BIASED THEORIES OF GALAXY FORMATION WITH ARBITRARY THRESHOLD FUNCTIONS AND BACKGROUND DISTRIBUTION

Biased theories of galaxy formation were initially introduced assuming that background matter distribution is Gaussian and only fluctuations above a fixed threshold can turn into observable objects. Both of these assumptions were later relaxed separately. Non-Gaussian background distributions were considered by several authors, and threshold functions different from a 9 (step) distribution were also debated. In the present paper, we introduce first a general formulation allowing us to take into account non-Gaussian backgrounds and non-θ thresholds simultaneously. This allows us to discuss the different effects of these two features. We then outline some general properties of non-θ thresholds which were previously obtained for some particular threshold only. We also relate tentatively the qualitative features of two particular threshold functions to the expected consequences of nonsphericity and merging in the process leading to galaxy clustering. The results obtained for these thresholds seem to show that neglecting such effects can lead to misleading conclusions, namely for very large mass scales. In particular, the threshold we relate to nonsphericity makes the observed number densities of Turner and Gott groups and Abell clusters naturally coherent. We discuss the possible physical relevance of this output. The comparison with observations, here performed on available two-dimensional data sets, seems to furnish a pattern suitable to parameterize more detailed data obtained from three-dimensional catalogs.