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7. Apparent magnitude and colors

The reduction of apparent B-magnitude to the RC3-system of magnitudes tex2html_wrap_inline1993 with photoelectric zero-point has been studied recently (Paturel et al. 1994). Apparent B-magnitudes reduced to the RC3-system will be designated as bt. Several effects were taken into account. The reduction of a given magnitude m to bt is given by:

where a, b, c, d, e, f, tex2html_wrap_inline2015, <t>, tex2html_wrap_inline2019, <de1950> are constant values given in Paturel et al. (1994, Table 6). The mean bt magnitude is calculated as a weighted mean where the weight is derived for each source of magnitude as the inverse square of the mean standard deviation. The final actual uncertainty sbt is derived from the total weight.

The cumulative completeness curve logN vs. bt is shown in Fig. 7 (click here). The completeness in apparent magnitude is satisfied up to bt=15.5. Apparent total magnitude bt is available for 76760 galaxies. The histogram of actual uncertainties sbt on bt is given in Fig. 8 (click here). More than 7 000 galaxies have an actual uncertainty on bt smaller than 0.02 mag.

Note that apparent diameter can be roughly converted into a magnitude m assuming that the mean surface brightness is constant for all galaxies. The conversion can be made using the relationship (Di Nella & Paturel 1994):


The standard deviation on m is about 0.5 mag. Using this relation, it is possible to obtain an estimate of the apparent magnitude for 93062 galaxies, 76760 magnitudes of which come from bt and 16302 from logd25. This magnitude m will be used for drawing a more general completeness curve (Fig. 11 (click here)).

Figure 7: Completeness curve for apparent magnitude bt. The completeness is satisfied up to the limit bt=15.5

Figure 8: Histogram of actual uncertainty on apparent magnitudes bt

Apparent bt magnitudes are corrected for galactic extinction, inclination and redshift effects according to the relation:

where ag is the galactic extinction in B (see Sect. 4), expressed in magnitude, ak is taken from de Vaucouleurs et al. (1976, RC2 p33, rel.25), v is the heliocentric velocity in tex2html_wrap_inline2067 (Sect. 9) and ai is given by Bottinelli et al. (1995) as:

where, tex2html_wrap_inline2071 is taken from Simien & de Vaucouleurs (1986), as a function of the morphological type code. tex2html_wrap_inline2073 is taken from Fouqué & Paturel (1985) as seen before (Sect. 6), C=0.04 (Bottinelli et al. 1995) and tex2html_wrap_inline2077. Note that this relation has been demonstrated for spiral galaxies only. For early type galaxies (t<0) we assume ai=0, in agreement with de Vaucouleurs et al. (1991).

Colors are given in the UBV systemgif. They are: total asymptotic colors ubt for tex2html_wrap_inline2091 ; bvt for tex2html_wrap_inline2095 and effective colors (i.e. colors within the effective aperture in which half the total B-flux is emitted) ube for tex2html_wrap_inline2101; bve for tex2html_wrap_inline2105. Total asymptotic colors are corrected for galactic extinction, inclination and redshift effects according to RC3. The corrected colors are bvtc and ubtc for tex2html_wrap_inline2111 and tex2html_wrap_inline2113 respectively.

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