Photometry of the Globular Cluster NGC 5466: Red Giants and
Blue Stragglers
Nassissie Fekadu and Eric L. Sandquist1,2
Department of Astronomy, San Diego state University, 5500 Campanile Drive, San Diego,
CA 92182
fekadu@sciences.sdsu.edu, erics@sciences.sdsu.edu
Michael Bolte1
University of California Observatories, University of California, Santa Cruz, CA 95064
bolte@ucolick.org
ABSTRACT
We present wide-field BV I photometry for about 11,500 stars in the low-
metallicity cluster NGC 5466. We have detected the red giant branch bump
for the first time, although it is at least 0.2 mag fainter than expected relative
to the turnoff. The number of red giants (relative to main sequence turnoff
stars) is in excellent agreement with stellar models from the Yonsei-Yale and
Teramo groups, and slightly high compared to Victoria-Regina models. This
adds to evidence that an abnormally large ratio of red giant to main-sequence
stars is not correlated with cluster metallicity. We discuss theoretical predictions
from different research groups and find that the inclusion or exclusion of helium
diffusion and strong limit Coulomb interactions may be partly responsible.
We also examine indicators of dynamical history: the mass function expo-
nent and the blue straggler frequency. NGC 5466 has a very shallow mass func-
tion, consistent with large mass loss and recently-discovered tidal tails. The
blue straggler sample is significantly more centrally concentrated than the HB or
RGB stars. We see no evidence of an upturn in the blue straggler frequency at
1Visiting Astronomer, Kitt Peak National Observatory, National Optical Astronomy Observatory, which
is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative
agreement with the National Science Foundation.
2Guest User, Canadian Astronomy Data Centre, which is operated by the Dominion Astrophysical Ob-
servatory for the National Research Council of Canada’s Herzberg Institute of Astrophysics.
http://arxiv.org/abs/0704.0827v1
– 2 –
large distances from the center. Dynamical friction timescales indicate that the
stragglers should be more concentrated if the cluster’s present density structure
has existed for most of its history. NGC 5466 also has an unusually low central
density compared to clusters of similar luminosity. In spite of this, the specific
frequency of blue stragglers that puts it right on the frequency – cluster MV
relation observed for other clusters.
Subject headings: equation of state — globular clusters: individual (NGC 5466)
— stars: blue stragglers — stars: evolution — stars: luminosity function
1. Introduction
The luminosity function (LF) is an observational tool used for analyzing the post-
main sequence evolutionary phases of low-mass (≈ 0.5-0.8M⊙) metal-poor stars in Galactic
globular clusters (GGC). Because of their age and richness, GGC typically contain hun-
dreds of stars that have evolved off the main sequence. The numbers of stars in evolved
phases are directly related to the evolutionary timescales and fuel consumed in each phase
(Renzini & Fusi Pecci 1988), so that they present us with an opportunity to test this aspect
of stellar evolution models.
The results of the most stringent tests have been mixed. Repeated studies of the metal-
poor cluster M30 (Bolte 1994; Bergbusch 1996; Guhathakurta et al. 1998; Sandquist et al.
1999) have found an excess number of red giant branch (RGB) stars relative to main sequence
(MS) stars. Stetson (1991) also uncovered an apparent excess of stars in a combined LF of
the metal-poor clusters M68, NGC 6397, and M92. However, the LFs of more metal-rich
clusters show no discrepancy (M5: Sandquist et al. 1996; M3: Rood et al. 1999; M12:
Hargis, Sandquist, & Bolte 2004). In a survey of 18 clusters, Zoccali & Piotto (2000) found
good agreement with model predictions with the possible exception of clusters at the high
metallicity end.
In this paper we present BV I photometry of NGC 5466, a high galactic latitude globular
cluster (l = 42.2◦ and b = 73.6◦), located in the constellation of Boötes (α = 14h05m27.s4,
δ = +28◦32′04′′ at a distance of R=15.9 kpc; Harris 1996). NGC 5466 is a loose cluster
(rc = 1.
′64) with extremely low metallicity ([Fe/H]= −2.22) and subject to little or no
reddening, (E(B − V ) ≃ 0) (Harris 1996).
In §2, we describe the process leading to the calibrated photometry, and compare with
previous studies of the cluster. In §3, we compare the observed color-magnitude diagram
and observed luminosity function with theoretical models, focusing on the relative number
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of stars on the lower RGB and around the MS turnoff. Finally, in §4, we present a new
examination of the blue straggler population of NGC 5466.
2. Observations and Data Reduction
The data used in this study were obtained with the Kitt Peak National Observatory
(KPNO) 0.9 m telescope (0.′′68 pix−1) on the nights of UT dates 1995 May 4, May 5, and
May 9. A complete list of the image frames, exposure times, and observing conditions is
given in Table 1.
The images obtained on the three nights were processed using IRAF1 tasks and pack-
ages. The reduction involved subtraction and trimming of the overscan region of all images,
subtraction of a master bias frame from flats and object frames, and flat fielding of the
object frames using images taken at twilight. Profile-fitting photometry was done using the
DAOPHOTII/ALLSTAR programs (Stetson 1987).
We also reduced archival ground-based photometry of the cluster core taken with the
High-Resolution Camera (HRCam) on the 3.6 m Canada-France-Hawaii Telescope (CFHT).
The V and I images were taken 30 and 31 May 1992 (observers J. Heasley and C. Christian),
and have not previously been described in the literature. The CCD images had 1024 × 1024
pixels, 0.′′13 per pixel, and excellent seeing (0.4 - 0.5 arcsec). The images were reduced using
the archived bias and twilight flat frames, and following a procedure similar to that for the
KPNO data. This allowed us to get excellent photometry to 2 magnitudes below the turnoff
in the cluster core. These images were used entirely for blue straggler identification (see §4).
2.1. Calibration against Primary Standard Stars
The conditions at KPNO on 1995 May 9 were photometric, and Landolt standard star
fields were observed at a range of air masses to determine photometric transformation coeffi-
cients. The standard values used for the calibration were chosen from the large compilation
of Stetson (2000), which is set to be on the same photometric scale as the earlier Landolt
(1992) values.
We conducted photometry on the standard stars and isolated cluster stars using multiple
1IRAF(Image Reduction and Analysis Facility) is distributed by the National Optical Astronomy Ob-
servatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under
contract with the National Science Foundation.
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synthetic apertures. We then used the DAOGROW (Stetson 1990) program to construct
growth curves to extrapolate measurements to a common aperture size. Using the CCDSTD
program, the standard star transformation equations were found to be:
b = B + ao + (−0.069± 0.005)(B − V ) + (0.255± 0.014)(X − 1.0)
v = V + bo + (0.027± 0.004)(B − V ) + (0.172± 0.010)(X − 1.0)
i = I + co + (−0.013± 0.005)(V − I) + (0.145± 0.018)(X − 1.0)
where X is the airmass, v, b and i are instrumental magnitudes, and V , B, and I are standard
magnitudes. These calibration equations are different than those used for our analysis of
M10 Pollard et al. (2005) and M12 Hargis et al. (2004), which were observed on the same
night, because our I−band exposures did not go as deep as the B and V exposures. As a
result, the (B − V ) color was a better choice for calibrating the V photometry down to our
faintest observed stars. The calibrated measurements for the standard stars are compared
with catalogue values in Fig. 1.
We note that there is slight evidence of trend in the residuals for the I band versus
magnitude, which might indicate nonlinearity. This impression is caused by one observation
of the PG1323-086 field. We did, however, have an additional observation of the same field
on the same night having the same exposure time that does not show the same (small) trend.
Because we do not have any reason to eliminate the frame and because its elimination has a
minimal effect on the transformation coefficients, we have decided to retain the measurements
from the image.
2.2. Calibration against Secondary Standard Stars
Aperture photometry for 165 cluster stars was used to calibrate the point-spread function
(PSF) photometry for the cluster. These secondary standard stars were chosen based on
relatively low measurement errors and location in relatively uncrowded regions of the cluster.
They were chosen from the asymptotic giant branch (AGB), upper RGB, and horizontal
branch (HB) of the cluster in order to cover the entire range of colors covered by cluster
stars.
The PSF-fitting photometry for the three nights of data was combined and averaged
after zero-point differences among the frames had been determined and corrected. The zero-
point corrections to the standard system were determined after fixing the color-dependent
terms at the values measured in the primary standard star calibration. (This was also done
in our studies of M10 and M12.) In Fig. 2, it can be seen that this procedure does not
introduce systematic color- or magnitude-dependent errors.
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2.3. Comparison with Previous Studies
We compared our photometric data set to those of Jeon et al. (2004), Rosenberg et al.
(2000), and Stetson (2000). The magnitude and color comparisons (BV I in this study versus
V I in Stetson and Rosenberg et al., and BV in Jeon et al.) as function of magnitude and
color are shown in Figs. 3 – 5. Though our calibrated magnitudes are slightly brighter than
those of Stetson (2000), the differences are small, and there is no color trend. The offsets
compared to the Rosenberg et al. (2000) are larger, but again there are no clear color trends.
The offsets compared to the Jeon et al. (2004) data are also significant, but more notable
are slight trends with color.
2.4. Calculation of the Luminosity Function
Artificial star tests were performed to empirically measure the precision of our photom-
etry and to correct for incompleteness in the detection of stars. We followed the procedure
described by Hargis et al. (2004) for the calculation of incompleteness corrections as function
of position and magnitude.
The inputs used for producing the artificial star tests were the reduced B and V
CCD frames, PSFs for each object frame, fiducial lines, and an estimate for the initial
LF (Sandquist et al. 1996). Artificial stars were randomly placed in cells on a spatial grid
and the entire grid was then shifted randomly from run to run in order to ensure the whole
imaged field was tested (Piotto & Zoccali 1999). Each star was placed in a consistent po-
sition relative to the cluster center on each image. If a detected star was found to coincide
with the input position of an artificial star, it was added to the archive. The new images
were reduced using the same procedure applied to the original data set. In this study, a
total of 100,000 artificial stars from 50 separate runs were added. The number of artificial
stars per trial was chosen so that the effects of crowding on the photometry was qualitatively
unchanged.
The recovered artificial stars were used to calculate 1) median magnitude and color
biases (δV and δB−V , where δ = median[output − input]), 2) median external error esti-
mates (σext(V ) = median[δV −median(δV )]/0.6745 and σext(B − V )), and 3) total recovery
probabilities (F (V ), which is the fraction of the stars that were recovered with any output
magnitude) in bins according to projected radius and magnitude. The values for the above
quantities are plotted in Figs.6 – 8.
Finally, an initial estimate of the “true” LF and the error distribution, magnitude biases
and the total recovery probability (F ) were used to compute the completeness fraction f
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(the ratio of the predicted number of stars to the actual number of observed stars). The
completeness fraction results are shown in Figure 9. We then interpolated to compute f
for the radial distance and magnitude of each detected star. For each observed star f−1
was added to the appropriate magnitude bin to determined the observed LF. (Note that the
completeness fraction was set to 1.0 for star brighter than the turnoff.) The observed LF
along with the upper and lower 1 σ error bars on log N are listed in Table 2.
3. Discussion
3.1. Reddening, Metallicity, Distance Modulus, and Age
Because NGC 5466 resides at high galactic latitude, it suffers little if any reddening.
Though Schlegel et al. (1998) found a reddening of E(B − V ) = 0.02 from the maps of dust
IR emission, we adopted E(B − V ) = 0.0 (Rosenberg et al. 2000). For our interests in this
paper, the small difference is of small importance. Most of the comparisons below between
observations and theory are relative, in which reference points (like the turnoff) are used to
determine magnitude and/or color shifts. This has the benefit of minimizing the influence
of uncertainties in reddening and distance modulus (see below).
As for abundances, there is only one high-resolution measurement for a cluster star, and
it is for the anomalous Cepheid V19. McCarthy & Nemec (1997) find [Fe/H]= −1.92±0.05,
while Pritzl et al. (2005) find [Fe/H]= −2.05 using the same data. Typically quoted metal-
licity values include [Fe/H] = −2.17 (Zinn 1980) from photoelectric photometry of integrated
light in selected filter bands, and [Fe/H] = −2.22, which was derived by Zinn & West (1984)
(ultimately from low-resolution spectral scans by Searle & Zinn 1978). When converted to
the widely-used metallicity scale of Carretta & Gratton (1997), this becomes [Fe/H] = −2.14.
More work could certainly be done on the composition of NGC 5466 stars, but the evidence
so far points to an abundance [Fe/H] . −2.0. Though the range in the above quoted metal-
licity values is relatively large for a globular cluster, the exact value is not critical for our
purposes since we will primarily be concerned with relative comparisons.
Our photometry does not extend faint enough to derive a new distance modulus from
subdwarf fitting to the main sequence. Harris (1996) obtained (m − M)V = 16.0 by cali-
brating the observed luminosity level of the horizontal branch with the relation MV (HB) =
0.15[Fe/H]+0.80 and adopting a reddening, E(B−V )=0.0 and a metallicity, [Fe/H]=−2.22.
Ferraro et al. (1999) determined distance moduli (m−M)V = 16.16 from their zero-age HB
estimate, assuming no reddening and metallicity on the Carretta & Gratton (1997) scale.
We will consider distance moduli in this range.
– 7 –
Most previous age estimates of NGC 5466’s age have it older than the recent deter-
mination of the age of the universe (13.7+0.13
−0.17 Gyr) obtained by the Wilkinson Microwave
Anisotropy Probe (WMAP) team (Spergel et al. 2006). Recent homogeneous studies of GGC
indicate that NGC 5466 is coeval with clusters of similar metallicity (Salaris & Weiss 2002;
Rosenberg et al. 2000). As a result, we will primarily consider ages in the range of 12 to 13
3.2. The Color-Magnitude Diagram
The color-magnitude diagrams (CMDs) for NGC 5466 show well-defined RGB, AGB,
and HB sequences (see Fig. 10), and stars extending from the tip of the RGB down to
V ≈ 22.5. Fiducial sequences for the MS and lower RGB were determined from the mode of
the color distribution of stars in magnitude bins. The SGB position was determined using
the magnitude distribution of the stars in color bins. The fiducial line for the rest of the
RGB was obtained from the mean color of stars in magnitude bins. The fiducial points are
listed in Table 3.
A comparison of the fiducial points derived for NGC 5466 with theoretical isochrones for
a range of ages from the Teramo (Cassisi et al. 2004), Victoria-Regina (VandenBerg et al.
2006), and Yonsei-Yale (Demarque et al. 2004) groups is displayed in Figures 11 and 12.
The isochrones have been shifted in color and magnitude (aligning the turnoff colors and
the magnitudes of the main sequence point 0.05 mag redder than the turnoff) according
to the technique of Vandenberg et al. (1990). This has the advantage of removing some of
systematic uncertainties associated with the color-Teff transformations. [In our comparisons,
we found that the Yonsei-Yale models could not match the fiducial line for any reasonable set
of input parameters when the transformations of Lejeune et al. (1998) were used. Therefore,
we only utilize models using the Green, Demarque, & King (1987) transformations. Even
then, we could not find a match with the slope of the upper giant branch for reasonable
metallicities ([Fe/H] . −1.9).] On the whole, the shape of the fiducial matches the models
well on the main sequence, subgiant branch, and lower giant branch. Neither the Teramo
nor the Victoria-Regina models include element diffusion processes, while the Yonsei-Yale
isochrones only include He diffusion. However, differences in Teff -color transformations are
likely to be the cause of some of the differences seen.
– 8 –
3.3. The Luminosity Function
The number of stars at a given luminosity in post-main-sequence phases is directly pro-
portional to the lifetime spent at that luminosity. It is well known that the LF of the RGB
probes the chemical stratification inside a star because the hydrogen abundance being sam-
pled by the thin hydrogen-fusion shell affects the rate of evolution, and hence star counts
on the RGB (Renzini & Fusi Pecci 1988). Setting aside the short pause at the RGB bump,
RGB evolution accelerates in a very regular way that is ultimately related to the structure
of degenerate core. The relationship between core mass and radius forces the fusion shell to
function at strictly controlled density and temperature conditions, which leads to a relation-
ship between core mass and luminosity. This causes the LF to be particularly sensitive to
certain physical details, which we discuss in §3.3.1 below.
Fig. 13 shows the observed luminosity function compared to theoretical LFs for the la-
beled values of metallicity, exponent of the initial mass function, and a range of age estimates
for NGC 5466, assuming our preferred distance modulus (m −M)V = 16.00. The theoret-
ical models were normalized to the observed LF at V ≈ 21.3 (sufficiently faint that stellar
evolution effects are minimized). The models agree well with the observed LF, implying an
age of approximately 12 - 13 Gyr.
3.3.1. Relative RGB and MS Numbers
Gallart et al. (2005) recently discussed theoretical luminosity functions calculated by
different groups. One of the primary differences they noted was in the number of giant stars
relative to main sequence stars. In order to show these differences in a parameter-independent
way, we follow the method of Vandenberg et al. (1990). In Fig. 14, the theoretical LFs were
shifted so that a point on the main sequence 0.05 mag redder than the turnoff color point
matched the corresponding point on the cluster fiducial line. The reason for using the point
(VTO+0.05) rather than the MSTO itself is that the MS has a significant slope and curvature
at this point, making it possible to accurately measure the point in both observational data
and isochrones (Vandenberg et al. 1990). The theoretical models were normalized to the two
bins in the observed LF on either side of the turnoff (V = 19.83 and 20.13). As can be seen,
age-related differences between the theoretical LFs nearly disappear when this procedure
is applied (see also Stetson 1991; Vandenberg et al. 1998). However, when different sets of
models are compared, there are small differences in the number of RGB stars relative to
MS stars, with the Victoria-Regina models predicting the smallest number of giants and the
Yonsei-Yale models predicting the largest.
– 9 –
To quantify the differences, we computed the ratio of the number of stars on the lower
giant branch to the number of stars near the main sequence. Pollard et al. (2005) introduced
this ratio and showed that it is insensitive to age and heavy-element abundance. For the
main sequence population, we used star counts in the two bins on either side of the turnoff
(19.682 < V < 20.282), and for the red giant branch we used the counts in the range
16.982 < V < 18.482. We derived model values from the same magnitude ranges relative to
the VTO+0.05 point on the main sequence. Values are compared in Table 4. The error in the
observed value is dominated by Poisson statistical scatter. The Yonsei-Yale models are in
best agreement with the observations, the Victoria-Regina models are out of agreement by
more than 2 σ, and the Teramo models are in between.
It is worth examining the possible causes of this difference both because it may help
improve the physics inputs for the models and because red giant stars are some of the largest
contributors to the integrated light of old stellar populations. Gallart et al. (2005) tabulated
most of the main physics inputs for the most widely-used model sets2. Earlier studies (Stetson
1991; Vandenberg et al. 1998) have shown that the LF-shifting method used above eliminates
nearly all sensitivity to model input parameters like mass function, age, convective mixing
length, and composition inputs with the exception of helium abundance, which we examine
first.
Older models (e.g. Fig. 9 of Ratcliff 1987, Fig. 7 of Stetson 1991, Fig. 3 of Vandenberg et al.
1998) seem to agree that an increase in initial helium abundance Y in non-diffusive models
by 0.1 results in an increase in the relative number of stars on the RGB (more precisely, a
reduction in the relative number of main sequence stars) by about 0.07-0.08 in logN . The
Teramo models (Y = 0.245) predict about 12% more giant stars relative to main sequence
stars compared to the Victoria-Regina models (Y = 0.235)3. This difference corresponds
to a shift of 0.05 in logN , which is about an order of magnitude too large for the helium
abundance difference.
The Yonsei-Yale models have the lowest assumed helium abundance (Y = 0.23), but
are the only set of the three that include helium diffusion. The inclusion of helium dif-
fusion reduces the age derived from the turnoff of a globular cluster by about 10-15%
2Since the Gallart et al. (2005) review was published, the Teramo group found an error in the evolution
scheme they used on the giant branch, which brings their models into better agreement with other groups.
We use their updated models in the comparisons here
3The Teramo models also assume a larger α-element enhancement ([α/Fe] = 0.4) than the Victoria-Regina
models ([α/Fe] = 0.3), which would tend to reduce the number of giants relative to main sequence stars.
However, because the relative number of RGB and MS stars is not sensitive to small differences in heavy
element abundance, this difference is probably unimportant.
– 10 –
(Proffitt & Vandenberg 1991; Straniero et al. 1997; VandenBerg et al. 2002), thanks to the
inward motion of helium. According to theoretical models (e.g. Fig. 8 of Proffitt & Vandenberg
1991), diffusion has a small effect on the LFs (∼ a few times 10−2 in logN , increasing for
increasing age), but it does increase the number of giants relative to MS stars. He diffusion
reduces the total core hydrogen fuel supply available to an MS star, but in itself this does not
strongly modify the LF, just changes the brightness of the turnoff. This magnitude change
is eliminated in our LF shifting procedure. The chemical composition profile left in the star
after it leaves the main sequence has a greater impact. Diffusion reduces the H abundance in
the fusion regions, thereby decreasing the evolutionary timescale. According to the models
of Proffitt & Michaud (1991), the changes to the He abundance profile are most considerable
immediately below the surface convection zone, and just outside the nuclear fusion regions
(where the composition gradient slows the inward settling of helium). However, over most
of the star, the changes in Y are limited to 0.01 - 0.02. Because the core portion of the
composition profile is consumed on the subgiant branch, the evolution timescales for giant
stars are only affected in a minor way, and the appearance of a deep convection zone on
the lower giant branch wipes out most of the effects of diffusion for the upper giant branch
evolution.
In spite of this, the Yonsei-Yale models have almost 23% more giants than the Victoria-
Regina models, and more than 9% more giants than the Teramo models (relative to MS
stars). The lower helium abundance in the Yonsei-Yale models compared to the other models
should partially counteract what effects helium diffusion might have had on the RGB/MS
ratio as well. Thus, it appears that neither He abundance nor He diffusion can completely
explain the differences between the Yonsei-Yale models and the other groups.
We can ask whether the LFs show similar disagreements at other metallicities. Hargis et al.
(2004) made comparisons between the Victoria-Regina and Yonsei-Yale theoretical LFs and
observational LFs for the clusters M3 (Rood et al. 1999), M5 (Sandquist et al. 1996), M12,
and M30. The overall impression from those comparisons was again that the Yonsei-Yale
models (having He diffusion) predict more giant stars relative to main-sequence stars than
do the Victoria-Regina models. In Fig. 15, we compare the LFs for these clusters with
the Teramo models. The degree of agreement or disagreement can be quantified with num-
ber ratios of lower RGB and MSTO stars, similar to the ones we computed earlier for
comparisons with NGC 5466. Our calculations are shown in Table 4. As can be seen, uncer-
tainties in the metallicity scale have some effect on the comparisons with the observations.
The Carretta & Gratton (1997) scale has higher [Fe/H] values than the Zinn & West (1984)
scale, and thus results in lower number ratios.
Fig. 16 shows the results of comparing the observed ratios with the models for different
– 11 –
[Fe/H] scales. On the Zinn & West 1984 scale (right panels), the observed values seem to
be in agreement to within about 1 − 1.5σ for most of the models, with the exception of
the the lowest metallicity clusters (M30 and NGC 5466) and the lowest helium abundance
(Victoria-Regina) models. On the Carretta & Gratton 1997 scale, the Yonsei-Yale models
have the best overall agreement, although the Teramo models only deviate noticeably for
the lowest metallicity clusters. The Victoria-Regina models predict too few giants for all of
the clusters.
The differences from model to model (as opposed to models versus observation) point
toward deficiencies elsewhere in the physics or computational algorithms used in the stel-
lar evolution codes. 4 The RGB LF is a robust prediction of the models because there is
a strong core mass — luminosity relationship: the conditions in the hydrogen fusion shell
of the giant are strongly dependent on the structure of the degenerate core and are al-
most independent of the details of the mass or structure of the envelope. As a result of
this, we can focus on factors affecting core structure. (As a non-standard physics exam-
ple, Vandenberg et al. 1998 describe the way in which core rotation relieves a giant star of
some of the need to support itself by gas pressure, which reduces the core temperature and
lengthens the evolutionary timescale.) Because model-to-model differences appear even on
the faint end of the giant branch, we can set aside factors that only become important to the
structure of the star near the tip of the giant branch [such as neutrino losses and conductive
opacities; see Bjork & Chaboyer 2006, for example], even though there are significant theo-
retical uncertainties in these quantities. Nuclear reaction rates in the fusion shell can also
be neglected, partly because the uncertainties in the reactions appear to be relatively small
Adelberger et al. (1998), but also because small changes in the reaction rates require only
tiny changes in the shell temperature to get the same energy production. This leads us to
examine the equation of state (EoS) in the core.
Although the behavior of degenerate electrons is thought to be very well understood,
their interactions with nuclei can have a measureable effect on the pressure. Particles of like
charge tend to cluster together, which modifies the free energy of the gas and reduces the gas
pressure for given density and temperature. Harpaz & Kovetz (1988) looked at the effects
of the inclusion of Coulomb interactions on giant stars, and their results are corroborated
by those of Cassisi et al. (2003). They found that for a given core mass the fusion shell
temperature was higher when the Coulomb interactions were included, which leads to faster
processing of hydrogen. Thus this is another example (like core rotation) where modification
of the pressure support of the core affects the evolutionary timescales, which results in
4For a comparison of these physical inputs for the different theoretical groups, see Table 1 of Gallart et al.
(2005).
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changes to the luminosity function. The Coulomb corrections to the pressure become more
important with increasing density for the core, but are small compared to the contribution
of the degenerate electrons.
All of the model sets we have considered here incorporate Coulomb interactions in some
form. The Teramo group used the most sophisticated “EOS1” version of the FreeEOS5,
which incorporates Coulomb corrections in a form that matches limits in both the weak
(Debye-Hückel) and strong (once-component plasma) Coulomb interaction limits as well
as (less importantly) electron exchange interactions. The strong interaction limit is most
relevant for giant star cores since the strong interaction parameter
where ζ is the rms nuclear charge and r0 is the average internuclear distance.
The Yonsei-Yale group used the OPAL EoS tables (Rogers et al. 1996), but falls back
on the group’s older EoS [e.g. (Guenther et al. 1992)] for conditions for high densities and
temperatures outside the OPAL tables. While the most recent OPAL tables probably contain
the most complete physical description of the Coulomb effect, the OPAL tables they used
(Y.-C. Kim, private communication) were computed prior to recent improvements to account
for relativistic electrons (Rogers & Nayfonov 2002), and as a result cut off at log ρ > 5.0.
The Yale EoS at higher densities only includes the Coulomb effect in the weak Debye-Hückel
limit, which for the highest densities in the core. The Victoria-Regina models also use
a modified version of the EFF EoS (Eggleton et al. 1973), with a correction for Coulomb
corrections in the weak Debye-Hückel limit (VandenBerg et al. 2000).
The differences in the implementation of the Coulomb effect may explain the fact that
the Teramo models generally predict more giants (relative to the main sequence) than the
Victoria-Regina models do. However, the smaller Coulomb corrections in the Yonsei-Yale
models would tend to result in fewer giants than the Teramo models (although the effects of
helium diffusion work in the opposite direction). So, we are unable to completely reconcile
the differences in the luminosity functions from the three groups.
Obviously more detailed study is needed by all of the modelling groups to identify the
causes of the differences, but such a study is beyond the scope of this paper. Still, we
believe that helium diffusion and strong interaction Coulomb corrections are physical effects
that should be considered first. There is, for example, good evidence from helioseismology
5FreeEOS is available at http://freeeos.sourceforge.net/, and the discussion of the implementation of the
Coulomb effect can be found at http://freeeos.sourceforge.net/coulomb.pdf.
http://freeeos.sourceforge.net/
http://freeeos.sourceforge.net/coulomb.pdf
– 13 –
for helium diffusion in the Sun Bahcall et al. (1995), despite the surface convection and
meridional flow (e.g., Hathaway 1996). It is expected that helium diffusion should also act
in globular cluster stars. A detailed study of the effect of equation of state uncertainties
has yet to be done [see, for example, Bjork & Chaboyer (2006) for a study of uncertainties
in other physical inputs]. Use of FreeEoS would make a study of equation of state effects
most stringent since it appears to be capable of modelling the most sophisticated tabular
EoS (OPAL), while also having the flexibility to allow individual bits of the physics to be
“turned off”.
As a final warning about the observations, we should remember the LF of the clus-
ter M10. Pollard et al. (2005) found that unusual variations in numbers of RGB stars at
different brightness levels in M10 (a virtual twin to M12). In particular there seemed to
a significant excess in the number of stars near the RGB bump in brightness, while the
lower RGB appeared normal (compared to Victoria-Regina and Yonsei-Yale models). A
similar excess may be present in the RGB LF of M13 (Cho et al. 2005). These kinds of
variations cannot be explained by the “global” physics that should apply to all globular
cluster stars. These anomalies point toward fluctuations in the stellar initial mass function
or composition-dependent effects.
3.3.2. The RGB Bump
A second feature of the LF presented here is a noticeable RGB bump. Typically, the
RGB bump appears as a peak in the differential LF and as a change of slope in the cumulative
LF (CLF). The bump provides a measure of the maximum depth reached by the outer
convection zone during first dredge-up since it is the result of a pause in the star’s evolution
when the shell fusion source begins consuming material of constant, lower helium content
(Fusi Pecci et al. 1990). Unfortunately, the number of stars occupying the bump gets smaller
and the luminosity of the bump increases as the metallicity of the cluster decreases, making
the bump harder to detect in metal-poor clusters. A small peak appears in our differential
LF at V ≈ 16.2, and a significant (2.5 − 3.5σ) change in slope occurs at the same position
as the peak in the differential LF, as shown in Fig. 17.
The relative brightness of the bump can be measured by comparing to the V -magnitude
of the HB at the level of the RR Lyrae instability strip ∆V
HB = Vbump−VHB (Ferraro et al.
1999). This indicator is a function of the total metallicity and the age of the cluster: an
increase in metallicity and/or a decrease in age are accompanied by a decrease in luminosity
of the bump (Ferraro & Montegriffo 2000). We find Vbump = 16.20 ± 0.05 mag, and VHB =
16.52 ± 0.11 (from interpolation between the average magnitudes of non-variable HB stars
– 14 –
at the blue and red ends of the RR Lyrae instability strip), giving ∆V
HB = −0.32 ± 0.12.
In the compilation of Ferraro et al. (1999), a zero-age HB reference point was calculated
using the relation VZAHB = VHB +0.106[Fe/H]
+0.236[Fe/H]+ 0.193. Ferraro et al. found
VZAHB = 16.62 ± 0.10, which is consistent with the value obtained here (VZAHB = 16.65 ±
0.11). Our value of ∆V
ZAHB = −0.45 ± 0.12 is considerably lower than tabulated values
for other clusters with similar metallicities (M68: −0.60 ± 0.07; M92: −0.65 ± 0.12; M15:
−0.65 ± 0.09). In a separate compilation, Zoccali et al. (1999) measured a smaller value
ZAHB = −0.45 ± 0.11 for M15, in better agreement with the value for NGC 5466. (The
difference is primarily because Zoccali et al. measured the bump position to be 0.16 mag
fainter than Ferraro et al. .) Clearly there is still some need for more precise comparisons of
bumps in metal-poors clusters with theory.
We believe, however, that the brightness of the bump should ultimately be judged using
hydrogen-fusing stars as references because it avoids any effects of the poorly-understood
physical processes (such as the helium flash and/or mass loss) associated with the creation
of an HB star. Using the cluster LF (as seen in Figure 14), we again find that the observed
RGB bump is fainter than model values by at least 0.3 mag when the models are shifted
to match the cluster’s main sequence. Hargis et al. (2004) did similar comparisons between
theoretical models and luminosity functions for M3, M5, M12, and M30 taken from the
literature. With the exception of M30 (because the bump could not be identified), the
position of the bump relative to the turnoff region agreed well with theory. NGC 5466 is
thus the most metal-poor cluster this comparison has been done for. So at present we are left
with the question of whether this might result from the cluster’s low metallicity, or whether
we have been the unfortunate victims of a fluctuation in the number of giant stars in this
low-mass cluster. We therefore encourage the examination of the luminosity function of more
massive metal-poor clusters to settle the question.
3.3.3. Mass Function Exponent
Two recent papers (Belokurov et al. 2006; Grillmair & Johnson 2006) reported the dis-
covery of tidal streams covering many degrees around NGC 5466 in Sloan Digital Sky Sur-
vey images. Gnedin & Ostriker (1997) examined the Milky Way globular clusters and found
NGC 5466 to be a cluster that has probably been strongly affected by disk shocking in the
recent past. In our examination of the LF, we found a rather low value for the global main se-
quence mass function slope. The mass function for a cluster is typically expressed as a power
law (N(M) ∝ M−(1+x)), where the slope x = 1.35 is the standard Salpeter value. Generally,
the present-day power-law index x varies from cluster to cluster. The mass function slopes
– 15 –
that best fit the upper LF of NGC 5466 around and above the MSTO have −1 . x . 0.
(Note that the best fit slope does depend on the models being used: the Yonsei-Yale models
require a flatter slope than the Victoria-Regina and Teramo models.) Such a shallow mass
function slope is unusual for a metal-poor cluster. For example, the cluster NGC 5053 has
similar metallicity, position relative to the galactic center and plane, and density structure,
but still has a steep x ∼ 2 mass function (Fahlman et al. 1991). Djorgovski et al. (1993)
found that mass function slopes in the range of 0.5 ≤ M
≤ 0.8 are influenced primarily by
the cluster’s position in the galaxy, and to some extent by cluster metallicity. Based on both
of those factors, NGC 5466 should have a larger mass function slope (x ∼ 3 according to the
multivariate formula in Djorgovski et al. 1993). Like other halo clusters, NGC 5466’s orbit
is quite eccentric and will take the cluster more than 30 kpc away from the Galactic center
(Dinescu et al. 1999), but it is currently on its way back into the halo after two relatively
recent passes through the Galactic disk. Recent losses of low-mass stars may explain the
recent identification of strong tidal tails near the cluster by Belokurov et al. (2006).
4. Blue Stragglers
Blue stragglers (BSSs) were first identified by Sandage (1953) in the globular cluster
M3. These stars are more massive than the turnoff mass and occupy the space in the CMD
just bluer and brighter than the MSTO. Blue stragglers are found in clusters, and relatively
more frequently in lower-luminosity clusters (Ferraro et al. 1993; Preston & Sneden 2000;
Piotto et al. 2004; Sandquist 2005). From the various models proposed for the formation
mechanism of BSSs, the “collision” theory (involving strong gravitational interactions be-
tween previously unassociated single or binary stars) and the “mass-transfer” theory (in
which the more massive star in a binary evolves and during its expansion transfers mass to
its companion) are the strongest possibilities. There is a continuing interest in the study of
BSSs because they may provide insight into the recent dynamical history of a cluster.
In order to identify BSSs over the entire observed area of the cluster out to a radius
of 11.′6, we used photometry from three datasets. In the core of the cluster we used the
CFHT data presented here for the first time. Outside of the CFHT field, we used the BV
photometry of Jeon et al. 2004, which covered a field 11.′6 on a side centered on the cluster.
Finally, we used our KPNO data for the least crowded outskirts of the cluster. Even though
NGC 5466 is a very low density cluster, the spatial resolution of the KPNO data was such
that blends of stars would have resulted in the spurious identification of 10 objects as BSS
in the intermediate portion of the field.
48 BSS candidates were identified in NGC 5466 by Nemec & Harris (1987), all located
– 16 –
between 0.′1 and 5.′6 from the cluster center. In spite of the low cluster density, we find new
BSS candidates at all radii and luminosity levels, and find several of their candidates are
spurious. According to the CFHT photometry, the object with ID 45 from Nemec & Harris
is a blend of several fainter stars, none of which is a BSS. In addition, IDs 6 and 24 were
identified as blends of stars using the Jeon et al. (2004) dataset. Our BSS list is presented
in Table 5. The list includes the nine known SX Phoenicis stars (ID 27, 29, 35, 38, 39, and
49, Nemec & Mateo 1990; ID 3 (SX Phe 3), 36 (SX Phe 2), and 50 (SX Phe 1), Jeon et al.
2004) and the three eclipsing binaries (ID 19, 30, and 31; Mateo et al. 1990). New straggler
candidates were given ID numbers that build upon the Nemec & Harris (1987) list. Figure
18 shows the CMDs used to select the 94 identified BSSs in each of the three datasets.
In order to use the BSSs to constrain cluster dynamics, we compared the normalized
cumulative radial distribution of the BSSs to the population of the giant branch, as shown
in Fig. 19. Nemec & Harris (1987) found a 97.8% probability that their BSS sample was
more centrally concentrated than red giants in the same magnitude range. Because their
photometry was taken in conditions of poorer seeing (compared to our CFHT photometry
and that of Jeon et al.), their samples are likely to be somewhat incomplete near the cluster
center.
Our RGB sample contains 350 stars with magnitude V < 18.5. Kolmogorov-Smirnov
(K−S) probability tests were used to test the hypothesis that both populations were drawn
from the same parent population. The K−S probability that the BSSs are drawn from
the same radial distribution as the RGB population is 8.1 × 10−7, and 2.4 × 10−4 for the
comparison with the HB population. By contrast there is a probability of 0.27 that the RGB
and HB samples are drawn from the same population. The concentration of BSSs toward
the cluster center as compared to the RGB and HB samples is consistent with the idea that
they are more massive than individual RGB stars, and as a result have been segregated by
mass deeper within the cluster potential well.
Piotto et al. (2004) recently used samples of stragglers from the cores of 56 globular
clusters to show that there was a strong correlation between FHBBSS = NBSS/NHB and inte-
grated cluster V magnitude, and a weaker anti-correlation with central density. Sandquist
(2005) examined an additional 13 low-luminosity globular clusters using similar selection
criteria. NGC 5466 is an interesting cluster in relation to these samples because it has an
integrated luminosity that puts it at the faint end of the Piotto et al. sample (MVt = −6.96;
Harris 1996), but with a central density that is nearly an order of magnitude lower than
any of their clusters [log(ρ0/(LV,⊙pc
−3)) = 0.88] but comparable to clusters in the Sandquist
sample. To put NGC 5466 in the context of the Piotto et al. and Sandquist samples, we
selected a subset of our BSSs that satisfied the selection criteria in those studies (brighter
– 17 –
than the MSTO, and bluer than the MSTO by 0.05 in B − V color). From mode fitting to
the turnoff region in the Jeon et al. (2004) and CFHT data, we find (B−V )TO = 0.367 and
(V − I)TO = 0.511. A color offset of 0.05 in B − V corresponds to an offset of about 0.075
in V − I (VandenBerg & Clem 2003) for NGC 5466’s metallicity. We find that 75 BSSs are
brighter than the cluster turnoff (VTO = 19.99±0.05) and 0.05 bluer than the cluster turnoff
in B − V . We have identified 97 HB stars in our datasets for NGC 5466, which gives a
specific frequency FHBBSS = 0.77± 0.12 (with the error estimate from Poisson statistics).
When compared to the Piotto et al. values (see Fig. 20), NGC 5466 falls within the
general trend versus MVt despite the cluster’s low central density. On the other hand, NGC
5466 has a lower FHBBSS value than other clusters of similar central density (but lower total
luminosity). As discussed by Sandquist (2005), this provides additional evidence that the
plateau in FHBBSS seen for clusters with log ρ0 . 2.5 is a result of the correlation between cluster
integrated magnitude and central density. The lowest luminosity clusters in the Sandquist
sample (E3 and Palomar 13) have central densities comparable to that of NGC 5466, but
BSS frequencies that are several times higher. Another moderate-luminosity, low-density
cluster (NGC 5053; Hiner et al., in preparation) similar to NGC 5466 shows a comparably
low straggler frequency. BSSs produced via purely collisional means are not likely to show
this kind of behavior. More likely is the scenario proposed by Davies et al. (2004) in which
binary stars that would normally produce BSSs are destroyed earlier in the cluster’s history.
More direct observational support for that hypothesis is needed though — for example, a
detailed study of the variation of the binary star fractions as a function of integrated cluster
magnitude.
Fig. 21 shows that the number and frequency
RBSS =
NBSS/N
Lsample/L
sample
of BSSs relative to the integrated V -band flux (derived from a King model profile) as a func-
tion of radius. Both frequencies increase toward the cluster center, and neither shows signs
of rising toward larger radii. As recent studies of denser clusters show (M3: Ferraro et al.
1993; M55: Zaggia et al. 1997; 47 Tuc: Ferraro et al. 2004; NGC 6752: Sabbi et al. 2004),
the BSS frequency generally decreases at intermediate radii and rises again at larger dis-
tances. However, the cluster Palomar 13 (Clark et al. 2004), which has a central density
similar to NGC 5466, shows no sign of an increase in straggler frequency at large distance.
In more massive clusters, the minimum in the BSS frequency is reached approximately
where the timescale for dynamical friction equals the age of the cluster (Warren et al. 2006).
A similar calculation for the current structure of NGC 5466 indicates that this occurs at about
270′′(about 2.8rc). This appears to be in the outer reaches of the core straggler distribution.
– 18 –
Because it is likely that NGC 5466 has lost a significant fraction of its mass, we expect
that the current density structure of the cluster has not existed throughout its history and
that NGC 5466 might have been able to dynamically relax stragglers to its core from larger
distances earlier in its history. This may be showing that the global BSS population differs
significantly between low-density/low-mass clusters and high-density/high-mass clusters. A
lack of stragglers at large distance may be signature of large-scale tidal stripping of the
cluster, which would remove both stragglers that would normally have formed in primordial
binaries in the outer reaches of the cluster and ones that formed in the core but were given
velocity kicks into orbits that would take them into the outer reaches.
The case against a rise at large radius in Palomar 13 is stronger because the cluster
has been surveyed out to 19 core radii, while in NGC 5466, we have only surveyed out to
about 10 core radii (or 7.5 half-mass radii). Still, NGC 5466 probably should have an even
more concentrated distribution of stragglers if its current density structure has existed for
most of its history. In more massive clusters, the secondary rise in straggler frequency is
observed between 8 and 10 rc. Unfortunately, further study of the stragglers in NGC 5466
will probably be complicated by the strong tidal tails observed in the cluster.
5. Conclusions
Examinations of the luminosity functions of globular clusters continue to produce inter-
esting tests of astrophysics. In this study, we found that NGC 5466 has a luminosity function
that is in better overall agreement with theoretical models than the anomalous cluster M30,
which has a similar low metallicity. In addition, we found that the relative numbers of red
giant and main sequence stars may produce a fairly sensitive test of the physics near the
core of red giants — specifically, helium diffusion and Coulomb interactions. However, we
are not yet able to fully explain the differences between sets of theoretical models.
Recent discoveries of large tidal tails associated with NGC 5466 suggest that this cluster
has been strongly disrupted by interactions with the Galaxy. Our measured flat (−1 . x . 0)
main-sequence luminosity function is unusual for a low-metallicity halo cluster. It is, however,
consistent with the emerging picture of mass-segregation followed by tidal stripping.
We have thoroughly re-examined the blue straggler population in the cluster, and de-
tected a total of 94. The radial distribution of stragglers is clearly more centrally concen-
trated than the RGB and HB populations. The frequency of blue stragglers in the cluster is
relatively low — consistent with the observed anti-correlation between frequency and cluster
luminosity, in spite of the cluster’s very low central density.
– 19 –
We would like to thank the anonymous referee for helpful comments on the manuscript,
Y. Jeon for providing us with an electronic copy of his photometric dataset, Y.-C. Kim for
information on the Yonsei-Yale isochrones, and S. Cassisi for providing us with access to
the Teramo set of models. This work has been funded through grants AST 00-98696 and
05-07785 from the National Science Foundation to E.L.S. and M.B.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 24 –
Fig. 1.— Photometric residuals (in the sense of this study minus those of Landolt 1992 and
Stetson 2000) of primary standard stars. The median residuals are listed in the panels with
the semi-interquartile range (half the magnitude difference between the 25% and 75% points
in the ordered list of residuals) given in parentheses.
– 25 –
Fig. 2.— Photometric residuals (in the sense of the final PSF photometry minus standard
aperture photometry values) of secondary standard stars.
– 26 –
Fig. 3.— Residuals (in the sense of this study minus Stetson 2000) from the star-by-star
comparison. The median residuals are listed in the panels with the semi-interquartile range
(see Fig.1) given in parentheses.
– 27 –
Fig. 4.— Residuals (in the sense of this study minus Rosenberg et al. 2000) from the star-
by-star comparison. The median residuals and the plots versus color have been restricted
to brighter stars (V < 20 and I < 19) to make the comparisons clearer. The numbers in
parentheses are the semi-interquartile ranges (see Fig.1).
– 28 –
Fig. 5.— Residuals (in the sense of this study minus Jeon et al. 2004) from the star-by-star
comparison. The median residuals and the plots versus color have been restricted to brighter
stars (B < 20 and V < 19.5) to make the comparisons clearer. The numbers in parentheses
are the semi-interquartile ranges (see Fig.1).
– 29 –
Fig. 6.— External V magnitude errors σext(V ) as a function of radius and magnitude
determined from artificial star tests, with exponential fits shown by the solid lines.
– 30 –
Fig. 7.— Magnitude biases δ(V ) determined from artificial star tests as a function of radius
and magnitude.
– 31 –
Fig. 8.— Total recovery probability F (V ) determined from artificial star tests as a function
of radius and magnitude.
– 32 –
Fig. 9.— Completeness fraction f(V ) determined from artificial star tests as a function of
radius and magnitude.
– 33 –
Fig. 10.— Color-magnitude diagrams for all stars measured in the KPNO and CFHT images.
The BV fiducial (Table 3) is also plotted in the left panel.
– 34 –
Fig. 11.— Comparison of the observed fiducial sequence of NGC 5466 with the isochrones
of the Teramo, Victoria-Regina, and Yonsei-Yale groups. The isochrones have been shifted
horizontally so that the turnoff colors align, and shifted vertically to align the main sequence
point 0.05 mag redder than the turnoff. On the giant branch, the ages increase from the
reddest to the bluest isochrone.
– 35 –
Fig. 12.— Same as Fig. 11, except for more metal-rich models.
– 36 –
Fig. 13.— Comparison of the observed V−band LF of NGC 5466 with theoretical models
of the Yonsei-Yale, Teramo, and Victoria-Regina groups assuming (m−M)V = 16.
– 37 –
Fig. 14.— Comparison of the observed V−band LF of NGC 5466 with theoretical models
of the Victoria-Regina, Yonsei-Yale, and Teramo groups using magnitude shifts that bring
the main sequence point 0.05 mag redder than the turnoff into alignment. The models have
been normalized to the two bins on either side of the turnoff (V = 19.94).
– 38 –
Fig. 15.— Comparison of the observed LFs of M3, M5, M12, and M30 with theoretical
models of the Teramo group using magnitude shifts that bring the main sequence point 0.05
mag redder than the turnoff into alignment. The models have been normalized to bins on
either side of the turnoff.
– 39 –
Fig. 16.— Fractional difference between the observed RGB-MS number ratios (for M5, M12,
M3, M30, and NGC 5466, from left to right) and the theoretical predictions from the Yonsei-
Yale, Teramo, and Victoria-Regina models. The left panels use the Carretta & Gratton
(1997) metallicity scale, and the right panels use the Zinn & West (1984) scale. The sense
is (observed − theoretical) / observed.
– 40 –
Fig. 17.— The cumulative luminosity function for bright RGB stars derived from the pho-
tometry of Jeon et al. (2004; 286 stars) and from the KPNO dataset (338 stars) presented
here. Dotted lines show fits to the data for stars above and below the position of the apparent
bump.
– 41 –
Fig. 18.— Blue straggler selection for NGC 5466. The stars plotted in each panel show the
entire sample used for the selection: stars from Jeon et al. (2004) in the middle panel are
only those stars outside the CFHT field, and KPNO stars in the right panel are only those
outside the Jeon et al. field. Open squares show stragglers identified by Nemec & Harris
(1987), and open circles are new candidates.
– 42 –
Fig. 19.— Normalized cumulative radial distributions for RGB stars (dashed line), HB stars
(dotted line), and BSSs (solid line).
– 43 –
Fig. 20.— Relative frequencies of blue stragglers as a function of cluster absolute magnitude
and central density. The solid square is NGC 5466, the open squares are globular clusters
from Sandquist (2005), and all other points are from Piotto et al. (2004). Open circles are
post-core-collapse clusters. In the left panel, symbols represent clusters in different ranges of
central density from the Piotto et al. sample: log ρ0 < 2.8: open triangles; 2.8 < log ρ0 < 3.6:
filled triangles; 3.6 < log ρ0 < 4.4: stars; log ρ0 > 4.4: filled circles.
– 44 –
Fig. 21.— Frequency of BSS relative to the integrated V -band flux of detected cluster stars
(top panel) and specific frequency of blue stragglers relative as a function of radius (bottom
panel).
– 45 –
Table 1. Photometric Observation Log for NGC 5466
UT Date Filters N Exposure Time (s) Airmass
1995 May 4 B,V 1,1 60 1.01,1.12
1995 May 4 B 2 300 1.03, 1.03
1995 May 4 B,V 2,1 600 1.0,1.11,1.0
1995 May 5 B,I 2,2 300 1.03,1.01,1.02,1.01
1995 May 9 B,V ,I 1,1,1 60 1.12,1.13,1.14
– 46 –
Table 2. V -Band Luminosity Function
V logN σhigh σlow
13.532 0.5005 0.1761 0.3010
13.832 −0.1015 0.3010 1.0000
14.132 −0.1015 0.3010 1.0000
14.432 0.5975 0.1605 0.2575
14.732 0.8985 0.1193 0.1651
15.032 0.6767 0.1487 0.2279
15.332 0.6767 0.1487 0.2279
15.632 0.5976 0.1606 0.2575
15.932 0.8986 0.1193 0.1651
16.232 1.2410 0.0839 0.1041
16.532 1.0127 0.1063 0.1411
16.832 1.0451 0.1029 0.1351
17.132 1.3306 0.0764 0.0928
17.432 1.4432 0.0678 0.0804
17.732 1.4777 0.0728 0.0876
18.032 1.6136 0.0630 0.0738
18.332 1.7575 0.0540 0.0617
18.632 1.7577 0.0540 0.0617
18.932 1.9624 0.0433 0.0481
19.232 2.2928 0.0301 0.0324
19.532 2.5143 0.0236 0.0249
19.832 2.6996 0.0192 0.0201
20.132 2.7738 0.0178 0.0185
20.432 2.8830 0.0159 0.0165
20.732 2.9327 0.0151 0.0157
21.032 3.0036 0.0142 0.0146
21.332 3.0496 0.0137 0.0142
21.632 3.1179 0.0132 0.0136
– 47 –
– 48 –
Table 3. Fiducial sequence for NGC 5466
V B − V Na
22.198 0.578 518
21.999 0.564 598
21.798 0.549 724
21.596 0.532 710
21.398 0.498 673
21.200 0.470 670
21.004 0.459 653
20.802 0.450 614
20.600 0.431 568
20.400 0.418 546
20.199 0.404 470
20.001 0.395 453
19.805 0.396 382
19.599 0.403 273
19.400 0.436 235
19.206 0.495 155
19.005 0.543 84
18.823 0.586 70
18.588 0.607 43
18.401 0.616 52
18.204 0.621 40
17.989 0.636 34
17.820 0.647 31
17.586 0.654 23
17.403 0.672 20
17.194 0.677 19
16.988 0.693 11
16.784 0.722 10
16.613 0.725 6
16.400 0.752 12
16.199 0.771 16
– 49 –
Table 3—Continued
V B − V Na
16.066 0.779 5
15.825 0.809 7
15.602 0.827 4
15.407 0.857 6
15.111 0.917 1
15.006 0.930 5
14.786 0.946 2
14.590 0.986 11
14.438 1.044 2
aNumber of stars
used to determine
fiducial point
– 50 –
Table 4. RGB-MSTO Number Ratios
Sourcea TO Sample RGB Sample Y NRGB/NMSTO [Fe/H]
NGC 5466 19.682 < V < 20.282 16.982 < V < 18.482 0.162± 0.013
VR 0.235 0.132 −2.22
VR 0.235 0.130 −2.14
T 0.245 0.148 −2.22
T 0.245 0.146 −2.14
YY 0.230 0.162 −2.22
YY 0.230 0.160 −2.14
M3 18.80 < V < 19.40 16.40 < V < 18.00 0.168± 0.008
VR 0.235 0.170 −1.66
VR 0.235 0.158 −1.34
T 0.246 0.181 −1.66
T 0.248 0.170 −1.34
YY 0.230 0.185 −1.66
YY 0.230 0.162 −1.34
M5 19.13 < B < 19.73 16.33 < B < 17.93 0.110± 0.006
VR 0.235 0.106 −1.40
VR 0.235 0.097 −1.11
T 0.248 0.114 −1.40
T 0.251 0.106 −1.11
YY 0.230 0.119 −1.40
YY 0.230 0.105 −1.11
M12 18.14 < V < 18.74 15.59 < V < 17.24 0.158± 0.011
VR 0.235 0.144 −1.40
VR 0.235 0.118 −1.14
T 0.248 0.155 −1.40
T 0.251 0.144 −1.14
YY 0.230 0.150 −1.40
YY 0.230 0.137 −1.14
M30 18.33 < V < 18.93 15.78 < V < 17.43 0.214± 0.017
VR 0.235 0.174 −2.13
VR 0.235 0.153 −1.91
– 51 –
Table 4—Continued
Sourcea TO Sample RGB Sample Y NRGB/NMSTO [Fe/H]
T 0.245 0.173 −2.13
T 0.246 0.165 −1.91
YY 0.230 0.194 −2.13
YY 0.230 0.180 −1.91
aVR: Victoria-Regina models (no diffusion); YY: Yonsei-Yale models (He
diffusion); T: Teramo models (no diffusion). All models are for an age of
12 Gyr.
– 52 –
Table 5. Selected Star Populations in NGC 5466
ID ∆α(′′) ∆δ(′′) B σB V σV I σI Alternate ID Ref.
a Notes
Blue Stragglers
1 137.74 32.86 19.1477 19.0038 605 J
1 137.74 32.86 19.1446 0.0122 19.0182 0.0280 18.7606 0.0400 809 K
2 −12.18 −5.60 18.7591 0.0116 18.5972 0.0061 10313 C
2 −12.18 −5.60 18.8461 0.0147 18.7209 0.0258 18.6245 0.0504 2176 K
3 −8.68 14.99 19.1710 0.0100 18.9595 0.0059 9339 C SX Phe (3)
3 −8.68 14.99 19.4373 0.0155 19.2441 0.0296 19.1073 0.0563 2129 K
4 −77.31 83.56 19.2057 19.0546 646 J
4 −77.31 83.56 19.2266 0.0123 19.0548 0.0256 18.8465 0.0460 2880 K
5 −81.70 65.06 18.5511 18.2697 389 J
5 −81.70 65.06 18.5632 0.0121 18.2740 0.0243 17.8309 0.0255 2895 K
7 −132.96 −3.18 18.8010 18.7046 504 J
7 −132.96 −3.18 18.8482 0.0113 18.7379 0.0217 18.5538 0.0386 3289 K
8 −144.85 3.07 18.8436 18.6640 498 J
8 −144.85 3.07 18.8726 0.0120 18.6345 0.0234 18.3367 0.0298 3358 K
9 −90.90 83.38 19.1757 19.0256 626 J
9 −90.90 83.38 19.1385 0.0144 18.9711 0.0257 18.7508 0.0387 2973 K
10 −44.94 96.04 19.3627 19.1882 751 J
10 −44.94 96.04 19.4145 0.0139 19.2190 0.0261 18.9077 0.0494 2520 K
aPhotometry Sources: K: KPNO data from this paper, C: CFHT data from this paper, J: Jeon et al. (2004)
Note. — The complete version of this table is in the electronic edition of the Journal. The printed edition contains
only a sample.
	Introduction
	Observations and Data Reduction
	Calibration against Primary Standard Stars
	Calibration against Secondary Standard Stars
	Comparison with Previous Studies
	Calculation of the Luminosity Function
	Discussion
	Reddening, Metallicity, Distance Modulus, and Age
	The Color-Magnitude Diagram
	The Luminosity Function
	Relative RGB and MS Numbers
	The RGB Bump
	Mass Function Exponent
	Blue Stragglers
	Conclusions

  We present wide-field BVI photometry for about 11,500 stars in the
low-metallicity cluster NGC 5466. We have detected the red giant branch bump
for the first time, although it is at least 0.2 mag fainter than expected
relative to the turnoff. The number of red giants (relative to main sequence
turnoff stars) is in excellent agreement with stellar models from the
Yonsei-Yale and Teramo groups, and slightly high compared to Victoria-Regina
models. This adds to evidence that an abnormally large ratio of red giant to
main-sequence stars is not correlated with cluster metallicity. We discuss
theoretical predictions from different research groups and find that the
inclusion or exclusion of helium diffusion and strong limit Coulomb
interactions may be partly responsible.
  We also examine indicators of dynamical history: the mass function exponent
and the blue straggler frequency. NGC 5466 has a very shallow mass function,
consistent with large mass loss and recently-discovered tidal tails. The blue
straggler sample is significantly more centrally concentrated than the HB or
RGB stars. We see no evidence of an upturn in the blue straggler frequency at
large distances from the center. Dynamical friction timescales indicate that
the stragglers should be more concentrated if the cluster's present density
structure has existed for most of its history. NGC 5466 also has an unusually
low central density compared to clusters of similar luminosity. In spite of
this, the specific frequency of blue stragglers that puts it right on the
frequency -- cluster M_V relation observed for other clusters.

Introduction
The luminosity function (LF) is an observational tool used for analyzing the post-
main sequence evolutionary phases of low-mass (≈ 0.5-0.8M⊙) metal-poor stars in Galactic
globular clusters (GGC). Because of their age and richness, GGC typically contain hun-
dreds of stars that have evolved off the main sequence. The numbers of stars in evolved
phases are directly related to the evolutionary timescales and fuel consumed in each phase
(Renzini & Fusi Pecci 1988), so that they present us with an opportunity to test this aspect
of stellar evolution models.
The results of the most stringent tests have been mixed. Repeated studies of the metal-
poor cluster M30 (Bolte 1994; Bergbusch 1996; Guhathakurta et al. 1998; Sandquist et al.
1999) have found an excess number of red giant branch (RGB) stars relative to main sequence
(MS) stars. Stetson (1991) also uncovered an apparent excess of stars in a combined LF of
the metal-poor clusters M68, NGC 6397, and M92. However, the LFs of more metal-rich
clusters show no discrepancy (M5: Sandquist et al. 1996; M3: Rood et al. 1999; M12:
Hargis, Sandquist, & Bolte 2004). In a survey of 18 clusters, Zoccali & Piotto (2000) found
good agreement with model predictions with the possible exception of clusters at the high
metallicity end.
In this paper we present BV I photometry of NGC 5466, a high galactic latitude globular
cluster (l = 42.2◦ and b = 73.6◦), located in the constellation of Boötes (α = 14h05m27.s4,
δ = +28◦32′04′′ at a distance of R=15.9 kpc; Harris 1996). NGC 5466 is a loose cluster
(rc = 1.
′64) with extremely low metallicity ([Fe/H]= −2.22) and subject to little or no
reddening, (E(B − V ) ≃ 0) (Harris 1996).
In §2, we describe the process leading to the calibrated photometry, and compare with
previous studies of the cluster. In §3, we compare the observed color-magnitude diagram
and observed luminosity function with theoretical models, focusing on the relative number
– 3 –
of stars on the lower RGB and around the MS turnoff. Finally, in §4, we present a new
examination of the blue straggler population of NGC 5466.
2. Observations and Data Reduction
The data used in this study were obtained with the Kitt Peak National Observatory
(KPNO) 0.9 m telescope (0.′′68 pix−1) on the nights of UT dates 1995 May 4, May 5, and
May 9. A complete list of the image frames, exposure times, and observing conditions is
given in Table 1.
The images obtained on the three nights were processed using IRAF1 tasks and pack-
ages. The reduction involved subtraction and trimming of the overscan region of all images,
subtraction of a master bias frame from flats and object frames, and flat fielding of the
object frames using images taken at twilight. Profile-fitting photometry was done using the
DAOPHOTII/ALLSTAR programs (Stetson 1987).
We also reduced archival ground-based photometry of the cluster core taken with the
High-Resolution Camera (HRCam) on the 3.6 m Canada-France-Hawaii Telescope (CFHT).
The V and I images were taken 30 and 31 May 1992 (observers J. Heasley and C. Christian),
and have not previously been described in the literature. The CCD images had 1024 × 1024
pixels, 0.′′13 per pixel, and excellent seeing (0.4 - 0.5 arcsec). The images were reduced using
the archived bias and twilight flat frames, and following a procedure similar to that for the
KPNO data. This allowed us to get excellent photometry to 2 magnitudes below the turnoff
in the cluster core. These images were used entirely for blue straggler identification (see §4).
2.1. Calibration against Primary Standard Stars
The conditions at KPNO on 1995 May 9 were photometric, and Landolt standard star
fields were observed at a range of air masses to determine photometric transformation coeffi-
cients. The standard values used for the calibration were chosen from the large compilation
of Stetson (2000), which is set to be on the same photometric scale as the earlier Landolt
(1992) values.
We conducted photometry on the standard stars and isolated cluster stars using multiple
1IRAF(Image Reduction and Analysis Facility) is distributed by the National Optical Astronomy Ob-
servatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under
contract with the National Science Foundation.
– 4 –
synthetic apertures. We then used the DAOGROW (Stetson 1990) program to construct
growth curves to extrapolate measurements to a common aperture size. Using the CCDSTD
program, the standard star transformation equations were found to be:
b = B + ao + (−0.069± 0.005)(B − V ) + (0.255± 0.014)(X − 1.0)
v = V + bo + (0.027± 0.004)(B − V ) + (0.172± 0.010)(X − 1.0)
i = I + co + (−0.013± 0.005)(V − I) + (0.145± 0.018)(X − 1.0)
where X is the airmass, v, b and i are instrumental magnitudes, and V , B, and I are standard
magnitudes. These calibration equations are different than those used for our analysis of
M10 Pollard et al. (2005) and M12 Hargis et al. (2004), which were observed on the same
night, because our I−band exposures did not go as deep as the B and V exposures. As a
result, the (B − V ) color was a better choice for calibrating the V photometry down to our
faintest observed stars. The calibrated measurements for the standard stars are compared
with catalogue values in Fig. 1.
We note that there is slight evidence of trend in the residuals for the I band versus
magnitude, which might indicate nonlinearity. This impression is caused by one observation
of the PG1323-086 field. We did, however, have an additional observation of the same field
on the same night having the same exposure time that does not show the same (small) trend.
Because we do not have any reason to eliminate the frame and because its elimination has a
minimal effect on the transformation coefficients, we have decided to retain the measurements
from the image.
2.2. Calibration against Secondary Standard Stars
Aperture photometry for 165 cluster stars was used to calibrate the point-spread function
(PSF) photometry for the cluster. These secondary standard stars were chosen based on
relatively low measurement errors and location in relatively uncrowded regions of the cluster.
They were chosen from the asymptotic giant branch (AGB), upper RGB, and horizontal
branch (HB) of the cluster in order to cover the entire range of colors covered by cluster
stars.
The PSF-fitting photometry for the three nights of data was combined and averaged
after zero-point differences among the frames had been determined and corrected. The zero-
point corrections to the standard system were determined after fixing the color-dependent
terms at the values measured in the primary standard star calibration. (This was also done
in our studies of M10 and M12.) In Fig. 2, it can be seen that this procedure does not
introduce systematic color- or magnitude-dependent errors.
– 5 –
2.3. Comparison with Previous Studies
We compared our photometric data set to those of Jeon et al. (2004), Rosenberg et al.
(2000), and Stetson (2000). The magnitude and color comparisons (BV I in this study versus
V I in Stetson and Rosenberg et al., and BV in Jeon et al.) as function of magnitude and
color are shown in Figs. 3 – 5. Though our calibrated magnitudes are slightly brighter than
those of Stetson (2000), the differences are small, and there is no color trend. The offsets
compared to the Rosenberg et al. (2000) are larger, but again there are no clear color trends.
The offsets compared to the Jeon et al. (2004) data are also significant, but more notable
are slight trends with color.
2.4. Calculation of the Luminosity Function
Artificial star tests were performed to empirically measure the precision of our photom-
etry and to correct for incompleteness in the detection of stars. We followed the procedure
described by Hargis et al. (2004) for the calculation of incompleteness corrections as function
of position and magnitude.
The inputs used for producing the artificial star tests were the reduced B and V
CCD frames, PSFs for each object frame, fiducial lines, and an estimate for the initial
LF (Sandquist et al. 1996). Artificial stars were randomly placed in cells on a spatial grid
and the entire grid was then shifted randomly from run to run in order to ensure the whole
imaged field was tested (Piotto & Zoccali 1999). Each star was placed in a consistent po-
sition relative to the cluster center on each image. If a detected star was found to coincide
with the input position of an artificial star, it was added to the archive. The new images
were reduced using the same procedure applied to the original data set. In this study, a
total of 100,000 artificial stars from 50 separate runs were added. The number of artificial
stars per trial was chosen so that the effects of crowding on the photometry was qualitatively
unchanged.
The recovered artificial stars were used to calculate 1) median magnitude and color
biases (δV and δB−V , where δ = median[output − input]), 2) median external error esti-
mates (σext(V ) = median[δV −median(δV )]/0.6745 and σext(B − V )), and 3) total recovery
probabilities (F (V ), which is the fraction of the stars that were recovered with any output
magnitude) in bins according to projected radius and magnitude. The values for the above
quantities are plotted in Figs.6 – 8.
Finally, an initial estimate of the “true” LF and the error distribution, magnitude biases
and the total recovery probability (F ) were used to compute the completeness fraction f
– 6 –
(the ratio of the predicted number of stars to the actual number of observed stars). The
completeness fraction results are shown in Figure 9. We then interpolated to compute f
for the radial distance and magnitude of each detected star. For each observed star f−1
was added to the appropriate magnitude bin to determined the observed LF. (Note that the
completeness fraction was set to 1.0 for star brighter than the turnoff.) The observed LF
along with the upper and lower 1 σ error bars on log N are listed in Table 2.
3. Discussion
3.1. Reddening, Metallicity, Distance Modulus, and Age
Because NGC 5466 resides at high galactic latitude, it suffers little if any reddening.
Though Schlegel et al. (1998) found a reddening of E(B − V ) = 0.02 from the maps of dust
IR emission, we adopted E(B − V ) = 0.0 (Rosenberg et al. 2000). For our interests in this
paper, the small difference is of small importance. Most of the comparisons below between
observations and theory are relative, in which reference points (like the turnoff) are used to
determine magnitude and/or color shifts. This has the benefit of minimizing the influence
of uncertainties in reddening and distance modulus (see below).
As for abundances, there is only one high-resolution measurement for a cluster star, and
it is for the anomalous Cepheid V19. McCarthy & Nemec (1997) find [Fe/H]= −1.92±0.05,
while Pritzl et al. (2005) find [Fe/H]= −2.05 using the same data. Typically quoted metal-
licity values include [Fe/H] = −2.17 (Zinn 1980) from photoelectric photometry of integrated
light in selected filter bands, and [Fe/H] = −2.22, which was derived by Zinn & West (1984)
(ultimately from low-resolution spectral scans by Searle & Zinn 1978). When converted to
the widely-used metallicity scale of Carretta & Gratton (1997), this becomes [Fe/H] = −2.14.
More work could certainly be done on the composition of NGC 5466 stars, but the evidence
so far points to an abundance [Fe/H] . −2.0. Though the range in the above quoted metal-
licity values is relatively large for a globular cluster, the exact value is not critical for our
purposes since we will primarily be concerned with relative comparisons.
Our photometry does not extend faint enough to derive a new distance modulus from
subdwarf fitting to the main sequence. Harris (1996) obtained (m − M)V = 16.0 by cali-
brating the observed luminosity level of the horizontal branch with the relation MV (HB) =
0.15[Fe/H]+0.80 and adopting a reddening, E(B−V )=0.0 and a metallicity, [Fe/H]=−2.22.
Ferraro et al. (1999) determined distance moduli (m−M)V = 16.16 from their zero-age HB
estimate, assuming no reddening and metallicity on the Carretta & Gratton (1997) scale.
We will consider distance moduli in this range.
– 7 –
Most previous age estimates of NGC 5466’s age have it older than the recent deter-
mination of the age of the universe (13.7+0.13
−0.17 Gyr) obtained by the Wilkinson Microwave
Anisotropy Probe (WMAP) team (Spergel et al. 2006). Recent homogeneous studies of GGC
indicate that NGC 5466 is coeval with clusters of similar metallicity (Salaris & Weiss 2002;
Rosenberg et al. 2000). As a result, we will primarily consider ages in the range of 12 to 13
3.2. The Color-Magnitude Diagram
The color-magnitude diagrams (CMDs) for NGC 5466 show well-defined RGB, AGB,
and HB sequences (see Fig. 10), and stars extending from the tip of the RGB down to
V ≈ 22.5. Fiducial sequences for the MS and lower RGB were determined from the mode of
the color distribution of stars in magnitude bins. The SGB position was determined using
the magnitude distribution of the stars in color bins. The fiducial line for the rest of the
RGB was obtained from the mean color of stars in magnitude bins. The fiducial points are
listed in Table 3.
A comparison of the fiducial points derived for NGC 5466 with theoretical isochrones for
a range of ages from the Teramo (Cassisi et al. 2004), Victoria-Regina (VandenBerg et al.
2006), and Yonsei-Yale (Demarque et al. 2004) groups is displayed in Figures 11 and 12.
The isochrones have been shifted in color and magnitude (aligning the turnoff colors and
the magnitudes of the main sequence point 0.05 mag redder than the turnoff) according
to the technique of Vandenberg et al. (1990). This has the advantage of removing some of
systematic uncertainties associated with the color-Teff transformations. [In our comparisons,
we found that the Yonsei-Yale models could not match the fiducial line for any reasonable set
of input parameters when the transformations of Lejeune et al. (1998) were used. Therefore,
we only utilize models using the Green, Demarque, & King (1987) transformations. Even
then, we could not find a match with the slope of the upper giant branch for reasonable
metallicities ([Fe/H] . −1.9).] On the whole, the shape of the fiducial matches the models
well on the main sequence, subgiant branch, and lower giant branch. Neither the Teramo
nor the Victoria-Regina models include element diffusion processes, while the Yonsei-Yale
isochrones only include He diffusion. However, differences in Teff -color transformations are
likely to be the cause of some of the differences seen.
– 8 –
3.3. The Luminosity Function
The number of stars at a given luminosity in post-main-sequence phases is directly pro-
portional to the lifetime spent at that luminosity. It is well known that the LF of the RGB
probes the chemical stratification inside a star because the hydrogen abundance being sam-
pled by the thin hydrogen-fusion shell affects the rate of evolution, and hence star counts
on the RGB (Renzini & Fusi Pecci 1988). Setting aside the short pause at the RGB bump,
RGB evolution accelerates in a very regular way that is ultimately related to the structure
of degenerate core. The relationship between core mass and radius forces the fusion shell to
function at strictly controlled density and temperature conditions, which leads to a relation-
ship between core mass and luminosity. This causes the LF to be particularly sensitive to
certain physical details, which we discuss in §3.3.1 below.
Fig. 13 shows the observed luminosity function compared to theoretical LFs for the la-
beled values of metallicity, exponent of the initial mass function, and a range of age estimates
for NGC 5466, assuming our preferred distance modulus (m −M)V = 16.00. The theoret-
ical models were normalized to the observed LF at V ≈ 21.3 (sufficiently faint that stellar
evolution effects are minimized). The models agree well with the observed LF, implying an
age of approximately 12 - 13 Gyr.
3.3.1. Relative RGB and MS Numbers
Gallart et al. (2005) recently discussed theoretical luminosity functions calculated by
different groups. One of the primary differences they noted was in the number of giant stars
relative to main sequence stars. In order to show these differences in a parameter-independent
way, we follow the method of Vandenberg et al. (1990). In Fig. 14, the theoretical LFs were
shifted so that a point on the main sequence 0.05 mag redder than the turnoff color point
matched the corresponding point on the cluster fiducial line. The reason for using the point
(VTO+0.05) rather than the MSTO itself is that the MS has a significant slope and curvature
at this point, making it possible to accurately measure the point in both observational data
and isochrones (Vandenberg et al. 1990). The theoretical models were normalized to the two
bins in the observed LF on either side of the turnoff (V = 19.83 and 20.13). As can be seen,
age-related differences between the theoretical LFs nearly disappear when this procedure
is applied (see also Stetson 1991; Vandenberg et al. 1998). However, when different sets of
models are compared, there are small differences in the number of RGB stars relative to
MS stars, with the Victoria-Regina models predicting the smallest number of giants and the
Yonsei-Yale models predicting the largest.
– 9 –
To quantify the differences, we computed the ratio of the number of stars on the lower
giant branch to the number of stars near the main sequence. Pollard et al. (2005) introduced
this ratio and showed that it is insensitive to age and heavy-element abundance. For the
main sequence population, we used star counts in the two bins on either side of the turnoff
(19.682 < V < 20.282), and for the red giant branch we used the counts in the range
16.982 < V < 18.482. We derived model values from the same magnitude ranges relative to
the VTO+0.05 point on the main sequence. Values are compared in Table 4. The error in the
observed value is dominated by Poisson statistical scatter. The Yonsei-Yale models are in
best agreement with the observations, the Victoria-Regina models are out of agreement by
more than 2 σ, and the Teramo models are in between.
It is worth examining the possible causes of this difference both because it may help
improve the physics inputs for the models and because red giant stars are some of the largest
contributors to the integrated light of old stellar populations. Gallart et al. (2005) tabulated
most of the main physics inputs for the most widely-used model sets2. Earlier studies (Stetson
1991; Vandenberg et al. 1998) have shown that the LF-shifting method used above eliminates
nearly all sensitivity to model input parameters like mass function, age, convective mixing
length, and composition inputs with the exception of helium abundance, which we examine
first.
Older models (e.g. Fig. 9 of Ratcliff 1987, Fig. 7 of Stetson 1991, Fig. 3 of Vandenberg et al.
1998) seem to agree that an increase in initial helium abundance Y in non-diffusive models
by 0.1 results in an increase in the relative number of stars on the RGB (more precisely, a
reduction in the relative number of main sequence stars) by about 0.07-0.08 in logN . The
Teramo models (Y = 0.245) predict about 12% more giant stars relative to main sequence
stars compared to the Victoria-Regina models (Y = 0.235)3. This difference corresponds
to a shift of 0.05 in logN , which is about an order of magnitude too large for the helium
abundance difference.
The Yonsei-Yale models have the lowest assumed helium abundance (Y = 0.23), but
are the only set of the three that include helium diffusion. The inclusion of helium dif-
fusion reduces the age derived from the turnoff of a globular cluster by about 10-15%
2Since the Gallart et al. (2005) review was published, the Teramo group found an error in the evolution
scheme they used on the giant branch, which brings their models into better agreement with other groups.
We use their updated models in the comparisons here
3The Teramo models also assume a larger α-element enhancement ([α/Fe] = 0.4) than the Victoria-Regina
models ([α/Fe] = 0.3), which would tend to reduce the number of giants relative to main sequence stars.
However, because the relative number of RGB and MS stars is not sensitive to small differences in heavy
element abundance, this difference is probably unimportant.
– 10 –
(Proffitt & Vandenberg 1991; Straniero et al. 1997; VandenBerg et al. 2002), thanks to the
inward motion of helium. According to theoretical models (e.g. Fig. 8 of Proffitt & Vandenberg
1991), diffusion has a small effect on the LFs (∼ a few times 10−2 in logN , increasing for
increasing age), but it does increase the number of giants relative to MS stars. He diffusion
reduces the total core hydrogen fuel supply available to an MS star, but in itself this does not
strongly modify the LF, just changes the brightness of the turnoff. This magnitude change
is eliminated in our LF shifting procedure. The chemical composition profile left in the star
after it leaves the main sequence has a greater impact. Diffusion reduces the H abundance in
the fusion regions, thereby decreasing the evolutionary timescale. According to the models
of Proffitt & Michaud (1991), the changes to the He abundance profile are most considerable
immediately below the surface convection zone, and just outside the nuclear fusion regions
(where the composition gradient slows the inward settling of helium). However, over most
of the star, the changes in Y are limited to 0.01 - 0.02. Because the core portion of the
composition profile is consumed on the subgiant branch, the evolution timescales for giant
stars are only affected in a minor way, and the appearance of a deep convection zone on
the lower giant branch wipes out most of the effects of diffusion for the upper giant branch
evolution.
In spite of this, the Yonsei-Yale models have almost 23% more giants than the Victoria-
Regina models, and more than 9% more giants than the Teramo models (relative to MS
stars). The lower helium abundance in the Yonsei-Yale models compared to the other models
should partially counteract what effects helium diffusion might have had on the RGB/MS
ratio as well. Thus, it appears that neither He abundance nor He diffusion can completely
explain the differences between the Yonsei-Yale models and the other groups.
We can ask whether the LFs show similar disagreements at other metallicities. Hargis et al.
(2004) made comparisons between the Victoria-Regina and Yonsei-Yale theoretical LFs and
observational LFs for the clusters M3 (Rood et al. 1999), M5 (Sandquist et al. 1996), M12,
and M30. The overall impression from those comparisons was again that the Yonsei-Yale
models (having He diffusion) predict more giant stars relative to main-sequence stars than
do the Victoria-Regina models. In Fig. 15, we compare the LFs for these clusters with
the Teramo models. The degree of agreement or disagreement can be quantified with num-
ber ratios of lower RGB and MSTO stars, similar to the ones we computed earlier for
comparisons with NGC 5466. Our calculations are shown in Table 4. As can be seen, uncer-
tainties in the metallicity scale have some effect on the comparisons with the observations.
The Carretta & Gratton (1997) scale has higher [Fe/H] values than the Zinn & West (1984)
scale, and thus results in lower number ratios.
Fig. 16 shows the results of comparing the observed ratios with the models for different
– 11 –
[Fe/H] scales. On the Zinn & West 1984 scale (right panels), the observed values seem to
be in agreement to within about 1 − 1.5σ for most of the models, with the exception of
the the lowest metallicity clusters (M30 and NGC 5466) and the lowest helium abundance
(Victoria-Regina) models. On the Carretta & Gratton 1997 scale, the Yonsei-Yale models
have the best overall agreement, although the Teramo models only deviate noticeably for
the lowest metallicity clusters. The Victoria-Regina models predict too few giants for all of
the clusters.
The differences from model to model (as opposed to models versus observation) point
toward deficiencies elsewhere in the physics or computational algorithms used in the stel-
lar evolution codes. 4 The RGB LF is a robust prediction of the models because there is
a strong core mass — luminosity relationship: the conditions in the hydrogen fusion shell
of the giant are strongly dependent on the structure of the degenerate core and are al-
most independent of the details of the mass or structure of the envelope. As a result of
this, we can focus on factors affecting core structure. (As a non-standard physics exam-
ple, Vandenberg et al. 1998 describe the way in which core rotation relieves a giant star of
some of the need to support itself by gas pressure, which reduces the core temperature and
lengthens the evolutionary timescale.) Because model-to-model differences appear even on
the faint end of the giant branch, we can set aside factors that only become important to the
structure of the star near the tip of the giant branch [such as neutrino losses and conductive
opacities; see Bjork & Chaboyer 2006, for example], even though there are significant theo-
retical uncertainties in these quantities. Nuclear reaction rates in the fusion shell can also
be neglected, partly because the uncertainties in the reactions appear to be relatively small
Adelberger et al. (1998), but also because small changes in the reaction rates require only
tiny changes in the shell temperature to get the same energy production. This leads us to
examine the equation of state (EoS) in the core.
Although the behavior of degenerate electrons is thought to be very well understood,
their interactions with nuclei can have a measureable effect on the pressure. Particles of like
charge tend to cluster together, which modifies the free energy of the gas and reduces the gas
pressure for given density and temperature. Harpaz & Kovetz (1988) looked at the effects
of the inclusion of Coulomb interactions on giant stars, and their results are corroborated
by those of Cassisi et al. (2003). They found that for a given core mass the fusion shell
temperature was higher when the Coulomb interactions were included, which leads to faster
processing of hydrogen. Thus this is another example (like core rotation) where modification
of the pressure support of the core affects the evolutionary timescales, which results in
4For a comparison of these physical inputs for the different theoretical groups, see Table 1 of Gallart et al.
(2005).
– 12 –
changes to the luminosity function. The Coulomb corrections to the pressure become more
important with increasing density for the core, but are small compared to the contribution
of the degenerate electrons.
All of the model sets we have considered here incorporate Coulomb interactions in some
form. The Teramo group used the most sophisticated “EOS1” version of the FreeEOS5,
which incorporates Coulomb corrections in a form that matches limits in both the weak
(Debye-Hückel) and strong (once-component plasma) Coulomb interaction limits as well
as (less importantly) electron exchange interactions. The strong interaction limit is most
relevant for giant star cores since the strong interaction parameter
where ζ is the rms nuclear charge and r0 is the average internuclear distance.
The Yonsei-Yale group used the OPAL EoS tables (Rogers et al. 1996), but falls back
on the group’s older EoS [e.g. (Guenther et al. 1992)] for conditions for high densities and
temperatures outside the OPAL tables. While the most recent OPAL tables probably contain
the most complete physical description of the Coulomb effect, the OPAL tables they used
(Y.-C. Kim, private communication) were computed prior to recent improvements to account
for relativistic electrons (Rogers & Nayfonov 2002), and as a result cut off at log ρ > 5.0.
The Yale EoS at higher densities only includes the Coulomb effect in the weak Debye-Hückel
limit, which for the highest densities in the core. The Victoria-Regina models also use
a modified version of the EFF EoS (Eggleton et al. 1973), with a correction for Coulomb
corrections in the weak Debye-Hückel limit (VandenBerg et al. 2000).
The differences in the implementation of the Coulomb effect may explain the fact that
the Teramo models generally predict more giants (relative to the main sequence) than the
Victoria-Regina models do. However, the smaller Coulomb corrections in the Yonsei-Yale
models would tend to result in fewer giants than the Teramo models (although the effects of
helium diffusion work in the opposite direction). So, we are unable to completely reconcile
the differences in the luminosity functions from the three groups.
Obviously more detailed study is needed by all of the modelling groups to identify the
causes of the differences, but such a study is beyond the scope of this paper. Still, we
believe that helium diffusion and strong interaction Coulomb corrections are physical effects
that should be considered first. There is, for example, good evidence from helioseismology
5FreeEOS is available at http://freeeos.sourceforge.net/, and the discussion of the implementation of the
Coulomb effect can be found at http://freeeos.sourceforge.net/coulomb.pdf.
http://freeeos.sourceforge.net/
http://freeeos.sourceforge.net/coulomb.pdf
– 13 –
for helium diffusion in the Sun Bahcall et al. (1995), despite the surface convection and
meridional flow (e.g., Hathaway 1996). It is expected that helium diffusion should also act
in globular cluster stars. A detailed study of the effect of equation of state uncertainties
has yet to be done [see, for example, Bjork & Chaboyer (2006) for a study of uncertainties
in other physical inputs]. Use of FreeEoS would make a study of equation of state effects
most stringent since it appears to be capable of modelling the most sophisticated tabular
EoS (OPAL), while also having the flexibility to allow individual bits of the physics to be
“turned off”.
As a final warning about the observations, we should remember the LF of the clus-
ter M10. Pollard et al. (2005) found that unusual variations in numbers of RGB stars at
different brightness levels in M10 (a virtual twin to M12). In particular there seemed to
a significant excess in the number of stars near the RGB bump in brightness, while the
lower RGB appeared normal (compared to Victoria-Regina and Yonsei-Yale models). A
similar excess may be present in the RGB LF of M13 (Cho et al. 2005). These kinds of
variations cannot be explained by the “global” physics that should apply to all globular
cluster stars. These anomalies point toward fluctuations in the stellar initial mass function
or composition-dependent effects.
3.3.2. The RGB Bump
A second feature of the LF presented here is a noticeable RGB bump. Typically, the
RGB bump appears as a peak in the differential LF and as a change of slope in the cumulative
LF (CLF). The bump provides a measure of the maximum depth reached by the outer
convection zone during first dredge-up since it is the result of a pause in the star’s evolution
when the shell fusion source begins consuming material of constant, lower helium content
(Fusi Pecci et al. 1990). Unfortunately, the number of stars occupying the bump gets smaller
and the luminosity of the bump increases as the metallicity of the cluster decreases, making
the bump harder to detect in metal-poor clusters. A small peak appears in our differential
LF at V ≈ 16.2, and a significant (2.5 − 3.5σ) change in slope occurs at the same position
as the peak in the differential LF, as shown in Fig. 17.
The relative brightness of the bump can be measured by comparing to the V -magnitude
of the HB at the level of the RR Lyrae instability strip ∆V
HB = Vbump−VHB (Ferraro et al.
1999). This indicator is a function of the total metallicity and the age of the cluster: an
increase in metallicity and/or a decrease in age are accompanied by a decrease in luminosity
of the bump (Ferraro & Montegriffo 2000). We find Vbump = 16.20 ± 0.05 mag, and VHB =
16.52 ± 0.11 (from interpolation between the average magnitudes of non-variable HB stars
– 14 –
at the blue and red ends of the RR Lyrae instability strip), giving ∆V
HB = −0.32 ± 0.12.
In the compilation of Ferraro et al. (1999), a zero-age HB reference point was calculated
using the relation VZAHB = VHB +0.106[Fe/H]
+0.236[Fe/H]+ 0.193. Ferraro et al. found
VZAHB = 16.62 ± 0.10, which is consistent with the value obtained here (VZAHB = 16.65 ±
0.11). Our value of ∆V
ZAHB = −0.45 ± 0.12 is considerably lower than tabulated values
for other clusters with similar metallicities (M68: −0.60 ± 0.07; M92: −0.65 ± 0.12; M15:
−0.65 ± 0.09). In a separate compilation, Zoccali et al. (1999) measured a smaller value
ZAHB = −0.45 ± 0.11 for M15, in better agreement with the value for NGC 5466. (The
difference is primarily because Zoccali et al. measured the bump position to be 0.16 mag
fainter than Ferraro et al. .) Clearly there is still some need for more precise comparisons of
bumps in metal-poors clusters with theory.
We believe, however, that the brightness of the bump should ultimately be judged using
hydrogen-fusing stars as references because it avoids any effects of the poorly-understood
physical processes (such as the helium flash and/or mass loss) associated with the creation
of an HB star. Using the cluster LF (as seen in Figure 14), we again find that the observed
RGB bump is fainter than model values by at least 0.3 mag when the models are shifted
to match the cluster’s main sequence. Hargis et al. (2004) did similar comparisons between
theoretical models and luminosity functions for M3, M5, M12, and M30 taken from the
literature. With the exception of M30 (because the bump could not be identified), the
position of the bump relative to the turnoff region agreed well with theory. NGC 5466 is
thus the most metal-poor cluster this comparison has been done for. So at present we are left
with the question of whether this might result from the cluster’s low metallicity, or whether
we have been the unfortunate victims of a fluctuation in the number of giant stars in this
low-mass cluster. We therefore encourage the examination of the luminosity function of more
massive metal-poor clusters to settle the question.
3.3.3. Mass Function Exponent
Two recent papers (Belokurov et al. 2006; Grillmair & Johnson 2006) reported the dis-
covery of tidal streams covering many degrees around NGC 5466 in Sloan Digital Sky Sur-
vey images. Gnedin & Ostriker (1997) examined the Milky Way globular clusters and found
NGC 5466 to be a cluster that has probably been strongly affected by disk shocking in the
recent past. In our examination of the LF, we found a rather low value for the global main se-
quence mass function slope. The mass function for a cluster is typically expressed as a power
law (N(M) ∝ M−(1+x)), where the slope x = 1.35 is the standard Salpeter value. Generally,
the present-day power-law index x varies from cluster to cluster. The mass function slopes
– 15 –
that best fit the upper LF of NGC 5466 around and above the MSTO have −1 . x . 0.
(Note that the best fit slope does depend on the models being used: the Yonsei-Yale models
require a flatter slope than the Victoria-Regina and Teramo models.) Such a shallow mass
function slope is unusual for a metal-poor cluster. For example, the cluster NGC 5053 has
similar metallicity, position relative to the galactic center and plane, and density structure,
but still has a steep x ∼ 2 mass function (Fahlman et al. 1991). Djorgovski et al. (1993)
found that mass function slopes in the range of 0.5 ≤ M
≤ 0.8 are influenced primarily by
the cluster’s position in the galaxy, and to some extent by cluster metallicity. Based on both
of those factors, NGC 5466 should have a larger mass function slope (x ∼ 3 according to the
multivariate formula in Djorgovski et al. 1993). Like other halo clusters, NGC 5466’s orbit
is quite eccentric and will take the cluster more than 30 kpc away from the Galactic center
(Dinescu et al. 1999), but it is currently on its way back into the halo after two relatively
recent passes through the Galactic disk. Recent losses of low-mass stars may explain the
recent identification of strong tidal tails near the cluster by Belokurov et al. (2006).
4. Blue Stragglers
Blue stragglers (BSSs) were first identified by Sandage (1953) in the globular cluster
M3. These stars are more massive than the turnoff mass and occupy the space in the CMD
just bluer and brighter than the MSTO. Blue stragglers are found in clusters, and relatively
more frequently in lower-luminosity clusters (Ferraro et al. 1993; Preston & Sneden 2000;
Piotto et al. 2004; Sandquist 2005). From the various models proposed for the formation
mechanism of BSSs, the “collision” theory (involving strong gravitational interactions be-
tween previously unassociated single or binary stars) and the “mass-transfer” theory (in
which the more massive star in a binary evolves and during its expansion transfers mass to
its companion) are the strongest possibilities. There is a continuing interest in the study of
BSSs because they may provide insight into the recent dynamical history of a cluster.
In order to identify BSSs over the entire observed area of the cluster out to a radius
of 11.′6, we used photometry from three datasets. In the core of the cluster we used the
CFHT data presented here for the first time. Outside of the CFHT field, we used the BV
photometry of Jeon et al. 2004, which covered a field 11.′6 on a side centered on the cluster.
Finally, we used our KPNO data for the least crowded outskirts of the cluster. Even though
NGC 5466 is a very low density cluster, the spatial resolution of the KPNO data was such
that blends of stars would have resulted in the spurious identification of 10 objects as BSS
in the intermediate portion of the field.
48 BSS candidates were identified in NGC 5466 by Nemec & Harris (1987), all located
– 16 –
between 0.′1 and 5.′6 from the cluster center. In spite of the low cluster density, we find new
BSS candidates at all radii and luminosity levels, and find several of their candidates are
spurious. According to the CFHT photometry, the object with ID 45 from Nemec & Harris
is a blend of several fainter stars, none of which is a BSS. In addition, IDs 6 and 24 were
identified as blends of stars using the Jeon et al. (2004) dataset. Our BSS list is presented
in Table 5. The list includes the nine known SX Phoenicis stars (ID 27, 29, 35, 38, 39, and
49, Nemec & Mateo 1990; ID 3 (SX Phe 3), 36 (SX Phe 2), and 50 (SX Phe 1), Jeon et al.
2004) and the three eclipsing binaries (ID 19, 30, and 31; Mateo et al. 1990). New straggler
candidates were given ID numbers that build upon the Nemec & Harris (1987) list. Figure
18 shows the CMDs used to select the 94 identified BSSs in each of the three datasets.
In order to use the BSSs to constrain cluster dynamics, we compared the normalized
cumulative radial distribution of the BSSs to the population of the giant branch, as shown
in Fig. 19. Nemec & Harris (1987) found a 97.8% probability that their BSS sample was
more centrally concentrated than red giants in the same magnitude range. Because their
photometry was taken in conditions of poorer seeing (compared to our CFHT photometry
and that of Jeon et al.), their samples are likely to be somewhat incomplete near the cluster
center.
Our RGB sample contains 350 stars with magnitude V < 18.5. Kolmogorov-Smirnov
(K−S) probability tests were used to test the hypothesis that both populations were drawn
from the same parent population. The K−S probability that the BSSs are drawn from
the same radial distribution as the RGB population is 8.1 × 10−7, and 2.4 × 10−4 for the
comparison with the HB population. By contrast there is a probability of 0.27 that the RGB
and HB samples are drawn from the same population. The concentration of BSSs toward
the cluster center as compared to the RGB and HB samples is consistent with the idea that
they are more massive than individual RGB stars, and as a result have been segregated by
mass deeper within the cluster potential well.
Piotto et al. (2004) recently used samples of stragglers from the cores of 56 globular
clusters to show that there was a strong correlation between FHBBSS = NBSS/NHB and inte-
grated cluster V magnitude, and a weaker anti-correlation with central density. Sandquist
(2005) examined an additional 13 low-luminosity globular clusters using similar selection
criteria. NGC 5466 is an interesting cluster in relation to these samples because it has an
integrated luminosity that puts it at the faint end of the Piotto et al. sample (MVt = −6.96;
Harris 1996), but with a central density that is nearly an order of magnitude lower than
any of their clusters [log(ρ0/(LV,⊙pc
−3)) = 0.88] but comparable to clusters in the Sandquist
sample. To put NGC 5466 in the context of the Piotto et al. and Sandquist samples, we
selected a subset of our BSSs that satisfied the selection criteria in those studies (brighter
– 17 –
than the MSTO, and bluer than the MSTO by 0.05 in B − V color). From mode fitting to
the turnoff region in the Jeon et al. (2004) and CFHT data, we find (B−V )TO = 0.367 and
(V − I)TO = 0.511. A color offset of 0.05 in B − V corresponds to an offset of about 0.075
in V − I (VandenBerg & Clem 2003) for NGC 5466’s metallicity. We find that 75 BSSs are
brighter than the cluster turnoff (VTO = 19.99±0.05) and 0.05 bluer than the cluster turnoff
in B − V . We have identified 97 HB stars in our datasets for NGC 5466, which gives a
specific frequency FHBBSS = 0.77± 0.12 (with the error estimate from Poisson statistics).
When compared to the Piotto et al. values (see Fig. 20), NGC 5466 falls within the
general trend versus MVt despite the cluster’s low central density. On the other hand, NGC
5466 has a lower FHBBSS value than other clusters of similar central density (but lower total
luminosity). As discussed by Sandquist (2005), this provides additional evidence that the
plateau in FHBBSS seen for clusters with log ρ0 . 2.5 is a result of the correlation between cluster
integrated magnitude and central density. The lowest luminosity clusters in the Sandquist
sample (E3 and Palomar 13) have central densities comparable to that of NGC 5466, but
BSS frequencies that are several times higher. Another moderate-luminosity, low-density
cluster (NGC 5053; Hiner et al., in preparation) similar to NGC 5466 shows a comparably
low straggler frequency. BSSs produced via purely collisional means are not likely to show
this kind of behavior. More likely is the scenario proposed by Davies et al. (2004) in which
binary stars that would normally produce BSSs are destroyed earlier in the cluster’s history.
More direct observational support for that hypothesis is needed though — for example, a
detailed study of the variation of the binary star fractions as a function of integrated cluster
magnitude.
Fig. 21 shows that the number and frequency
RBSS =
NBSS/N
Lsample/L
sample
of BSSs relative to the integrated V -band flux (derived from a King model profile) as a func-
tion of radius. Both frequencies increase toward the cluster center, and neither shows signs
of rising toward larger radii. As recent studies of denser clusters show (M3: Ferraro et al.
1993; M55: Zaggia et al. 1997; 47 Tuc: Ferraro et al. 2004; NGC 6752: Sabbi et al. 2004),
the BSS frequency generally decreases at intermediate radii and rises again at larger dis-
tances. However, the cluster Palomar 13 (Clark et al. 2004), which has a central density
similar to NGC 5466, shows no sign of an increase in straggler frequency at large distance.
In more massive clusters, the minimum in the BSS frequency is reached approximately
where the timescale for dynamical friction equals the age of the cluster (Warren et al. 2006).
A similar calculation for the current structure of NGC 5466 indicates that this occurs at about
270′′(about 2.8rc). This appears to be in the outer reaches of the core straggler distribution.
– 18 –
Because it is likely that NGC 5466 has lost a significant fraction of its mass, we expect
that the current density structure of the cluster has not existed throughout its history and
that NGC 5466 might have been able to dynamically relax stragglers to its core from larger
distances earlier in its history. This may be showing that the global BSS population differs
significantly between low-density/low-mass clusters and high-density/high-mass clusters. A
lack of stragglers at large distance may be signature of large-scale tidal stripping of the
cluster, which would remove both stragglers that would normally have formed in primordial
binaries in the outer reaches of the cluster and ones that formed in the core but were given
velocity kicks into orbits that would take them into the outer reaches.
The case against a rise at large radius in Palomar 13 is stronger because the cluster
has been surveyed out to 19 core radii, while in NGC 5466, we have only surveyed out to
about 10 core radii (or 7.5 half-mass radii). Still, NGC 5466 probably should have an even
more concentrated distribution of stragglers if its current density structure has existed for
most of its history. In more massive clusters, the secondary rise in straggler frequency is
observed between 8 and 10 rc. Unfortunately, further study of the stragglers in NGC 5466
will probably be complicated by the strong tidal tails observed in the cluster.
5. Conclusions
Examinations of the luminosity functions of globular clusters continue to produce inter-
esting tests of astrophysics. In this study, we found that NGC 5466 has a luminosity function
that is in better overall agreement with theoretical models than the anomalous cluster M30,
which has a similar low metallicity. In addition, we found that the relative numbers of red
giant and main sequence stars may produce a fairly sensitive test of the physics near the
core of red giants — specifically, helium diffusion and Coulomb interactions. However, we
are not yet able to fully explain the differences between sets of theoretical models.
Recent discoveries of large tidal tails associated with NGC 5466 suggest that this cluster
has been strongly disrupted by interactions with the Galaxy. Our measured flat (−1 . x . 0)
main-sequence luminosity function is unusual for a low-metallicity halo cluster. It is, however,
consistent with the emerging picture of mass-segregation followed by tidal stripping.
We have thoroughly re-examined the blue straggler population in the cluster, and de-
tected a total of 94. The radial distribution of stragglers is clearly more centrally concen-
trated than the RGB and HB populations. The frequency of blue stragglers in the cluster is
relatively low — consistent with the observed anti-correlation between frequency and cluster
luminosity, in spite of the cluster’s very low central density.
– 19 –
We would like to thank the anonymous referee for helpful comments on the manuscript,
Y. Jeon for providing us with an electronic copy of his photometric dataset, Y.-C. Kim for
information on the Yonsei-Yale isochrones, and S. Cassisi for providing us with access to
the Teramo set of models. This work has been funded through grants AST 00-98696 and
05-07785 from the National Science Foundation to E.L.S. and M.B.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 24 –
Fig. 1.— Photometric residuals (in the sense of this study minus those of Landolt 1992 and
Stetson 2000) of primary standard stars. The median residuals are listed in the panels with
the semi-interquartile range (half the magnitude difference between the 25% and 75% points
in the ordered list of residuals) given in parentheses.
– 25 –
Fig. 2.— Photometric residuals (in the sense of the final PSF photometry minus standard
aperture photometry values) of secondary standard stars.
– 26 –
Fig. 3.— Residuals (in the sense of this study minus Stetson 2000) from the star-by-star
comparison. The median residuals are listed in the panels with the semi-interquartile range
(see Fig.1) given in parentheses.
– 27 –
Fig. 4.— Residuals (in the sense of this study minus Rosenberg et al. 2000) from the star-
by-star comparison. The median residuals and the plots versus color have been restricted
to brighter stars (V < 20 and I < 19) to make the comparisons clearer. The numbers in
parentheses are the semi-interquartile ranges (see Fig.1).
– 28 –
Fig. 5.— Residuals (in the sense of this study minus Jeon et al. 2004) from the star-by-star
comparison. The median residuals and the plots versus color have been restricted to brighter
stars (B < 20 and V < 19.5) to make the comparisons clearer. The numbers in parentheses
are the semi-interquartile ranges (see Fig.1).
– 29 –
Fig. 6.— External V magnitude errors σext(V ) as a function of radius and magnitude
determined from artificial star tests, with exponential fits shown by the solid lines.
– 30 –
Fig. 7.— Magnitude biases δ(V ) determined from artificial star tests as a function of radius
and magnitude.
– 31 –
Fig. 8.— Total recovery probability F (V ) determined from artificial star tests as a function
of radius and magnitude.
– 32 –
Fig. 9.— Completeness fraction f(V ) determined from artificial star tests as a function of
radius and magnitude.
– 33 –
Fig. 10.— Color-magnitude diagrams for all stars measured in the KPNO and CFHT images.
The BV fiducial (Table 3) is also plotted in the left panel.
– 34 –
Fig. 11.— Comparison of the observed fiducial sequence of NGC 5466 with the isochrones
of the Teramo, Victoria-Regina, and Yonsei-Yale groups. The isochrones have been shifted
horizontally so that the turnoff colors align, and shifted vertically to align the main sequence
point 0.05 mag redder than the turnoff. On the giant branch, the ages increase from the
reddest to the bluest isochrone.
– 35 –
Fig. 12.— Same as Fig. 11, except for more metal-rich models.
– 36 –
Fig. 13.— Comparison of the observed V−band LF of NGC 5466 with theoretical models
of the Yonsei-Yale, Teramo, and Victoria-Regina groups assuming (m−M)V = 16.
– 37 –
Fig. 14.— Comparison of the observed V−band LF of NGC 5466 with theoretical models
of the Victoria-Regina, Yonsei-Yale, and Teramo groups using magnitude shifts that bring
the main sequence point 0.05 mag redder than the turnoff into alignment. The models have
been normalized to the two bins on either side of the turnoff (V = 19.94).
– 38 –
Fig. 15.— Comparison of the observed LFs of M3, M5, M12, and M30 with theoretical
models of the Teramo group using magnitude shifts that bring the main sequence point 0.05
mag redder than the turnoff into alignment. The models have been normalized to bins on
either side of the turnoff.
– 39 –
Fig. 16.— Fractional difference between the observed RGB-MS number ratios (for M5, M12,
M3, M30, and NGC 5466, from left to right) and the theoretical predictions from the Yonsei-
Yale, Teramo, and Victoria-Regina models. The left panels use the Carretta & Gratton
(1997) metallicity scale, and the right panels use the Zinn & West (1984) scale. The sense
is (observed − theoretical) / observed.
– 40 –
Fig. 17.— The cumulative luminosity function for bright RGB stars derived from the pho-
tometry of Jeon et al. (2004; 286 stars) and from the KPNO dataset (338 stars) presented
here. Dotted lines show fits to the data for stars above and below the position of the apparent
bump.
– 41 –
Fig. 18.— Blue straggler selection for NGC 5466. The stars plotted in each panel show the
entire sample used for the selection: stars from Jeon et al. (2004) in the middle panel are
only those stars outside the CFHT field, and KPNO stars in the right panel are only those
outside the Jeon et al. field. Open squares show stragglers identified by Nemec & Harris
(1987), and open circles are new candidates.
– 42 –
Fig. 19.— Normalized cumulative radial distributions for RGB stars (dashed line), HB stars
(dotted line), and BSSs (solid line).
– 43 –
Fig. 20.— Relative frequencies of blue stragglers as a function of cluster absolute magnitude
and central density. The solid square is NGC 5466, the open squares are globular clusters
from Sandquist (2005), and all other points are from Piotto et al. (2004). Open circles are
post-core-collapse clusters. In the left panel, symbols represent clusters in different ranges of
central density from the Piotto et al. sample: log ρ0 < 2.8: open triangles; 2.8 < log ρ0 < 3.6:
filled triangles; 3.6 < log ρ0 < 4.4: stars; log ρ0 > 4.4: filled circles.
– 44 –
Fig. 21.— Frequency of BSS relative to the integrated V -band flux of detected cluster stars
(top panel) and specific frequency of blue stragglers relative as a function of radius (bottom
panel).
– 45 –
Table 1. Photometric Observation Log for NGC 5466
UT Date Filters N Exposure Time (s) Airmass
1995 May 4 B,V 1,1 60 1.01,1.12
1995 May 4 B 2 300 1.03, 1.03
1995 May 4 B,V 2,1 600 1.0,1.11,1.0
1995 May 5 B,I 2,2 300 1.03,1.01,1.02,1.01
1995 May 9 B,V ,I 1,1,1 60 1.12,1.13,1.14
– 46 –
Table 2. V -Band Luminosity Function
V logN σhigh σlow
13.532 0.5005 0.1761 0.3010
13.832 −0.1015 0.3010 1.0000
14.132 −0.1015 0.3010 1.0000
14.432 0.5975 0.1605 0.2575
14.732 0.8985 0.1193 0.1651
15.032 0.6767 0.1487 0.2279
15.332 0.6767 0.1487 0.2279
15.632 0.5976 0.1606 0.2575
15.932 0.8986 0.1193 0.1651
16.232 1.2410 0.0839 0.1041
16.532 1.0127 0.1063 0.1411
16.832 1.0451 0.1029 0.1351
17.132 1.3306 0.0764 0.0928
17.432 1.4432 0.0678 0.0804
17.732 1.4777 0.0728 0.0876
18.032 1.6136 0.0630 0.0738
18.332 1.7575 0.0540 0.0617
18.632 1.7577 0.0540 0.0617
18.932 1.9624 0.0433 0.0481
19.232 2.2928 0.0301 0.0324
19.532 2.5143 0.0236 0.0249
19.832 2.6996 0.0192 0.0201
20.132 2.7738 0.0178 0.0185
20.432 2.8830 0.0159 0.0165
20.732 2.9327 0.0151 0.0157
21.032 3.0036 0.0142 0.0146
21.332 3.0496 0.0137 0.0142
21.632 3.1179 0.0132 0.0136
– 47 –
– 48 –
Table 3. Fiducial sequence for NGC 5466
V B − V Na
22.198 0.578 518
21.999 0.564 598
21.798 0.549 724
21.596 0.532 710
21.398 0.498 673
21.200 0.470 670
21.004 0.459 653
20.802 0.450 614
20.600 0.431 568
20.400 0.418 546
20.199 0.404 470
20.001 0.395 453
19.805 0.396 382
19.599 0.403 273
19.400 0.436 235
19.206 0.495 155
19.005 0.543 84
18.823 0.586 70
18.588 0.607 43
18.401 0.616 52
18.204 0.621 40
17.989 0.636 34
17.820 0.647 31
17.586 0.654 23
17.403 0.672 20
17.194 0.677 19
16.988 0.693 11
16.784 0.722 10
16.613 0.725 6
16.400 0.752 12
16.199 0.771 16
– 49 –
Table 3—Continued
V B − V Na
16.066 0.779 5
15.825 0.809 7
15.602 0.827 4
15.407 0.857 6
15.111 0.917 1
15.006 0.930 5
14.786 0.946 2
14.590 0.986 11
14.438 1.044 2
aNumber of stars
used to determine
fiducial point
– 50 –
Table 4. RGB-MSTO Number Ratios
Sourcea TO Sample RGB Sample Y NRGB/NMSTO [Fe/H]
NGC 5466 19.682 < V < 20.282 16.982 < V < 18.482 0.162± 0.013
VR 0.235 0.132 −2.22
VR 0.235 0.130 −2.14
T 0.245 0.148 −2.22
T 0.245 0.146 −2.14
YY 0.230 0.162 −2.22
YY 0.230 0.160 −2.14
M3 18.80 < V < 19.40 16.40 < V < 18.00 0.168± 0.008
VR 0.235 0.170 −1.66
VR 0.235 0.158 −1.34
T 0.246 0.181 −1.66
T 0.248 0.170 −1.34
YY 0.230 0.185 −1.66
YY 0.230 0.162 −1.34
M5 19.13 < B < 19.73 16.33 < B < 17.93 0.110± 0.006
VR 0.235 0.106 −1.40
VR 0.235 0.097 −1.11
T 0.248 0.114 −1.40
T 0.251 0.106 −1.11
YY 0.230 0.119 −1.40
YY 0.230 0.105 −1.11
M12 18.14 < V < 18.74 15.59 < V < 17.24 0.158± 0.011
VR 0.235 0.144 −1.40
VR 0.235 0.118 −1.14
T 0.248 0.155 −1.40
T 0.251 0.144 −1.14
YY 0.230 0.150 −1.40
YY 0.230 0.137 −1.14
M30 18.33 < V < 18.93 15.78 < V < 17.43 0.214± 0.017
VR 0.235 0.174 −2.13
VR 0.235 0.153 −1.91
– 51 –
Table 4—Continued
Sourcea TO Sample RGB Sample Y NRGB/NMSTO [Fe/H]
T 0.245 0.173 −2.13
T 0.246 0.165 −1.91
YY 0.230 0.194 −2.13
YY 0.230 0.180 −1.91
aVR: Victoria-Regina models (no diffusion); YY: Yonsei-Yale models (He
diffusion); T: Teramo models (no diffusion). All models are for an age of
12 Gyr.
– 52 –
Table 5. Selected Star Populations in NGC 5466
ID ∆α(′′) ∆δ(′′) B σB V σV I σI Alternate ID Ref.
a Notes
Blue Stragglers
1 137.74 32.86 19.1477 19.0038 605 J
1 137.74 32.86 19.1446 0.0122 19.0182 0.0280 18.7606 0.0400 809 K
2 −12.18 −5.60 18.7591 0.0116 18.5972 0.0061 10313 C
2 −12.18 −5.60 18.8461 0.0147 18.7209 0.0258 18.6245 0.0504 2176 K
3 −8.68 14.99 19.1710 0.0100 18.9595 0.0059 9339 C SX Phe (3)
3 −8.68 14.99 19.4373 0.0155 19.2441 0.0296 19.1073 0.0563 2129 K
4 −77.31 83.56 19.2057 19.0546 646 J
4 −77.31 83.56 19.2266 0.0123 19.0548 0.0256 18.8465 0.0460 2880 K
5 −81.70 65.06 18.5511 18.2697 389 J
5 −81.70 65.06 18.5632 0.0121 18.2740 0.0243 17.8309 0.0255 2895 K
7 −132.96 −3.18 18.8010 18.7046 504 J
7 −132.96 −3.18 18.8482 0.0113 18.7379 0.0217 18.5538 0.0386 3289 K
8 −144.85 3.07 18.8436 18.6640 498 J
8 −144.85 3.07 18.8726 0.0120 18.6345 0.0234 18.3367 0.0298 3358 K
9 −90.90 83.38 19.1757 19.0256 626 J
9 −90.90 83.38 19.1385 0.0144 18.9711 0.0257 18.7508 0.0387 2973 K
10 −44.94 96.04 19.3627 19.1882 751 J
10 −44.94 96.04 19.4145 0.0139 19.2190 0.0261 18.9077 0.0494 2520 K
aPhotometry Sources: K: KPNO data from this paper, C: CFHT data from this paper, J: Jeon et al. (2004)
Note. — The complete version of this table is in the electronic edition of the Journal. The printed edition contains
only a sample.
	Introduction
	Observations and Data Reduction
	Calibration against Primary Standard Stars
	Calibration against Secondary Standard Stars
	Comparison with Previous Studies
	Calculation of the Luminosity Function
	Discussion
	Reddening, Metallicity, Distance Modulus, and Age
	The Color-Magnitude Diagram
	The Luminosity Function
	Relative RGB and MS Numbers
	The RGB Bump
	Mass Function Exponent
	Blue Stragglers
	Conclusions
