Limber equation for luminosity dependent correlations
arXiv:astro-ph/9911208 · doi:10.1016/S1384-1076(99)00046-9
Abstract
The passage from angular to spatial correlations, in the case of spatial clustering length depending on the average distance between nearby objects is studied. We show that, in a number of cases, the scaling law of angular correlation amplitudes, which holds for constant spatial clustering length, is still true also for a luminosity dependent spatial correlation. If the Limber equation is then naively used to obtain `the' spatial clustering length from the angular function amplitude, a quantity close to the average object separation is obtained. The case of cluster clustering is explicitly considered.
10 pages, LaTeX, no figures, Accepted for publication in New Astronomy