Description of small-scale fluctuations in the diffuse X-ray background.

An analytical study of the fluctuations on a small angular scale expected in the diffuse X-ray background in the presence of unresolved sources is presented. The source population is described by a function N(S), giving the number of sources per unit solid angle and unit apparent flux S. The distribution of observed flux, s, in each angular resolution element of a complete sky survey is represented by a function Q(s). The analytical relation between the successive, higher-order moments of N(S) and Q(s) is described. The goal of reconstructing the source population from the study of the moments of Q(s) of order higher than the second (i.e., the rms fluctuations) is discussed.