Optical Bias and Hierarchical Clustering

Recent statistical results obtained in the frame of biased theories of galaxy origin are transferred to the direct analysis of the luminosity field on the celestial sphere. Correlation functions on the celestial sphere should therefore obey a number of relations similar to those worked out for biased theories of galaxy origin (in a Gaussian or non-Gaussian context). The relation between this view and the view based on the Limber equation is discussed, and a tentative explanation of a number of peculiarities of observed spatial correlations is proposed. These ideas are also checked by performing a fit with the Zwicky catalog data. A discussion on the meaning of spatial statistical data worked out from angular measures is also performed.