Preliminary Report on a Statistical Analysis of the Lick Galaxy Counts.
Abstract
The spatial distribution of galaxies may be related to a continuous probability density P1(r,0, (p) which is a statistically homogeneous and isotropic random function of position (Astron. J. 61, 383, t956). The distribution of galaxy images on the celestial sphere is then related in an exactly analogous way to a two-dimensional probability density P1 (0, (p), defined as a weighted integral over depth of P1 (r,0, (p). Galaxy counts give information directly about P2, but only indirectly about P1. We have accordingly undertaken to analyze the Lick galaxy counts of Shane, Wirtanen, and Mayall along the following lines: (a) calculate the mean lagged products of the corrected counts in 5 0-wide galactic-latitude zones; (b) for each latitude zone construct a smoothed autocorrelation function; (c) calculate the corresponding Fourier transforms (spectrum functions); (d) by allowing for differential galactic absorption and for the effects of finite cell size, derive the spectrum function associated with P2 (0, ~); (e) find what this information implies about the spectrum function associated with P1 (r,0, ~). We have completed all steps but the final one in this program. The two-dimensional spectrum function appears to be rather flat in the limited wave- number region about which the data contain useful information. Consequently, the angular correlation distance of the counted numbers-a quantity that played an important part in the analyses of Neyman and Scott and of Limber-actually depends chiefly on the size of the cells used for the counts, rather than on any property of the spatial distribution. The Lick counts do not, therefore, contain useful information about correlation distances or mean cluster diameters in physical space. They do contain information about a limited part of the clustering spectrum. Information about other parts of the clustering spectrum can come from analyses like the present one of galaxy counts to different limiting magnitudes and with different cell sizes.
- Publication:
-
The Astronomical Journal
- Pub Date:
- October 1963
- DOI:
- 10.1086/109011
- Bibcode:
- 1963AJ.....68..540L