There has been a great deal of study of Globular Cluster (GC) systems around other galaxies as well as our own. They are a powerful diagnostic of many galactic processes from star formation history and chemical evolution to galactic dynamics and structure. With increasing telescope resolution and more sophisticated search techniques, more and more systems are being explored.
Elliptical galaxy systems are by far the easiest to study. Unplagued by complex spiral structure or star-forming regions, the galactic brightness profile is easily modeled and subtracted. Any remaining bright points are either globulars, foreground stars or background galaxies. Exposures in several bands give color information which helps winnow the candidate list further.
With spiral galaxies, the search process is more complicated. Nearby spirals such as M31 and M33 are close enough that many GCs can be resolved with HST. Since globulars inhabit the halo and spend much of their orbits far from the galactic disk, certain farther galaxies, which happen to be highly inclined, can be studied with deep imaging. Other detection techniques include color diagnostics, velocity determinations and radial light profiles. This will be discussed in more detail in §5.
Certain characteristics of GC systems have become apparent. In a number of well-studied populations, a Globular Cluster Luminosity Function (GCLF) has been observed that is Gaussian in nature with a characteristic peak magnitude and dispersion. Harris (1991) lists these parameters for 18 galaxies in his Table 2; M 
is typically -7.0 and 
=1.2. Ashman & Zeph (1998) cite M =-7conclusions.33, =1.23 for the Milky Way and M =-7.51, =1.05 for M31. Della Valle et al. (1998) get M 
=-7.08, M =-7.62, M 
=-8.14 for the Milky Way. Secker (1992) and Sandage & Tammann (1995) find M =-7.5 for MW and M31. Figure 1 shows the observed GCLF for the Milky Way.
Globulars also inhabit a well-defined region of color space. While GCs have a mean spectral type of F8 (Mihalas & Binney, 1981), they do have a distribution in color. Well-populated elliptical systems such as M81 (Whitmore et al. 1995) and NGC3923 (Zeph et al. 1995) show a bimodal distribution of colors and hence metalicities from 0.8 > V-I > 1.4 with blue and red peaks at about V-I=0.95 and V-I=1.2. The bluer peak represents metal-poor systems while the red peak is higher in metalicity. These likely reflect age differences among the clusters. The color bimodality is present in spirals as well, but the red peak is noticeably suppressed implying an older cluster population. Milky Way GCs lie in the color range 0.7 < V-I < 1.2 (Figure 2).
Specific frequency (S 
) is a parameter often used in the study of GC systems to describe relative population per unit luminosity. S relates the total number of globulars, N 
, with host galaxy luminosity by the empirical relationship
(Ashman & Zeph 1998). Elliptical galaxies usually have much higher S than do spirals. Early type galaxies tend to have more globulars than late-type, and this is reflected in their specific frequencies. The Milky Way, for reference, has a population of 180 
20 GCs and a specific frequency of 0.5 0.1; certain giant ellipticals have S 
10 and over 10,000 clusters.
In §2 we describe our galaxy selection process and in §3 the data reduction and photometry. In §4, we discuss what we expect to see. In §5 we discuss the GC search criteria employed by other authors and our search techniques and results. Our conclusions are presented in §6.
In choosing our data we wanted an object included in both initial coverage of the Sloane Digital Sky Survey and by Hubble Space Telescope images. Our aim was to use HST for deep, spatially resolved imaging while using SDSS for a five-color data-set of the brighter objects. As of 1999 March, the only SDSS runs have been along the celestial equator plus or minus about a degree in declination. We cross-referenced a list of equatorial NED objects with radial velocity less than 10,000 km/s with the edge-on spiral catalog of Guthrie (1992). Thirty one objects were found most of which were judged unusable because of strange morphology or extreme distance.
We choose for our study the galaxy NGC4437, also known as NGC4517--the only object to meet all our criteria. It is a type SA(s)cd galaxy in the direction of Virgo. With an inclination of 82 
(Gutherie 1992) it appears nearly edge-on to us and is thus ideal for a globular cluster search in the halo. The angular extent is roughly 12 x 1.5 arc minutes with the long axis very nearly in the east-west direction; thus we can use declination as a measure of distance from the plane of the galaxy. Bottinelli et al. (1985) list the distance modulus as derived from HI line widths as 29.30 0.19 giving a distance of 7.24 0.60 Mpc. The observed radial velocity, however, is 1129km/s (Shostak, 1975). When corrected for solar motion, this becomes 1118 km/s. Given H 
=75, the kinematic distance modulus is 30.86 and d=14.9Mpc. NGC4437 may lie in the foreground or it may be at the distance of the Virgo cluster, though several degrees to the south. At Virgo cluster distances, one arcsecond is approximately 78 pc. Thus we would expect one HST Wide Field pixel to correspond to about 8pc so that each WFC chip will cover about 6kpc. We will adopt a distance modulus of 30.0 for the remainder of our analysis.
The data distribution network for SDSS data is still in the awkward, prototype stages. At JHU, we have the full FITS files for run 94 and parts of run 211. Unfortunately, the image of the central part of the disk and halo of NGC4437 is in run 752, camera 4, field 298 (Figure 3). This data was discovered on the web site http://sdsslnx.fnal.gov:8015/ and painstakingly gathered by hand one object at a time.
Searching the STScI image archives, we found WFPC2 observations of NGC4437 (Figure 4). Four exposures in F555W for a total of 400 seconds and four in F814W for a total of 640 seconds were obtained by HST in 1997 March. The F555W filter is similar to the Johnson-Cousins V-band while the F814W is similar to the I-band. The pointing includes a narrow band of the galactic disk near the core and a piece of the inner halo (Figure 5). According to the exposure time calculator on the STScI web page, we should reach S/N>10 for the V=25 objects we expect to see. Observational details are presented in Table 1.
The HST data were retrieved from the archive and processed with IRAF. Originally in GEIS format, each file was split into its four component chip images and mosaics were made. Although helpful in gaining a feel for the full field, the mosaics were otherwise unnecessary. It became clear early on that better photometry would be obtained by treating each chip separately.
The next step was to align the four images taken in each filter. The task used was IMALIGN, with at least three reference stars in each field. In the PC chip there were no discernible objects, and we elected not to include it in further analysis.
After the images were aligned, they were combined with IMCOMBINE-a task that averages the pixel values in the four images and uses CRREJ to get rid of cosmic rays. For each frame we chose to use the first set of images as the base image, and found that the pointing was steady enough so that no further image shifting was needed to align V and I-band images. Because of this alignment, the deeper exposure and WFPC2s greater sensitivity in the I-band, we were able to choose photometry candidates in the I-band alone. We selected the objects for photometry iteratively, working to get a combination of PSF FWHM, standard deviation, and detection level that included as many of the visible objects as possible. The parameters settled upon for the DAOFIND task were FWHM=3, =0.52 counts, detection for 4 . Using TVMARK we could see that all of those candidates we might have chosen by sight were included, as well as many we might not have. Background was determined by getting image statistics on a visually blank area in each frame. All were very close to 0.52 counts/pixel.
Instrumental magnitudes were obtained using two different aperture photometry packages-APPHOT for the less crowded WF3 and WF4 fields, DAOPHOT for WF2. In both cases an aperture of 5 pixel radius was chosen, along with a sky annulus of 15 pixel inner radius, 5 pixel diameter. Taking a scale factor of 0".1/pixel, this aperture radius corresponds to 0".5. It is not a coincidence that this is the exact aperture used for all calibrations by Holtzmann et al. (1995). Other parameters set for determining instrumental magnitudes include a gain of 7 and the zero points listed below for each chip in each filter.
WFPC2 Zero points by Chip filter WF2 WF3 WF4 f555w 22.571 22.561 22.538 f814w 21.665 21.659 21.641 (obtained from WFPC2 tutorial online http://www.stsci.edu/ftp/instrument_news/WFPC2_doc.html#hand )
Next the instrumental magnitudes were converted into apparent magnitudes using the equations and transformation coefficients given in Holtzmann et al. (1995). We did not use the zero points listed there but did correct our instrumental magnitudes by -0.1 each, owing to the fact that the zero points quoted above are for infinite aperture. The final apparent magnitudes, corrected for color are given by the equation
also, the transformation coefficients are (from Table 7, Holtzmann, 1995)
filter T1 T2 f555w -0.052+/-0.007 0.027+/-0.002 f814w -0.062+/-0.009 0.025+/-0.002
with SCOL as the solution to the quadratic equation for coefficients with a=T2V-T2I, b=T1V-T1I-1, c=mi-mv. "mi" and "vi" are the instrumental magnitudes such that SCOL is uniquely determined for each object. The resulting color magnitude diagram for all objects is shown in Figure 6.
Using M31 and the Milky Way as model systems, we expect the GCLF to peak at roughly M =-7.4. With a distance modulus of 30.0, we expect to see m =22.6 1.5. Typical V-I=1.0 and thus our expected I magnitude range will be 21.6 1.5 magnitudes.
The bad news is that there probably will not be very many clusters in our field of view. Two well-studied Sc/Scd galaxies, M33 and NGC253 have S of 0.5 0.2 and 0.2 0.1, respectively. Harris (1991) gives a mean S equal to that of M33. The observed magnitude of NGC4437 is m =11.10 and at a distance modulus of 30, gives M =-19, roughly equivalent to M33. If we adopt S =0.5, this gives us N =20. For reference, M33 has at least 30 GCs while NGC253 has 24 observed GCs. However, our data only covers a small portion of the galactic halo where we would expect to see the GCs. We can expect to see, at most, a few GCs in our search area.
The field will be contaminated by other objects. However, foreground stars will probably not be a problem. Since the galactic latitude of NGC4437 is 62.61 degrees, we are not looking through very much of the Galactic disk. Main sequence stars in our own galaxy with spectral type near F8 will have M near 4.0. Thus a 23rd magnitude main sequence star in our color range will have a distance of of roughly 60kpc-many scale heights out in the halo. Even an 18th magnitude star is at an estimated distance of 6kpc. It seems unlikely that we will see very many foreground stars.
To be seen, individual stars in NGC4437 will have to be of absolute magnitude equal to the globular clusters. These will only be the very brightest of the O stars and supergiants and, unless they are heavily reddened, they won't appear as spectral type F. Again, it seems unlikely that a very hot young star would be simultaneously ejected into the halo of NGC4437 and reddened sufficiently to appear in our survey.
Background galaxies will probably be the major problem in our search. Just from looking at the images, it is clear that there are of order ten obvious galaxies in the WFPC2 field. A NED search reveals six 20th magnitude galaxies within 5' of the HST pointing and there are undoubtedly numerous fainter, uncataloged background objects. In fact, there may be a cluster or group in the background. Some of these will undoubtedly have the same color and magnitude characteristics as GCs, though the number of background galaxies per color bin should be a constant across our V-I range.
Other authors have used various techniques for finding Globular Clusters. Kissler-Patig et al. (1999) studied the spiral galaxies NGC4565 and NGC5907. Their data-similar to ours-used WFPC2 images in F450W and F814W. As selection criteria they chose objects with B-I > 1.2, m > 20.0 = M > -10, which would not exclude the brightest globulars in our galaxy or M31. The distance modulus of these galaxies is comparable to NGC4437. Most interestingly, Kissler-Patig et al. used the radial profiles of their candidate objects as a key diagnostic. Artificial stars and artificial GCs were generated using TINY TIM (Krist & Hook 1997). The resulting FWHM in B were between 1.5 and 2.5 pixels for the artificial GCs, while those for stars were in the range 0.8 to 1.5 pixels. They classified their objects accordingly.
Battistini et al. (1984) studied the Scd spiral NGC 2403. With a distance modulus in the range 26.7 to 27.6, it is substantially closer than NGC4437 or the objects studied by Kissler-Pattig et al., and Battistini et al. were working from B and V photographic plates. Thus they used for selection cirteria magnitude and color: V < 20, 0.54 < B-V < 1.2. They found 19 objects which they further classified by color: B-V < 0.54 were classified as "populous clusters", those with 0.54 < B-V < 1.2 were "classic globulars". Anything redder than 1.2 were classified as background galaxies.
Fleming et al. (1995) use V-band photometry and detailed study of the radial profiles to find GCs in NGC4565 (spiral). Meanwhile, Harris et al. (1985) looked at the spiral NGC2683 with a IIIa-J photographic plate. They divided the image up into annular rings and then chopped each ring into 20 degree sectors omitting any sector with galactic interference. Their selection criterion is not mentioned but is probably visual identification. They find 100 31 clusters and estimate the total population for this galaxy at 321 108.
Out of the 3198 objects found and processed by DAOPHOT, we started making cuts by position. Since the galaxy has a position angle very close to 90 degrees, we specified a declination cut at 0.105 degrees to remove sources in the disk of NGC4437. This reduced the number of objects to 200. Twenty-one of these objects were within one arc second of objects in the SDSS database. Of these 200, a color-magnitude diagram revealed a wide scatter of points (Figure 6). Whitmore et al (1995) and others show that the expected GC color distribution in an elliptical system is 0.8 < V-I < 1.4, but what scanty data we have for spirals shows a lack, or at least strongly diminished red bump and a blue bump shifted to smaller V-I. Thus we set our color criteria as 0.6 < V-I < 1.4 and selected 32 objects.
The resolution of the wide field chips is approximately 0.1 arc second per pixel corresponding to about 8pc at a distance modulus of 30. For Milky Way GCs, the mean half-light diameter is 8.8pc (Ashman & Zeph 1998) so they may be slighly resolved by the WFCs. However the radial profiles of NGC4437 GCs will likely be only marginally wider than the PSF. A close look at the WFC images revealed that six of these objects were obviously extended and showed definite non-stellar radial profiles. These objects were classified as galaxies and removed. Figure 8 shows a histogram of the remaining objects (dashed line) with a promising Gaussian profile of the type expected.
Radial profiles were generated in both bands for each of the 26 remaining objects; some example radial plots are shown in Figure 7. The authors examined each object sorting them as candidates or rejects, with GC candidates showing reasonably gaussian profiles and FWHM near 1.5 pixels (as per Kissler-Pattig et al. 1999). A few objects displayed exemplary radial profiles in one band but not in the other; these were accepted. Rejected objects included a few which were too bright and classified as stars. Any object with extended wings or obviously non-radial profiles was rejected as a probable galaxy. A number of the fainter sources did not show discernable peaks at all or appeared to be negative features and were rejected as noise. It is distinctly possible that some of these rejected objects are, in fact, globular clusters, but without deeper imaging, we cannot say with more certainty. Our candidates and rejects are presented in Table 2a and 2b respectively .
Two SDSS objects made it through all our cuts. One, object 3-50, is located very close to an obvious background galaxy-probably the SDSS object. The other crossover detection, object 3-65, is magnitude 20.7 in V and shows a very sharp profile. While this puts it on the very bright wing of the GCLF, its R-I=0.23 whereas the Milky Way GC population tends to run the range 0.4 < R-I < 1.3. It is probably not a cluster.
The result of our study of the globular cluster system of N4437 is a list of 11candidate objects (Table 2a). It is quite clear that not all of these can be GCs, based on a reasonable specific frequency, however they are possible detections. A histogram of the GC candidates is not inconsistent with a Gaussian profile.
What can we conclude? Firstly, there are most likely resolvable GCs in the WFPC2 field of N4437. They are probably the most luminous of the system, but that gives impetus to study this system more closely, or to search for closer edge-on spirals. The latter is especially desirable considering the SDSS data that should soon be available for a much larger portion of the sky. Obviously having the five filters of Sloan is much preferable to the two of WFPC2. Having both sets of observations, for a closer galaxy, would make quite a difference-considering the limiting magnitude of SDSS.
As for possible improvements to our current study, we could dream of taking deep fields of the entire galaxy, as well as spectroscopy of our candidates. Knowing radial velocities would go a long way toward weeding out background galaxies. It is also evident in the literature that producing a definitive list of GCs is an iterative process. Technology improves. Those who come later get the benefit of many lists, more study on the parent galaxy. The system for M31, in particular, has been studied this way (Reed, Harris & Harris 1992). Yet in the absence of all of these things, the fact remains that we have reasonable candidates.
We would like to thank the following people for the extensive help they gave us in aquiring, reducing and analysing our data: Zlatan Tsvetanov, Peter Kunszt, Wei Zheng, Eric Neilsen, Eric Peng, Rupali Chandar, Gyula Szokoly, Chris Pickens, Alan Uomoto, and Christy Tremonti.
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Figure 1: The GC luminosity function for the Milky Way (Ashman & Zeph 1998).
Figure 2: The metalicity (and color) distribution for the Milky Way (Ashman & Zeph 1998).
Figure 3: Sloan Digital Sky Survey image of NGC4437.
Figure 4: Digitized Sky Survey image with WFPC2 field overlayed.
Figure 5: WFPC2 combined I-band image.
Figure 6: Color-Magnitude diagram for all 3198 objects found by DAOFIND. The squares are the 26 objects which passed by the declination cut-off and the color range cutoff after being screened for obvious galaxies.
Figure 7: Radial profiles in V (top panels) and I (bottom panels) for object 3-65 (left), a starlike object; object 4-40 (center), a GC candidate; and 2-1131 (right), a non-detection.
Figure 8: Histogram of our objects in V-I space. Dashed line is our full 26 candidates. Solid line are the 11 objects in our candidate list.
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