The angular three-point correlation function in the quasi-linear regime

We calculate the normalized angular three-point correlation function (3PCF), q, as well as the normalized angular skewness, s(3), assuming the small-angle approximation, for a biased mass distribution in Bat and open cold dark matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of the assumed redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of (z) over bar similar or equal to 1 (such as the VLA FIRST Survey). Qualitatively, many of the results found for s(3) and q are similar to those obtained in a related treatment of the spatial skewness and 3PCF, such as a leading-order correction to the standard result for s(3) in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of q to both cosmological and biasing models. We show that since angular correlation functions (CFs) are sensitive to clustering over a range of redshifts, the various evolutionary dependences included in our predictions imply that measurements of q in a deep survey might better discriminate between models with different histories, such as evolving versus nonevolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation, valid for open, closed, and flat models, to obtain the angular bispectrum from the spatial bispectrum in the small-angle approximation.