Astron. Astrophys. 348, 418-436 (1999)

2. The data

2.1. Observations

We used the WFPC2 aboard the HST to obtain F555W (WFPC2 broadband V) and F814W (WFPC2 broadband I) images of a region near the nucleus of NGC 5128. The data were obtained on July 27, 1997 for the cycle 6 program GO-6789. The WFPC2 had an operating temperature of C and a nominal gain setting of 7 /ADU. The observations are listed in Table 1.

Table 1. Log of the observations.

Exposures were taken in each field with each of the F555W and the F814W filters. Cosmic rays impact pixels per second on each WFPC2 CCD, but by combining the multiple exposures per filter for each field, the number of pixels lost to cosmic ray events is negligible. Therefore, we did not apply any processing explicitly to remove cosmic rays from the images. The data were preprocessed through the standard STScI pipeline for WFPC2 data. Known bad pixels were flagged and not used in the data analysis. No corrections were made for geometric distortions in the area of the WFPC2 pixels.

The survey consists of six fields that cover a total area of approximately centered on (J2000 coordinates), the nucleus of NGC 5128. Adjacent fields overlap by giving a total effective area of for the survey.

2.2. Data reductions

We combined the exposures for each field by taking the average of the three images in each filter (four images for the F555W exposures of Field 2). No re-registration of the images was performed since the shifts between the images were typically less than 0.1 pixel ( on the WFC and on the PC). We estimate that combining the images in this way may result in the sizes of the GC candidates being systematically overestimated by no more than . We prefer to introduce this simple systematic offset than deal with the poorly-understood systematic uncertainties that arise from interpolating flux across fractional-pixel shifts.

2.2.1. Identifying globular cluster candidates

At the distance of NGC 5128 ( Mpc), the mean King core- and tidal-radii of the Milky Way GCs would appear to be and , respectively. Therefore, any GCs in NGC 5128 will appear to be semi-stellar and be strongly affected by the point spread function (PSF) of the WFPC2. After some experimentation, we adopted the following procedure for identifying GC candidates. We wish to stress that this procedure is quite strict and will probably result in the rejection of some legitimate GC candidates. However, we prefer to reject real GCs rather than have our sample contaminated with stars or background galaxies.

In order to increase the signal-to-noise ratio (S/N) of the GC candidates - a particularly important point for the faint () GC candidates - we combined the F555W and F814W images for each field to get finding images. The dust lane introduces variations in the background on spatial scales of , comparable to the expected sizes of the GC candidates in NGC 5128. To reduce the effects of the uneven background light, large-scale spatial variations in the background were removed by running a ring median filter (Secker 1995) over the finding image, subtracting the resulting smoothed background, and adding back the mean background value. The median filter radius was set to , which is times the expected full-width at half maximum (FWHM) of a typical GC candidate. This choice of filter radius ensures that the cores of the GC candidates will not be altered by the median filter and that any background structure larger than a typical GC candidate will be removed. Since the most extended Milky Way GCs have tidal radii that are significantly greater than 2.5 times their FWHM, and extended halos have been detected around several Galactic and extra-Galactic GCs (Grillmair et al. 1995; 1996; Holland et al. 1997), this approach will alter the distribution of light in the outer regions of most of the GC candidates. However, this is not important since the finding images are used only to construct a preliminary list of GC candidates. A more rigorous set of criteria, based on the structures of the GC candidates as determined from the original images, will be applied to the preliminary list to obtain a final list of GC candidates in the central regions of NGC 5128.

The first step in our identification procedure was to run the DAOPHOT II (Stetson 1987; 1994) FIND routine on the background-subtracted images to identify GC candidates. The finding thresholds were set to for the PC images and for the WFC images. Tests with artificial GCs suggested that any detections below these thresholds would be rejected at some point in our identification process. DAOPHOT II FIND has an algorithm for rejecting non-stellar objects based on two parameters called "sharpness" and "round". This algorithm was turned off since images of GCs can have different shapes and concentrations from images of stars.

Next, the DAOPHOT II PHOTOMETRY routine was used to obtain aperture photometry for each of these detections. The photometry was performed separately on each of the combined F555W and F814W frames, not on the combined finding frame. An aperture radius of was used since most Galactic GCs, if moved to the distance of NGC 5128, would appear to have core radii smaller than this. Therefore, the signal within the aperture will be dominated by the light from the object and not from the background. Candidate objects with within the photometry aperture were discarded since the signal was not strong enough to determine reliable shape parameters. The sky brightness was determined in an annulus with an inner radius of and an outer radius of . This annulus was chosen to be far enough from the center of the GC candidate that the light in the annulus will be dominated by the background, yet near enough to the GC candidate that the light in the annulus will be a reasonable approximation of the mean background at the location of the object. For large GC candidates this annulus will be inside the tidal radius of the object so our estimate of the background will be contaminated. However, the values determined at this stage are only preliminary estimates, which will be improved upon later in the identification process when Michie-King models are fit to the GC candidates. The lists of GC candidates in each of the F555W and F814W images were matched using the DAOMATCH and DAOMASTER software. Only objects that appeared in both the F555W and F814W images, and whose centers matched to within ( pixel on the PC images and pix on the WFC images), were considered to be real GC candidates.

Distinguishing bona fide GCs from stars and background galaxies is challenging. The colors of the objects can not be used since we are interested in studying the color distribution of GCs in NGC 5128 and do not wish to bias our sample. To make matters worse, the presence of dust in NGC 5128 will add a significant amount of scatter to the intrinsic color distribution, and may cause legitimate GCs to be rejected if a color-based identification scheme is used. The solution is to identify GC candidates by their structural parameters, although the best choice of structural parameters is not obvious. At the distance of NGC 5128 a typical Galactic GC would appear to have an intrinsic FWHM of , or approximately twice the FWHM of the WFPC2 PSFs. Therefore, the observed FWHM, concentration, and ellipticity of a GC candidate can be heavily influenced by the PSF. Since the PSF varies strongly with position on the WFPC2 CCDs, the potential for confusion between stellar images and concentrated GC candidates is great if the PSF is not removed, in some way, from the data. Therefore, the observed shape of an object can not be directly used to classify it as a star, GC candidate, or galaxy.

After some experimentation with adding and recovering artificial GCs and artificial stars, we found that the following procedure was reasonably reliable for identifying GC candidates. For each GC candidate we took all the pixel values within of the center of the object and subtracted an estimate of the local background (the center and background were determined by the DAOPHOT II PHOTOMETRY algorithm). A one-dimensional Moffatian (Moffat 1969),

was fit to each candidate using the effective radius, , instead of the true distance from the center of the candidate in order to compensate for any ellipticity that might be introduced by the PSF. The effective radius of an ellipse is defined by , where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. For each pixel the effective radius from the center of the GC candidate was computed using:

where x and y are the coordinates of the pixel on the CCD, and and are estimates of the ellipticity and position angle of the GC candidate. The latter two quantities were estimated from the moments of the light from each object.

In order to determine which combinations of and corresponded to stars and which corresponded to GC candidates, a series of artificial stars and artificial GCs were added to the images. The artificial stars were added using the DAOPHOT II ADDSTAR routine and the appropriate PSFs scaled to magnitudes of . The artificial GCs, also with integrated magnitudes of , were added using the IRAF ¹ v2.10.4 task NOAO.ARTDATA.MKOBJECT . The artificial GCs all had ellipticities of , concentrations of , and core radii of (corresponding to physical core radii of between and pc at the distance of NGC 5128). Therefore, the artificial GCs had a range of structures similar to those of the Milky Way's GCs. The procedure described above was used to determine the Moffat and for each artificial object. The results are presented in Fig. 1 and were used to determine which combinations of and represent stars and which represent GC candidates. These limits on and were then applied to the GC candidates found on the WFPC2 images of NGC 5128.

Fig. 1. This figure shows the best-fitting Moffatian and parameters for the artificial stars (circles) and artificial GCs (crosses). Based on the distribution of objects in this diagram we assumed that any objects that lie inside the wedge formed by the solid lines were GC candidates. No upper limit was placed on the value of .

Figs. 2 and 3 show the Moffatian and parameters for the 3800 objects that were successfully fit by Moffatians. There are 403 objects with Moffat parameters that lie inside the wedge (see Fig. 1). Our simulated data suggest that these are extended objects such as GCs, background galaxies, dust features, open clusters, star forming regions, or blended stars.

Fig. 2. This figure shows the best-fitting Moffatian and parameters for each object (small circles) on the F555W images. Simulated data (see Fig. 1) suggest that objects that lie inside the wedge formed by the solid lines are extended objects. Therefore we consider any objects that lie inside the wedge to to be GC candidates. The solid squares show the locations of the GC candidates from Table 2.

Fig. 3. This figure shows the best-fitting Moffatian and parameters for each object (small circles) on the F814W images. Simulated data (see Fig. 1) suggest that objects that lie inside the wedge formed by the solid lines are extended objects. Therefore we consider any objects that lie inside the wedge to to be GC candidates. The solid squares show the locations of the GC candidates from Table 2.

2.2.2. Fitting Michie-King models

We fit a two-dimensional, PSF-convolved, single-mass Michie-King model to each of the 403 GC candidate using software developed by Holland (1997). This software assumes that the surface brightness profile along the effective radius axis of a GC candidate with an ellipticity of and a position angle of has a King profile with a concentration of c and a core radius of . It then builds a two-dimensional model based on this surface brightness profile, , and . The two-dimensional model is convolved with the appropriate PSF for the location on the CCD and a chi-square minimization is performed between the PSF-convolved model and the original data image. The software uses CERN's MINUIT function minimization package to fit simultaneously the concentration, core radius, total flux in the object, ellipticity, position angle, and mean background. Objects located within 32 pixels of the edge of a CCD ( for the WFC and for the PC) were not fit to avoid the edges of the CCD biasing the fits. Once a best fit had been determined, the King tidal radius, , and the half-mass radius, , of the model were computed.

Separate fits were made to the F555W images and the F814W images and an object was considered to be GC candidate only if a Michie-King model could be fit in both colors. We were able to fit Michie-King models to 98 of the 403 potential GC candidates. Mean structural parameters were calculated for these object by taking the mean of the values found in each filter. Four objects (#8, #113, #128, and #129) (see Tables 2, 3, and 3) were identified on multiple fields. In these cases we computed the mean of the structural parameters measured in each field.

Table 2. The GC candidates in the central regions of NGC 5128.

Table 3. Extended objects with and in the central regions of NGC 5128

Table 3. (continued)

We elected to separate GC candidates from background galaxies based on their fitted ellipticities and half-mass radii (see Fig. 4). Half-mass radii are preferred to tidal radii or core radii because Fokker-Planck models of spherical stellar systems show that half-mass radii remain reasonably constant over periods of several Gyr (e.g. Cohn 1979; Takahashi 1997), making it a unique length scale for GCs. The mass interior to the half-mass radius tends to undergo a gravo-thermal collapse and become concentrated at the center of the GC over time (i.e. core-collapse), which results in the core radius shrinking. Meanwhile, the mass exterior to the half-mass radius tends to expand outwards, causing the tidal radius to grow. Since we are interested in finding young, intermediate-age, and old GCs in NGC 5128, it is useful to have a selection criterion that does not depend on the age of the GC candidate. Galactic GCs have half-mass radii of approximately pc (W. Harris 1996), which corresponds to at the distance of NGC 5128. There is no evidence that the radius of a Galactic GC depends on its mass (van den Bergh et al. 1991). Therefore, we have assumed that only objects with ( pc at the distance of NGC 5128) were GC candidates. It is possible that some of the objects in Fig. 4 that have high ellipticities and low half-mass radii are double clusters. However, Innanen et al. 1983have shown that a binary GC could not survive a single Galactic orbit in the Milky Way so it is unlikely that there are any old, or intermediate-age double GCs in NGC 5128. It is possible that very young multiple GCs that formed within the last Gyr could have survived to the present day, but we are unable to differentiate between them and background galaxies.

Fig. 4. The ellipticity vs. half-mass radius of the best-fitting single-mass Michie-King model for each object where a Michie-King model was successfully fit. Objects with ( pc) have not been plotted. The solid box in the lower left of the plot shows the region occupied by Galactic GCs. Based on this plot we have assumed that any object with ( pc) and (the dashed box) is a GC candidate in the NGC 5128 system.

The most elliptical Galactic GC is M19 with (White & Shawl 1987) and the most elliptical GC known is NGC 2193 in the Large Magellanic Cloud (LMC) which has (Geisler & Hodge 1980). Geisler & Hodge (1980) modelled the distribution of observed ellipticities for 25 GCs in the LMC and found that it was unlikely that the largest true ellipticity exceeded . The LMC contains both dynamically young and dynamically old GCs, so the largest ellipticity seen in the LMC is a reasonable estimate of the largest ellipticity that we can expect to see in NGC 5128. Therefore, only objects with were considered to be GC candidates.

The final step was to examine visually the WFPC2 images of each GC candidate to ensure that the Michie-King model fits looked realistic. We found that 20% of the objects were either located on diffraction spikes from saturated stars, or exhibited unusually large residuals when the best-fitting Michie-King models were subtracted. These spurious identifications were discarded.

Fig. 4 shows the measured half-mass radii and ellipticities for the surviving objects in NGC 5128 and Table 2 shows the final list of GC candidates that we find in the central regions of NGC 5128. The second and third columns show the J2000 coordinates of the objects as determined using the IRAF/STSDAS (v2.0.1) task STSDAS.TOOLBOX.IMGTOOLS.XY2RD . Column 4 is the observed (projected) distance of the GC candidate from the center of NGC 5128 in arcminutes. The center of NGC 5128 was taken to be , (Johnston et al. 1995). Columns 5 and 6 give the field (from Table 1) and CCD that the object was found on. Columns 7 and 8 give the X and Y coordinates (in pixels) on the CCD. Column 9 lists the identification number of the object in Table 1 of Minniti et al. (1996).

Table 3 lists the coordinates for the 61 extended objects with and . Some of these objects may be GCs in NGC 5128 while others may be background galaxies with structures similar to those of Michie-King models. Six of these objects have been previously identified as GCs by Minniti et al. (1996) and Sharples (1988).

Figs. 5 through 10 show the locations of the 21 GC candidates on the F814W-band WFPC2 images. Only objects that pass all of the criteria described above are marked on these figures. Objects (such as #15) were only marked on the fields that they were identified as GC candidates in. In most of the cases where a GC candidate is present in multiple fields, but only identified in one field, the GC candidate was located very near the edge of one of the CCDs. Spatial variations in the PSF are largest near the edges of the CCDs so the Michie-King model fits are less reliable near the edges of the CCDs.

Fig. 5. A finding chart for Field 1. The GC candidates are circled with their identification numbers (see Table 2) printed near each object.

Fig. 6. A finding chart for Field 2.

Fig. 7. A finding chart for Field 3.

Fig. 8. A finding chart for Field 4.

Fig. 9. A finding chart for Field 5.

Fig. 10. A finding chart for Field 6.

The structural parameters of the best-fitting Michie-King models, as well as the fitted ellipticities and position angles, for each GC candidate are listed in Table 4. The first column contains the object ID (from Table 2). The various radii are given in units of seconds of arc, and the position angles are measured in degrees with being north and increasing to the east. The values are the reduced goodness of fit values returned by the fitting software. The uncertainties () are the standard deviations in the values for the parameters that were measured in each filter. The position angles for GC candidates with small ellipticities () are not reliable. All of the are significantly less than one, which suggests that the formal uncertainties in the model's parameters are not reliable. Therefore, we have elected to estimate the uncertainties in the fits through monte-carlo simulations as described in Sect. 2.4.

Table 4. The best-fitting structural parameters for the NGC 5128 GC candidates. The values are the means of the structural parameters derived from the F555W and F814W images.

2.3. Contamination

Our data will contain images of Galactic foreground stars, and supergiants in NGC 5128. From the work of Bahcall & Soneira (1981) we expect to find Galactic stars with in our fields. The brightest stars in the halo of NGC 5128 have (Soria et al. 1996) while the brightest young stars in the central regions of NGC 5128 are expected to have approximately . The morphological selection criteria that we applied to our data are very effective at rejecting stars (see Figs. 1, 2, and 3), and the HST images show all of the 21 GC candidates to be extended objects, so we believe that stellar contamination is not a problem in our data.

The galaxy counts of Tyson (1988) suggest that there will be background galaxies in our images down to . However, many of these galaxies will be obscured by the dust lane, so we will detect significantly fewer than this. The morphological criteria that we applied to obtain our list of GC candidates will reject any galaxies that are not morphologically similar to the GCs found in the Milky Way or LMC. AM97 used a comparison field located northeast of the nucleus to estimate that % of the objects that they detect in their search for GCs in the inner regions of NGC 5128 are foreground stars or background galaxies. Since the morphological criteria that we applied are stricter than those of AM97, we believe that 20% is a reasonable upper limit on the amount of contamination in our list of GC candidates.

2.4. Uncertainties in the structural parameters

The MINUIT package provides an estimate of the formal uncertainty in each parameter based on the covariance matrix of the fit. In general the formal uncertainties were % of the best-fit value of each parameter. This is consistent with the uncertainties quoted in Table 4 that were determined from the differences between the best fitting structural parameters determined from the F555W images and the F814W images.

In order to test the formal uncertainty estimates, and to look for systematic differences between the recovered structural parameters and the true structural parameters of the NGC 5128 GC candidates, we constructed a series of artificial GCs and added them to the NGC 5128 images. The total of 810 artificial GCs were added to the WFPC2 images with randomly assigned concentrations between , core radii between , ellipticities of , and magnitudes of . We found that the recovered concentrations for the brightest artificial GCs () were within % of their true values 95% of the time. For the faintest artificial GCs () the recovered values were within 22% of the true values 95% of the time. Systematic shifts were negligible for artificial GCs with concentrations greater than , but grew rapidly for artificial GCs with concentrations less than this. The uncertainties in the structural parameters increased as the concentration decreased. Other structural parameters behaved in very similar manners.

A second source of uncertainty in the fitted structural parameters is the uncertainty in the PSF. Each GC candidate was fitted with a Michie-King model that was convolved by an estimate of the PSF at the location of the object on the CCD. We used PSFs that were created by Peter Stetson (1996, private communication) from WFPC2 observations of stars in the Galactic GC Centauri. However, the NGC 5128 images were taken approximately three years after the Cen ones, so long-term variations in the focus of the WFPC2 (e.g. Suchkov & Casertano 1997) raise the possibility of a mismatch between the actual and adopted PSFs. If this is the case then the derived structural parameters would be in error, as the fitted Michie-King models were convolved with a PSF constructed using a slightly different focus from that of our images. In order to estimate the possible errors introduced by uncertainties in the PSF, we repeated the Michie-King model fitting procedure with the wrong PSFs. In other words, we fit Michie-King models to the GC candidates on the WF3 CCD using both the F555W and the F814W PSFs from the WF2, WF3, and WF4 CCDs. This gave us six estimates of the structural parameters of each object obtained using six variations of the WF PSF. For each of these estimates we computed the difference between as determined using the correct PSF, and the five s determined using the incorrect PSFs (). We then computed the mean () and standard error in the mean of these five values for each GC candidate. This gave us an estimate of the systematic uncertainty in the value of that we derived for each GC candidate. Finally, we computed the mean, standard error in the mean, and median of the individual values for all the GC candidate. This gave an estimate of the systematic uncertainty for a typical GC candidate in our data. These values, along with analogous estimates of the systematic errors in the other structural parameters, are presented in Table 5.

Table 5. Systematic errors due to uncertainties in the PSF.

This technique is not mathematically rigorous since the variations in the PSF from one CCD to another, and from one filter to another, are not the same as the variations due to changes in the focus of the HST over a period of two or three years. However, Suchkov & Casertano (1997) find that long-term changes in focus introduce changes of a few percent in the photometric calibrations, which corresponds to changes of a few percent in the shape of the PSF. The variations in the PSF from one CCD to the next can be much larger than this so we believe that the systematic errors derived here represent an over-estimate of the true systematic errors introduced by possible long-term variations in the PSF.

© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999
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