Stroemgren photometry of Galactic Globular Clusters. I. New Calibrations of the metallicity index

Abstract

We present a new calibration of the Stroemgren metallicity index m1 using red giant (RG) stars in 4 globular clusters (GCs:M92,M13,NGC1851,47Tuc) with metallicity ranging from [Fe/H]=-2.2 to -0.7, marginally affected by reddening (E(B-V)<0.04) and with accurate u,v,b,y photometry.The main difference between the new metallicity-index-color (MIC) relations and similar relations available in the literature is that we adopted the u-y/v-y colors instead of the b-y.These colors present a stronger sensitivity to effective temperature, and the MIC relations show a linear slope. The difference between photometric estimates and spectroscopic measurements for RGs in M71,NGC288,NGC362,NGC6397, and NGC6752 is 0.04+/-0.03dex (sigma=0.11dex). We also apply the MIC relations to 85 field RGs with metallicity raning from [Fe/H]=-2.4 to -0.5 and accurate reddening estimates. We find that the difference between photometric estimates and spectroscopic measurements is-0.14+/-0.01dex (sig=0.17dex). We also provide two sets of MIC relations based on evolutionary models that have been transformed into the observational plane by adopting either semi-empirical or theoretical color-temperature relations. We apply the semi-empirical relations to the 9 GCs and find that the difference between photometric and spectroscopic metallicities is 0.04+/-0.03dex (sig=0.10dex).A similar agreement is found for the sample of field RGs, with a difference of -0.09+/-0.03dex (sig=0.19dex).The difference between metallicity estimates based on theoretical relations and spectroscopic measurements is -0.11+/-0.03dex (sig=0.14dex) for the 9 GGCs and -0.24+/-0.03dex (sig=0.15dex) for the field RGs. Current evidence indicates that new MIC relations provide metallicities with an intrinsic accuracy better than 0.2dex. Comment: 51 pages, 19 figures, accepted for submission to ApJ

Full text

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arXiv:0707.1019v1 [astro-ph] 6 Jul 2007
Str¨ omgren photometry of Galactic Globular Clusters. I. New
Calibrations of the metallicity index.1
A. Calamida2,3, G. Bono2,4, P. B. Stetson5,10,11, L. M. Freyhammer6, S. Cassisi7F.
Grundahl8, A. Pietrinferni7, M. Hilker4, F. Primas4, T. Richtler9M. Romaniello4, R.
Buonanno3, F. Caputo2, M. Castellani2, C. E. Corsi2, I. Ferraro2, G. Iannicola2, L. Pulone2
ABSTRACT
We present a new calibration of the Stroemgren metallicity index m1using
red giant (RG) stars in a sample of Galactic globular clusters (GGCs: M92, M13,
NGC1851, 47 Tuc) that cover a broad range in metallicity (−2.2 ≤ [Fe/H] ≤
−0.7), are marginally affected by reddening uncertainties (E(B–V) ≤ 0.04) and
for which accurate u,v,b,y Stroemgren photometry is available to well below
1Based in part on observations collected with the 1.54m Danish telescope operated at ESO (La Silla)
and with the Nordic Optical Telescope (NOT) operated at La Palma (Spain).
2INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00040, Monte Porzio Catone, Italy;
bono@mporzio.astro.it, caputo@mporzio.astro.it, corsi@mporzio.astro.it, ferraro@mporzio.astro.it, giac-
into@mporzio.astro.it, pulone@mporzio.astro.it
3Universit` a di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy;
nanno@mporzio.astro.it, calamida@mporzio.astro.it
buo-
4European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching bei Munchen, Germany;
mhilker@eso.org, fprimas@eso.org, mromanie@eso.org
5Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council,
5071 West Saanich Road, Victoria, BC V9E 2E7, Canada; Peter.Stetson@nrc-cnrc.gc.ca
6Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK; lmfreyham-
mer@uclan.ac.uk
7INAF-Osservatorio Astronomico di Collurania, via M. Maggini, 64100 Teramo, Italy; cassisi@oa-
teramo.inaf.it, adriano@oa-teramo.inaf.it
8Department of Physics and Astronomy, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark;
fgj@phys.au.dk
9Universidad
tom@mobydick.cfm.udec.cl
deConcepcion,Departamento deFisica, Casilla106-C, Concepcion,Chile;
10Guest User, Canadian Astronomy Data Centre, which is operated by the Herzberg Institute of Astro-
physics, National Research Council of Canada.
11Guest Investigator of the UK Astronomy Data Centre.

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the turnoff region. The main difference between the new empirical metallicity–
index–color (MIC) relations and similar relations available in the literature is
that we have adopted the u–y and v–y colors instead of the b–y color. These col-
ors present a stronger sensitivity to effective temperature, and the MIC relations
show a linear and well-defined slope. The net difference between photometric
estimates and spectroscopic measurements, for RG stars in five GGCs: M71,
NGC288, NGC362, NGC6397, NGC6752, is 0.04±0.03 dex with σ = 0.11 dex.
We also apply the new MIC relations to a sample of field stars for which spectro-
scopic metallicity (−2.4 ≤ [Fe/H] ≤ −0.5), accurate Str¨ omgren photometry, and
reddening estimates (Anthony-Twarog & Twarog 1994, 1998) are all available.
We find that the difference between photometric estimates and spectroscopic
measurements is on average −0.14 ± 0.01 dex, with σ = 0.17 dex.
We also provide two independent sets of MIC relations based on evolutionary
models that have been transformed into the observational plane by adopting ei-
ther semi-empirical or theoretical color-temperature relations (CTRs). We apply
the semi-empirical α−enhanced MIC relations to the nine GCs and find that
the difference between photometric estimates and spectroscopic measurements
is 0.04 ± 0.03 dex, with σ = 0.10 dex. A similar agreement is also found for
the sample of field stars, and indeed the difference is −0.09 ± 0.03 dex, with
σ = 0.19 dex. The difference between metallicity estimates based on theoretical
scaled-solar and spectroscopic measurements −0.11±0.03 dex, with σ = 0.14 dex
for the nine GGCs and −0.24 ± 0.03 dex, with σ = 0.15 dex for the field stars.
On the whole, current findings support the evidence that new Str¨ omgren MIC
relations provide metallicity estimates with an intrinsic accuracy better than 0.2
dex.
Subject headings: globular clusters: general — globular clusters: individual (M13,
M71, M92, NGC288, NGC362, NGC1851, NGC6397, NGC6752, 47 Tuc) —
stars: abundances — stars: evolution
1.Introduction
The intermediate-band Str¨ omgren photometric system (Str¨ omgren 1966; Crawford
1975; Bond 1980; Schuster & Nissen 1988, hereinafter SN88) presents several indisputable
advantages when compared with broad-band photometric systems such as the Johnson-
Cousins-Glass system (Johnson & Morgan 1953; Cousins 1976; Bessell 2005, and references
therein). The key advantages of Str¨ omgren photometry for A- to G-type stars are: i) the

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ability to provide robust estimates of intrinsic stellar parameters such as the metal abun-
dance (the m1= (v–b) −(b–y) index, Richter et al. 1999; Anthony-Twarog & Twarog 2000,
hereinafter ATT00; Hilker 2000, hereinafter H00; Hilker & Richtler 2000, hereinafter HR00),
the surface gravity (the c1= (u–v) − (v–b) index), and the effective temperature (the Hβ
index, Nissen 1988; Olsen 1988; ATT00). The Hβ index is marginally affected by reddening,
and therefore can also be compared to a simple color such as b–y to provide individual esti-
mates of reddening corrections (Nissen & Schuster 1991). The same outcome applies to the
reddening free [c1] index, and indeed theoretical and empirical evidence (e.g., Stetson 1991;
Nissen 1994; Calamida et al. 2005) suggests that a simple color such as u–y compared to [c1]
(which is a temperature index for stars hotter than 8,500 K) provides a robust reddening
index for blue horizontal branch stars. ii) The ([c1],v–y) color-color plane provides robust
estimates of the age of Galactic Globular Clusters (GGCs), since it is completely indepen-
dent of cluster distance and marginally affected by uncertainties in interstellar reddening
corrections. Moreover, the region around the main-sequence turnoff (TO) presents a cuspy
shape in this diagram (see Fig. 2 in Grundahl et al. 1998), and therefore its identification is
more robust than in the typical Johnson-Cousins bands. In the latter photometric system
the region around the TO presents a steep slope (Rosenberg et al. 2000). iii) The (u,u–y)
Color-Magnitude Diagram (CMD) provides the opportunity to identify a jump among hot
Horizontal Branch stars at 11,500 ? Teff ? 12,000 K caused by radiative levitation of
metals (Grundahl et al. 1998, 1999). iv) Detailed empirical investigations characterized the
Str¨ omgren system not only for A−G type dwarfs (Crawford 1975, 1979; Nissen 1988; Olsen
1988; Schuster & Nissen 1989, hereinafter SN89; Nordstrom et al. 2004), but also for G−K
type giants (Bond 1980; Richtler 1989; Twarog & Anthony-Twarog 1991; Grebel & Richtler
1992; Anthony-Twarog & Twarog 1994, hereinafter ATT94; H00). v) The use of the m1
versus color plane can also be safely adopted to distinguish cluster and field stars (ATT00;
Rey et al. 2004). vi) Accurate Str¨ omgren photometry can also be adopted to constrain the
ensemble properties of stellar populations in complex stellar systems like the Galactic bulge
(Feltzing & Gilmore 2000) and disk (Haywood 2001). vii) Str¨ omgren photometry has been
recently adopted to investigate the membership and the metallicity distribution of Red Giant
(RG) stars in the Local Group dwarf spheroidal galaxy Draco (Faria et al. 2007). Moreover,
it has also been adopted to remove the degeneracy between age and metallicity in other
stellar systems hosting simple stellar populations (GCs, elliptical galaxies), to investigate
age and metallicity distributions of dwarf elliptical galaxies in the Coma and Fornax galaxy
clusters (Rakos & Schombert 2004, 2005).
On the other hand, the Str¨ omgren system presents two substantial drawbacks. i) the
u and v bands have short effective wavelengths, namely λeff = 3450 and λeff = 4110˚ A.
As a consequence the ability to perform accurate photometry with current CCD detectors is

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hampered by their reduced sensitivity in this wavelength region. ii) The intrinsic accuracy of
the stellar parameters, estimated using Str¨ omgren indices, strongly depends on the accuracy
of the absolute zero-point calibrations. This typically means an accuracy better than 0.03
mag. This limit could be easily accomplished in the era of photoelectric photometry, but it
is not trivial at all in the modern age of CCDs.
The use of Str¨ omgren photometry was also hampered by the lack of accurate bolometric
corrections (BCs) and color-temperature relations (CTRs) based on recent and homogeneous
sets of atmosphere models. This gap was partially filled by the new semi-empirical set of
BCs and CTRs provided by Clem et al. (2004, hereinafter CVGB04) and by the new theo-
retical calibration of the Hβ index provided by Castelli & Kurucz (2006, hereinafter CK06).
Moreover and even more importantly, current empirical calibrations of Str¨ omgren metallicity
indices are based either on field stars (ATT94) or on a mix of cluster and field stars (H00).
However, empirical spectroscopic evidence suggests that field and cluster stars present differ-
ent heavy element abundance patterns (Gratton, Sneden & Carretta 2004). Moreover, the
occurrence of CN and/or CH rich stars in GGCs (Anthony-Twarog, Twarog, & Craig 1995;
Grundahl, Stetson, & Andersen 2002) along the RG (HR00), the subgiant branch, and the
main sequence (Stanford et al. 2004; Kayser et al. 2006) also suggests the opportunity for
an independent calibration1of the Str¨ omgren metallicity index based only on cluster stars
as originally suggested by Richtler (1989).
To fill this gap we plan to provide new empirical, semi-empirical, and theoretical calibra-
tions of the m1metallicity index using cluster stars, and new sets of semi-empirical and the-
oretical transformations. This is the first paper of a series devoted to Str¨ omgren photometry
of GGCs. The structure of the current paper is as follows. In §2 we discuss in detail the
photometric catalogs we adopted for the new empirical calibration and for validating current
metallicity-index–color (MIC) relations. Section 3 deals with the selection criteria adopted
to select the GCs for the calibration together with the optical-NIR two-color planes and
the proper-motion selection adopted to identify candidate field and cluster RG stars. In §4
we discuss the approach adopted to calibrate the Str¨ omgren metallicity index, while in §5
we present the different tests we performed to validate the current empirical calibrations
and the comparison between photometric estimates and spectroscopic measurements of iron
abundances. Section 6 deals with the calibration of both semi-empirical and theoretical MIC
relations. In this section we also discuss the validation of the new relations and the com-
parison with spectroscopic abundances and with other calibrations of the Str¨ omgren MIC
relations available in the literature. We summarize the results and briefly discuss further
1The referee noted that the calibration of the metallicity index based on a mixing of field disk stars and
open cluster stars does not show any drawback (Twarog et al. 1997)

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improvements and applications of the new MIC relations in §7.
2.Observations and data reduction
The photometric catalogs of globular clusters adopted in this investigation were collected
with the 2.56m Nordic Optical Telescope (NOT) on La Palma and with the 1.54m Danish
Telescope on La Silla (ESO), using the uvby filter sets available there (see Table 1 for a
log of the observations). Data secured with the NOT were collected during three observing
runs in 1995, 1997, and in 1998. Stars from the lists of Olsen (1983, 1984) and SN88 were
observed on two nights in 1995 and four nights in 1998 under photometric conditions, to
derive the transformation between the instrumental magnitudes and the standard system.
The data for M13 have already been described in Grundahl et al. (1998), while those for
M92 (NGC 6341) were collected with a thinned AR coated 2048 × 2048 pixel CCD camera
on the HiRAC instrument, with 0.′′11 per pixel, thus covering a sky area of approximately
3.75 × 3.75 arcmin2. Most of the observations were collected using tip/tilt correction, and
the seeing FWHM of the entire set of images ranges from ∼0.′′45 to ∼1.′′0. There was no
significant variation of the point spread function (PSF) over the field of view. We observed
two overlapping fields in M92, with one field on the cluster center to ensure a large sample
of HB and red-giant branch (RGB) stars. Data for M71 were collected between June 26
and July 2, 1995, and we observed a field 2′north of the cluster center (for more details see
Grundahl et al. 2002).
The images from the 1.54m Danish Telescope were acquired during two observing runs
in May and in October 1997. For both runs we used the Danish Faint Object Spectrograph
and Camera (DFOSC) equipped with a thinned, AR coated 2048 × 2048 pixel CCD camera.
The field of view covered by these data is approximately 11 arcmin across. During the
October observing run data were collected for NGC104, NGC288, NGC1851, NGC362, and
NGC6752, and during the run in May for NGC6397 (see Table 1). The selected clusters
were observed on several photometric nights, and approximately 150 different standard stars
from the list collected by Olsen (1983, 1984) and by SN88 were also observed. These images
were secured during seeing conditions ranging from 1.′′3 to 2.′′2. Flat fields were obtained
on each night during evening and morning twilight. Photometry for the defocused standard
stars was derived from large-aperture photometry.
The photometryofthecluster and standardframeswas performed with
DAOPHOTIV/ALLFRAME and DAOGROW (Stetson 1987, 1991, 1994). Based on the
frame–to–frame scatter for the bright stars in the clusters with calibrated photometry we
estimate that the errors in the photometric zero points are below 0.02 mag for the ob-

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servations from NOT, and less than 0.03 mag for the data from the 1.54m Danish Tele-
scope. The reader interested in more details concerning the observations, data reduction
and calibration procedures is referred to Grundahl et al. (1999) and Grundahl, Stetson &
Andersen (2002). The final calibrated cluster catalogs include ∼ 15,000–30,000 stars. The
Str¨ omgren catalogs adopted in this investigation can be retrieved from the following URL:
http://www.mporzio.astro.it/spress/stroemgren.php.
3.Globular cluster selection
In order to calibrate the metallicity index m1we selected four globular clusters, namely
M92, M13, NGC1851, NGC104, that cover a broad range in metallicity (−2.2 < [Fe/H] <
−0.7), are marginally affected by reddening (E(B–V) ≤ 0.04), and for which accurate
Str¨ omgren photometry is available to well below the turnoff region (Grundahl et al. 1998;
Grundahl et al. 1999, Grundahl, Stetson & Andersen 2002). We performed several tests
by including among the calibrating clusters other GCs that also have low reddening val-
ues (NGC288, NGC362, NGC6752), but the intrinsic accuracy of the calibration did not
improve, since their iron abundances are very similar either to M13 or to NGC1851. The
metallicities and the reddening values for these clusters are listed in Table 2. Empirical
evidence suggests that the m1versus color relation of RG stars presents a linear trend and a
good sensitivity to iron abundance (Bond 1980; Richtler 1989; Twarog & Anthony-Twarog
1991; Grebel & Richtler 1992; ATT94; H00). Therefore, we selected cluster stars from the
tip to the base of the RGB with a photometric accuracy σu,v≤ 0.03 mag and σb,y≤ 0.02
mag for each cluster in our sample.
However, in order to avoid subtle systematic uncertainties in the empirical calibrations,
actual cluster RG stars need to be distinguished from contaminating field stars. To ac-
complish this goal we decided to use optical-NIR color–color planes to split cluster from
field stars. In particular, we cross-identified stars in common with our Str¨ omgren catalogs
and the Near-Infrared (NIR) Two Micron All Sky Survey (2MASS) catalog (Skrutskie et
al. 20062). Moreover, we also re-identified a subsample of our optical catalog in the second
US Naval Observatory CCD Astrograph proper motion catalog (UCAC2, Zacharias et al.
2004). In both cases, the cross identification was performed following these steps: i) IRAF’s
IMMATCH package was used to establish a preliminary spatial transformation from the
Str¨ omgren catalog’s CCD coordinates to the reference catalog’s Equatorial (J2000.0) sys-
tem for a subsample of matched stars; ii) the full Str¨ omgren catalog was transformed onto
2See also http://www.ipac.caltech.edu/2mass/releases

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and matched with the reference catalog, on the basis of radial distance and initially also on
apparent stellar brightness; iii) the previous steps were reiterated 2–3 times until the trans-
formation permitted a near-complete matching, and then, iv) the final, matched sample of
common stars was obtained by rejecting entries separated by more than, typically, 0.′′8–1.′′3.
In certain cases the stellar magnitudes were used also to reject mismatches while tak-
ing into account possible ranges of color differences in the available bands. Note that our
Str¨ omgren photometry mostly covers relatively small and off-center fields of the analyzed
clusters. The stated UCAC2 proper-motion errors are about 1–3 mas yr−1for stars to 12th
magnitude and 4–7 mas yr−1for fainter stars to 16th magnitude, while the precision of the
positions is 15–70 mas, depending on magnitude, with estimated systematic errors of 10 mas
or below. The 2MASS catalog has limiting magnitudes for the J, H, and Ks−bands of
about 15.8, 15.1, and 14.3 mag, respectively, while the astrometric accuracy is of the order
of 100 mas.
Finally, we selected for each cluster only the RG stars with at least three NIR mea-
surements (J,H,K) and all four Str¨ omgren magnitudes. We found that (u–J, b–H) is the
best optical-NIR color-color plane to properly identify field and cluster stars. Fig. 1 shows
three isochrones at fixed cluster age (t = 12 Gyr) and different chemical compositions in this
plane. The evolutionary models and the atmosphere models adopted to transform theoret-
ical predictions into the observational plane have been constructed adopting a scaled-solar
abundance mixture. The evolutionary phases plotted in this figure range from the base (hot
end) to the tip (cool end) of the RGB. The systematic drift, at fixed b–H, toward redder
colors when moving from metal-poor to metal-rich structures is clear. It is noteworthy that
a difference of 1,200 K (Z=0.0001) and of 2,000 K (Z=0.02) between the base and the tip of
the RGB are covered by ∼ three and by more than seven magnitudes, respectively. Together
with the RG evolutionary phases Fig. 1 also shows the central H-burning phases up to the
turnoff point for the same metal abundances and cluster ages (solid colored lines). A partial
degeneracy between metal-poor and metal-intermediate dwarfs and RG stars takes place
only in the hot corner of this color-color plane, while at solar chemical composition it covers
a broader color range. However, typical halo and thin disk field populations possess iron
abundances systematically more metal-poor than the solar value (Castellani et al. 2002).
We did not use the K-band photometry because it is less accurate in the faint magnitude
limit when compared with J- and H-band magnitudes. A similar procedure but based on
Johnson-Cousins optical magnitudes and NIR magnitudes was adopted by Castellani et al.
(2007) to identify probable cluster and field stars in ω Centauri. The interested reader is
referred to this paper for a detailed discussion concerning the approach adopted to select
field and cluster stars.

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Fig. 1.— Optical-Near-Infrared color-color plane for isochrones at fixed cluster age and
different chemical compositions (see labeled values). Evolutionary phases included between
the base (hot end) and the tip (cool end) of the RGB are shown in black. Evolutionary
phases included between the central H-burning and the turnoff point are shown in colors.
Evolutionary tracks have been computed assuming scaled-solar compositions (Pietrinferni
et al. 2004). Theoretical predictions have been transformed into the observational plane
by adopting atmosphere models based on the same scaled-solar abundances adopted in the
evolutionary computations.
Fig. 2 shows NGC6397 RG stars (449 of them) plotted on the aforementioned color–
color plane. Metal-poor cluster stars form a narrow sequence ranging from b–H ∼ 2.5 to
b–H ∼ 4.0, while more metal-rich candidate field stars are distributed along a separate
sequence, systematically redder in u–J at fixed b–H color. The referee noted that in this
color-color plane the different stellar populations present a slope very similar to the slope
of the reddening vector. This means that the selection between cluster and field stars is
minimally affected by a difference in reddening. The objects with b–H > 5.0 are probably
metal-rich field star candidates. Once we identified the fiducial cluster sequence in the
(u–J, b–H) plane we performed a linear fit, u–J = α + β(b–H), for the candidate cluster
stars. Then, we estimated the difference in u–J color between individual RG stars and the

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Fig. 2.— Top – RG stars of NGC6397 plotted in the optical–NIR color–color (u–J, b–H)
plane. Red dots are candidate field stars (Non-Member stars, NMs = 144). The solid line
is the fitted cluster fiducial sequence. The arrow shows the reddening vector. Bottom –
Distribution of the difference between the u–J color of individual stars and the u–J color of
the fiducial cluster sequence. The dash–dotted line displays the Gaussian function that fits
the main peak in the color difference distribution. Objects with ∆(u–J) ≤ 3 × σu–Jwere
considered candidate cluster RG stars (Member stars, Ms = 305).
fiducial line at the same b–H color. The bottom panel of Fig. 2 shows the distribution of
the color excess ∆(u–J) for the entire sample. We fitted the distribution with a Gaussian
function and we considered only those stars with ∆(u–J) ≤ 3 × σu–Jas bona fide cluster
RG stars. The red dots in the top panel of Fig. 2 mark the candidate field stars after
this selection. The original sample was thus reduced by roughly 40%. Subsequently, we
also applied a selection by proper motion. In particular, we considered as cluster members
those stars with proper motions smaller than 35 mas/yr, and |arctan(PRA
additional selection decreased the sample of candidate RG members by less than 10%.
PDEC)| ≤ 1.0. This

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Fig. 3.— Top: RG stars in NGC6397 plotted in the (m1, u–y) plane (left). Candidate cluster
stars were selected according to the optical-NIR color-color plane (∆(u–J) ≤ 3.0 × σu–J)
and to the proper motion velocity (≤ 35mas/yr and |arctan(PRA
mark probable field stars selected according to optical-NIR colors (NMs = 144). The error
bars account for uncertainties in intrinsic photometric errors. The arrow shows the reddening
vector. The black dots in the middle panel display the candidate cluster RG stars according
to the optical-NIR color-color plane selection (Ms = 305). Blue dots mark probable field
stars according to the PM selection (NMs = 31). The right panel shows candidate cluster
RG stars (Ms = 274) according to the two selection criteria. Bottom: Str¨ omgren Color-
Magnitude Diagrams y,u–y(left), y,v–y(middle), and y,b–y(right) for cluster and field star
candidates.
PDEC)| ≤ 1.0). The red dots
In order to verify the reliability of the selection procedure that we devised to distin-
guish probable cluster and field stars, the top panels of Fig. 3 show from left to right the
distribution in the (m1,u–y) color–color plane of the original RG sample (449 stars), of the
candidate cluster RGs after the selection in the optical–NIR color-color plane (305), and
of the candidate RGs after the selection by proper motion (274). A few interesting fea-
tures of the (m1,u–y) plane must be discussed in detail: i) we adopted the u–y color as a
temperature index. The main advantage of this color over b–y is the stronger temperature

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sensitivity. The RG stars in NGC6397 cover more than two magnitudes in u–y while the
same objects cover only 0.5 mag in b–y. Obviously, the reddening correction for the u–y
color is larger than for the b–y color, but the reddening toward the selected calibrating GCs
is relatively well known and they are not affected, according to current empirical evidence,
by differential reddening. ii) Data plotted in the top left panel of Fig. 3 show a double
stellar sequence. The sequence that attains larger m1at fixed u–y values almost completely
disappears after the selection in the color–color plane (see the middle panel). The Proper
Motion (PM) selection decreases by roughly the 10% the sample of candidate cluster stars.
It was originally suggested by Bell & Gustafsson (1978) and more recently by ATT94, H00,
and by Grundahl et al. (2002) that stars with large m1values present an over-abundance of
carbon and/or nitrogen, i.e. they might be CN- and/or CH-rich stars. As a matter of fact,
two strong cyanogen (CN) molecular absorption bands are located at λ = 4142 and λ = 4215
˚ A, i.e. very close to the effective wavelength of the v filter (λeff = 4110, ∆λ = 190˚ A).
Moreover, the strong CH molecular band located in the Fraunhofer’s G−band (λ = 4300
˚ A) might affect both the v and the b magnitude. It is noteworthy that the molecular NH
band at λ = 3360˚ A, and the two CN bands at λ = 3590 and λ = 3883˚ A might affect
the u (λeff = 3450, ∆λ = 300˚ A) magnitude (see e.g. Smith 1987). However, current
evidence based on optical-NIR color-color and on proper motion selections suggests that the
stars with larger m1values in NGC6397 could be field stars. Note that a mild correlation
between a NIR (H–K) color-excess and the strength of the CN band at λ = 4215˚ A–based
on the Cmindex of the DDO photometric system– was detected by Smith (1988) in a sample
of Population I CN-rich field giants. However, we are not aware of any empirical evidence
suggesting that CN-rich stars in GCs also show a NIR color-excess.
As a further check, the same RGs samples have been plotted in three different CMDs
in the bottom panels of Fig. 3, namely (y,u–y) (left) (y,v–y) (middle), and (y,b–y) (right).
A glance at the data plotted in this figure shows that the bona fide cluster RG stars (black
dots) are distributed along a very narrow color-magnitude sequence. On the other hand, a
large fraction of the sequence with large m1values (red dots) covers a broad range in both
color and magnitude. It is noteworthy that several of these stars and a good fraction of the
stars with large PM values possess magnitudes and colors that are very similar to candidate
cluster RG stars. This finding further supports the use of the optical-NIR color-color plane
to properly separate field and cluster stars. However, we cannot exclude the possibility that
a fraction of current candidate non-members are cluster stars with peculiar spectra.
As a final validation of the selection procedure, we compared the radial distributions
of candidate cluster and field stars. The top panel of Fig. 4 shows the two distributions
and the flat distribution of field stars (dashed line) is quite evident when compared with
the steeper and more centrally concentrated distribution of bona fide cluster stars (solid

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Fig. 4.— Top - Radial distribution of candidate cluster RG stars (solid line) and of probable
field stars (dashed line) for the GC NGC 6397. The latter sample includes stars selected
according to the color-color plane and to the proper motions. R is the distance from the
center of the cluster in arcminutes. Bottom - Same as the top, but for the GC M92.
line). The mild decrease in the number of field stars in the outer reaches of the cluster
suggests that the color-color selection we applied is very conservative, and some real cluster
members might have been erroneously rejected. These objects deserve spectroscopic follow-
up to determine whether their peculiar optical-NIR colors are caused either by a significantly

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different chemical composition or by the presence of secondary companions or both.
The same approach was adopted for selecting the bona fide cluster RG stars of the other
calibrating clusters. In particular, Fig. 5 shows the selection applied to RGs in the metal-
poor GC M92. For this cluster we considered only those stars with ∆u–J ≤ 1.5 × σu–Jas
candidate RG members. Once again the original sample was reduced by approximately 40%
after the selection in the color-color plane was applied.
Fig. 5.— Same as Fig. 2, but for RG stars in the GC M92. Only the objects with ∆(u–J) ≤
1.5 × σu–Jwere considered candidate cluster RG stars.
Proper motion measurements for this cluster are not available in the UCAC2 catalog,
therefore we adopted the measurements provided by Cudworth (1976). We cross-identified
our Str¨ omgren catalog with the Cudworth catalog and we found 50 RG stars in common.

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Fig. 6.— Same as Fig. 3, but for RG stars in the GC M92. Only the RG stars with a
membership probability Pc ≥ 90 were considered candidate cluster members (Cudworth
1976).
Among them three have a cluster membership probability Pc< 90, and two were removed
according to the optical-NIR color-color selection. The top panels of Fig. 6 show the M92 RG
stars in the (m1,u–y) plane before (left), after the optical-NIR color-color selection (middle),
and after the proper motion selection (right). It is worth noting that the stars that attain
large m1values, at fixed u–y color, disappear after the selection in the (u–J, b–H) plane.
Moreover, almost all candidate field stars (red dots in Figs. 5 and 6) present magnitudes and
colors similar to candidate cluster RG stars (see bottom panels of Fig. 6). The same outcome
applies to the RG stars in M13, and indeed after the selection in the optical-NIR color-color
plane the cluster RG candidates occupy a narrow and well-defined sequence. Data plotted
in the bottom panel of Fig. 4 show that the radial distribution of probable field stars in M92
is quite flat in the external regions, but becomes similar to the candidate cluster RG stars in
the innermost regions. However, as already mentioned above and by ATT00 the key point in
current selections is more to leave the probable nonmembers out than to keep the candidate
members in.

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The referee suggested that we comment on the different distribution of field stars in the
optical-NIR color-color plane between NGC 6397 and M92. In order to provide a quantitative
estimate we performed two simulations of the field star distribution using the Galactic model
developed by Cignoni et al. (2006, and references therein). We find that the field across
NGC 6397 consists of 19% halo, 39% thick disk, and 42% thin disk stars (Castellani et al.
2001). On the other hand, the field across M92 consists of 38% halo, 36% thick disk, and
26% thin disk stars. The above numbers indicate that the main difference in the M92 field
is due to the substantial decrease in the fraction of more metal-rich thin disk stars and in
the increase in the fraction of less metal-rich halo stars.
Fig. 7.— Same as Fig. 2, but for RG stars in the GC NGC1851. Only the objects with
∆(u–J) ≤ 1.5 × σu–Jwere considered candidate cluster RG stars.
On the other hand, RG stars in NGC1851 and in NGC104 present, after the selection