THE ANGULAR-CORRELATION HIERARCHY IN THE QUASI-LINEAR REGIME

For Gaussian initial conditions the perturbation theory predicts a ver y specific hierarchy for the projected matter p-point correlation func tions. In the small angle approximation and assuming a power-law spect rum I derive the exact expressions of the coefficients s(p) relating t he averaged p-order angular correlation function, <(omega)over bar>(p) to the second one, <(omega)over bar> = s(p)<(omega)over bar>(p-1)(2). These results are valid for any selection function, but for a top-hat angular filter only. These coefficients are found to be significantly higher than their 3D counterparts, S-p = <(xi)over bar>/<(xi)over bar >(p-1)(2). For the coefficient s(3) I discussed the accuracy of the sm all angle approximation by computing, for particular examples, its ang ular dependence with Monte-Carlo numerical integrations. It is found t hat the accuracy of the small angle approximation for theta approximat e to 1 degrees slightly depends on the selection function. Using the s election function expected for galaxy catalogues the approximation is found to be reasonably good. The measurements of the s(p) parameters m ade in the APM angular survey are found to give systematic lower value s than the theoretical predictions. How significant this discrepancy i s and what the implications would be for galaxy formation models is di scussed in the last section.