3 Abell 496 image processing

Abell 496 is a class 1 rich cluster, Bautz Morgan type I (Abell et al. 1989), dominated by a single central cD galaxy, MGC -02-12-039 ( $\alpha_{2000} = 4^h 33' 37.7''$, $\delta_{2000} = -13^\circ 15' 43.2''$, z=0.032). The peak of the X-ray emission lies inside the core of the cD galaxy (Table 1). CCD observations of the cluster were carried out during the first observing run from 24 to 27 December 1994. The effective field of the DFOSC camera and Thomson THX 31156 CCD is $8.68 \times 8.68$arcmin with a single pixel corresponding to 0.508  arcsec. The total area of the observed field is 224 arcmin² for each filter (Fig. 2). We list the journal of the observations in Table 2.

Figure 3: The calibration straight line for filter r. For each of the three standard star, the typical uncertainty on the offset measure is 0.02 magnitude. Moreover, the 3 different average offset values show a linear dependence on the colour of the star. By the linear fit, we extrapolate the offset value corresponding to g-r=0

3.1 Flat-fielding and magnitude calibration

Basic data reduction, including bias subtraction, flat-field correction, magnitude calibration and cosmic rays subtraction, is done using the ESO-MIDAS software environment.

For each filter we build two different flat-field frames. For the first we use the dithering method to obtain the flat field frame directly from scientific exposures (see for example Molinari et al. 1996). The second flat field frame is built using the median of the distribution of the sunset and twilight sky images. We obtain the minimum value of the ratio noise/sky, at both small and big scales in the frames, using the first flat-fielding procedure for filter i. For the g and r filters we adopt the average between the two different flat-field frames, since this gives the minimum rms. After the reduction, the typical rms of the sky is $1.5\%,~ 1\%,~ 0.75\%$ of the background for the g, r, i frames, respectively.

   

Table 2: The journal of observations. The Date, Universal Time, air mass, exposure time, and seeing for each frame are shown. In each frame seeing is calculated as the FWHM of the stars

Object	Filter	Date	U.T.	airmass	E.T.	Seeing
field0	g	25-12-94	1:54	1.071	900s.	1.25
			2:48	1.040	"	1.25
			3:41	1.060	"	1.50
			4:33	1.133	"	1.50
	r		1:37	1.092	"	1.25
			3:05	1.041	"	1.25
			3:24	1.048	"	1.50
			4:50	1.171	"	1.50
	i		2:12	1.054	"	1.25
			2:31	1.044	"	1.25
			3:58	1.077	"	1.50
			4:16	1.102	"	1.50
field1	g	26-12-94	1:45	1.076	"	1.50
			2:14	1.050	"	1.50
			3:41	1.063	"	1.15
			4:06	1.093	"	1.15
	r		1:12	1.128	"	1.50
			2:32	1.042	"	1.50
			3:24	1.050	"	1.15
			4:23	1.121	"	1.15
	i		1:28	1.100	"	1.50
			2:50	1.039	"	1.50
			3:07	1.042	"	1.15
			4:40	1.157	"	1.15
field2	g	27-12-94	1:21	1.105	"	1.30
			5:04	1.233	"	1.35
			5:22	1.298	"	1.35
		28-12-94	1:49	1.064	"	1.25
	r	27-12-94	1:05	1.134	"	1.30
			4:47	1.184	"	1.35
			5:39	1.372	"	1.35
		28-12-94	1:32	1.083	"	1.25
	i	27-12-94	1:38	1.080	"	1.30
			1:56	1.061	"	1.30
		28-12-94	0:58	1.140	"	1.25
			1:16	1.106	"	1.25
field3	g	28-12-94	2:14	1.046	900s.	1.25
			4:11	1.114	"	1.50
			5:35	1.371	"	1.50
			5:52	1.462	600s.	1.50
	r		2:31	1.040	900s.	1.25
			4:28	1.147	"	1.50
			5:18	1.297	"	1.50
			6:04	1.538	600s.	1.50
	i		2:48	1.040	900s.	1.25
			4:45	1.189	"	1.50
			5:02	1.240	"	1.50
			6:15	1.618	600s.	1.50

Cosmic rays are identified by their appearance in only one of the dithered images. The stars observed as standard are selected in the photometric system of Thuan & Gunn (1976) and are listed in Table 3. The offset of the calibration is measured as the difference between instrumental magnitude (as measured with the g, r, i filters at ESO telescope) and the magnitude of the standard stars. In spite of the fact that we evaluate a relation between the colour of the standard star and the magnitude off-set, we decided not to account for the colour relation due to the paucity of the data and the possibility of systematic errors. Most importantly, we could not apply the colour correction to galaxies which have been detected only in one or two filters (40% of the sample). Choosing the best compromise, we applied in all cases the magnitude correction equivalent to g-r = 0. Because of this assumption, our photometric data differ slightly from the photometric Gunn system (typically 0.1 magnitude for an object with g-r=1). The colours we measure, however, match very well the Gunn system, because the slopes of the calibration straight lines in the three filters are similar.

   

Table 3: Standard stars used for calibration

Name	$\alpha_{1950}$	$\delta_{1950}$	g	r	i
HD 84937	09 46 12.1	+13 59 17.0	8.325	8.383	8.43
Ross 683	08 47 46.6	+07 49 08.0	11.40	11.08	-
BD $-15^\circ 6290$	22 50 37.5	-14 31 42.0	10.754	9.544	8.334

   

Table 4: k correction (Buzzoni 1995) and galactic extinction (Burstein & Heiles 1982) values used for the E/S0 galaxies in Abell 496

filter	g	r	i
k corr.	0.02	0.01	0.01
gal. ext.	0.07	0.04	0.03

3.2 Object search and analysis

Automatic object detection and magnitude evaluation have been done by using the INVENTORY package (West & Kruszewski 1981) implemented in the MIDAS environment. Galaxies of the sample span a very large range in magnitude from the magnitude limit (mag $\sim24$, see next section) to the isophotal magnitude (mag $\sim 13$) of the cD central galaxy. This range corresponds to a comparable range in the size of the galaxies. It varies from the PSF limit ($\sim 3$ pixels) to the isophotal radius of the cD galaxy ($\sim 100$ pixels). Because of this inherent heterogeneity, the sample is not perfectly suitable for automatic search and analysis of the sources. In particular, we must separate the signal of very extended objects from the rest of the image to avoid the problem of multiple detection. The procedure we use is composed of the following three points. First, we model and subtract the light of the most extended objects. Second, we apply the INVENTORY standard research and analysis procedure to frames in which the remaining objects are comparable in size. Finally, we apply the INVENTORY analysis routine to the single-object images of the modelled and rebuilt extended objects. Here we describe only the first point of the procedure which is the original part.

Figure 4: Isophotes of the cD galaxy of Abell 496 from the raw image (left panel), and from the rebuilt model (right panel). The coordinate refer to the pixels of the image: 1 pixel = 0.508 arcsec. In the left panel the circular path at 24 pixel radius is marked; the intensity profile along this path is reported in the panel A of Fig. 5. The model is built using raw data where possible and fit value when an external object is superimposed on the line of sight

We model and rebuild the extended sources, typically giant elliptical galaxies, with a procedure similar to the one described by Molinari et al. (1996). We improved their algorithm by making it more flexible. First, for each distance from the centre of the galaxy, the algorithm analyses the azimuthal intensity profile along the circular paths (see the left panel in Fig. 4). The projection of an elliptical isophote on the circular paths yields a periodic variation of surface brightness, as shown in the panel A of Fig. 5. It corresponds to the intensity profile along the circular path marked on the left panel of Fig. 4. The maxima correspond to the intersections of the circular path with the major semi-axis of the isophote. Then the algorithm fits the profile using a Fourier series and a low-pass filter. This procedure eliminates the physical and geometrical high frequency noise due to the discrete nature of the CCD pixel grid. Finally, we calculate the distribution of the differences between the data and the fit: we exclude from the profile the points whose intensity is greater than 3 times the standard deviation of the distribution (Fig. 5, panel B). Those points are replaced by the exact fit values. By iterating a few times the procedure, we can separate the signals of the superimposed sources (Fig. 5 panels C), without any assumption on the shape of the isophotes.

Figure 5: Steps of the modelling procedure. A). The raw elliptical isophote is projected on a circular path. The profile shown here corresponds to the 24 pixel radius of the cD galaxy of Abell 496 as shown with a marked line in the left panel of Fig. 4. The azimuthal coordinate has the zero point toward the right of the image, and it increases counterclockwise. The periodic shape of period $\pi$ of the profile is evident: the two maxima are at 90 and 270 degrees, corresponding to the intersections between the path and the major axis of the elliptical isophotes (see Fig. 4). The profile of a superimposed source is evident at 30 degrees as a departure from the periodic shape. We can find the superimposed object along the path marked in Fig. 4 at30 degrees from the 0 point of the azimuthal coordinate. The high frequency noise in the profile shape is due both to Poissonian and geometrical noises. B). Fit procedure is performed repeatedly excluding step by step the external object identified at 3 $\sigma$. C). When an external object is identified, the extended object is rebuilt using the fit value. Otherwise, the profile is left untouched

We also made the algorithm more flexible by introducing other geometrical parameters. In particular, we allow for the exclusion of selected angular profiles intervals from the calculation of the Fourier coefficient of the trigonometric series. Intervals to be excluded are selected by visual inspection. The exclusion option is useful when two objects of comparable size overlap and have very close intensity maxima. In this way, we can rebuild the hidden isophothes assuming a central symmetry. In Fig. 4 we compare the isophotes of the raw image of the cD galaxy (left panel) with the rebuilt model (right panel). The rebuilt model is then subtracted from the original frame to keep the photometric analysis of very extended sources separated.

Although time-consuming (due to its interactiveness), this procedure yields accurate photometric measurements of both the extended and small sources. The described procedure, in fact, allows the complete photometric analysis of the surface brightness of the extracted objects (see Sect. 5.1 for the Abell 496 cD). Contrary to other popular automated programs (e.g. SExtractor, Bertin & Arnout 1996), we do not assign a pixel and its value to a unique object, but partition the flux in each pixel among the different objects detected. Thus the isophotes are recovered in their shape and intensity for all sources.