3 The photometry

3.1 Data analysis

The photometric reduction of the combined U-, V- and $K_{\rm s}$-band images was performed using the DAOPHOT II programme (Stetson 1987,1994). First, we located all the objects that were >3$\sigma$ above the background on individual images. More than 50 relatively bright, not saturated, isolated, stellar objects were chosen to create the variable PSF for each image. ALLSTAR fitting of the PSF to all the objects produced the object lists that were matched with DAOMATCH and DAOMASTER, where only objects with good photometry in at least two frames were kept. The final photometric catalogue was obtained with ALLFRAME which uses as input information photometry lists from ALLSTAR and fits the PSF to all frames (in U, V and K-band) simultaneously. Again, only the objects detected in at least 2 images were kept. Using the information on the location of stars in all bands simultaneously improved our photometry, which is deeper by $\sim$1 mag with respect to ALLSTAR photometry. Moreover, the treatment of close companions, in particular the ones that have different colors, is much better with ALLFRAME.

NGC 5128 is close enough that its globular clusters appear slightly resolved, in the sense of having a larger FWHM and non-stellar PSF (Minniti et al. 1996; Rejkuba 2001). Restricting the sharpness and goodness of the fit parameters to -0.7< SHARP <0.7, we rejected most of the galaxies, star clusters and other extended objects as well as remaining blemishes and cosmic rays from the final photometry list. Also stars with large photometric uncertainties in one or more filters ( $\sigma \ge 0.5$ mag) were rejected.

Figure 3: Photometric calibration of Landolt (1992) stars during the nights of observations in U and V filters. Left panels: the scatter for the calibration without the color term; right panels: the scatter for the calibration with the color term.

Finally the images were visually checked and a few remaining extended background objects (e.g. partially resolved star forming region in a background spiral galaxy) were discarded. With this selection our final U,V photometry catalogue contains 1581 and 1944 stars in Fields 1 and 2, respectively, while the V,K catalogue contains 5172 and 8005 stars and the numbers of stars with good photometry in U, Vand K-band are 508 and 663 in Fields 1 and 2, respectively.

3.2 The photometric calibration

For the photometric calibration of the optical images, standard stars from the catalogue of Landolt (1992) were used. We checked the photometric quality of the two nights separately and since both were photometric, with almost identical zeropoints, we combined the standard stars for the two nights. Using a total of 14 stars in 4 different fields, spanning the color range -1.321<(U-V)< 4.162, we derived the following calibration transformations:

 

$$u_{\rm inst} U - 24.262(\pm0.089 ) + 0.379 (\pm0.068 )*X$$ =

$$- \,\,\,0.042(\pm0.007)*(U-V)$$ (1)

$$v_{\rm inst} = V - 27.348 (\pm 0.042) + 0.213 (\pm 0.034)*X$$ (2)

where X is the mean airmass of the observations, $u_{\rm inst}$ and $v_{\rm inst}$ are instrumental magnitudes and U and V magnitudes from the Landolt (1992) catalogue. The one-sigma scatter around the mean was 0.031 mag for the U band and 0.023 mag for the V band (Fig. 3, left panel). Adding the color term (U-V) in the transformations slightly reduces the scatter in the V-band to 0.017 mag (Fig. 3, right panel). However, the calibration equation without the color term for the V-band was preferred, since the scientific data in that filter go much deeper and Umagnitudes for some objects could not be measured accurately enough.

Observations at our reference $K_{\rm s}$-band epoch (G in Table 1) were taken in photometric conditions. During the same night, July 8 2000, three standard stars from the list of Persson et al. (1998) were observed. Each standard star was observed at 5 different positions on the IR-array. In this way, a total of 15 independent measurements were obtained. However, the number of measurements with different airmass was only 3, so that we preferred to adopt the mean extinction coefficients measured on Paranal for $K_{\rm s}$-band of 0.05 mag/airmass. The derived zeropoint of the G-epoch observations is $24.23\pm 0.04$. The following calibration equation was applied to our data:

$$k_{\rm s,\rm inst} = K_{\rm s} - 24.23 \,(\pm 0.04) + 0.05 * X$$ (3)

where X is the airmass of observations, $k_{\rm s,\rm inst}$ is the instrumental magnitude and $K_{\rm s}$ is the calibrated magnitude. The photometry of all other K-band epochs were measured with respect to the reference epoch.

   
3.3 Completeness and contamination

Figure 4: The completeness and photometric uncertainties as a function of magnitude and color. The thin vertical dotted lines indicate the value of input U-V colors. The full line defines the 90% completeness limit and the dashed line is for 50% completeness limit.

Figure 5: The completeness and photometric uncertainties as a function of magnitude and color. The thin dotted line indicate the value of input V-K colors. The dashed line defines the 50% completeness limit.

Figure 6: The completeness as function of radial distance from the center of NGC 5128 calculated around 90% completeness limit for U- and V-band (for (U-V)=0.7) and around 65% for $K_{\rm s}$-band.

We made extensive tests to measure completeness and magnitude uncertainties as a function of magnitude and radial distance from the center of the galaxy. The completeness for the U, V and $K_{\rm s}$-band photometry has been calculated using the ADDSTAR programme within DAOPHOT. We made twenty artificial star experiments, adding each time $\sim$3000 stars to the first frame. The stars were added on a regular grid separated by $2 \times R_{PSF} +$ 1 pixels in order not to alter crowding (where R_PSF is the PSF radius used for fitting the image with the worst seeing) and having magnitudes randomly distributed in the observed range. The position of the first star in the list was chosen randomly, so that over 20 different experiments the added stars were uniformly distributed over the whole field. After the appropriate coordinate shifts were applied and magnitudes changed to the instrumental system taking into account the observed magnitudes and colors, the same stars from the first frame were added also to all other frames. Their photometry was recomputed in the same way as for the original images. The stellar PSF obtained from the field stars for the respective image was used in the simulations. Incompleteness in Field 1, defined by a recovery rate of 50% from the artificial-star experiment, sets in around magnitude 25 in the U-band (but depends strongly on U-Vcolor; see Fig. 4) and 22.5 in $K_{\rm s}$-band (Fig. 5). The corresponding numbers for Field 2 are 25 for U-band and 21.3 for $K_{\rm s}$-band. The difference at $K_{\rm s}$-band between the two fields is due to (1) better seeing in Field 1 ( ${\it FWHM}=2.1$ pix vs. 2.7 pix) and (2) higher surface brightness in Field 2.

Dependence of the completeness on radial distance from the center of the galaxy ( $\alpha_{2000}=13^{\rm h}25^{\rm m}26\hbox{$.\!\!^{\rm s}$ }4$, $\delta_{2000}=-43^\circ 01\hbox{$^\prime$ }05\hbox{$.\!\!^{\prime\prime}$ }1$) was calculated for the magnitude bin around 90% level of completeness in U- and V-band (Fig. 6) and around 65% of completeness in $K_{\rm s}$-band. There is no significant spatial variation of completeness in our data.

To assess the accuracy of our photometry, we calculated the difference between the input and recovered magnitudes for each magnitude bin (Figs. 4, 5). Our photometry is reliable down to the incompleteness limit and blending does not seriously affect our data (see the discussion in Sect. 4.2). For magnitudes fainter than the 50% completeness limit, the measured values are systematically brighter, because of the bias towards brighter fluctuations and blending due to crowding. The colors of the recovered stars with magnitudes fainter than the 50% completeness limits are redder than the input colors in the UV CMDs (Fig. 4), due to the larger incompleteness in the U- than in the V-band. In the VK CMDs the colors of the recovered stars range from slightly redder than the input color for the very red stars, due to the dominant incompleteness in the V-band, to bluer for the faintest and bluest stars, due to the dominant incompleteness in the K-band (Fig. 5). We did not correct our data for this systematic shift, because magnitudes fainter than the 50% completeness limit will not be used in further analysis.

Contamination by foreground Galactic stars and unresolved background galaxies is important because of the low Galactic latitude of our fields ( $b=19\hbox{$.\!\!^\circ$ }5$) and the very deep photometric limits observed. We used the Besançon group model of stellar population synthesis of the Galaxy available through the Web (Robin & Creze 1986; Robin et al. 1996) to simulate the total number and optical magnitude and color distribution of Galactic foreground stars in our fields. The simulated catalogue has 1827 stars in the FORS1 field ( $6\hbox {$.\mkern -4mu^\prime $ }8 \times 6\hbox {$.\mkern -4mu^\prime $ }8$) in the magnitude interval 18<V<30. In order to get a realistic estimate for the number of stars that would be observed in our fields, the correction for completeness is necessary. Therefore, we added the stars from the simulated catalogue (with magnitudes scaled to correspond to instrumental magnitudes) to our images and re-measured their magnitudes. In this way, realistic photometric uncertainties were applied and the number of stars recovered in two fields was corrected for completeness. A total of 340 and 350 stars with U- and V-band photometry satisfying profile fitting and photometric uncertainty selection criteria were measured in Field 1 and 2, respectively. Most of the foreground stars have 0<U-V<3 (Fig. 7). All of the stars in the red part of the Field 2 CMD brighter than $V\sim22$ are expected to be foreground stars (see Sect. 4.1). In order to adjust for the expected number of Galactic stars we normalized the models to the observed number of reddest stars in Field 2. Thus the total number of foreground stars was increased by 31% in both fields.

The Galaxy model simulation supplies not only the colors of the simulated stars, but also their metallicities, ages, spectral types and luminosity classes. Using all these data and the Kurucz (1998) model atmospheres, we derived the foreground contamination in the K-band. After correction for completeness, the expected number of foreground stars in ISAAC images is 112 and 91 in the VK CMD of Field 1 and 2, respectively. All of the foreground stars have 1.0< V-K < 4.5(Fig. 7 right panel).

The measured number of compact background galaxies on the FORS1 images, taken in similar observing conditions, is 400 in the magnitude range V=20-25 mag for the selection of sharpness parameter $-1<{\rm sharp}<1$ (Jerjen & Rejkuba 2001). Our tighter selection criteria ( $-0.7<{\rm sharp}<0.7$) eliminated most of them. In the smaller field of view of ISAAC, the predicted number of background galaxies is $\sim$330 in the interval of magnitudes $16<K_{\rm s}<23$ and $\sim$180 between $16<K_{\rm s}<22$(Saracco et al. 2001). Most of the background galaxies are resolved and rejected by sharp and magnitude uncertainty parameter requirements on our photometry. Only few compact galaxies might contaminate the sample.

Figure 7: UV (left) and VK (right) color-magnitude diagrams for foreground Galactic stars simulated using the Besançon group model. The correction for completeness and realistic photometric uncertainties have been applied by adding the simulated stars to our Field 2 images and re-measuring them. The reddening vector E(B-V)=0.1 is plotted in the upper right corner.

3.4 Comparison with published data

Several recent studies of resolved stellar populations in NGC 5128 exist in the literature, all but one made with HST in F606W (V) and F814W (I) or F110W (J) and F160W (H) photometric bands, which are not very sensitive to the recent star formation. Our Field 2 is centered on the field of Soria et al. (1996), which was also observed in the near-IR (F110W and F160W filters) by Marleau et al. (2000), but the direct comparison is not possible due to different photometric bands used.

The only possible direct comparison is for our Field 1 photometry, which partially overlaps with the HST photometry of Mould et al. (2000) and the ground based photometry of Fasset & Graham (2000). The last authors observed a wider field than ours in U, B and V Glass filters, but due to smaller telescope aperture (2.5 m), their photometry is much shallower. The HST photometry is deeper, but covers a much smaller area. The mean difference between V magnitudes of Fasset & Graham and Mould et al. photometry is $-0.13\pm 0.07$ mag, in the sense of HST photometry having a systematically fainter zero point (Fasset & Graham 2000). Comparison of 26 stars in common between our data and that of Fasset & Graham for the brightest blue stars (their Table 3) is presented in Fig. 8.

Figure 8: Comparison of our photometry with that of Fasset & Graham (2000) for 26 bright blue stars in common. In the upper panned the comparison of V band magnitudes is presented and in the lower panel U-band magnitudes are compared. The two extended objects (#4 and #5 in Table 2) noted by Rejkuba (2001) are plotted with filled symbols. The mean offset of -0.13 mag in U-band is indicated with the dashed line.

The mean difference for all 26 stars is negligible for V-band photometry, but it amounts to 0.13 mag in U-band. From Fig. 8 a systematic trend with the magnitude is apparent in V and U band. Excluding the star #10 (see Table 2),

 

 

Table 2: Comparison with Fasset & Graham (FG) photometry; the numbers of stars in the first column are from FG.

#	$V_{\rm FG}$	$(B-V)_{\rm FG}$	$(U-B)_{\rm FG}$	$V_{\rm FORS1}$	$U_{\rm FORS1}$
1	19.94	+0.23	-0.54	19.987	19.498
4a	21.07	+0.12	-1.26	20.871	19.711
5b	21.19	+0.04	-1.26	20.925	19.717
7c	21.51	-0.07	-0.34	$\cdots$	20.291
10	21.65	+0.04	-1.16	20.986	20.440
12	21.72	+0.21	-0.20	21.722	21.580
13	21.75	+0.11	-0.84	21.667	20.600
15	21.86	+0.09	-0.61	21.885	21.099
16	21.94	-0.05	-0.92	21.978	20.862
17	21.95	+0.34	-0.82	21.963	21.391
18d	22.01	+0.30	-0.84	$\cdots$	$\cdots$
20	22.10	+0.07	-0.82	22.150	21.144
21	22.12	-0.08	-1.00	22.127	20.942
26	22.25	+0.08	-0.98	22.323	21.234
27	22.35	-0.03	-0.91	22.331	21.295
28	22.40	-0.05	-0.87	22.412	21.323
30	22.51	+0.20	-0.56	22.631	22.032
32	22.53	+0.13	-0.50	22.579	22.217
33	22.54	+0.07	-0.76	22.623	21.528
35	22.55	+0.11	-0.55	22.503	21.968
36	22.58	-0.08	-0.88	22.606	21.535
37	22.58	+0.02	-1.06	22.777	21.549
39	22.69	-0.12	-0.82	22.706	21.585
42	22.82	+0.00	-1.02	22.856	21.646
46	22.89	+0.31	-0.12	22.919	23.260
47	22.90	-0.05	-1.00	22.934	21.737
48	22.96	+0.08	-0.74	23.051	22.149
50	22.99	-0.04	-0.81	23.134	22.027

^a f1.GC-8 (Rejkuba 2001).
^b f1.GC-25 (Rejkuba 2001).
^c Saturated in FORS1 V image.
^d Extended in FORS1 images.

which has HST V magnitude of 21.04 (thus close to our value; star R4 in Table 1 of Mould et al.), and extended sources #4, #5 (see Rejkuba 2001; filled triangles in Fig. 8) and #18, these trends can be represented by the following equations:

$$V_{\rm FORS1}-V_{\rm FG} = 0.030 \times V_{\rm FORS1} - 0.65$$ (4)

$$U_{\rm FORS1}-U_{\rm FG} = 0.089 \times U_{\rm FORS1} - 2.05$$ (5)

with rms equal to 0.055 for V and 0.096 for U. At least part of this difference may be due to different filters used (Bessell 1995). Fasset & Graham further neglected the color term in their calibration due to insufficient color coverage of their standards, while we found that the color term is important for our U-band calibration.