Distances, Space Distribution and Luminosity Function of Quasi-stellar Objects

Abstract

THE question of the distances of quasi-stellar objects may be dealt with on the basis of The following statistical consideration. Consider a multitude of objects of some sort, distributed according to Poisson's law in an infinite space. The mean density of these objects is D. There is an observer, whose position is chosen randomly, and the objects have been enumerated in order of increasing distance from this observer. The distance of the kth object from the observer is denoted by r_k. Designating the volume of the sphere of radius r_k by V_k it can be shown easily^1,2 that the mean value of V_k is equal to Each of the values can be considered as “density determined by means of the xth object”. It can be shown that the dispersion of D_k decreases when k increases. The values of D_k determined using the distances of several neighbours can serve as different approximations to the mean density D.