3. Morphological analysis
We present below the global morphological properties of ABCG 194 both from optical and X-ray data. After obtaining maps of the various components, we will discuss the main cluster orientations at various scales, and compare the density profiles for the galaxy distribution and for the X-ray gas.
3.1. Optical analysis
In order to illustrate the galaxy distribution, we have derived a Dressler map of the galaxy distribution (Dressler 1980), the main directions at various radii and the galaxy density profile.
The Dressler smoothing method has been applied to the sample of galaxies with velocities in the cluster; the result is displayed in Fig. 5. One can see that in the central part the cluster is elongated along PA50 with a second component visible in the south east, along a direction roughly perpendicular to the main one.
We estimate these quantities with a momentum method, using the Salvador-Solé & Sanromá (1989) software: from a distribution of points in a disc of radius , this method gives the ellipticity and major axis direction, as well as the points which are involved in the actual ellipse (displayed in Fig. 6a), leading to an equivalent radius . The position angles and axial ratios - defined as the ratio of the small axis b to the large axis a - for the three concentric discs of radii , and arcsec are given in Table 1. The axial ratio is seen to increase with radius, showing that despite its classification as "linear" ABCG 194 is elongated only in its central parts.
Table 1. Equivalent radius, number of galaxies located in the disc (see text), minor to major axis ratio, direction of the major axis and center of the ellipse (in arcseconds relative to the cluster center).
Chapman et al. (1988) have fit the ABCG 194 profile (for azimuthally averaged counts) with the following model:
(resulting parameters are indicated in Table 2). The choice of this profile is questionable in comparison with a more general -model:
However, recent profile fits obtained from the ENACS data are consistent with a King model with a small dispersion on the values of (Adami et al. 1998). C. Adami has kindly performed several fits to our data; his results are given in Table 2 (elliptical profiles are used, assuming ). It is interesting to notice that even when is free in the fitting process (rows 3-5), its value is close to 1, in agreement with ENACS values. The axial ratio is 0.8, in agreement with the values given in Table 1.
Table 2. Values for the -model distribution of galaxies. Notes: (1) Chapman et al. (1988), the cluster is supposed to be spherical; (2) fixed to 1, but the axial ratio is free; (3) and the axial ratio are both free; (4) in a rectangle of 100002 arcsec2, with the ratio fixed at the previous value; (5) in a rectangle of 80002 arcsec2.
With = 360 km s-1 and =2.6 keV, we can calculate and find a value of 0.93, consistent with the values given in Table 1.
3.2. X-ray analysis
Keeping in mind the weakness of the signal to noise ratio, we have tried to derive as much information as possible from the X-ray data.
While two privileged directions are found from the optical analysis (see previous subsection), only one is found at first sight from the X-ray image. We have therefore made an analysis of the number of counts in angular sectors centered on the X-ray -model center and wide, rotating with a step of . Fig. 7 shows the existence of four peaks; the two strongest peaks correspond to PA=50 (the main principal direction of the cluster) and PA=140 pointing towards the south east optical enhancement. The third peak, which is symmetrical to that at PA=50 is very weak. The fourth peak is symmetrical to the second one, and shows that there is also X-ray emission towards the north west. Note that the first peak is certainly contaminated by the bright X-ray source labeled F in Fig. 6b.
We performed a multi scale wavelet analysis on this image to eliminate the noise and identify structures at various scales (see a full description of the method e.g. in Slezak et al. 1994). This was done in the central 35´ diameter region (within the PSPC annulus), as illustrated in Fig. 6b. This obviously corresponds only to the central part of the cluster (see Fig. 1). The limiting radius is 1540 arcsec, or 0.8 Mpc.
At the largest scale (32 PSPC pixels, or 4 arcmin), one can observe elliptical emission with a major axis of about 50o and an axial ratio .
At a smaller scale (16 PSPC pixels, or 2 arcmin), the general behavior is similar. Due to the weight of the powerful X-ray emitting point-like source (F), the (X,Y) origin has shifted toward the west along the major axis.
The temperature was fixed to the constant value of 2.60.15 keV measured by ASCA (Fukazawa et al. 1998). We calculated the bolometric X-ray luminosity by normalizing a photo-electric absorbed (galactic ) mekal model (metal abundances = , ) to the source masked and background subtracted total diffuse emission (found to be 0.42 counts/sec). We find erg s-1.
We have performed a pixel by pixel fit to the data as described by Pislar et al. (1997). A -model was used for the density law, including or not the strong point-like sources. The sources detected by Snowden's software were not included in these fits. The center is found at coordinates: , , i.e. displaced to the south west relatively to the optical center given by CGH. The background found (0.24 counts/pixel) is consistent with the mean background taken in an annulus far enough from the center to be flat on a wide area. Results are shown in Fig. 8: the isocontours appear rather satisfactory, but the various parameters are not well constrained (the MINOS routine from MINUIT was unable to find error boundaries). We then made a -model fit on the profile obtained by summing the counts in elliptical bins (with their center, PA and ellipticity given by the pixel by pixel fit). This fit leads to similar values, and to very large error bars. Fig. 9 shows how badly is constrained: the contour of stays open for very large values of . The , and values are defined for , 4 and 9 respectively.
Note that the ellipticity found in X-rays is comparable to that in the optical (see Table 3).
Table 3. Results of different fits of the diffuse emission over the whole image. The sources detected by Snowden's software were not included in these fits.
The X-ray gas mass was calculated by integrating the -model given in Table 3. At the limiting radius =0.8 Mpc (defined as the radius where the X-ray background is reached), the X-ray gas mass is , with limits corresponding to 1 errors: . The very large error bars are mostly due to the fact that the parameter is not well constrained.
The stellar mass Mstellar was calculated by integrating the King model given in Table 2, assuming =10 /. At the X-ray limiting radius , the stellar mass is . However, the galaxies extend much further out, up to a radius of about 3 Mpc, where the corresponding stellar mass is . Note that these values are not well constrained: besides the usual errors on the central density and core radius, the dominant source of error is the incompleteness of our data. In the central part of the cluster (for radii smaller than 2100 arcsec) faint galaxies are relatively more numerous than in the outskirts: 9 galaxies have magnitudes fainter than 16 while 34 are brighter than this value. The stellar luminosity inside radius R is: , where I is the integration of the King distribution. The error on the luminosity is in fact that on , which is independent of radius; the error on I is negligible. We therefore consider that the error on the stellar mass due to incompleteness at faint magnitudes is at most 25%.
The Mgas/Mstellar ratio is about unity for radii smaller than 200 kpc, and reaches a value of for (applying error propagation equations).
The hydrostatic equation applied to the X-ray gas allows us to estimate the total cluster dynamical mass, with hypotheses on the X-ray gas temperature. Since we have no X-ray gas temperature map, we will assume the gas to be isothermal. The corresponding mass profile is displayed in Fig. 10. The dynamical mass at radius is Mdyn = , with limits corresponding to 1 errors: . Although the dynamical mass derived from the X-rays is not very accurate, it agrees with the virial mass estimated by Girardi et al. (1998).
The ratios of the X-ray and stellar masses and of the sum of these two quantities to the dynamical mass are 0.12, 0.04 and 0.16 respectively (for ) at radius . These values are only indicative within a factor of 2, due to the large error bars on the masses.
© European Southern Observatory (ESO) 1999
Online publication: August 25, 1999