed TO stars doesn’t permit to infer the actual
fraction.
c© 0000 RAS, MNRAS 000, 000–000
Berkeley 32 and King 11 7
Figure 6. The range of statistically acceptable ages for King 11. Results for
different sets of tracks are shown.
of the observed clump (whose membership is also confirmed by ra-
dial velocity estimates). Figure 6 shows the results 4; error bars cor-
respond to ages for which an appropriate combination of distance
and reddening exists. Considering our findings, one can provision-
ally accept a range of ages between 3 and 5 Gyr. Only BBC models
for Z=0.004 are rejected by the KS test for all ages (meaning that no
solution for age, reddening and distance has been found). Figures
7, 8, 9 show a selection of our best synthetic CMDs. To further pro-
ceed in the selection, we have used the morphology of the RGB (a
poorly populated region, therefore ignored by our statistical test)
to give additional constraints on the parameter space. An exami-
nation of this evolutionary phase reveals that: 1) the residual BBC
models (Z=0.02 and Z=0.008) are all rejected, because they pre-
dict excessively red RGBs (the upper panel of Figure 7 shows the
best BBC model: age=4.5 Gyr, Z=0.02, E(B − V )=0.93 and (m-
M)0=11.85); 2) the same problem exists with the FRA models: the
RGB is systematically too red (the lower panel of Figure 7 shows
the best FRA model: age=3 Gyr, Z=0.02, E(B−V )=1.01 and (m-
M)0=11.95); 3) the FST models seem in good agreement with the
data independently of the adopted metallicity. We thus restrict the
next considerations only to the FST models.
Figure 8 shows the theoretical FST CMDs that best repro-
duce the V,B − V data. The best fit parameters turn out to be:
Z=0.02, age 4 Gyr, E(B − V )=0.94 and (m-M)0=11.95 (panel a);
Z=0.01, age 4.25 Gyr, E(B − V )=1.04 and (m-M)0=11.75 (panel
b); Z=0.006, age 4.75 Gyr, E(B − V )=1.09 and (m-M)0=11.65
(panel c).
To solve the degeneracy we have made use of the V, V − I
CMD: although not complete in the bright part, it remains use-
ful, since only models of the right metallicity can fit the ob-
served CMDs in all passbands (see also the case of Be 32). Be-
cause of the very large reddening, we adopt the reddening law by
Dean, Warren, & Cousins (1978, see Appendix, eq. A1): E(V −
I) = 1.25×E(B−V )× [1+0.06(B−V )0+0.014E(B−V )],
which takes into account a colour dependence. This relation tends
to the usual E(V − I) = 1.25 × E(B − V ) for B − V → 0 and
E(B − V ) → 0).
In Fig. 9 we show the synthetic cases of Fig. 8 both in the
4 FRANEC models for Z=0.006 and Z=0.01, providing the same age of
Z=0.02, are not shown in the figure.
1.0 2.0
BBC−0.02
FRA−0.02
Figure 7. The upper panel shows the best solution for King 11 for BBC
models: Z=0.02, E(B − V )=0.93 and (m-M)0=11.85); 2) the lower panel
shows the best FRANEC model: age=3 Gyr, Z=0.02, E(B − V )=1.01 and
(m-M)0=11.95). Both these models predict RGBs that are too red.
V,B − V and V, V − I diagrams and with no photometric error,
to allow for a more immediate visualization of the theoretical pre-
dictions. We can see from Fig. 9 that the three competing models,
indistinguishable in B−V (left panel), do separate in V − I (right
panel): the best fit is reached for Z=0.01. The solar composition
seems definitely ruled out (the MS is too blue), but the Z=0.006
model lies only slightly too red and cannot be completely excluded.
This seems to confirm the findings by Friel et al. (2002), who based
the analysis on spectroscopic indices. In contrast, Aparicio et al.
(1991) preferred a solar abundance on the basis of their CMDs, but
in this case different stellar models have been employed. While we
are rather confident on a subsolar metallicity, a definitive answer
will require analysis of high resolution spectra.
The assumption of different levels of core overshooting (η =
0.2 or 0.3) has a minor effect on the results, as expected: King 11
is a sufficiently old cluster that the upper MS stars have masses
with small convective cores, and therefore with small overshoot-
ing. Comfortably, the predicted number of stars in RGB and clump
phase is close to the observed one, confirming that the evolutionary
lifetimes of the theoretical models are correct.
Finally, in order to evaluate the contribution of the adopted bi-
nary fraction and IMF, we performed several tests. Larger fractions
of binaries could help to fit the MS, yielding slightly larger distance
moduli (with minor effects on the age). Viceversa, if distance, red-
dening and age are fixed, the stellar multiplicity that is consistent
with the data is wide (between 10% and 60%). In fact, only frac-
tions higher than 60% produce an evident plume over the turn-off
region, which is not observed. If the same test (fixing distance, red-
dening and age) is performed also for the IMF, the results allow
c© 0000 RAS, MNRAS 000, 000–000
8 Tosi et al.
1.0 2.0
1.0 2.0
1.0 2.0
1.0 2.0
b c d
Figure 8. Comparison between observational and synthetic CMDs for King 11. Panel a shows the data CMD for the central 2′ radius region. Panels b, c and
d show the CMDs of the best fitting cases (FST tracks): (b) age 4 Gyr, E(B − V )=0.94 and (m-M)0=11.95, (c) Z=0.01, age 4.25 Gyr, E(B − V )=1.04 and
(m-M)0=11.75, (d) Z=0.006, age 4.75 Gyr, E(B − V )=1.09 and (m-M)0=11.65.
to rule out only exponents larger than 3.3, for which the synthetic
RGBs appear underpopulated.
In conclusion, the best parameters for King 11 can be summa-
rized in the following intervals:
• Z=0.01;
• age between 3.5 to 4.75 Gyr;
• distance modulus between 11.67 and 11.75;
• reddening 1.03 6 E(B − V ) 6 1.06.
4.2 Berkeley 32
For Be 32, we have chosen as reference CMDs those of the region
within 3′ from the cluster centre (top panels in Fig. 10), which con-
tains 608 stars with magnitudes measured in all the three B, V, I
bands. The same area in the control field contains 332 stars with
B, V, I . Taking this contamination into account, as well as the cir-
cumstance that 27 of the stars within the central area are shown by
the RVs not to belong to Be 32, we assume the cluster members to
be 249. The top panel of Fig. 10 shows the CMD of the stars located
within 3′ from the cluster centre, with the larger symbols indicating
the 48 objects whose RVs indicate most probable membership. To
help in the RGB definition, also the two brightest RGB members
are shown, although outside the selected 3′ radius.
The synthetic CMDs have been generated with 249 objects,
the incompleteness of Table 2 and the photometric errors described
by D06. We have generated the synthetic CMDs with and without
binary systems. As for most of our sample clusters, a fraction of
30% of binaries seems more consistent with the data, for all sets
of stellar models. We notice, though, that binaries are not sufficient
to cover the whole colour extension of the MS: a differential red-
dening of about ∆E(B − V ) = ±0.01 would provide a better
reproduction of the MS thickness.
The results of our analysis are the following. A solar metallic-
ity is out of the question, because the synthetic CMDs show V − I
colours definitely too blue for all cases when the B − V colours
are correct. Of all the synthetic models, only those with metal-
licity Z=0.008 are always able to simultaneously reproduce both
the B − V and V − I colours of all the evolutionary phases. For
Z<0.008, if B−V is reproduced, V − I tends to be too red, while
for Z>0.008, if B−V is fine, V − I tends to be too blue. Unfortu-
nately, Z=0.008 is available only for the BBC tracks. For the FRA
models, an acceptable colour agreement is achieved for Z=0.006,
but when we take into account also the shape of the MS and the
TO, Z=0.01 may be better. With the FST models, instead, Z=0.006
seem slightly better than Z=0.01. This ambiguity further suggests
that the actual metallicity is in between, i.e, Z=0.008.
In order to obtain an in depth exploration of the preferred
metallicity Z=0.008, we have also applied our statistical procedure.
Although the contamination by field stars is quite high, the turn-
off region, also thanks to the partial cleaning from non members
by the RVs, appears better defined than in King 11. The KS test
is simultaneously applied to the V, B-V and V-I distributions, se-
lecting only models giving a KS probability above 5 percent. The
c© 0000 RAS, MNRAS 000, 000–000
Berkeley 32 and King 11 9
1.5 1.75 2 2.25
2 2.5 3
Z=0.02
Z=0.01
Z=0.006
2 2.5
Z=0.01
Figure 9. Choice of the metallicity for King 11: the left panel shows the V,B− V data and the three best solutions (at Z=0.006, 0.01, 0.02) that all reproduce
the observed CMD of the central zone, while the right panel shows the same models overimposed on the V, V − I data (in this case stars from the whole field
are shown). Only the solution at Z=0.01 (for an easier understanding it is isolated in the small panel on the right) can well fit at the same time the two different
CMDs.
only acceptable models resulted to have age between 5 and 6.1
Gyr, distance moduli (m − M)0 = 12.5 − 12.6 and reddening
0.085 < E(B − V ) < 0.12.
Whatever the metallicity, it is not easy to reproduce the shape
of all the evolutionary phases covered by the stars in Be 32. The
BBC models, in spite of the excellent reproduction of the colours,
shape and position of MS, SGB and RGB, do not fit precisely the
morphology of the TO and predict a clump slightly too bright. The
FRA models are the only ones with a TO hooked enough to fit the
bluest supposed member of Fig. 10 (which however is in the tail
of the RV distribution and is the least safe member), but not for
the ages which better reproduce the other CMD sequences. When
the TO morphology is fine, the clump is too bright and vice versa.
Moreover, the MS of the FRA models is slightly too red at its faint
end. The FST models, independently of the overshooting choice η,
have TO not much hooked and excessively vertical RGBs, whose
brightest portion is therefore too blue.
As usual, models without overshooting (FRA) lead to the
youngest age. The FST models with maximum overshooting
η=0.03 provide results totally equivalent to those with η=0.02; this
has been noted also for King 11 and all OC’s old enough to have
stars with small (or no) convective cores.
The best compromise for each set of stellar models is:
• Z=0.008, age 5.2 Gyr, E(B−V )=0.12, (m-M)0=12.6 (BBC);
• Z=0.01, age 4.3 Gyr, E(B − V )=0.14, (m-M)0=12.6 (FRA);
• Z=0.006, age 5.2 Gyr, E(B − V )=0.18, (m-M)0=12.4 (FST).
The CMDs corresponding to these three best cases are shown in
Fig. 10, where in V,B−V we plot only the synthetic stars to allow
for a direct comparison of the different models, while in V, V − I
we overplot the control field objects on the synthetic stars to facili-
tate the comparison between theoretical and observational CMDs.
The uncertainties mentioned above obviously affect the iden-
tification of the best age; however, all our independent tests con-
sistently favour an age between 5.0 and 5.5 Gyr with overshooting
models (both BBC and FST, although the BBC ones perform better,
possibly because of the more appropriate metallicity Z=0.008).
Finally, another useful piece of information can be inferred
from the comparison of the pure synthetic CMDs of the bottom
panels of Fig. 10 with the observational ones of the top panels. The
synthetic MSs don’t reach magnitudes fainter than V ≃21 for BBC
and FST and V ≃20 for FRA. This limit corresponds to the min-
imum stellar mass available in the adopted sets of models: 0.6M⊙
in the BBC and FST sets and 0.7M⊙ in the FRA ones. In the cen-
tral row panels, where the external field CMD is overimposed to
the synthetic one, the faintest portions are therefore populated only
by foreground/background stars. Yet, the synthetic LFs don’t differ
too much from the observational one, suggesting that contamina-
tion dominates at that magnitude level.
5 SUMMARY AND DISCUSSION
The context of this work is the large BOCCE project
(Bragaglia & Tosi 2006), devoted to the systematic study of the
Galactic disc through open clusters. Distance, reddening and phys-
ical properties of the open clusters King 11 and Be 32 have been
explored. To this end, synthetic CMDs have been built and com-
pared with data using both morphological and statistical criteria.
A morphological analysis exploits all the evolutionary phases, but
leads to some level of subjectiveness. On the other hand, a pure
statistical treatment can establish the significance for each model
c© 0000 RAS, MNRAS 000, 000–000
10 Tosi et al.
Figure 10. Comparison between observational and synthetic CMDs for Be 32. Panels a and b show the stars measured in B, V, I in the central 3′ radius
region. The larger symbols (red in the electronic version) in panel b indicate the objects with higher membership probability from the RVs (see text for details).
Panels f, g and h show the B − V CMDs of the best fit case, mentioned in the text, for each type of stellar models. Panels c, d and e show the corresponding
V − I CMDs, overimposed to the CMD of the same area in the control field for a more direct comparison.
(reducing the subjectiveness of the comparison), but is truly selec-
tive only in case of very well defined TOs.
In order to extract the maximum level of information, we have
used both approaches: 1) we generate synthetic CMDs to best re-
produce the main CMD features, especially the late evolutionary
phases (RGB, red clump luminosity, SGB); 2) TO and main se-
quence are explored by KS test (LF and colour distribution). The
final results come from the intersection of these.
During the analysis, King 11 and Be 32 have presented differ-
ent problems. For King 11, whose metallicity is unknown, the sta-
c© 0000 RAS, MNRAS 000, 000–000
Berkeley 32 and King 11 11
Table 5. Comparison of our results and selected literature data for the two clusters.
Authors age (Gyr) Z or [Fe/H] (m −M)0 E(B-V) Notes
King 11
This work 3.5-4.75 0.01 11.67–11.75 1.03-1.06 BV I
Kaluzny ∼ 5 (m −M)V ∼ 15.3 Shallow BV R, comparison to M67/red clump mag
Aparicio et al. 5± 1 0.02 11.7 1.00 BV R, synthetic V,B − V CMD
Salaris et al. 5.5 −0.23± 0.15 δV , [Fe/H] from liter., age-metallicity-δV relation
Berkeley 32
This work 5.0-5.5 0.008 12.4–12.6 0.12 BV I
Kaluzny & Mazur 6 −0.37± 0.05 12.45±0.15 0.16 Morphological Age Ratio/MS fitting
D’Orazi et al. 6.3 0.008 12.5–12.6 0.10 BV I , isochrone fitting/red clump mag
Richtler & Sagar 6.3 −0.2 12.6±0.15 0.08 V I , isochrone fitting/red clump mag
Sestito et al. −0.29± 0.04 0.14 High-res spectra
tistical treatment has the advantage to explore very quickly a mul-
tidimensional parameter space. Nevertheless, King 11 has a very
noisy TO, therefore, a morphological analysis plays a key role in
refining the results. On the other hand, Be 32 is characterized by
well defined TO and MS (and a well defined metallicity), and the
statistical approach has provided an independent estimate of the
parameters.
For King 11, our analysis has produced the following re-
sults: (1) the FST tracks give the best chance to reproduce the
LF, the colour distribution and the morphological constraints (the
clump luminosity, the bottom of the RGB and the RGB colour);
(2) the metallicities Z=0.006, Z=0.01, Z=0.02 all produce synthetic
V,B − V CMDs whose goodness of fit are indistinguishable but
the use of the I band permits to select the right cluster metallicity,
i.e. Z=0.01; (4) the synthetic CMDs generated with the FST tracks
are consistent with a reddening 1.03 6 E(B − V ) 6 1.06, a dis-
tance modulus between 11.67 and 11.75, a cluster age between 3.5
and 4.75 Gyr (the best fit is obtained with 1.04, 11.75 and 4.25,
respectively).
Our results confirm that King 11 is among the true “old open
cluster”, contradicting the Dias et al. (2002) value, but in line with
all past direct determinations. For an immediate comparison, Table
5 shows our results together with literature ones. Our derived ages
are consistent with the Aparicio et al. (1991) finding (age 5 ± 1
Gyr). The difference (our estimates are systematically younger)
may be easily ascribed to the input physics: Aparicio et al. (1991)
adopted the Bressan, Bertelli & Chiosi (1981) tracks, characterized
by strong core overshooting: although King 11 masses are only
marginally affected by this phenomenon, a conspicuous amount
of overshooting goes in the direction of rising the estimated age.
A similar age is recovered also by Kaluzny (1989), but that work
is based on a very shallow sample. Salaris et al. (2004), adopting
[Fe/H]=−0.23, provide an age of about 5.5 Gyr from their recali-
bration of the relation between δV , metallicity and age, based on
ten clusters. The large reddening we have found is in good agree-
ment with literature values, in particular with the E(B−V ) = 0.98
derived by the Schlegel et al. (1998) maps. Our choice of metallic-
ity is in good agreement with the one by Friel et al. (2002) and
slightly discrepant with the other derivation based on photome-
try (Aparicio et al. 1991), which, however, is more uncertain since
those authors found discrepant results with different methods.
In the case of Be 32 our CMDs constrain fairly well the clus-
ter metallicity. The BBC tracks for Z=0.008 reproduce all the stel-
lar phases in all bands, while other metallicities have problems to
simultaneously best fit both the V,B − V and the V, V − I dia-
grams. This is in perfect agreement with the finding by Sestito et al.
(2006), based on high resolution spectra ([Fe/H]= −0.29± 0.04).
The best estimate of the age ranges between 5.0 and 5.5 Gyr,
slightly older than King 11. The age derived by D06 with isochrone
fitting was 6.3 Gyr, consistent with what we find here once we
consider the coarseness of the isochrone grid. Slightly older ages
(6.3 and 6.0 Gyr, respectively) were found also by Richtler & Sagar
(2001) and Kaluzny & Mazur (1991), while Hasegawa et al. (2004)
reach exactly our same conclusion (5.2 Gyr).
In addition, the present data for Be 32 suggests a distance
modulus (m − M)0 = 12.4 − 12.6, in fair agreement with past
studies, and reddening most likely around 0.12. The latter is con-
sistent but slightly larger than the E(B − V ) = 0.10 we deter-
mined in D06 assuming an older age, and slightly smaller than the
value E(B − V ) = 0.16 quoted by Kaluzny & Mazur (1991).
A clearly lower reddening (E(B − V ) = 0.08) was found by
Richtler & Sagar (2001), but we recall that their study was based
only on two passbands and may be plagued by uncertainties like
the ones we found in the case of our analysis of King 11. The com-
parison to the Schlegel et al. (1998) maps is too uncertain, given
the very low latitude of the cluster. We suggest the possibility of a
differential reddening of the order of ∆E(B − V ) ≃0.02.
We have computed the distances of the two OCs adopting the
preferred distance moduli: King 11 has a distance of about 2.2-3.4
kpc from the Sun and about 9.2-10 kpc from the Galactic centre
(assuming the Sun to be at 8 kpc from the centre), with a height
above the Galactic plane of 253-387 pc; the corresponding values
for Be 32 are 3.0-3.3 kpc, 10.7-11 kpc, and 231-254 pc, respec-
tively. Neither cluster is far enough from the Galactic centre to be
of relevance in the current debate about the metallicity distribution
in the outer disc. However, both contribute to enlarge the still small-
ish number of old OCs and their metallicity (specially once that of
King 11 is confirmed by dedicated high resolution spectroscopy
studies) will be important in defining the (possible) variation of the
radial metallicity distribution over the Galactic disc lifetime.
ACKNOWLEDGEMENTS
The King 11 data reduction was performed by Roberto Gualandi
of the Loiano Telescope staff. We are grateful to Sofia Randich for
the RVs of Be 32 provided in advance of publication. We gratefully
acknowledge the use of software written by P. Montegriffo, and of
the BDA database, created by J.C. Mermilliod, and now operated
c© 0000 RAS, MNRAS 000, 000–000
12 Tosi et al.
at the Institute for Astronomy of the University of Vienna. This
project has received partial financial support from the Italian MIUR
under PRIN 2003029437.
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c© 0000 RAS, MNRAS 000, 000–000
	Introduction
	Observations and data reduction
	The colour - magnitude diagrams
	Cluster parameters
	King 11
	Berkeley 32
	Summary and discussion

  We have obtained CCD BVI imaging of the old open clusters Berkeley 32 and
King 11. Using the synthetic colour-magnitude diagram method with three
different sets of stellar evolution models of various metallicities, with and
without overshooting, we have determined their age, distance, reddening, and
indicative metallicity, as well as distance from the Galactic centre and height
from the Galactic plane. The best parameters derived for Berkeley 32 are:
subsolar metallicity (Z=0.008 represents the best choice, Z=0.006 or 0.01 are
more marginally acceptable), age = 5.0-5.5 Gyr (models with overshooting;
without overshooting the age is 4.2-4.4 Gyr with poorer agreement),
(m-M)_0=12.4-12.6, E(B-V)=0.12-0.18 (with the lower value being more probable
because it corresponds to the best metallicity), Rgc ~ 10.7-11 kpc, and |Z| ~
231-254 pc. The best parameters for King 11 are: Z=0.01, age=3.5-4.75 Gyr,
(m-M)_0=11.67-11.75, E(B-V)=1.03-1.06, Rgc ~ 9.2-10 kpc, and |Z| ~ 253-387 pc.

Introduction
	Observations and data reduction
	The colour - magnitude diagrams
	Cluster parameters
	King 11
	Berkeley 32
	Summary and discussion
