The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field.

Abstract

In this paper the theory recently developed by the writer for the analysis of counts of the extra-galactic nebulae in terms of a fluctuating density field has been applied to the counts obtained by Shane and Wirtanen at the Lick Observatory. The observational data have been reduced to the forms required for this analysis, and the corresponding theoretical functions have been obtained for several sets of values for the parameters involved. The comparison of the theory with the observations indicates that the effects of fluctuations in the absorption within our own Galaxy can be neglected in a first approximation ; further, the theoretical expectations for the case in which there is a dispersion of 2 mag. in the absolute magnitudes of the nebulae are found to be in best accord with the observations. The mean square of the deviations in the space density of the nebulae from the mean is found to be about twenty-five times the square of the mean density. The value for the microscale, ro, characterizing the "eddy" distribution of the nebulae and the value for the mean density of the nebulae in space, p, are both dependent upon the particular values used for the limiting apparent magnitude of the counts, m^, the mean absolute magnitude of the nebulae, Mo, and the optical half-thickness of the galaxy, T1/2; for given values of these quantities it is shown how the corresponding values of ro and p can be deduced on the basis of the theory. From a straightforward analysis of the counts as they are given, the value fi/2 = 0.76 is obtained. If this value is taken as that which is appropriate to the observational material and if the best available values for w'o and Mo are used, it is found that ro = 3.0 X 10 6 parsecs and p = 6.0 X 10-19 nebulae per cubic parsec. I. INTRODUCTION In a previous paper 1 the writer has developed a method for analyzing the counts of the extragalactic nebulae in terms of a fluctuating density field for the nebulae in space. In the present paper the counts obtained by C. D. Shane and C. A. Wirtanen at the Lick Observatory are analyzed according to the proposed model. Here-as in Paper I-we shall consider an idealized model such that the absolute magnitude, M, the apparent magnitude, m, and the distance, r, for a particular nebula are related in the following way: M = w + 5-5 logio r-2.5 T logio e , (i) where r is the optical thickness of the Galaxy in the direction considered. We shall further assume that the universe of those nebulae which are recorded in the counts is static in time and homogeneous with respect to the absolute magnitudes and the spatial-distribution properties of the nebulae within it. Deviations from the conditions of these assumptions most certainly exist ; and, if well determined, the effects introduced by such deviations could be taken into account at the expense of some mathematical simplicity. However, it is felt that such deviations are not yet well enough known to warrant their inclusion. It is further felt that in the proposed type of statistical treatment such refinements are hardly justified in any case. II. THE OBSERVATIONAL DATA AND THEIR REDUCTION TO THE REQUIRED FORMS