Count laws and projection effects in clusters of galaxies

Abstract

We show that a 2D projection is representative of its corresponding 3D distribution at a confidence level of 90 % if it follows a King profile and if we consider the whole spatial distribution. The level is significantly lower and not decisive in the vicinity of the 2D cluster center. On another hand, if we verify the reciprocal statement of the Mattig's distribution (1958) -i.e. a flux limited sample is represented by a 0.6 slope of its count law-, we point out that, due to the usual unaccuracy of the slope determination, a slope of 0.6 is not a sufficiently strict criterion for completeness and uniformity of a sample as often used in the literature.