The angular correlation hierarchy in the quasilinear regime.

Abstract

For Gaussian initial conditions the perturbation theory predicts a very specific hierarchy for the projected matter $p$-point correlation functions. In the small angle approximation and assuming a power-law spectrum I derive the exact expressions of the coefficients $s_p$ relating the averaged $p$-order angular correlation function, $\omb_p$ to the second one, $\omb_p=s_p\ \omb_2^{p-1}$. 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, $S_p=\xib_p/\xib_2^{p-1}$. For the coefficient $s_3$ I discussed the accuracy of the small angle approximation by computing, for particular examples, its angular dependence with Monte-Carlo numerical integrations. It is found that the accuracy of the small angle approximation for $θ\approx 1^o$ slightly depends on the selection function. Using the selection function expected for galaxy catalogues the approximation is found to be reasonably good. The measurements of the $s_p$ parameters made in the APM angular survey are found to give systematic lower values than the theoretical predictions. How significant this discrepancy is and what the implications would be for galaxy formation models is discussed in the last section.