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THE ASTROPHYSICAL JOURNAL, 527:230È235, 1999 December 10
1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.(
THE COLOR-MAGNITUDE DIAGRAM OF THE GLOBULAR CLUSTER NGC 6362 AND THE
CANONICAL TILT OF HORIZONTAL BRANCHES
E. BROCATO1
Osservatorio Astronomico di Collurania, Via M. Maggini, I-64100 Teramo, Italy; brocato=astrte.te.astro.it
V. CASTELLANI2
Dipartimento di Fisica, di Pisa, Piazza Torricelli 2 I-56100 Pisa, Italy;Universita
`vittorio=astrte.te.astro.it
G. RAIMONDO1
Osservatorio Astronomico di Collurania, Via M. Maggini, I-64100 Teramo, Italy; raimondo=astrte.te.astro.it
AND
A. R. WALKER
Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatories,3Casilla 603, La Serena, Chile; awalker=noao.edu
Received 1999 January 8; accepted 1999 July 21
ABSTRACT
In this paper we present new and accurate photometry for stars in the Galactic globular cluster NGC
6362. The color-magnitude diagram discloses two peculiarities in the distribution of stars : (1) a slightly
tilted horizontal branch (HB) mag) and (2) a clump of stars near the red edge of the HB. We(*V
tilt \ 0.1
perform a detailed comparison with theoretical stellar models in both the HB and red giant branch
(RGB) phases. It appears that in the moderately metal rich NGC 6362 the tilted HB can be explained
as a natural product of canonical evolutionary theories, being a consequence of the minimum in the
bolometric correction near 7500 K. We also investigate the e†ect of decreasing the efficiency of con-
vective transport in stars climbing the RGB. Adopting Z\0.002 and Y\0.23, and performing a global
Ðtting with the theoretical isochrones and zero-age HB, an age of 12 ^1 Gyr is found, together with
and E(B[V)\0.08.(m[M)V\14.68
Subject headings : globular clusters : individual (NGC 6362) È Hertzsprung-Russell diagram È
stars: evolution È stars : horizontal-branch È stars : interiors
1.INTRODUCTION
Galactic clusters have long been the stellar systems most
suitable for testing the predictions of stellar evolution theo-
ries over the main evolutionary phases of both H- and He-
burning structures. In more recent times, the
color-magnitude diagrams (CMDs) of Galactic globular
clusters (GCs) have become of critical importance in eluci-
dating the early phases of galactic evolution, as well as
providing severe constraints to the age of the universe. This
has stimulated much e†ort on both the theoretical (see, e.g.,
Cassisi et al. 1998 and references therein) and observational
fronts.
In a recent paper, Piotto et al. (1999) present a B,VCMD
for the GC NGC 6362 obtained with the Hubble Space
Telescope (HST ) Wide Field Planetary Camera 2, and com-
prising 4104 stars covering the center of the cluster. This
CMD is notable for showing a well-deÐned sequence of blue
straggler (BS) stars and a main sequence (MS) that extends
almost 2 mag deeper than that shown here, allowing a
careful study of the cluster luminosity function. However,
due to the small area covered by HST , the evolved star
sequences, such as the horizontal branch (HB), are not well
populated and have lower photometric accuracy than here;
thus, the two CMDs to a great extent complement each
other.
1Istituto Nazionale di Fisica Nucleare, LNGS, I-67100 LÏAquila, Italy.
2Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56100 Pisa,
Italy.
3Operated by the Association of Universities for Research in
Astronomy, under cooperative agreement with the National Science Foun-
dation.
In this paper we present a new and accurate CMD for
stars in the Galactic GC NGC 6362. In °2 we will discuss
the observational data and present CMDs for the cluster
stars. We Ðnd that NGC 6362 is a further representative of
the globular clusters showing a tilted HB. In °3 we discuss
this point, showing that (at least in this case) the tilted HB is
the natural product of canonical evolutionary theories,
without invoking the intervention of more sophisticated
mechanisms. In the same section we show that the observed
cluster CMD is well Ðtted by a 12 Gyr isochrone, i.e., the
same age already found on the basis of the same theoretical
scenario for much more metal poor clusters. A Ðnal dis-
cussion will close the paper.
2.OBSERVATIONS AND DATA REDUCTION
NGC 6362 lies at a2000 \17h31m55s,d2000 \
[67¡02@52A. With Galactic coordinates b\(l\325¡.55,
and an estimated distance modulus of about 15[17¡.57)
mag (Fourcade 1974; Alcaino & Liller 1986), the cluster is
placed at the periphery of the Galactic bulge. Zinn & West
(1984) Ðnd the metallicity of NGC 6362 to be [Fe/H] \
[1.08 ^0.09, and Rutledge, Hesser, & Stetson (1997)
give [Fe/H] \[1.18 ^0.06 on the same scale, or
[Fe/H] \[0.99 ^0.03 on the scale of Carretta & Gratton
(1997), who themselves, based on only two stars, Ðnd
[Fe/H] \[0.96. Suntze†, Kinman, & Kraft (1991) give
[Fe/H] \[1.08. Thus, NGC 6362 is one of the most metal
rich clusters known with halo kinematics. Despite the high
metallicity, NGC 6362 has an extensive population of RR
Lyrae and many blue HB stars. Early reddening estimates
range between E(B[V)\0.08 (Fourcade 1974) and 0.12
(Harris & Racine 1979).
230
NGC 6362 AND CANONICAL TILT OF HORIZONTAL BRANCHES 231
As part of a program studying the RR Lyrae variables in
selected Galactic GCÏs, 315 CCD frames in the B,V, and I
passbands were obtained of a Ðeld centered on13@.6 ]13@.6
NGC 6362 during Ðve observing runs in 1993È1995, with
the CTIO 0.9 m telescope and Tektronix 2048 No. 3 CCD.
An analysis of the RR Lyrae observations will be given
elsewhere (A. R. Walker, in preparation). The clusters NGC
6981 (M72) and NGC 1851 were also observed as part of
the same program, and similar observing and reduction
techniques were followed for each, as described by Walker
(1998).
Photoelectric standards have been observed in the vicin-
ity of NGC 6362 by Alcaino (1970), in Vand Bonly, and in
UBV RI by Alcaino & Liller (1986). Many of these latter
stars have faint companions, and given the large CCD Ðeld
here, a new set of local standards was set up. The 21 stars
selected have Vmagnitudes between 14.6 and 16.8, and
were measured on 36 sets of frames on six fully photometric
nights on three di†erent observing runs. During each night
many standard stars were observed from Landolt (1992), in
order to determine color equations, extinction, and zero
points. Reductions for the primary and local standards fol-
lowed exactly the same procedures, to mitigate the intro-
duction of systematic errors. The rms scatter for the local
standards, looking at mean values for each of the six nights,
is typically very small, >0.01 mag, and thus the error in the
magnitude system for the local standards will be dominated
by the tie-in to the primary standards and should not be
signiÐcantly greater than ^0.01 mag.
Photometry for the stars on the 315 CCD frames utilized
the programs DAOPHOT and ALLSTAR (Stetson 1987,
1995), using scripts to efficiently process all the frames. At
the completion of the photometry, the lists of stars for each
frame were matched and cross-referenced using programs
DAOMATCH and DAOMASTER (Stetson 1995). Photo-
metry for the nonvariable stars was combined using the
following algorithm, remembering that there are up to 105
measurements in each color. If there were fewer than 20
measurements in each color, the star was rejected. For those
remaining, the measurements for each color were sorted,
and the median and the lower tenth percentile found.
The sorted lists were then clipped both below and above
the median using the di†erence between the median and the
lower tenth percentile, on the assumption that most
systematic measurement errors (cosmic rays, two stars
measured as one, etc.) bias the measured magnitude
brighter. The mean of the remaining measurements was
then calculated.
The resulting V,B[Vand I,V[ICMDs (Figs. 1 and 2)
show tightly deÐned sequences, superimposed on a large
Ðeld population. The RR Lyrae variables are plotted at
their mean magnitude values. The reddening and metallicity
can be derived from the CMD by a variety of methods
(A. R. Walker, in preparation). Mean values are
E(B[V)\0.05 ^0.02, rather smaller than the earlier esti-
mates, and [Fe/H] \[1.1 ^0.1, in good agreement with
values quoted above. This reddening value is in excellent
agreement with that obtained by Piotto et al. (1999),
E(B[V)\0.06 ^0.03, and indeed a careful comparison
shows that the two studies are in excellent photometric
agreement over the whole CMD, with di†erences of less
than 0.01 mag in Vand B[Vwhen Ðducials are compared.
Piotto et al. (1999) show that the center of NGC 6362
contains a extensive, narrow sequence of BS stars, but they
FIG. 1.ÈV,B[Vcolor-magnitude diagram
are not able to determine whether there is any di†erence in
radial distribution of these stars compared to other cluster
members. The BS stars are also apparent on our CMD, and
they are much more centrally concentrated than the other
cluster stars. We quantify this by comparing the number of
BS stars as a function of radial distance. For this compari-
son we use a CMD containing stars with a less stringent
error cuto† than the one used for accurately delineating the
CMD sequences, containing 8078 stars compared to 4054 ;
many of the extra stars are those measured with higher
errors in the crowded central regions of the cluster. We
count BS stars in the photometric box V\17È18,
B[V\0.25È0.40 and compare to a MS box V\18.5È
19.5, B[V\0.5È0.6, and for the inner two annuli, to a box
containing RGB stars between V\16.5 and 17.5. The BS
box is deliberately chosen to be well separated from the
FIG. 2.ÈI,V[Icolor-magnitude diagram
232 BROCATO ET AL. Vol. 527
cluster MS, so that it will not be contaminated by MS stars
with large photometric errors. The results are given in Table
1. These data should not be overinterpreted, since particu-
larly for the inner annulus the incompleteness factor is large
and uncertain. For this reason, we compare the BS counts
in the inner two annuli with samples both brighter (RGB)
and fainter (MS) than the BS sample. Corrections for Ðeld
star contamination are ascertained from counting stars at a
radius greater than 1000 pixels, excluding those that clearly
lie on the cluster MS and RGB. The Ðeld stars are sub-
tracted o† in the ““ corrected ÏÏ columns and are seen to be
very small. The results show that there are at least a factor
of 2 more BS stars than in the MS and RGB samples in the
innermost (0È200 pixel) annulus compared to the more
distant annuli. Similar selections using Piotto et al. (1999)
data provide for BS, MS, and RGB star counts of 12, 712,
and 61, respectively, with ratios BS/MS \0.017 and
BS/RGB \0.20, which can be compared to data in
Table 1. These values conÐrm our results for the bright part
of the diagram and show the large incompleteness
(crowding) a†ecting our MS counts in the inner annulus.
3.COMPARISON WITH THEORETICAL PREDICTIONS
Inspection of the CMDs reveals that in the V,B[V
plane the HB of NGC 6362 does not show a continuously
decreasing Vmagnitude when moving from the cool toward
the hot portion of the branch, and indeed the HB is bright-
est around B[V\0.2. An additional very interesting
feature, seen in both the V,B[Vand I,V[Idiagrams,
occurs at the red boundary of the HB, where a clump of
stars extends over some tenths of a magnitude in brightness
at near constant color.
Figures 3 and 4 show the observed distribution of HB
stars in the V,B[Vand I,V[ICMDs. According to data
in Figure 3, it is apparent that NGC 6362 appears as a
representative of globular clusters with a tilted HB, to be
added to NGC 1851 (Walker 1998) and perhaps NGC 6229
(Borissova et al. 1997, 1999) and the extreme cases of NGC
6388 and NGC 6441 (Piotto et al. 1997; Rich et al. 1997 ;
Layden et al. 1999). This feature, appearing in the B[V
color, is not seen in the I,V[Idiagram of NGC 6362
(Fig. 4).
In the case of NGC 6362 (and also in NGC 1851) the tilt
is of the order of mag, where is a measure-*V
tilt \ 0.1 *V
tilt
ment of the luminosity increase occurring from the red side
to the blue, i.e., the maximum luminosity distance of the HB
from a straight line drawn at the lower level of the red HB,
while in the two clusters NGC 6441 and NGC 6388 it is
mag. The matter has been recently discussed by*V
tilt D0.5
Sweigart & Catelan (1998), who suggest that such a severely
tilted HB should be regarded as evidence for the occurrence
FIG. 3.ÈObserved distribution of HB stars in the V,B[Vplane,
plotted together with the theoretical ZAHBs calculated for three di†erent
values of the mixing length. Symbols mark the location of stars with mass
0.80, 0.75, 0.70, 0.67, 0.65, 0.64, 0.63, 0.62, 0.61, and 0.60 M_.
of some unusual mechanism, such as rotation or di†erential
He enrichment of the external layers. However, one should
note that the occurrence of a tilted HB is not ignored by
available theoretical predictions concerning canonical HB
sequences, as already presented in the current literature.
For example, by looking, e.g., at Figures 8 and 9 in Castel-
lani, Chieffi, & Pulone (1991), one Ðnds that in the V,B[V
diagram, a very metal poor HB (Z\0.0001) has a lumi-
nosity that regularly slopes down when the temperature is
increasing, while by Z\0.001 the HB starts to tilt up.
Thus, metal-rich GCs are theoretically expected to have a
tilted HB.
The reason for the canonical tilt appears to be rather
obvious: whereas theoretical luminosities decrease when
the temperature of zero-age HB (ZAHB) stars is increasing,
the bolometric corrections have a minimum around Te\
7500 K. As a consequence, the bolometric correction (BC)
tends to push toward a brighter Vmagnitude around this
temperature. At lower metallicities, the resulting HB magni-
tude is dominated by the slope of the theoretical luminosity-
temperature relation, and theory predicts that the V
magnitude will continuously increase from the red to the
blue side of the branch. However, for higher metallicities the
theoretical slope decreases, and a minimum Vappears
TABLE 1
NUMBER OF STARS IN THE SELECTED EVOLUTIONARY PHASES
Annulus Radii
(pixels) BS MS RGB BScorr MScorr RGBcorr BScorr/MScorr BScorr/RGBcorr
0È200.......... 12 230 63 11.9 229 62 0.052 0.19
200È300 ....... 4 336 46 3.85 334 46 0.012 0.08
300È400....... 4 456 36 3.8 454 36 0.008 0.10
400È500 ....... 1 428 26 0.75 425 26 0.002 0.03
[1000 ........ 1 88 10 0 77 5 ... ...
NOTE.ÈSubscript ““ corrÏÏ indicates the correction for the Ðeld star contamination.
No. 1, 1999 NGC 6362 AND CANONICAL TILT OF HORIZONTAL BRANCHES 233
FIG. 4.ÈAs in Fig. 3, but in the I,V[Iplane. Symbols mark the
location of stars with mass 0.80, 0.75, 0.70, 0.67, 0.65, 0.64, 0.63, 0.62, and
0.61 M_.
within the HB. This is not the case for the Imagnitude,
since in that case the BC is much less dependent on the
stellar temperature.
To examine this problem in more detail, we used our
updated evolutionary code (see Cassisi et al. 1998) to
compute a set of evolutionary sequences, taking into
account element di†usion and for an original chemical com-
position that should be suitable for NGC 6362, namely,
Z\0.002, Y\0.23. Figure 5 shows theoretical predictions
concerning the ZAHB luminosity, as derived for three dif-
ferent assumptions about the mixing length parameter,
FIG. 5.ÈTheoretical ZAHBs as derived for the labeled values of the
mixing length. Symbols mark the location of stars with mass 0.80, 0.75,
070, 0.67, 0.65, 0.64, 0.63, 0.62, 0.61, 0.60, 0.58, 0.56, and 0.55 M_.
which governs the efficiency of the external convection that
a†ects the envelopes of the cooler stars. Figure 3 shows the
same theoretical result, but translated into the V,B[V
diagram, adopting model atmospheres from Castelli,
Gratton, & Kurucz (1997) and best Ðtted to the observation
with the labeled value of the cluster reddening and distance
modulus. In all cases, one Ðnds that theoretical predictions
appear to be in reasonable agreement with observations
and, in particular, that the theory shows a minimum V
magnitude at B[V^0.3. The assumption about the effi-
ciency of superadiabatic convection plays a relevant role in
governing the predicted location of the HB red portion.
Thus, the tilt observed in NGC 6362 must be regarded as a
natural expectation from canonical theories.
Turning now to the clump of stars at the cool end of the
red HB, we Ðrst note that Fusi Pecci et al. (1992) predict
that this location is close to where blue straggler descen-
dants should be found, which is relevant since NGC 6362
appears to be fairly rich in blue stragglers. However, the
Piotto et al. (1999) data do not show an excess of stars
clumped near the red HB, which would be expected given
the large number (D30) of BS stars, thus apparently ruling
out this possibility. In addition, this feature disappears in
the Ðeld population (i.e., for stars at radius greater than
1000 pixels); thus, it is not due to a chance superimposition
of Ðeld stars. Therefore, we suggest that either we are facing
evolutionary e†ects (see, e.g., the synthetic HB of Catelan et
al. 1998 and Brocato et al. 1999) on a clump of red ZAHB
stars with mixing length parameter a\1.0, or the ZAHB
follows the a\1.6 predictions but with a disagreement
between theory and observations of the order of 0.05 mag.
By relying again on Castelli et al. (1997) model atmo-
spheres and adopting the above reported values for the
cluster reddening and distance modulus, one can translate
the theoretical results onto the observational I,V[I
diagram. We adopted E(V[I)\1.25E(B[V) from Bessell
& Brett (1988), and thus dI\1.75E(B[V). The Ðtting, as
shown in Figure 4, appears quite satisfactory.
The theoretical scenario has Ðnally been used to derive
cluster isochrones for a suitable range of ages. According to
the discussion given in Brocato et al. (1998), the cluster
reddening and distance modulus can be Ðrmly established
by Ðtting the HB. Following the quoted procedure, we
derive and E(B[V)\0.08(m[M)V\14.68 ^0.05
^0.02, in good agreement with De Santis & Cassisi (1999).
The reddening is slightly higher than the value obtained in
°2, but the observational and Ðtted values do agree within
their estimated uncertainties. Figures 6 and 7 show that
with the already given values of DMs, E(B[V), and
E(V[I), stars at the cluster turno† and along the subgiant
branch appear very nicely Ðtted by the 12 Gyr isochrone,
with a\2.3.
The mismatch between theory and observation in the
upper portion of the RGB may be due to the adopted color
temperature relation being incorrect, as discussed by
Lejeune, Cuisinier, & Buser (1997). An alternative explana-
tion is that the efficiency of convective transport is progres-
sively decreasing with respect to the predictions of
evolution with a constant value for the mixing length, in the
sense that a lower value of the mixing length is needed in
order to Ðt the observations. To explore this possibility, we
computed evolutionary models in which we progressively
varied the aparameter, i.e., the mixing length, as stars start
to climb the RGB. We parameterize the[log (L/L_)º0.5]
234 BROCATO ET AL. Vol. 527
FIG. 6.ÈFit of the NGC 6362 data to the theoretical isochrone aged 12
Gyr.
mixing length as a linear function of the stellar luminosity:
where is the usual value and bisa\a0[blog (L/L_), a0
the decreasing rate that needs to be calibrated. The best Ðts
are obtained by adopting a decreasing rate of b\0.20, as
shown in Figures 8 and 9, where we also plot the isochrones
derived with b\0.10 and b\0.15.
4.FINAL REMARKS
In this paper we have shown that the occurrence of tilted
HBs, at least up to mag, is a natural prediction of*V
tilt \ 0.1
current evolutionary theories for old GCÏs with moderate to
large metallicities. The Ðtting between theory and obser-
vations of stars in NGC 6362 appears quite satisfactory,
predicting a cluster age of about 12 Gyr. Such an age is
similar to the ages derived adopting the same theoretical
scenario for other Galactic globular clusters with much
lower metallicity, such as M68 (Z\0.0004, t^11 Gyr;
Cassisi et al. 1999), so that no evidence can be found here to
FIG. 7.ÈFit of the NGC 6362 data to the theoretical isochrone aged 12
Gyr.
FIG. 8.ÈE†ect of di†erent decreasing rates of the aparameter. The thin
solid line corresponds to a constant value (a\2.3), as in Fig. 6; dotted line
corresponds to b\0.10, and long-dashed line to b\0.15. The best Ðt is
performed with b\0.20 (thick solid line).
FIG. 9.ÈAs in Fig. 8, but in the I,V[Iplane. The thin solid line
corresponds to a constant value (a\2.3), as in Fig. 7; the dotted line
corresponds to b\0.10, and the long dashed line to b\0.15. The best Ðt
is performed with b\0.20 (thick solid line).
support a possible correlation between age and metallicity.
Note also that similar ages have also been measured for old
globular clusters in the Large Magellanic Cloud (Brocato et
al. 1996; Olsen et al. 1998).
However, the explanation for the clumping of stars at the
red boundary of the HB remains an open question, for
which we have only suggested some possible alternative
explanations.
We thank Frank Valdes for advice on combining mea-
surements. G. R. acknowledges the Amm. Provinciale di
Teramo for a fellowship.
No. 1, 1999 NGC 6362 AND CANONICAL TILT OF HORIZONTAL BRANCHES 235
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