The theory of the fluctuations in brightness of the Milky Way. IV

Abstract

In this paper the integral equation governing the fluctuations in brightness of the Milky Way is solved, quite generally, for the case when the system of the stars and clouds extends to infinity in the direction of the line of sight and the transparency factor, q, characterizing the clouds is governed by an arbitrary frequency function, ψ(q)(O ≤ q ≤ 1). The solution is obtained in the form of a series in Laguerre polynomials with coefficients depending only on the moments of ψ(q). It is further shown that the solutions found in Paper II for two particular forms of ψ(q) can be obtained as special cases of the general solution given here.