On the absolute age of the Globular Cluster M92

Abstract

We present precise and deep optical photometry of the globular M92. Data were collected in three different photometric systems: Sloan Digital Sky Survey (g',r',i',z'; MegaCam@CFHT), Johnson-Kron-Cousins (B, V, I; various ground-based telescopes) and Advanced Camera for Surveys (ACS) Vegamag (F475W, F555W, F814W; Hubble Space Telescope). Special attention was given to the photometric calibration, and the precision of the ground-based data is generally better than 0.01 mag. We computed a new set of {\alpha}-enhanced evolutionary models accounting for the gravitational settling of heavy elements at fixed chemical composition ([{\alpha}/Fe]=+0.3, [Fe/H]=-2.32 dex, Y=0.248). The isochrones -- assuming the same true distance modulus ({\mu}=14.74 mag), the same reddening (E(B-V)=0.025+-0.010 mag), and the same reddening law -- account for the stellar distribution along the main sequence and the red giant branch in different Color-Magnitude Diagrams (i',g'-i' ; i',g'-r' ; i',g'-z' ; I,B-I ; F814W,F475W-F814W). The same outcome applies to the comparison between the predicted Zero-Age-Horizontal-Branch (ZAHB) and the HB stars. We also found a cluster age of 11 +/- 1.5 Gyr, in good agreement with previous estimates. The error budget accounts for uncertainties in the input physics and the photometry. To test the possible occurrence of CNO-enhanced stars, we also computed two sets of {\alpha}- and CNO-enhanced (by a factor of three) models both at fixed total metallicity ([M/H]=-2.10 dex) and at fixed iron abundance. We found that the isochrones based on the former set give the same cluster age (11 +/- 1.5 Gyr) as the canonical {\alpha}-enhanced isochrones. The isochrones based on the latter set also give a similar cluster age (10 +/- 1.5 Gyr). These indings support previous results concerning the weak sensitivity of cluster isochrones to CNO-enhanced chemical mixtures. Comment: This paper makes use of data obtained from the Isaac Newton Group Archive which is maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency

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arXiv:1006.5217v1 [astro-ph.SR] 27 Jun 2010
Draft version 2010 June 29
Preprint typeset using LATEX style emulateapj v. 6/22/04
ON THE ABSOLUTE AGE OF THE GLOBULAR CLUSTER M921
A. Di Cecco2, R. Becucci3, G. Bono2,4, M. Monelli5, P. B. Stetson6,13,14, S. Degl’Innocenti3,7, P. G. Prada
Moroni3,7, M. Nonino8, A. Weiss9, R. Buonanno2,10, A. Calamida11, F. Caputo4, C. E. Corsi4, I. Ferraro4, G.
Iannicola4, L. Pulone4, M. Romaniello11, and A. R. Walker12
(Dated: drafted 2010 June 29 / Received / Accepted)
Draft version 2010 June 29
ABSTRACT
We present precise and deep optical photometry of the globular M92. Data were collected in three
different photometric systems: Sloan Digital Sky Survey (g′,r′,i′,z′; MegaCam@CFHT), Johnson-
Kron-Cousins (B,V ,I; various ground-based telescopes) and Advanced Camera for Surveys (ACS)
Vegamag (F475W, F555W, F814W; Hubble Space Telescope).
the photometric calibration, and the precision of the ground-based data is generally better than
0.01 mag. We computed a new set of α-enhanced evolutionary models accounting for the gravi-
tational settling of heavy elements at fixed chemical composition ([α/Fe]=+0.3, [Fe/H]=–2.32 dex,
Y =0.248). The isochrones—assuming the same true distance modulus (µ=14.74 mag), the same red-
dening (E(B–V)=0.025±0.010 mag), and the same reddening law—account for the stellar distribution
along the main sequence and the red giant branch in different Color-Magnitude Diagrams (i′,g′− i′;
i′,g′−r′; i′,g′−z′; I,B−I; F814W,F475W −F814W). The same outcome applies to the comparison
between the predicted Zero-Age-Horizontal-Branch(ZAHB) and the HB stars. We also found a cluster
age of 11±1.5 Gyr, in good agreement with previous estimates. The error budget accounts for uncer-
tainties in the input physics and the photometry. To test the possible occurrence of CNO-enhanced
stars, we also computed two sets of α- and CNO-enhanced (by a factor of three) models both at fixed
total metallicity ([M/H]=–2.10 dex) and at fixed iron abundance. We found that the isochrones based
on the former set give the same cluster age (11±1.5 Gyr) as the canonical α-enhanced isochrones. The
isochrones based on the latter set also give a similar cluster age (10±1.5 Gyr). These findings sup-
port previous results concerning the weak sensitivity of cluster isochrones to CNO-enhanced chemical
mixtures.
Subject headings: globular cluster: individual (M92) — stars: evolution — stars: horizontal-branch
— stars: main sequence — stars: Population II — stars: red giants
Special attention was given to
1. INTRODUCTION
1This paper makes use of data obtained from the Isaac Newton
Group Archive which is maintained as part of the CASU Astro-
nomical Data Centre at the Institute of Astronomy, Cambridge.
This research used the facilities of the Canadian Astronomy Data
Centre operated by the National Research Council of Canada with
the support of the Canadian Space Agency.
2Dipartimento di Fisica, Universit` a di Roma Tor Vergata,
via della Ricerca Scientifica 1, 00133 Rome, Italy;
dra.dicecco@roma2.infn.it
3Dipartimento di Fisica, Universit` a di Pisa, Largo B. Pontecorvo
2, 56127 Pisa, Italy
4INAF–OAR, via Frascati 33, Monte Porzio Catone, Rome,
Italy
5IAC, Calle Via Lactea, E38200 La Laguna, Tenerife, Spain
6DAO–HIA, NRC, 5071 West Saanich Road, Victoria, BC V9E
2E7, Canada
7INFN–Pisa, via E. Fermi 2, 56127 Pisa, Italy
8INAF–OAT, via G.B. Tiepolo 11, 40131 Trieste, Italy
9Max-Planck-Institut fr Astrophysik, Karl-Schwarzschild-Str.
1, 85748 Garching, German
10ASI–Science Data Center, ASDC c/o ESRIN, via G. Galilei,
00044 Frascati, Italy
11
ESO, Karl-Schwarzschild-Str.
Munchen, Germany
12CTIO–NOAO, Casilla 603, La Serena, Chile
13Visiting Astronomer, Kitt Peak National Observatory, Na-
tional Optical Astronomy Observatory, which is operated by the
Association of Universities for Research in Astronomy (AURA) un-
der cooperative agreement with the National Science Foundation.
14Visiting Astronomer, Canada-France-Hawaii Telescope oper-
ated by the National Research Council of Canada, the Centre Na-
tional de la Recherche Scientifique de France and the University of
Hawaii.
alessan-
2,85748 Garching bei
The Galactic globular cluster (GGC) M92 (NGC 6341)
is among the oldest and most metal-poor ([Fe/H]=–
2.38, Kraft & Ivans 2003; 2004) Galactic stellar sys-
tems. It is located well above the Galactic plane
(l=68.34◦, b=34.86◦, Harris 1996), is minimally affected
by field star contamination, and is only slightly reddened
(E(B–V)=0.02, Harris 1996). However, the cluster’s ab-
solute age is far from being well established.
estimates based on updated cluster isochrones indicate
that the absolute age of M92 ranges from 12.3±0.9 Gyr
(Salaris & Weiss2002) to 14.8±2.5 Gyr (Carretta et
al. 2000; Grundahl et al. 2000).
timate of the absolute age of M92 was also provided
by VandenBerg et al. (2002).
timate of both distance modulus (DM) and redden-
ing (DMV=14.60±0.12, E(B–V)=0.023 mag) using the
unique field, metal-poor ([Fe/H]?–2.3) subdwarf calibra-
tor with an accurate trigonometric parallax from Hip-
parcos (σπ/π ≤0.1).By adopting the quoted values
and a set of cluster isochrones ([Fe/H]=–2.3, [α/Fe]=0.3
dex) including gravitational settling and radiative ac-
celerations they found an absolute age of 13.5±1.0-1.5
Gyr.Similar cluster ages have been found using the
luminosity function (LF) of evolved stars, and indeed
Cho & Lee (2007) found an age of ∼13.5 Gyr, while
Paust, Chaboyer & Sarajedini (2007) found an age of
14.2±1.2 Gyr. Precise estimates of the GC absolute ages
rely, from an empirical point of view, on four ingredients:
distance, total metallicity, reddening, and photometric
Recent
A very accurate es-
They gave a new es-

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2 Di Cecco et al.
zero-points (Renzini 1991). Recent estimates of the clus-
ter distance modulus based on different standard can-
dles agree quite well. The true DM (µ) of M92 based on
main sequence (MS) fitting ranges from µ = 14.64±0.07
mag (Carretta et al. 2000) to µ = 14.75 ± 0.11 mag
(Kraft & Ivans 2003).Distances based on the near-
infrared (NIR) Period-Luminosity (PL) relation of RR
Lyrae stars (Bono et al. 2001; Cassisi et al. 2004; Cate-
lan 2004; Del Principe et al. 2005, 2006; Sollima et al.
2006) suggest a similar mean value, i.e., µ=14.65±0.10
mag. Thus, the different distance estimates agree within
their current uncertainties (1σ).
The uncertainty in the reddening correction for low-
reddening GCs is typically of the order of 0.02 mag (Grat-
ton et al. 2003; Bono et al. 2008 ). Experience has shown
that the typical uncertainty in the zero-point of photom-
etry from a given observing run is still of the order of
0.01–0.02 mag (e.g., Stetson, Bruntt & Grundahl 2003;
Stetson, McClure & VandenBerg 2004; Stetson 2005). In
the case of M92, this uncertainty may occasionally have
been still larger (0.03 mag, Carretta et al. 2000). How-
ever, we believe that this systematic uncertainty can be
reduced by averaging the photometric results of many
observing runs, each of which has been individually cali-
brated to a common photometric standard system. The
uncertainty affecting the total metallicity is of the order
of 0.2 dex, if we include cluster-to-cluster uncertainties
in iron and α-element abundances as well as systematic
uncertainties in the overall metallicity scale (Carretta et
al. 2009).
Dating back to the seventies, spectroscopic measure-
ments showed quite clearly the occurrence of star-to-star
variations of C and N abundances in several GGCs (M5,
M10, M13, M92, ω Cen, Osborn 1971; Cohen 1978). Sub-
sequent investigations also found variations in Na (Cohen
1978; Peterson 1980), in Al (Norris et al. 1981) and in O
(Pilachowski et al. 1983; Leep, Wallerstein & Oke 1986).
The observational scenario was further enriched by the
evidence that the molecular band-stregths of CN and CH
appear to be anticorrelated (Smith 1987; Kraft 1994,
and references therein). Both this anticorrelation and
an anticorrelation between O–Na and Mg–Al have been
observed in evolved (red giant branch [RGB], Horizontal
Branch [HB]), and in unevolved MS stars of all GCs stud-
ied in sufficient detail (Suntzeff & Smith 1991; Cannon
et al. 1998; Harbeck, Grebel & Smith 2003; Gratton et
al. 2001; Ramirez & Cohen 2002; Carretta et al. 2007).
A working hypothesis to explain these observations is
that a previous generation (first generation) of asymp-
totic giant branch (AGB) stars expelled processed ma-
terial during thermal pulses, thus the subsequent stel-
lar generation (second generation) formed with mate-
rial that had already been polluted (Ventura et al.
2001; Gratton, Sneden & Carretta 2004, and references
therein). In this scenario, the surface abundance of the
second stellar generation is characterized by a significant
He enrichment and by well defined C-N-O-Na anticor-
relations. It has been suggested that typically the frac-
tion of stars belonging to the second generation might
be of order 50% (D’Antona & Caloi 2008). Alternative
hypotheses are that cluster self-pollution is caused ei-
ther by evolved RGB stars that experienced extra-deep
mixing (Denissenkov & Weiss 2004) or by fast rotat-
ing intermediate-mass stars (Maeder & Meynet 2006;
Prantzos & Charbonnel 2006; Decressin et al. 2007).
M92 shows the typical variations in [C/Fe] and [N/Fe]
(Carbon et al. 1982; Langer et al.
al. 2001), together with the usual anticorrelations (Pi-
lachowski 1988; Sneden et al. 1991; Kraft 1994). How-
ever, up to now no evidence has been found concerning
the occurrence of multiple stellar populations (Piotto et
al. 2007; Cassisi et al. 2008). Therefore, M92 is a per-
fect laboratory to constrain the impact of canonical and
CNO-enhanced mixtures on the estimate of the cluster
age.
We take advantage of deep and accurate multiband op-
tical images collected with both ground-based and space
telescopes to constrain the absolute age of M92.
1986; Bellman et
2. DATA REDUCTION AND THEORETICAL FRAMEWORK
To provide robust estimates of the absolute age of
M92, we secured optical images collected in three dif-
ferent photometric systems. In particular, we adopted
both ground-based and space images. The ground-based
data were collected either with MegaCam — the mosaic
camera available at the Canada-France-Hawaii Telescope
(CFHT: Sloan filters, field of view [FoV]: 1◦x1◦, spatial
resolution: 0′′.19/pixel) — or with several small/medium
telescopes (Johnson-Cousins bands).
were collected with the Advanced Camera for Surveys
(ACS) on the Hubble Space Telescope (HST) using
both the Wide Field Channel (WFC, FoV: 202′′x202′′,
0′′.05/pixel) and the High Resolution Channel (HRC,
FoV: 0′.5x0′.5, 0′′.025/pixel). The sky coverage of the
different data sets is plotted in Fig. 1.
The CFHT data set includes 1440 CCD images col-
lected in the Sloan bands –g′,r′,i′,z′– with different ex-
posure times (ETs). In particular, the shallow images
were acquired with ETs of 5 (g′,r′,i′) and 15 (z′) s,
while the deep images had ETs of 250 (g′,r′), 300 (i′)
and 500 (z′) s. The mean seeing in the different bands
ranges from ∼ 0′′.75 (g′,r′,i′) to ∼ 0′′.85 (z′). These im-
ages were pre-processed using Elixir (Magnier & Cuil-
landre 2004). For each chip of the mosaic camera we
performed standard Point Spread Function (PSF) fit-
ting photometry with DAOPHOT IV and ALLSTAR
(Stetson 1987). The individual chips were rescaled to
a common geometrical systems defined by a 1◦.5×1◦.5
Sloan Digital Sky Service (SDSS) reference image us-
ing DAOMATCH/DAOMASTER. We performed the fi-
nal photometry by running ALLFRAME (Stetson 1994)
simultaneously over the entire data set. We ended up
with a photometric catalog including ∼84,000 stars with
at least one measurement in two different photometric
bands. The absolute calibration was performed using
local secondary standards provided by Clem, Vanden-
Berg & Stetson(2007). Fig. 2 shows three different
Color-Magnitude Diagrams (CMDs) based on this cata-
log. Data plotted in this figure were selected according to
photometric error ≤ 0.01 mag, sharpness15abs(sha)≤1,
and separation16sep≥2.5. Moreover, to overcome the
central crowding and contamination by field stars we se-
lected stars in an annulus 60′′≤ r ≤ 700′′. Special atten-
tion was paied to the absolute and relative photometric
The space data
15The sharpness is an index that quantify the similarity between
the shape of the measured objects and of the adopted PSF.
16The separation index quantifies the degree of crowding (Stet-
son et al. 2003)

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3
Fig. 1.— Left – sky area across the globular cluster M92 covered by the different ground-based data sets. The red box shows the area
covered by CFHT images, while the blue box shows the area covered by the Johnson-Cousins images. The orientation is shown in the
bottom right corner. Right – same as the left, but for space data sets collected with the Advanced Camera for Surveys (ACS) on board the
HST. The dots display the area covered by the images collected with the Wide Field Channel (WFC), while the red square those collected
with the High Resolution Channel (HRC). The red cross marks the cluster center.
zero-points. The precision for a single star is typically
better than 0.02 mag. The precision of the different cal-
ibrations is supported by the very good agreement be-
tween the ridge lines (red lines in Fig. 2) provided by
Clem et al. and our measurements of the cluster stars.
The error budget accounting for intrinsic and calibration
errors is smaller than 0.01 mag down to Main Sequence
Turn-Off (MSTO) stars (i′∼19 mag).
In addition to the Sloan data, we also analyzed 782
CCD images collected in the Johnson-Cousins bands;
these were reduced and calibrated by one of us (PBS)
in an ongoing effort to provide homogeneous photometry
on the Landolt (1992) photometric system17. These data
were obtained in the course of 44 independent observ-
ing runs on nine telescopes (CFHT; DAO; INT; JKT;
KPNO 0.9, 2.1, 4.0; NOT) from 1984 to 2002. Based
upon frame-to-frame repeatability, we infer that at least
some stars have magnitudes and colors individually pre-
cise to<
∼0.01mag as faint as V ∼ 20, which is ∼ 1.5mag
fainter than the MSTO. Given the large number of in-
dependently calibrated observing runs, we believe that
systematic calibration uncertainties should be well un-
der 0.01mag.
The ground-based images were supplemented with
space images collected with ACS@HST. In particular,
we used twelve images in two different pointings acquired
with the WFC (see right panel of Fig. 1). The innermost
WFC images18were three with the F814W-band (ETs
of 0.5, 6, and 100 s) and covering the center of the clus-
ter. The outermost WFC images19were: three with the
F475W (ETs of 3, 20, 40 s) and three with the F814W
17For more details see the following URL: http://www4.cadc-
ccda.hia-iha.nrc-cnrc.gc.ca/ community/ STETSON/ standards/
18GO-9453, PI: T. Brown
19GO-10505, PI: C. Gallart
(ETs of 1, 10, 20 s) filters, located ∼ 2′S–E from the
cluster center. We used the FLT versions of these images
and did not apply any cosmic ray mask, since the indi-
vidual ETs are short. To overcome the crowding of the
innermost regions (concentration c=1.81, Harris 1996),
we also considered a set of images collected with the HRC
(see right panel of Fig. 1). This data set includes 155
F555W drizzled images collected with different exposure
times (74×10 s, 4×120 s, 10×40 s, 4×80 s, 34×100 s,
8×200 s, 4×400 s, 9×500 s, 8×1000 s)20. These images
were pre-reduced using the HST pipeline. To reduce the
ACS data, individual PSF were modeled for both chips
using DAOPHOT/ALLFRAME programs, and the indi-
vidual catalogs were calibrated following the Sirianni et
al. (2005) prescriptions.
To compare the observations with the models we com-
puted evolutionary tracks with an updated version of the
FRANEC evolutionary code (Chieffi & Straniero 1989;
Degl’Innocenti et al. 2008). For these models the OPAL
2006 equation of state (EOS) was adopted (Iglesias &
Rogers 1996), together with radiative opacity tables by
the Livermore group (Iglesias & Rogers 1996)21for tem-
peratures higher than 12,000oK; in this way the EOS and
the opacity are fully consistent. The conductive opacities
are from Shternin & Yakovlev (2006, see also Potekhin
1999) while the atmospheric opacities are from Fergu-
son et al. (2005). All the opacity tables were calculated
for the Asplund, Grevesse & Sauval (2005, hereinafter
AG05) solar mixture. The nuclear reaction rates, are
from the NACRE compilation (Angulo et al. 1999). It is
worth mentioning that the use of the new measurement
of the14N(p,γ)15O capture cross section (Formicola et
al. 2004) would imply a systematic increase of ∼1 Gyr
20GO-10335, PI: H. Ford
21http://opalopacity.llnl.gov/opal.html

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4Di Cecco et al.
Fig. 2.— The i′,g′− r′(left), i′,g′− i′(middle) and i′,g′− z′(right) CMD based on images collected with the MegaCam@CFHT. The
red lines display the ridgelines provided by Clem et al. (2007). The error bars on the left show the mean intrinsic photometric error in
magnitude and in color, while the black arrows the reddening vectors.
in the estimate of the GC absolute age (Imbriani et al.
2004). Our models include atomic He and metal diffu-
sion, with diffusion coefficients given by Thoul, Bahcall
& Loeb (1994). The reader interested in a detailed dis-
cussion of the uncertainties affecting the diffusion coeffi-
cients is referred to Bahcall, Pinsonneautl & Wasserburg
(1995), Castellani et al. (1997) and to Guzik, Watson &
Cox (2005). To model external convection we adopted,
as usual, the mixing length formalism (Bohm-Vitense
1958). The mixing length parameter, α, governing the
efficiency of convection, was set at α=2.0.
The metallicity adopted for the models is directly re-
lated to the observed [Fe/H] (when the AG05 solar mix-
ture is assumed)
Z =
1 − YP
1
1 +∆Y
∆Z+
(Z/X)⊙× 10−[Fe/H]. (1)
and α-element abundances according to formula origi-
nally suggested by Salaris et al. (1993).
We adopted the value [Fe/H]=–2.32, given by spec-
troscopic measurements ([Fe/H]=–2.38) by Kraft &
Ivans (2003,2004), but rescaled to the AG05 solar iron
abundance.The adopted α-element enhancement is
[α/Fe]=+0.3, while for the primordial helium content,
we adopted the recent cosmological value Yp=0.248 (Pe-
imbert et al. 2007; Izotov, Thuan & Stasi´ nska 2007).
Note that the change from the old Grevesse & Sauval
(1999) to the new AG05 solar mixture causes at fixed iron
and α-element abundances a decrease from Z=0.00014to
Z=0.00010. The difference is mainly caused by the de-
crease in CNO solar abundances. The interested reader is
referred to the recent investigation by Caffau et al. (2010)
for a new and independent measurements of solar CNO
abundances.The cluster isochrones were transformed
into the observational plane using the bolometric correc-
tions (BCs) and the color-temperature relations (CTRs)
provided by Brott & Hauschild (2005), while for the zero-
age horizontal-branch (ZAHB) models we used the BCs
and CTRs provided by Castelli & Kurucz (2003). In the
following, the evolutionary models constructed assum-
ing the above chemical abundances are called “canonical
models”.
To account for C-N-O-Na anticorrelations, we used the
same mixture adopted in the literature (Salaris et al.
2006; Cassisi et al. 2008; Pietrinferni et al. 2009) which
is based on a mean value of the observed anticorrelations

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5
provided by Carretta et al. (2005). The changes in ele-
mental abundance relative to the canonical α-enhanced
models are the following: N increased by 1.8 dex, C de-
creased by 0.6 dex, Na increased by 0.8 dex, and O de-
creased by 0.8 dex. These changes give an enhancement
of ≈ a factor of three (+0.5 dex) in the [C+N+O/Fe]
abundance. We did not include the Mg–Al anticorrela-
tion because it minimally affects the evolutionary prop-
erties (Salaris et al. 2006). The increase in the total CNO
abundance causes, at fixed iron abundance, an increase
in the total metallicity from Z=0.00010 to Z=0.00023.
This increase in metallicity makes the MSTO fainter and
cooler as originally suggested by Bazzano et al. (1982)
and by VandenBerg (1985).
of the different chemical mixtures, the CNO-enhanced
models were constructed both at fixed total metallic-
ity ([M/H]=–2.10) and at fixed iron content ([Fe/H]=–
2.32). Note that the net effect of element diffusion in
α-enhanced models is to decrease the surface CNO abun-
dances from [C/Fe]=0.00, [N/Fe]=0.00, [O/Fe]=0.30 at
the zero age main sequence to [C/Fe]=-0.06, [N/Fe]=-
0.04, [O/Fe]=0.27 dex at the MSTO. The α and CNO-
enhanced models show a similar decrese, and indeed
the surface CNO abundances change from [C/Fe]=-0.60,
[N/Fe]=1.80, [O/Fe]=-0.5 at the zero age main sequence
to [C/Fe]=-0.65, [N/Fe]=1.76, [O/Fe]=-0.53 dex at the
MSTO.
Transforming these evolutionary models into the ob-
servational plane requires a set of BCs and CTRs com-
puted for the same mixtures, but they are not available
yet. However, Cassisi et al. (2008) and Pietrinferni et al.
(2009) found that BCs and CTRs computed assuming
simple α-enhanced mixtures mimic the same behaviour.
Moreover, we found that BCs and CTRs hardly depend,
at fixed total metallicity, on changes in the mixture. Ac-
cordingly, to transform the CNO-enhanced models con-
structed at fixed iron abundance, we adopted [Fe/H]=–
2.32 and [α/Fe]=+0.72 to obtain the same total metal-
licity.
To constrain the impact
3. COMPARISON BETWEEN THEORY AND
OBSERVATIONS
To compare theory and observations we assumed a
true distance modulus µ = 14.74 mag, in good agree-
ment with the distance estimated by Kraft & Ivans
(2003, µ=14.75) and a cluster reddening of E(B–V ) =
0.025 ± 0.010 (Zinn 1985; Schlegel, Finkbeiner, & Davis
1989; Gratton et al. 1997; Kraft & Ivans 2003; Car-
retta et al. 2000). Moreover, we adopted a total to se-
lective absorption ratio of RV=3.10 and the empirical
reddening laws provided by Cardelli, Clayton & Mathis
(1989). In particular, for the Sloan bands available at
CFHT, we computed the following ratios: Ag′/AV=1.21,
Ar′/AV=0.87, Ai′/AV =0.66 and Az′/AV=0.48. For the
Johnson-Cousins filters we adopted AB/AV=1.32 and
AI/AV=0.59, while for the ACS filters AF475W/AV=1.20
and AF814W/AV=0.55, respectively.
The top panels of Fig. 3 show the comparison between
data collected in different photometric bands and α-
enhanced isochrones at fixed total metallicity ([M/H]=–
2.10 dex) and two cluster ages 10 (red line) and 12 (green
line) Gyr. The CFHT data (the first three panels from
left to right) were selected according to photometric er-
ror (σ(color)≤ 0.04), sharpness (abs(sha) ≤ 1) and ra-
dial distance (60′′≤ r ≤ 400′′). The same selection was
adopted for the Johnson data (fourth panel), while the
ACS data (fifth panel) were only selected on the basis of
the photometric error. To validate the adopted values of
the true distance modulus and the cluster reddening we
also plotted the predicted ZAHB for the same chemical
composition (blue line). We found that using the same
distance and the same reddening the predicted “canoni-
cal” ZAHB agrees quite well with observations in the five
different CMDs. Moreover, the comparison between the-
ory and observations gives a cluster age of 11±1.5 Gyr.
The error budget is mainly driven by observational un-
certainties affecting the metallicity measurements, and
theoretical uncertainties in the input physics of the evo-
lutionary models and transformations.
To constrain the impact of the CNO abundance on the
age of M92, we performed the same comparison at fixed
total metallicity, but using the CNO-enhanced models.
The middle panels of Fig. 3 show the same data as plot-
ted in the top panel, but the cluster isochrones are based
on evolutionary models that are enhanced in both α el-
ements and CNO. The same enriched composition was
also adopted to compute the ZAHB and we found no
significant differences compared to the canonical models.
Therefore, we assumed the same true distance modulus
and cluster reddening as for the canonical predictions.
The comparison between theory and observations indi-
cates that α and CNO enriched isochrones provide, at
fixed total metallicity, the same cluster age (11±1.5 Gyr)
as the canonical α-enhanced models. Data plotted in the
bottom panels show the comparison between theory and
observations for α and CNO enhancements at fixed iron
abundance ([Fe/H]=–2.32). Note that the total metallic-
ity of the isochrones and of the ZAHB is now increased to
[M/H]=–1.75. The cluster age we found is, for the same
true distance and cluster reddening, minimally younger
(10±1.5 Gyr), but still agrees quite well (±1 σ) with the
above estimates. It is worth noticing that canonical and
CNO-enhanced isochrones show very similar morpholo-
gies in optical CMDs, as originally suggested by Salaris
et al. (2006).This indicates that broad-band optical
photometry like that investigated here cannot be safely
adopted to constrain the occurrence of CNO-enhanced
subpopulations in GCs.
To further constrain the impact of the CNO enhance-
ment on the evolutionary properties of metal-poor GCs
we also compared the observed star count ratios with the
evolutionary lifetime ratios.
theory and observations was performed using evolved
(RGB, HB) and MS stars. The MS stars were selected
in a magnitude interval of 0.25 mag across the MSTO
(Mi′ = 18.8), while the RGB stars were selected in the
magnitude interval 15.0 ≤ i′≤ 17.2 (see the left panel
of Fig. 4). To provide robust star counts over the en-
tire body of the cluster we used ACS/HRC data for the
regions across the very center of the cluster (≤ 35′′),
the ACS/WFC data up to radial distances of 75′′and
the CFHT data for the remaining regions. To homoge-
nize the star counts, the ACS/HRC and the ACS/WFC
data collected in the F814W-band were transformed into
the i′-band, while those ones collected in the F475W
and in the F555W-band were transformed into the g′
and r′-band.The accuracy of the transformations is
better than 0.02 mag. To estimate the completeness
The comparison between

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6Di Cecco et al.
of the CFHT data in the regions outside the internal
ACS/WFC pointing, we adopted the ACS/WFC data of
the external pointing. We found that the completeness
for i′≤ 22 mag is ∼54% for 75′′≤ r ≤ 150′′, ∼82% for
150′′≤ r ≤ 200′′, and complete for larger distances. To
investigate possible radial trends (Castellani et al. 2007;
Sandquist & Martel 2007) the cluster was divided into
eight annuli up to r=400′′. Each annulus includes the
same number of stars (∼ 12,200).
The right panel of Fig. 4 shows the star count ratios
HB/RGB (top), RGB/MS (middle) and HB/MS (bot-
tom) as a function of the radial distance. Data plotted
in this figure show the star counts are, within the errors,
constant across the cluster. To estimate the lifetime ra-
tios of the same evolutionary phases we adopted for the
α-enhanced models the evolutionary track of a stellar
structure with M(TO)/M⊙=0.78, [M/H]=–2.10. Note
that this is the TO mass of the 11 Gyr cluster isochrone.
For the α- and CNO-enhanced models with the same to-
tal metallicity we adopted the same stellar mass, while
for those with the same iron abundance ([Fe/H]=–2.32)
we adopted a stellar mass of M(TO)/M⊙=0.80. This
is the TO mass of the 10 Gyr cluster isochrone. The
HB evolutionary lifetime was estimated using a struc-
ture with stellar mass of M/M⊙=0.70. This mass value
relies on the mean mass for HB stars found by Cassisi et
a. (2001) and by Cho & Lee (2007) using synthetic HB
models. Note that a change of 0.05 M⊙has a minimal
impact on the HB lifetime (3-4%). By using the same
true distance modulus and cluster reddening adopted to
estimate the cluster age, we found that observed and
predicted ratios agree quite well (1σ, see Table 1). It
is worth mentioning that the stated uncertainties in the
star counts include Poisson uncertainties and complete-
ness uncertainties. For the predicted ratios we assumed
an uncertainty of 10% for each of the different evolu-
tionary phases (Castellani et al. 2007, and references
therein).
The anonymous referee suggested that we specify the
impact of the different chemical mixtures on both the
opacities and the burning processes. To disentangle the
effects, we performed a series of numerical experiments
following the approach recently adopted by Pietrinferni
et al. (2009) for a chemical composition that is at the
metal-rich end of GCs, namely [Fe/H]=–0.7 dex, by Ven-
tura et al. (2009) for the metal-intermediate ([Fe/H]∼ –
1.2 dex) GC NGC 1851 and by Di Criscienzo et al. (2010)
for the metal-poor ([Fe/H]∼ –2 dex) GC NGC 6397.
We performed these experiments at fixed iron content
to reveal the differential effects produced by either α-
enhanced or α- plus CNO-enhanced mixtures. The green
solid and the blue dashed lines plotted in Fig. 5 show
two evolutionary tracks constructed at fixed stellar mass
(M=0.80 M⊙), iron content ([Fe/H]=–2.32) and helium
content (Y =0.248), but the former assumes a canonical
α-enhanced mixture ([M/H]=–2.10, Z=0.00010), while
the latter assumes the α- and CNO-enhanced mixture
([M/H]=–1.75, Z=0.00023). As expected, the difference
is minimal along the MS, but becomes relevant between
the TO and the base of the RGB. During these evolu-
tionary phases the track with the α- and CNO-enhanced
mixture is, at fixed effective temperature, systematically
fainter.The MSTO is fainter and cooler.
bump, i.e., the evolutionary phases during which the H-
The RGB
burning shell encounters the chemical discontinuity in
the envelope left over by the first dredge-up is slightly
fainter in the α- and CNO-enhanced track than in the
α-enhanced track. The difference is caused by the fact
that the convective envelope during the earlier RGB
phases deepens more in the former than in the latter case
(Salaris et al. 2006; Pietrinferni et al. 2009; Di Cecco et
al. 2010), because the increase in the total metallicity
causes an increase in the opacity.
To further investigate the specific impact of α- and
CNO-enhanced mixture on the opacity we also con-
structed an evolutionary track in which the nuclear burn-
ing processes use an α-enhanced mixture, while the opac-
ity is based on an α and CNO-enhanced mixture. The
red dashed-dotted line plotted in Fig. 5 shows that this
track is, at fixed effective temperature, slightly fainter
than the track using an α-enhanced mixture (green solid
line) both in the nuclear burning and in the opacity. As a
consequence, the MSTO of the former track is marginally
cooler, while the RGB bump is minimally fainter than in
the latter one.
To study the impact of α- and CNO-enhanced mixture
on the nuclear network we also constructed an evolu-
tionary track in which the nuclear burning processes use
an α- and CNO-enhanced mixture, while the opacity is
based on an α-enhanced mixture. The pink dotted line
plotted in Fig. 5 shows that this track is, at fixed effective
temperature, minimally brighter than the track with an
α- and CNO-enhanced mixture both in the nuclear burn-
ing and in the opacity. The same outcome applies to the
MSTO and to the RGB bump.
These findings indicate that the changes in the lumi-
nosity and in the effective temperature of the MSTO,
when switching from an α-enhanced to an α- and CNO-
enhanced mixture, are caused by changes both in the
nuclear burning and in the opacity. On the other hand,
the change in the luminosity of the SGB is caused pri-
marily by the change in the nuclear burning processes.
The same outcome applies for the decrease in the lu-
minosity of the RGB bump. These results support the
dependences found by Pietrinferni et al. (2009) for more
metal-rich stellar structures.
4. CONCLUSIONS
We present different optical data sets for M92 col-
lected in three different photometric systems (SDSS,
g′,r′,i′,z′; Johnson-Cousins, BV I;
F475W, F555W, F814W) and with ground-based and
space (HST) telescopes. Special attention was given to
the precision of the photometric zero-points. By using
the same true distance modulus and cluster reddening
our canonical α-enhanced isochrones constructed assum-
ing [Fe/H]=–2.32, [α/Fe]=0.3 and Y =0.248, account for
the observed features in five different CMDs. We found
a cluster age of 11±1.5 Gyr, supporting previous results
based on cluster isochrones and luminosity functions.
The same outcome applies to the comparison between
the HB stars and the predicted ZAHB. We also investi-
gated the impact of a CNO enriched chemical composi-
tion and we found that α- and CNO- enhanced isochrones
at fixed total metallicity ([M/H]=–2.10) provide, within
the errors, the same cluster age. Moreover, α- and CNO-
enhanced isochrones at fixed iron abundance ([Fe/H]=–
2.32, [M/H]=–1.75) give a cluster age that is minimally
ACS Vegamag,

Page 7

7
TABLE 1
Star count ratios and evolutionary lifetime
ratios.
RatiosHB/RGBRGB/MSHB/MS
Empiricala
Theoryb
Theoryc
Theoryd
0.29 ± 0.05
0.31 ± 0.04
0.29 ± 0.04
0.32 ± 0.04
0.38 ± 0.04
0.33 ± 0.05
0.33 ± 0.05
0.30 ± 0.04
0.11 ± 0.01
0.10 ± 0.01
0.10 ± 0.01
0.09 ± 0.01
aMean star count ratios from the very center up to
∼7.′
bLifetime ratios based on an evolutionary model
constructed assuming M(TO)/M⊙=0.78, and an α-
enhanced mixture ([Fe/H]=–2.32, [α/Fe]=0.3).
cLifetime ratios based on an evolutionary model con-
structed assuming M(TO)/M⊙=0.78, and an α- and
CNO-enhanced mixture, but the same total metallic-
ity ([M/H]=–2.10) as the α-enhanced model.
dLifetime ratios based on an evolutionary model con-
structed assuming M(TO)/M⊙=0.80, and an α- and
CNO-enhanced mixture, but the same iron abundance
([Fe/H]=–2.32) as the α-enhanced model.
younger (10±1.5 Gyr).
We also investigated the star count ratios for evolved
(RGB,HB) and MSTO stars. We found that they do
not show any radial trend when moving from the very
center to the outermost cluster regions. Moreover and
even more importantly, star count ratios agree quite well
(within 1σ) with the lifetime ratios of the same evolu-
tionary phases.
The above results indicate that the occurrence of CNO
enriched subpopulations has a minimal impact on the
cluster age in the metal-poor domain. The same outcome
applies to star count ratios and evolutionary lifetimes.
These findings appear quite robust, since they rely on
different photometric data sets covering the entire body
of the cluster and on the same evolutionary framework.
We also note that isochrones including atomic He and
metal diffusion give cluster ages that are ≈1 Gyr younger
than canonical isochrones (Castellani et al. 1997). This
means that current findings support previous theoret-
ical predictions for typical GCs by Salaris et al. (2006)
and recent age estimates for metal-poor GCs provided by
Marin-Franch et al. (2009). Finally, it is worth emphasiz-
ing that current age estimates agree quite well with the
cluster age provided by VandenBerg et al. (2002) using
an independent but similar theoretical framework. The
difference is larger than one σ only for the cluster age
based on the CNO-enhanced models computed at fixed
iron content (10±1.5 vs 13.5±1.5 Gyr). This difference
can be explained if we account for the mild change in
the shape of the SGB region of these isochrones when
compared with the canonical ones.
It is a real pleasure to thank an anonymous referee for
his/her positive comments on the results of this investiga-
tion and for his/her suggestion. We also thank S. Cassisi
and A. Pietrinferni for several useful discussions concern-
ing low-mass stars and chemical mixtures. This project
was partially supported by the grant Monte dei Paschi
di Siena (P.I.: S. Degl’Innocenti) and PRIN-MIUR2007
(P.I.: G. Piotto).
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