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6. Diameter and axis ratio

Many papers were devoted to the study of diameters and specially to the reduction to the standard system defined by the isophote at the brightness of 25 B-tex2html_wrap_inline1907. The conclusion of these studies was published by Paturel et al. (1991).

The diameters are expressed to 0.01' in log of 0.1' according to the convention of Second Reference Catalog (de Vaucouleurs et al. 1976). They are designated as logd25. For instance a diameter of 10' will be given as logd25=2.00. Axis ratios are expressed in log of the ratio of the major axis to the minor axis. They are designated as logr25.

The main catalogs are reduced to the tex2html_wrap_inline1921-standard system using a relationship

where D is the diameter and R is the ratio of the major axis to the minor axis in a given catalog. The constants a, b and a' are given in Paturel et al. (1991, Tables 1a and 1b) for the most common catalogs. Diameters and axis ratios extracted from LEDA images or from COSMOS database were converted into the standard system using the same relationships but with different coefficients (Paturel et al. 1996; Garnier et al. 1996; Rousseau et al. 1996).

The completeness curve logN vs. the limiting logd25 is shown in Fig. 3 (click here). The completeness is satisfied down to the limit logtex2html_wrap_inline1937 (i.e. 0.8' in diameter). Diameters logd25 are available for 82033 galaxies. The histogram of actual uncertainty slogd25 on apparent diameter logd25 is given in Fig. 4 (click here). More than 13 000 galaxies have a diameter with an actual uncertainty smaller than 0.05 (in logd25). The distribution of logarithms of axis ratios is shown in Fig. 5 (click here). This distribution is close to the one expected if the orientation of galaxies is randomly distributed.

Figure 3: Completeness curve for logd25. The completeness is satisfied down to the limit logtex2html_wrap_inline1951 (i.e. 0.8' in diameter)

Figure 4: Histogram of actual uncertainty slogd25 on apparent diameter logd25

The position angle of the major axis is noted PA. It is counted from North towards East, between tex2html_wrap_inline1959 and tex2html_wrap_inline1961 and is almost randomly distributed (Fig. 6 (click here)). A small excess of galaxies appears at PA = tex2html_wrap_inline1963 and PA = tex2html_wrap_inline1965 which seems to be an artifact.

Figure 5: Histogram of log of axis ratio logr25. The solid curve shows the distribution of logr25 for random orientation

Figure 6: Distribution of major axis position angles

In RC2 apparent diameters were corrected for galactic extinction and inclination effect according to Heidmann & de Vaucouleurs (1972a,b,c). Recently, this question was revisited after the result by Valentijn (1990, 1994) that galaxy disks are opaque. Our conclusion (Bottinelli et al. 1995) leads to the following correction:

where C=0.04, ag is the galactic extinction (see section about coordinates) and tex2html_wrap_inline1975 is given by Fouqué & Paturel (1985) as 0.094 for spiral galaxies and 0.081-0.016.t for early type galaxies with morphological type code t<0.

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