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\begin{document}

\vspace*{\fill}

\title{THE LUMINOSITY FUNCTIONS OF OLD AND INTERMEDIATE-AGE GLOBULAR
CLUSTERS IN NGC 3610\/\altaffilmark{1}}

\author{Bradley C.\ Whitmore}

\affil{Space Telescope Science Institute\\
3700 San Martin Drive\\
Baltimore, MD 21218\\
Electronic mail: whitmore@stsci.edu}

\author{Fran\c cois Schweizer}

\affil{Carnegie Observatories\\
813 Santa Barbara Street\\
Pasadena, CA 91101-1292\\
Electronic mail: schweizer@ociw.edu}

\author{Arunav Kundu}

\affil{Michigan State University\\
Physics \& Astronomy Department\\
East Lansing, MI 48824-1116\\
Electronic mail: akundu@pa.msu.edu}

\author{Bryan W.\ Miller}

\affil{AURA/Gemini Observatory\\
Casilla 603\\
La Serena, Chile\\
Electronic mail: bmiller@gemini.edu}

\vspace{1in}
\centerline{\titlelarge To be published in the July issue of the \emph{Astronomical Journal}}
\received{5 February 2002}
\accepted{21 March 2002}
\sluginfo
\vfill

\altaffiltext{1}{Based on observations with the NASA/ESA \textit{Hubble Space 
Telescope}, obtained at the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy,
Inc., under NASA contract NAS5-26555.}

\begin{abstract}
The Wide Field and Planetary Camera~2 on board the \textit{Hubble Space
Telescope} has been used to obtain high-resolution images of NGC~3610,
a dynamically young elliptical galaxy in a group environment. These
observations supersede shorter, undithered HST observations where an
intermediate-age population of globular clusters was first
discovered. The new observations show the bimodal color distribution
of globular clusters more clearly, with peaks at \vi~= 0.95 and
1.17. The luminosity function of the blue, metal-poor population of
clusters in NGC~3610 turns over, consistent with a Gaussian
distribution with a peak $M_V\approx-7.0$, similar to old
globular-cluster populations in elliptical galaxies. The red,
metal-rich population of clusters has a luminosity function which is
more extended toward both the bright and faint ends, as expected for a
cluster population of intermediate age. It is well fit by a power law
$\phi(L)dL \propto L^{\alpha} dL$, with an exponent of $\alpha = -1.78
\pm 0.05$, or $\alpha = -1.90 \pm 0.07$ when corrected for
observational scatter.  A Kolmogorov-Smirnov test confirms the
significant difference between the luminosity functions of the red and
blue clusters, with a probability of less than 0.1\% that they come
from the same population.  A comparison with the Fall \& Zhang
cluster disruption models shows marginal agreement with the observed
data when comparing both the luminosity functions and the mean color
distributions, although there are differences in detail.  In
particular, there is no clear evidence of the predicted turnover at
the faint end, although deeper observations will be required to make a
definitive test. A by-product of the analysis is the demonstration
that, at any given metallicity, the peak of the luminosity function should remain nearly constant from 1.5--12~Gyr, since the effect of the disruption of faint
clusters is almost perfectly balanced by the fading of the
clusters. This may help explain the apparent universality of the peak
of the globular cluster luminosity function.
\end{abstract}

\keywords{galaxies: globular clusters, galaxies: interactions, galaxies: elliptical, galaxies: individual (NGC 3610)}

\section{INTRODUCTION}

Until recently, all globular clusters were considered to be among the
oldest objects in the universe, and various theories were
developed to explain their formation some 15~Gyr ago. However, the
discovery of young massive compact clusters in merging and
starbursting galaxies (e.g., Holtzman \etal\/ 1992, 1996; Whitmore \etal\/
1993; Whitmore \& Schweizer 1995; Meurer \etal\ 1995, Schweizer \etal\/ 1996,
Zepf \etal\/ 1999) provides a means to study the formation of what appear to 
be young globular clusters in the \textit{local} universe.

Young merger remnants (e.g., $\la1$ Gyr) are generally easy to identify,
both because of their disturbed morphologies and the burst of
star formation that accompanies the interaction. Intermediate-age merger
remnants (e.g., 1--5~Gyr) are more difficult to identify since the
main body has had time to relax into a relatively symmetric configuration
and the newly-formed stellar populations have had time to fade and
redden (Schweizer \& Seitzer 1992). In particular, newly formed metal-rich
globular clusters with ages in the range 1--2~Gyr will have roughly
the same \vi\/ colors as old metal-poor globular
clusters (see Whitmore \etal\/ 1997; hereafter Paper~I), making it
difficult to distinguish the two.  Fortunately, the intermediate-age
clusters will still be 1--2~mag brighter than the old clusters.

Recently, a number of studies have identified intermediate-age
globular clusters in several merger remnants. This helps provide the
``missing link'' between young merger remnants and elliptical
galaxies.  For example, in Paper~I we estimated that NGC~3610 suffered an
interaction $4\pm2.5$~Gyr ago.  The case for NGC~1700 was less
clear, although the data were compatible with an age of $\sim4$~Gyr.
A recent study by Brown \etal\/ (2000) yields an estimated age of 2--5~Gyr 
for NGC~1700 globulars.  Similar results have been obtained for
NGC~6702, with Georgakakis, Forbes, \& Brodie (2001) estimating an age
of 2--5~Gyr for its red globular clusters. Currently, the best example 
of an early-type galaxy with intermediate-age globular clusters is 
probably NGC~1316, where photometric and spectroscopic observations of 
its red clusters yield ages of $3\pm0.5$~Gyr (Goudfrooij \etal\/ 2001a,b). 

The luminosity functions for clusters in young mergers, such as ``The
Antennae,'' are power laws with indices of $\alpha\approx -2$
(Whitmore \etal\/ 1999b; Whitmore 2001).  This distribution is markedly
different from the peaked Gaussian profiles found for luminosity
functions of old globular clusters (e.g., Figure~3 of Zhang \& Fall
1999). However, various destruction mechanisms---such as 2-body
evaporation, bulge and disk shocking, and stellar mass loss---should 
remove the less massive, more diffuse clusters as the galaxy ages. 
Hence, this process may eventually yield a peaked distribution of 
clusters similar to what is seen for old globular clusters.  
Intermediate-age remnants, such as NGC~3610 (Scorza \& Bender 1990, 
Schweizer \& Seitzer 1992), offer the possibility of observing this 
process in action.  While the blue, metal-poor globular clusters should 
have a distribution similar to old globular clusters in elliptical 
galaxies, peaking at $M_V\approx-7.2$ with a dispersion of $\sigma\approx1.3$ 
(Whitmore 1997), the red, metal-rich clusters should extend to both brighter 
and fainter luminosities and may show a dropoff one or two magnitudes fainter 
than is seen for the old globular clusters (Fall \& Zhang 2001, Goudfrooij
\etal\/ 2001b).

In the following we adopt a Hubble Constant of $H_0 = 75$~km~s$^{-1}$
Mpc$^{-1}$ and a mean corrected group velocity of 2251~km~s$^{-1}$
(Paper~I), which places NGC~3610 at a distance of 30.0~Mpc, corresponding 
to a distance modulus of 32.39~mag.  At this distance the projected scale 
is $1'' = 146$~pc, and 1~pixel of the Planetary Camera ($0\farcs04554$) covers 
6.63~pc.

\section{OBSERVATIONS AND REDUCTIONS}

\subsection{WFPC2 Observations}

Our previous WFPC2 observations of NGC~3610 consisted of $2\times500$~s 
exposures in F555W and $2\times600$~s exposures in F814W. The
exposures were undithered. The new Cycle~7 observations (Proposal ID~=
7468), obtained on November~3, 1999, consisted of $4\times1200$~s
exposures in F555W and $4\times1400$~s exposures in F814W. In both
passbands we observed at two positions (offset from each other by 
$\sim5.5$~pixels in the Planetary Camera (hereafter PC) and $\sim2.5$~pixels 
in the Wide Field Camera (hereafter WF)) to permit subpixel
dithering. The DRIZZLE software developed by Fruchter \& Hook (1998)
was used to combine the images in each passband, with parameters set
to \textit{pixfrac}~=~0.6 and \textit{scale}~= 0.5 (i.e., pixel size).  
The factor of $\sim5$ increase in the total exposure time, the use of 
dithering, and the use of a new search algorithm allowed us to reach a 
factor of $\sim2$ fainter in luminosity than with our 1994 observations, 
as can be seen by comparing the new completeness functions of Figure~1 with
the corresponding functions of Figure~7 in Paper~I.

\subsection{New Search Algorithm}

Our primary goal for the Cycle~7 observations of NGC~3610 was to push
the detection threshold as faint as possible, in order to determine
whether the luminosity function for the intermediate-age clusters
continues as a power law to fainter magnitudes or turns over, as
predicted by theory (e.g., Fall \& Zhang 2001).
We therefore developed a new search algorithm in order to reach
magnitudes as faint as possible. The first step of this algorithm
uses the DAOFIND task from the daophot package (Stetson 1987) to
identify potential sources down to a very faint limit (2~$\sigma$ of
background) on the $V$, $I$, and summed $V+I$ images.
This results in a relatively large number of false detections in the
bright inner regions of the galaxy. Such detections are then filtered
out by requiring a $\geq5~\sigma$ detection on a median-subtracted $V+I$
image (with aperture radii for object/inner background/outer background 
set to 2/2/4 pixels on the dithered image, corresponding to 1/1/2 pixels 
on the original image). The algorithm then performs photometry of the 
surviving candidate sources on both the drizzled $V$ and $I$~images. 
Sources are further selected by requiring a $\ge5~\sigma$ detection in 
one of the two bands, and values for the concentration index  (the 
difference in magnitude using apertures with~1 and 6~drizzled-pixel 
radii on the PC, or~1 and 4~drizzled pixels on the WF) between 1.4 and 
2.05 on the WF images and greater than 1.8 on the PC image. This choice of concentration indices filters out both hot pixels and background galaxies
(see Miller et~al.\ 1997 for an example of how the size criteria work
for undithered images). Note that there is no upper limit for the 
concentration index on the PC because objects very near the center have 
large apparent values of the index, due to the very strong galaxy 
background. A visual inspection and simple statistics suggest that most
or all of these objects are globular clusters rather than background
galaxies. 

Figure~2 shows a median-subtracted F555W image of the central region of 
NGC~3610.  The apparent warp of the central disk first described in Paper~I 
is prominent. The red clusters with \vi~= 1.025--1.5 are circled, while the 
blue clusters with \vi~= 0.5--1.025 are marked by squares. The bright clusters 
from Table~1 are marked with larger symbols and labeled. 
A comparison with our earlier HST data shows that 22 of the 23
clusters in the overlap region with Figure~3b of Paper~I are recovered.
In addition, 11 new candidate clusters are found, primarily in the
inner region where our new search technique makes it possible to identify 
clusters in regions of higher background. These newly discovered objects
include nine of the 50 brightest clusters (i.e., \#1, 4, 8, 14, 15, 16,
29, 47, and 48). Eight of these nine clusters are red, emphasizing the
preponderance of bright red clusters near the center of the galaxy. 

\vspace{-6pt}
\subsection{Photometry}

Aperture corrections were determined by measuring magnitudes through 
various apertures for several well exposed clusters on each of the four 
chips.  The aperture corrections for the PC were $-0.304$~mag in $V$ and 
$-0.363$~mag in $I$, using aperture radii for object/inner
background/outer background of 6/10/16 pixels on the dithered image 
(i.e., 3/5/8 pixels on the original image). The corrections on the WF 
were $-0.312$~mag in $V$ and $-0.370$~mag in $I$, using aperture radii
of 4/10/16 pixels on the dithered image. Small chip-to-chip corrections 
were also applied using the values in Table~28.1 of the HST Data Handbook 
(Voit 1997).

A comparison of our new photometry with the $V$ magnitudes of 40 bright 
clusters found earlier (Paper~I, Table~4) shows a median difference of 
0.10~mag, with Paper~I values being fainter. The comparison is especially 
poor for four clusters very near the center of the galaxy, where differences 
in $V$ can be as large as 1~mag. Although we realized in Paper~I that these 
clusters had large uncertainties (i.e., error estimates ranging from 0.44 
to 1.05~mag), the main reason for this difference now appears to be our use 
of larger apertures for both the objects and the background in the older
observations. The very strong background gradients in the inner regions and 
the larger sky annuli resulted in our overestimating the background in the 
Paper~I photometry.  After removing the outliers near the center of the 
galaxy the dispersion of the differences in $V$ is 0.09~mag, with a mean 
difference 0.07 (Paper~I values fainter).  The comparison for \vi\ colors 
is better, with a mean difference of only 0.03~mag (Paper~I values redder) 
and a dispersion of 0.09~mag.

Completeness tests were performed for five background levels on the PC and 
four background levels on the WFC by using the task \textit{addstar} in the 
DAOPHOT package. This program adds artificial objects derived by using high 
S/N images of isolated clusters from the same chip. Figure~1 shows the 
resulting completeness functions. The completeness thresholds used in the 
present paper are defined as the magnitude at which only half the artificial 
objects are identified.  Corrections for non-optimal charge transfer 
efficiency on the CCDs of WFPC2 were applied using the formulae by Whitmore, 
Heyer, \& Casertano (1999). Finally, the instrumental magnitudes were 
transformed to the Kron-Cousins system via the formulae by Holtzman \etal\/ 
(1996).

\vspace{-6pt}
\section{ANALYSIS}

\centerline{\it 3.1 Color Distribution}

Figure~3 shows the new \vi\/ vs.\ $V$ color-magnitude diagram for NGC~3610 
clusters. This diagram looks quite similar to the corresponding diagram 
of Paper~I, but now extends to a fainter detection limit of $V\approx26.5$ 
at 50\% completeness. We again find a clear trend for the brighter clusters 
to be redder.

Figure~4 shows histograms of \vi\/ indices of candidate clusters within 
50$''$ from the center of NGC~3610.  The \textit{left panel} shows
all candidate clusters brighter than $V=26.5$ while the \textit{right
panel} shows only those brighter than $V=25$.  Note that the clusters
in the PC (i.e., the area shaded black) show clearly bimodal color
distributions in either case, while in the combined PC\,+\,WF area the
brighter clusters show bimodality more cleary, presumably
because of the higher signal-to-noise.  This diagram was
obtained as follows.  All candidate clusters within 50$''$ from the
center and with \sigvi~$\leq 0.4$~mag were binned in 0.05-mag
intervals and corrected for contamination by background objects.  The
latter correction was derived by selecting objects beyond 85$''$ from
the center according to the same selection criteria, smoothing their
color distribution with a 7-bin triangular weight function to diminish
small-number noise, and subtracting their surface-number density from
that of the clusters within the central 50$''$.  The corrected numbers
of clusters is shown as a solid line in Figure~4, while the numbers
before background correction are indicated by a dotted line.  Since
the background-object selection region beyond 85$''$ presumably still
contains some halo globular clusters, the correction for contamination
by background objects is a maximum, and the true color distribution of
globulars in NGC~3610 must lie somewhere between the solid and dotted
lines (likely close to the solid lines).

The most central dozen of the selected clusters all lie close to, or 
within the, central warped stellar disk (Figure~2). Although all but two 
of these twelve clusters look round and symmetric, one might question 
whether some of them are disk clumps or noise of uniform color and, 
therefore, contribute unduly to the red peak of the bimodal color 
distribution. To check for this possibility, we excluded these twelve 
clusters by requiring that the level of the surrounding background in 
$V$ be less than 130 counts per pixel.  The resulting color distributions 
looks nearly identical to Figure~4.  We conclude that the very pronounced 
red peak of the central clusters is not an artifact of disk noise, but 
simply reflects the strong central concentration of this subpopulation of
globulars.

The bimodality is more pronounced than in Paper~1, perhaps because of 
smaller measuring errors due to the longer exposures and dithered data. 
We used the KMM test developed by Ashman, Bird, \& Zepf (1994) to 
objectively estimate the probability of a bimodal distribution. A wide 
range of selection criteria were employed to test the robustness of the
estimates.  In essentially all cases the distribution was found to
be bimodal, with probabilities ranging between 93\% and 97\% if we 
restrict the sample to $0.7<$~\vi~$<1.5$, $\sigma(V-I) < 0.3$, and use
projected distances from the center of less than 20$''$ (n~= 39), 30$''$
(n~= 57), and 40$''$ (n~= 74). The mean values for the two peaks of the
distributions fall in the ranges \vi~= 0.94--0.96 and 1.16--1.17 for 
these three spatial subsamples, very similar to the values found for 
many elliptical galaxies (e.g., Kundu \& Whitmore 2001).  Roughly 30\% 
of the clusters appear to be members of the bluer, metal-poor population, 
according to the KMM test.  If we extend the sample to larger projected 
distances the bimodality probabilities become smaller (e.g., 82\% for 
$R<50''$ and 74\% for the full field of view), presumably because of 
increasing contamination by background objects in the outer regions, and 
perhaps also because of larger photometric errors for the fainter clusters, 
which tend to be found in the outer regions.
  
A close look at Figure~3 shows that most of the clusters in the brightest 
2--3~mag range belong to the red, metal-rich population, with colors in the 
range \vi~= 1.025--1.30. However, at a magnitude of  $V\approx25$ it appears 
that the dominant population is the blue, metal-poor clusters, with colors 
in the range 0.80--1.025. We note that a typical value of $M_V$ for an old
globular cluster population is $-7.2$ (Whitmore 1997). Hence we expect a 
peak in the blue population at $M_V\approx25.2$, given the distance modulus 
of $m-M = 32.39$.  Near the completeness limit at $V \approx 26.5$, the 
metal-rich population again appears to dominate. This alternating dominance 
of red and blue clusters is consistent with expectations from a superposition 
of an old metal-poor population of globular clusters and an intermediate-age 
metal-rich population of globular clusters, if the latter has a luminosity 
function extending farther to both brighter and fainter magnitudes (i.e.,
more similar to a power law).

The statistical significance of this trend can be better quantified by
computing the mean \vi\/ as a function of $V$, as shown in Figure~5. We
first trim the distribution to only include objects in the range $0.8< V-I 
< 1.3$, since Figures~3 and~4 show that most candidate clusters fall in 
this range. Figure~5 \textit{(top)} shows the \vi\/ means without any 
restriction on the radius. This diagram supports the first visual 
impression from the color-magnitude diagram: the brightest clusters at 
$V \approx 22$ have a mean \vi~$=1.15\pm0.04$.  The mean then migrates to 
\vi~$=1.05\pm0.02$ at $V \approx 25$, and finally shifts back toward the 
red with \vi~$=1.09\pm0.02$ at $V=26.25$. Excluding clusters in the range 
$V=24$--26, the data represent a 5~$\sigma$ deviation from a value of 
\vi~$= 1.05$.

If we restrict the sample to objects within $r<20''$ (middle panel in 
Fig.~5), we once again find the brighter clusters with redder colors. 
However, objects at fainter magnitudes are missing due to the brighter 
completeness correction limit of the PC.

Finally, if we restrict the sample to objects within the annulus of
$20'' < r < 50''$ (bottom panel in Fig.~5), we again find the
bell-shaped curve indicative of redder mean colors at both the bright 
and faint ends. In addition, we are able to observe to fainter magnitudes 
since the objects lie on the WF chips. Here we find a continuation of the 
trend to redder colors, with mean \vi~$=1.11\pm0.02$ at $V = 27.2$.

\subsection{Luminosity Functions of Blue and Red Clusters}

The derivation of the luminosity function (hereafter LF) of a cluster
population on a strongly varying galaxy background presents a serious
challenge.  The detected-cluster counts need to be corrected for
incompleteness as a function of both the cluster magnitude and the
local level of galaxy background.  Yet, the experimentally determined
completeness functions of Figure~1 (\S2.3) show a strong dependence on
the background level and differ sharply between the PC and WF cameras.
As a result, piecing together an incompleteness-corrected luminosity
function from clusters imaged by the two different cameras and
lying on backgrounds of very different brightness is nearly impossible.

The problem is alleviated if one restricts oneself to clusters
imaged on the WF chips.  Not only are the background variations much
reduced (since NGC~3610 was centered on the PC), but equal detection
probability is reached at $V$~magnitudes nearly 1.0~mag fainter on
the WF images than on the PC image.  Therefore, we restrict our
discussion of the LF of globular clusters in NGC 3610 to the LF
determined from clusters imaged on Chips WF2--WF4. The LF on the PC is
consistent with the following results, but the low number statistics
make it impossible to draw any firm conclusions.

Figure~6 shows the luminosity functions of blue and red globular
clusters determined separately.  The LFs corrected for contamination
by background objects are shown as solid lines and are shaded black
above the 50\%-completeness limits (marked by dashed vertical lines).
For comparison, the LFs \textit{un}corrected for background contamination
are shown as dotted lines.

These luminosity functions were determined as follows.  First, candidate
clusters were separated into two subsamples of blue ($0.80 \leq
V\!-\!I \leq 1.025$) and red ($1.025 < V\!-\!I \leq 1.30$) clusters.
For each of these subsamples, all candidate clusters imaged on WF chips
and lying within a limiting radius $R_{\rm lim}\!= 50''$, 65$''$, or 80$''$
from the center were selected, subject to the conditions that 
$19 \leq V \leq 28$, \sigvi~$< 0.60$~mag, and the galaxy-background level
be $0.1 \leq V_{\rm bkg} \leq 100$ counts/pixel.  Each cluster was
then corrected for incompleteness by dividing its count of one by the
completeness fraction corresponding to its $V$~magnitude and background
level.  This fraction itself was obtained from the functions shown in
Figure~1 by bilinear interpolation. The corrected (i.e., weighted) 
cluster count was then added to the appropriate bin in $V$~magnitude, 
with bin sizes of typically 0.25~mag.

The resulting raw luminosity functions were further corrected for
contamination by fore- and background objects (i.e., stars and distant
galaxies).  To that effect, objects were selected at distances
$R_{\rm bkg} > 85''$ from the center and subject to the same color,
magnitude, and galaxy-background selection criteria as the objects in
the inner search zones. The ``luminosity functions'' of these objects 
were determined in a similar manner as described above, then smoothed 
by a 7-bin triangular weighting function to diminish small-number noise, 
scaled to the areas of the inner search zones, and subtracted from the 
above raw LFs.  It is these corrected LFs that are shown as solid lines 
(and shaded black above the 50\% completeness limits) in Figure~6.

As Figure~6 illustrates, the luminosity functions of blue and red
globular clusters in NGC~3610 differ dramatically.  While the LF for
the blue globulars is approximately Gaussian, that for the red
globulars is more nearly power-law shaped.  When compared to the blue
clusters, there are more red clusters both at the bright end and near
the 50\%-completeness limit, consistent with the mean colors discussed
in \S3.1 and shown in Figure~5.  The LFs shown are for 205 candidate
globular clusters (64 blue, 141 red) on the WF chips out to $R_{\rm
lim}\!= 80''$.  The same shape difference is observed for the LFs of
clusters out to $R_{\rm lim}\!= 50''$ and 65$''$, though with more
noise due to smaller cluster numbers.

The statistical significance of this result can be better quantified
by performing a Kolmogorov-Smirnov test on the populations of red
globular clusters and blue globular clusters, as defined above.
Figure~7 shows the results based on the completeness- and
background-corrected luminosity functions from Figure~6.  The top
panel shows the fraction of each distribution as a function of 
$V$~magnitude for the clusters on the WF chip.  The value of the largest
discrepancy is shown on the figure, as is the probability that the two
populations come from the same distribution (i.e., only a 1.1 \%
chance). We note that the nature of the trend, with more red globular
clusters at both the bright and faint ends, tends to cancel out the
value of the largest discrepancy. The two lower panels in Figure~7
show the results if we break the cumulative distributions in two at
the cross-over point, $V\approx25$. The largest fractional
discrepancies are now $\approx0.4$. While the small number of
clusters in the bright part of the WF sample results in a relatively
large value of the probability (2.1\%), the faint sample now shows a
very small probability (0.09\%) that the red and blue globular
clusters are drawn from the same sample.

\subsection{Comparison with the Fall \& Zhang (2001) Cluster Disruption
Models}

Fall and Zhang (2001) have developed models for the disruption of
globular clusters, which include two-body relaxation, gravitational
shocks, and stellar evolution.   Figure~4 in Fall \& Zhang (2001) 
demonstrates how an initial power-law or Schechter  mass function will
evolve toward a peaked distribution, typical of an old globular
cluster population. As the fainter clusters are destroyed, the peak of
the distribution shifts toward larger mass. However, the luminosities
of the clusters fade at almost exactly the same rate (e.g., see Figure~13
in Paper~I), hence compensating for the effect. The net result is that, at 
a given metallicity, the peak luminosity remains almost constant with time 
in the range 1.5--12~Gyr. This may help explain the apparent universaility 
of the globular cluster luminosity function, as demonstrated by various 
studies (e.g., Harris, 1991)

Figure~8 demonstrates this effect.  We combined the Fall \& Zhang (2001) 
model that employs a Schechter initial mass function (i.e., the bottom 
left panel in their Figure~4) and the prediction for fading from the 
Bruzual \& Charlot (1996, unpublished) stellar evolution models in order
to predict the relative shifts between the peaks of the various distributions. 
Solar metallicity is used for the young and intermediate-age clusters while 
0.02~solar metallicity is used for the old (12~Gyr) population. The models are normalized at $V=25$. The top panel shows the luminosity function on a log 
scale while the bottom panel shows it on a linear scale. The predicted peaks 
for the 1.5, 3, and 6~Gyr models are essentially identical.  The only reason
for the shift in the peak of the 12~Gyr old population is the lower metallicity. 
If we were to use solar rather than 0.02~solar metallicity for the 12~Gyr 
population, we would find that the peaks of the distributions vary by only 
$\sim0.10$~mag over the full range from 1.5--12~Gyr.

The tail of the predicted LF at the faint end is nearly identical for all three intermediate ages, but the bright end shows some variation. In particular, the 
1.5~Gyr population is predicted to have more bright clusters than the 12~Gyr old clusters while the 6~Gyr population is predicted to have fewer. Based on this fact alone it would appear that the intermediate-age clusters in NGC~3610 would fall
in the range 1.5--3~Gyr. We note that the turnover in the 12~Gyr population is predicted to be about 1.5~magnitudes brighter than our completeness limit of 
$\sim26.6$, but the predicted turnover in the intermediate-age population is only $\approx0.5$~magnitudes brighter. Figure~6 does not show any clear evidence for a turnover of the red population out to the completeness limit, although there is
a hint that it may flatten out beyond this point. Deeper observations will be 
required to make a definitive test, however.

While the young clusters in recent mergers  appear to have roughly solar 
metallicity (e.g., Schweizer \& Seitzer, 1998), the metallicity for older 
remnants is more uncertain, and may tend to be lower since the merger event 
happened further in the past. If we adopt 0.4~solar for the metallicity of 
the 1.5--6~Gyr populations we would find that the peak luminosities move toward brighter magnitudes by $\sim0.3$~mag, reducing only slightly the difference 
between the metal-poor 12~Gyr population and the metal-rich younger populations.

These models can also be used to predict how the values of mean (\vi\/) change 
with magnitude. Figure~9 shows the predicted mean colors, based on the models 
in Figure~8. We find the same qualitative behavior as shown by our data for 
NGC~3610 in Figure~5, with redder colors for both bright and faint clusters 
and a mean color $\approx1.05$ in the intermediate range. The best agreement 
appears to be with the 1.5~Gyr models. However, we note that the bluest mean 
colors are predicted to be in the range $V \approx23$--24, while the observed 
peak is $V \approx 25.4$. One possible explanation for this difference might 
be the fact that the models assume a  zero-age burst of cluster formation, 
while there is good evidence---both observationally (Whitmore et~al.\ 1999b) 
and theoretically (Mihos et~al.\ 1993)---that clusters can be produced for 
roughly half a billion years during a merger. 

\subsection{Fits and Simulations of the Blue and Red  Populations}

Figure~10 shows a Gaussian fit to the blue clusters (upper panel) and
a variety of power-law and Fall \& Zhang (2001) model fits to the red
clusters (lower panel).  The Gaussian fit to the blue population
yields a peak at $V = 25.44 \pm 0.10$ and a width $\sigma = 0.66
\pm0.19$.  This corresponds to a value of M$_V = -6.95$, similar to
the value found for normal elliptical galaxies (e.g., Whitmore 1997
finds M$_V = -7.21 \pm 0.26$).  We note, however, that the value of
$\sigma$ is considerably smaller than typically found for giant
elliptical galaxies (e.g., 1.1--1.5, according to Kundu \& Whitmore
2001).  Fixing $\sigma$ to these values yields peaks in a range from
$V = 25.61 \pm 0.15$ (using $\sigma = 1.1$) to $V = 26.04 \pm 0.3$
(using $\sigma = 1.5$).  However, as Figure~10 shows, even the fit
with $\sigma = 1.1$ is clearly too wide, hence we adopt the original
value of $V = 25.44$ as our best-fit.  

The lower panel of Figure~10 includes a best-fit power law $\phi(L)dL
\propto L^{\alpha} dL$, with an exponent of $\alpha = -1.78 \pm 0.05$ 
(thick solid line), and a set of Fall \& Zhang (2001) models ranging 
from zero age to 12~Gyr. The best fitting Fall \& Zhang model is the 
1.5~Gyr model (dotted line). The fits to the 0 and 3~Gyr models are 
quite similar while the fits to the 6 and 12~Gyr population are
clearly unreasonable.  Hence, the simple power law provides the best
overall fit to the red population, partly because the bright end
slopes of the Fall \& Zhang models using the Schechter initial mass
distribution appear to be a bit too steep.

Fall \& Zhang (2001) also calculated models using a shallower power-law 
of index $-2$ for the initial mass distribution (i.e., the top left
diagram in their Figure~4). Figure~11 shows the fits to the data using
these models. While the agreement is better at the bright end, the fit
on the faint end is essentially unchanged.  In particular, there is no
clear evidence for the predicted flattening.  However, the current
data is not deep enough to make a definitive test.

Goudfrooij \etal\/ (2001a) claimed that the luminosity function for
the red clusters in the 3~Gyr old merger remnant NGC~1316 has a
shallower slope, with $\alpha = -1.2\pm0.3$. However, a comparison
of their Figure~13a with our Figure~6 shows that the two luminosity
functions are actually quite similar. It appears that an error was
made in the calculation of $\alpha$. Goudfrooij (2002; private
communication) has corrected the problem and now finds $\alpha \approx
-1.7\pm0.1$ for the red clusters in NGC~1316, which is similar to
the value we find in NGC~3610. We note that the fits are actually
computed by using the log Number vs.\ $V$ correlation (e.g., the bottom
plot in Figure~10) and then converting it to the form
$\phi(L)dL \propto L^{\alpha} dL$ via the formula $\alpha = 2.5 \times
\beta +1$, where $\beta$ is the slope in the log Number vs.\ $V$~diagram.

One of the difficulties of extracting the luminosity function for the
red and blue clusters is the necessity of defining color bins which
are smaller than the observational uncertainies at faint magnitudes. 
For example, this means that an intrinsically blue cluster may fall 
outside the $0.80<V<1.025$ range simply due to large observational 
measuring errors. Conversely, an intrinsically red cluster may be 
counted as a blue cluster because it is scattered into the blue bin.

We can correct for this effect by using simulations similar to those
developed in Paper~I. These are designed to approximately match the 
color-magnitude diagram, the total luminosity function, and the color 
histogram for the brighter clusters. We then use these simulations 
to determine correction fractions for the blue and red populations 
as a function of magnitude.

For the blue clusters we adopt a Gaussian mass function with parameters 
designed to approximately match the fit shown in the upper panel of 
Figure~10, an age of 15~Gyr, and a metallicity [Fe/H]~$= -1.3$. This 
results in a mean value of $V-I = 0.95$.  For the red clusters we adopt 
a power-law mass function with $\alpha = -1.8$, an age of 6~Gyr, and 
metallicity [Fe/H]~= 0.0. This results in a mean value of $V-I = 1.17$.  
We scale the observational uncertainies so that they mimic the scatter 
in the color-magnitude diagram and color histogram.  The resulting age 
determination of 6~Gyr is consistent with our estimate of $4\pm2.5$~Gyr 
from Paper~I, but is larger than the estimate of 1.5~Gyr based on a 
comparison with the Fall \& Zhang (2001) models. However, we note that 
the uncertainties in both estimates are roughly a factor of two, hence 
there is no serious discrepancy in the comparison.

Figure 12 shows the color magnitude diagram for the simulation. This
demonstrates how the data points for some blue and red clusters are
scattered into regions outside the appropriate color bins. We note
that Figure~12 looks somewhat different than Figure~3 for two reasons. 
First, the open and filled symbols in Figure~12 are the intrinsic blue 
and red clusters while in Figure~3 they are the clusters on the PC and 
WF. Second, Figure~3 includes background objects that are not included 
in the simulation.

Figure 13 shows both the intrinsic (dotted line) and apparent (solid
line) luminosity functions for the simulation from Figure~12. This
demonstrates how observational scatter can affect our determinations
of the LFs for the blue and red populations.  In particular, the scatter  
results in an underestimate in the slope of the power law for the red 
population, although the effect is relatively minor (i.e., the value of 
$\alpha$ changes from $1.77\pm0.06$ to $1.90\pm0.07$).

\section{SUMMARY}

New, deeper, dithered observations using the WFPC2 on board the 
\textit{Hubble Space Telescope} have been used to extend our study of 
NGC~3610, an elliptical galaxy that is a likely intermediate-age merger 
remnant. Our primary results are the following.
\begin{enumerate}
\item The inner globular clusters show a clear bimodal color
distribution, with peaks at \vi~$= 0.95$ and 1.17. The KMM test
developed by Ashman, Bird, \& Zepf (1994) yields probabilities for
bimodality ranging between 93\% and 97\% if we restrict the
sample to have  projected distances from the center of less than 
20$''$ (n~= 39), 30$''$ (n~= 57), and 40$''$ (n~= 74). Bimodality 
probabilities become smaller in the outer regions (e.g., 74\% for 
the full field of view), presumably because of increasing 
contamination by background objects and larger photometric errors 
for fainter objects.

\item The luminosity function of the blue, metal-poor population (i.e.,
$0.8<$~\vi~$\leq1.025$) of clusters in NGC~3610 turns over, with a peak 
$M_V \approx -7$, similar to values typical for old globular-cluster 
populations in elliptical galaxies.

\item The red, metal-rich population ($1.025\leq$~\vi~$<1.3$) of
clusters has a luminosity function which is more extended toward both
the bright and faint ends, as expected for an intermediate-age cluster
population.  This is evident in both the luminosity function and the
distribution of mean colors.  The red population is well fit by a
power law $\phi(L)dL \propto L^{\alpha} dL$, with an exponent of
$\alpha = -1.78 \pm 0.05$, or $\alpha = -1.90 \pm 0.07$ when corrected 
for observational scatter using a simulation of the data. A 
Kolmogorov-Smirnov test indicates that the probability that the red 
and blue clusters come from the same population in NGC~3610 is less 
than 0.1\%.

\item A comparison with the Fall \& Zhang (2001) cluster disruption
models shows marginal agreement with the observed data when comparing 
both the luminosity functions and the mean color distributions. For 
example, the model predicts the bluest mean colors should occur in the 
range $V \approx23$--24 while the observed peak occurs at $V\approx25.4$. 
The models also predict a flattening and turnover of the peak in the LF 
of the red clusters at $V\approx26$. While there is no clear evidence of 
the predicted turnover, deeper observations will be required to make a 
definitive test.

\item A by-product of the analysis is the demonstration that, at any given 
metallicity, the peak of the luminosity function should remain nearly constant
from 1.5--12~Gyr, since the effect of the disruption of faint clusters is 
almost perfectly balanced by the fading of the clusters. This may help explain 
the apparent universality of the peak of the globular cluster luminosity function. 
\end{enumerate}

\acknowledgements
We thank Paul Goudfrooij and Michael Fall for useful discussions. This work 
was supported by NASA grant GO-07468.01-A.  Partial support by the NSF 
through Grant AST~99-00742 to F.S.\ is also gratefully acknowledged. Partial 
support to B.W.M.\ was provided by the Gemini Observatory, which is operated 
by the Association of Universities for Research in Astronomy, Inc., on behalf 
of the international Gemini parthership of Argentina, Australia, Brazil, 
Canada, Chile, the United Kingdom and the United States of America. A.K.\ 
acknowledges support from NASA LTSA grant NAG5-11319, and from NASA grant 
HST-AR-08755.04-A.

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\begin{figure}%1
\centering
\includegraphics[width=4in,angle=-90]{fig1.eps}
\caption{Completeness curves as determined from artificial
star experiments for different background levels on the PC and WF.
The background levels are given in units of DN (Data Number).}
\end{figure}

\begin{figure}%2
\centering
\includegraphics[width=3.5in,angle=-90]{fig2.ps}
\caption{Median-subtracted image in F555W showing the inner
region of NGC~3610. Squares are blue clusters while circles are
red clusters. Larger symbols are used for the 50 brightest
clusters.}
\end{figure}

\begin{figure}%3
\centering
\includegraphics[width=3.5in,angle=-90]{fig3.eps}
\caption{\vi\/ vs.\ $V$ color-magnitude diagram for cluster
candidates in NGC~3610. Open circles are used for the objects on the
PC while filled circles are used for the WF.}
\end{figure}

\begin{figure}%4
\centering
\includegraphics[width=3.25in]{fig4.ps}
\caption{Color distributions of NGC 3610 candidate clusters within 50$''$
from the center; all clusters (solid lines) and clusters on PC chip only
(shaded black). The dotted lines show clusters before correction for
background-object contamination.  \textit{Left panel} shows all candidate
clusters brighter than $V=26.5$, while \textit{right panel} shows only
those brighter than $V=25$.  Note that the clusters in the PC area
show clearly bimodal color distributions in either case, while
in the combined PC\,+\,WF area the brighter clusters show bimodality
more clearly.}
\end{figure}

\begin{figure}%5
\centering
\includegraphics[width=2.75in]{fig5.eps}
\caption{Mean values of \vi\/ for clusters in the range $0.8<$~\vi~$<1.3$ 
as a function of $V$ for various radial ranges in NGC~3610. In all cases 
the smallest mean value is near $V=25$, with higher values on both the 
bright and faint ends. This shows that the distribution of red globular 
clusters is more extended (i.e., is more like a power law) than the 
distribution of blue globular clusters (which is more like a Gaussian).}
\end{figure}

\begin{figure}%6
\centering
\includegraphics[width=3.25in]{fig6.ps}
\caption{Luminosity functions of blue (\textit{left}) and red
(\textit{right}) globular clusters in NGC~3610 within 80$''$ from the center.  
The 50\% completeness limits (\textit{vertical dashed}) mark the boundary 
up to which the LFs can be trusted.  Areas \textit{shaded dark} mark 
background-corrected LFs, \textit{dotted lines} the uncorrected LFs.  Notice 
the nearly lognormal shape of LF for blue globulars and the nearly power-law 
LF for red globulars.}
\end{figure}

\begin{figure}%7
\centering
\includegraphics[width=2.75in]{fig7.eps}
\caption{Kolmogorov-Smirnov tests comparing the populations of blue 
globular cluster ($0.8<$~\vi~$\leq1.025$) and red globular cluster 
($1.025<$~\vi~$\leq1.3$). The largest discrepancies are listed along with 
the probability that the two samples come from the same population. The 
cross-over near $V=25$ tends to cancel out the differences in the two 
populations, hence the bottom two panels break the cumulative distribution 
in half. In all cases we find strong evidence that the two populations are statistically different.}
\end{figure}

\begin{landscape}
\begin{figure}%8,9
\begin{minipage}[t]{0.48\linewidth}
\centering
\includegraphics[width=3in]{fig8.eps}
\caption{Predicted luminosity functions (log in the top panel; linear in 
the bottom panel) based on a combination of the Fall \& Zhang (2001) cluster 
disruption models and the Bruzual \& Charlot (1996) population synthesis 
models. Solar metallicity is assumed for the young and intermediate-age 
clusters while 0.02 solar is assumed for the 12~Gyr population. Note that 
the fading predicted by the BC96 models almost exactly cancels out the 
increase in the mean mass predicted by the Fall and Zhang models, resulting 
in nearly identical distributions at the faint end for the 1.5, 3, and 
6~Gyr models.}
\end{minipage}\hfill
%\end{figure}
%\begin{figure}%9
\begin{minipage}[t]{0.48\linewidth}
\centering
\includegraphics[width=2.5in]{fig9.eps}
\caption{Predicted values of mean \vi\/ for the models shown in Figure~8. 
Note that while the 1.5 and 3~Gyr models have the same qualitative behavior 
as shown in Figure~5, the predicted position of the peak is bluer than found 
for the observations of NGC~3610.}
\end{minipage}
\end{figure}


\begin{figure}%10,11
\begin{minipage}[t]{0.48\linewidth}
\centering
\includegraphics[width=3in]{fig10.eps}
\caption{Fits to the luminosity functions of blue ({\it
upper\/}) and red ({\it lower\/}) globular clusters in NGC~3610.  The
upper panel shows our best-fit Gaussian (thick solid line; $V = 25.44
\pm 0.10$, $\sigma = 0.66 \pm 0.19$) for the blue clusters, along
with a fit with $\sigma = 1.1$ (dotted line), which is clearly
unreasonable.  The lower panel shows a best-fit power law (thick solid
line; slope = $-1.78 \pm 0.05$), and a range of Fall \& Zhang (2001)
models using Schechter initial mass functions and ages ranging from
zero age (thin solid line) to 12~Gyr (3dot - dash line). The best
fitting Fall \& Zhang model is the 1.5~Gyr model (dotted line).  The~0
and 3~Gyr models give similar results, while the 6~and 12~Gyr models
result in unreasonable fits.}
\end{minipage}
%\end{figure}
\begin{minipage}[t]{0.48\linewidth}
%\begin{figure}%11
\centering
\includegraphics[width=3in]{fig11.eps}
\caption{Same as Figure~10, but using Zhang \& Fall
(2001) models with a power-law distribution for the
initial mass function.}
\end{minipage}
\end{figure}
\end{landscape}

\begin{figure}%12
\centering
\includegraphics[width=3in]{fig12.eps}
\caption{A simulation of the 
\vi\/ vs.~$V$ color-magnitude diagram for cluster
candidates in NGC~3610. Filled circles are intrinsically
red clusters while open circles are intrinsically
blue clusters. Note how observational measuring
errors can scatter the data points into the wrong color
bins. See text for details about the simulation parameters.}
\end{figure}

\begin{figure}%13
\centering
\includegraphics[width=3in]{fig13.eps}
\caption{The intrinsic (dotted line) and apparent (solid line)
luminosity functions for the simulation shown in Figure~12. 
This shows that observational scatter can result in an overestimate
in the value of~$V$ for the peak of the blue population and
an underestimate in the slope of the power law for the red population.}
\end{figure}

\clearpage

\newcommand\cola {\null}
\newcommand\colb {&}
\newcommand\colc {&}
\newcommand\cold {&}
\newcommand\cole {&}
\newcommand\colf {&}
\newcommand\colg {&}
\newcommand\colh {&}
\newcommand\coli {&}
\newcommand\eol{\\}
\newcommand\extline{&&&&&&&&\eol}

\begin{deluxetable}{rccccccccr}
\tablewidth{0pt}
\tablecaption{Positions, magnitudes,  and colors of the 50 brightest 
cluster candidates in NGC 3610}
\tablehead{
\colhead{} &\colhead{} &\colhead{} &\colhead{} &\colhead{Projected}\\
\colhead{\#} &\colhead{Paper I \#\tablenotemark{a}} &\colhead{RA} &\colhead{DEC} 
	&\colhead{Radius\tablenotemark{b}} &\colhead{$V$\tablenotemark{c}}
	&\colhead{$\pm$\tablenotemark{d}} &\colhead{$V-I$\tablenotemark{c}} 
	&\colhead{$\pm$\tablenotemark{d}} &\colhead{M$_V$\tablenotemark{e}}\\
&\colhead{} &\colhead{(h:m:s)} &\colhead{(deg:$'$:$''$)} &\colhead{($''$)} 
	&\colhead{(mag)} &\colhead{(mag)} &\colhead{(mag)} &\colhead{(mag)} 
	&\colhead{(mag)}\\
\colhead{(1)} &\colhead{(2)} &\colhead{(3)} &\colhead{(4)} &\colhead{(5)} 
	&\colhead{(6)} &\colhead{(7)} &\colhead{(8)} &\colhead{(9)} &\colhead{(10)}
}
\startdata
%
      1\cola  &   --- \colb  11:18:25.27\colc  58:47:10.08\cold   \phn1.14\cole  20.78
\colf   0.12\colg    1.30\colh   0.17\coli $-$11.61\eol
%
      2\cola &    10 \colb  11:18:25.25\colc  58:47:12.35\cold   \phn1.27\cole  21.09
\colf   0.13\colg   1.27\colh    0.17\coli  $-$11.30\eol
%
      3\cola &  \phn1   \colb  11:18:27.96\colc  58:47:16.05\cold  21.95\cole  21.53
\colf   0.05\colg   1.05\colh   0.05\coli $-$10.86\eol
%
      4\cola &   ---  \colb  11:18:25.00\colc  58:47:12.82\cold   \phn2.34\cole  21.54
\colf   0.13\colg   1.28\colh   0.17\coli $-$10.85\eol
%
      5\cola &  \phn2   \colb  11:18:24.57\colc  58:47:13.24\cold    \phn5.40\cole   21.70\colf   0.06\colg   1.14\colh   0.06\coli $-$10.69\eol
%
      6\cola &   ---  \colb  11:18:28.03\colc  58:47:05.11\cold   22.70\cole  21.79
\colf   0.05\colg   1.24\colh   0.05\coli  $-$10.60\eol
%
      7\cola &   \phn8  \colb  11:18:27.46\colc  58:47:07.18\cold  17.91\cole  21.92
\colf   0.05\colg    1.10\colh   0.05\coli $-$10.47\eol
%
      8\cola &   ---  \colb  11:18:24.89\colc  58:47:13.59\cold   \phn3.51\cole  21.95
\colf    0.10\colg   1.21\colh   0.13\coli $-$10.44\eol
%
      9\cola &  \phn3   \colb  11:18:33.84\colc  58:46:53.75\cold  69.31\cole  21.96
\colf   0.05\colg   1.15\colh   0.05\coli $-$10.43\eol
%
     10\cola &  \phn4  \colb  11:18:32.95\colc  58:46:15.41\cold  81.98\cole    22.00
\colf   0.05\colg   0.94\colh   0.05\coli $-$10.39\eol
%
     11\cola &  \phn7  \colb  11:18:23.79\colc  58:47:02.90\cold  13.74\cole  22.09
\colf   0.05\colg   1.19\colh   0.05\coli  $-$10.30\eol
%
     12\cola &  ---  \colb  11:18:24.45\colc  58:47:26.87\cold  16.84\cole   22.10
\colf   0.05\colg   0.99\colh   0.05\coli $-$10.29\eol
%
     13\cola &  \phn6  \colb  11:18:25.70\colc  58:47:05.55\cold   \phn6.73\cole  22.11
\colf   0.06\colg   1.16\colh   0.06\coli $-$10.28\eol
%
     14\cola &  ---  \colb  11:18:25.45\colc  58:47:11.09\cold   \phn1.85\cole  22.14
\colf   0.21\colg   1.27\colh   0.28\coli $-$10.25\eol
%
     15\cola &  ---  \colb  11:18:25.41\colc  58:47:11.47\cold   \phn1.62\cole  22.14
\colf   0.22\colg   1.14\colh   0.32\coli $-$10.25\eol
%
     16\cola &  ---  \colb  11:18:25.18\colc  58:47:13.01\cold   \phn1.91\cole  22.14
\colf   0.21\colg    1.40\colh    0.27\coli $-$10.25\eol
%
     17\cola &  \phn5  \colb  11:18:27.34\colc  58:46:55.51\cold  22.73\cole  22.39
\colf   0.05\colg   1.19\colh   0.05\coli   $-$10.00\eol
%
     18\cola &  12  \colb  11:18:26.15\colc  58:47:14.31\cold   \phn8.01\cole  22.48
\colf   0.05\colg    1.20\colh   0.05\coli  $-$9.91\eol
%
     19\cola &  \phn9  \colb  11:18:25.88\colc  58:47:11.92\cold    \phn5.30\cole  22.48
\colf   0.06\colg   1.15\colh   0.06\coli  $-$9.91\eol
%
     20\cola &  11  \colb  11:18:20.97\colc  58:46:33.72\cold  49.86\cole  22.53
\colf   0.05\colg   1.08\colh   0.05\coli  $-$9.86\eol
%
     21\cola &  23  \colb  11:18:25.55\colc  58:47:09.22\cold   \phn3.28\cole  22.57
\colf   0.27\colg   1.14\colh    0.40\coli  $-$9.82\eol
%
     22\cola &  13  \colb  11:18:32.23\colc  58:46:15.43\cold  77.97\cole  22.68
\colf   0.05\colg   1.06\colh   0.05\coli  $-$9.71\eol
%
     23\cola &  14  \colb  11:18:25.17\colc  58:47:19.48\cold   \phn8.37\cole  22.68
\colf   0.05\colg   1.08\colh   0.05\coli  $-$9.71\eol
%
     24\cola &  22  \colb  11:18:25.15\colc  58:47:14.11\cold   \phn3.03\cole  22.68
\colf   0.13\colg   1.13\colh   0.19\coli  $-$9.71\eol
%
     25\cola &  ---  \colb  11:18:19.13\colc  58:46:20.82\cold  69.03\cole  22.71
\colf   0.05\colg   1.03\colh   0.05\coli  $-$9.68\eol
%
     26\cola &  16  \colb  11:18:24.03\colc  58:47:14.80\cold   \phn9.85\cole  22.71
\colf   0.05\colg   1.14\colh   0.05\coli  $-$9.68\eol
%
     27\cola &  29  \colb  11:18:25.64\colc  58:47:08.42\cold   \phn4.27\cole  22.72
\colf   0.16\colg   0.97\colh   0.26\coli  $-$9.67\eol
%
     28\cola & 15   \colb  11:18:24.71\colc  58:45:53.33\cold  77.89\cole  22.85
\colf   0.05\colg   1.07\colh   0.05\coli  $-$9.54\eol
%
     29\cola &  ---  \colb  11:18:25.34\colc  58:47:12.74\cold   \phn1.92\cole  22.89
\colf   0.27\colg   1.26\colh   0.38\coli   $-$9.50\eol
%
     30\cola &  18  \colb  11:18:30.02\colc  58:47:28.42\cold  41.21\cole  23.01
\colf   0.05\colg   1.09\colh   0.05\coli  $-$9.38\eol
%
     31\cola &  17  \colb  11:18:26.45\colc  58:46:29.29\cold  42.92\cole  23.08
\colf   0.05\colg   1.18\colh   0.05\coli  $-$9.31\eol
%
     32\cola &  19  \colb  11:18:32.75\colc  58:46:03.85\cold   89.20\cole  23.09
\colf   0.05\colg   1.16\colh   0.05\coli   $-$9.30\eol
%
     33\cola &  20  \colb  11:18:25.69\colc  58:46:42.79\cold  28.57\cole  23.31
\colf   0.05\colg   1.26\colh   0.05\coli  $-$9.08\eol
%
     34\cola &  21  \colb  11:18:23.84\colc  58:47:23.44\cold  16.28\cole  23.33
\colf   0.05\colg   1.22\colh   0.05\coli  $-$9.06\eol
%
     35\cola &  ---  \colb  11:18:25.52\colc  58:46:52.45\cold  18.82\cole  23.34
\colf   0.05\colg   1.17\colh    0.06\coli  $-$9.05\eol
%
     36\cola &  ---  \colb  11:18:23.96\colc  58:46:52.65\cold  20.88\cole  23.35
\colf   0.05\colg   1.18\colh   0.06\coli  $-$9.04\eol
%
     37\cola &  25  \colb  11:18:25.21\colc  58:47:02.60\cold   \phn8.51\cole  23.36
\colf   0.06\colg   1.13\colh   0.06\coli  $-$9.03\eol
%
     38\cola &  24  \colb  11:18:25.27\colc  58:47:02.34\cold   \phn8.79\cole  23.36
\colf   0.06\colg   0.89\colh   0.07\coli  $-$9.03\eol
%
     39\cola &  ---  \colb  11:18:24.88\colc  58:47:15.39\cold   \phn4.99\cole  23.43
\colf   0.17\colg   1.02\colh   0.25\coli  $-$8.96\eol
%
     40\cola &  30  \colb  11:18:23.51\colc  58:46:11.92\cold  60.65\cole  23.51
\colf   0.05\colg   1.14\colh   0.05\coli  $-$8.88\eol
%
     41\cola &  28  \colb  11:18:26.28\colc  58:45:58.20\cold  73.39\cole  23.55
\colf   0.05\colg   0.91\colh   0.05\coli  $-$8.84\eol
%
     42\cola &  27  \colb  11:18:25.62\colc  58:46:39.96\cold  31.32\cole  23.57
\colf   0.05\colg   1.12\colh   0.05\coli  $-$8.82\eol
%
     43\cola &  36  \colb  11:18:23.62\colc  58:47:01.10\cold   15.90\cole  23.61
\colf   0.05\colg   1.16\colh   0.05\coli  $-$8.78\eol
%
     44\cola &  32  \colb  11:18:29.13\colc  58:47:09.59\cold  30.55\cole  23.62
\colf   0.05\colg   1.15\colh   0.05\coli  $-$8.77\eol
%
     45\cola &  37  \colb  11:18:25.83\colc  58:46:50.43\cold  21.24\cole  23.65
\colf   0.06\colg   1.13\colh   0.06\coli  $-$8.74\eol
%
     46\cola &  34  \colb  11:18:32.93\colc  58:47:38.61\cold  66.03\cole  23.72
\colf   0.05\colg   0.96\colh   0.05\coli  $-$8.67\eol
%
     47\cola &  ---  \colb  11:18:24.54\colc  58:47:15.64\cold    \phn6.90\cole  23.73
\colf   0.13\colg   1.38\colh   0.17\coli  $-$8.66\eol
%
     48\cola &  ---  \colb  11:18:24.90\colc  58:47:09.79\cold   \phn2.76\cole  23.74
\colf   0.31\colg   0.81\colh   0.54\coli  $-$8.65\eol
%
     49\cola &  33  \colb  11:18:31.40\colc  58:46:41.14\cold  56.71\cole  23.78
\colf   0.05\colg   1.34\colh   0.05\coli  $-$8.61\eol
%
     50\cola &  ---  \colb  11:18:31.40\colc  58:45:48.25\cold  95.83\cole  23.79
\colf   0.05\colg   0.63\colh   0.06\coli   $-$8.60\eol
\enddata
\tablenotetext{a}{Corresponding ID number from Table~4 of Paper~I. Note how the new search algorithm is able to identify new clusters close to the center of NGC~3610. Most of the missing clusters in the outer regions are due to different orientations of the two sets of observations.}
\tablenotetext{b}{Using a central position of 11h 18m 25.209s and 58$^{\circ}$ 47$'$ 11.12$''$.}
\tablenotetext{c}{No correction for extinction was made since Burstein and Heiles
(1984) give A$_V = 0.00$~mag.}
\tablenotetext{d}{A value of 0.05~mag has been added in quadrature to approximate
the error introduced by uncertainties in  zeropoint, aperture corrections, and CTE corrections.}
\tablenotetext{e}{Using H$_0 = 75$ km s$^{-1}$ Mpc$^{-1}$ and $m-M = 32.39$.}
\end{deluxetable}

\end{document}

