Statistical analysis of catalogs of extragalactic objects. VII - Two- and three-point correlation functions for the high-resolution Shane-Wirtanen catalog of galaxies

Abstract

We present estimates of the two- and three-point angular correlation functions for the highresolution (10') Shane-Wirtanen catalog of galaxies. Special attention is given to statistical corrections for plate-to-plate variations of limiting magnitude, counting error, and the effect of the 10' x 10' counting cell. The two-point function is well approximated by a power law for o < 2?5, corresponding to a projected distance of 9h-' Mpc (H = IOOh km s- Mpc-1), but breaks sharply below the power law at larger angles. Several arguments indicate that the break is an intrinsic feature of the galaxy distribution, not an artifact of the analysis. New scaling relations taking account of red shift and curvature are derived and used to compare the correlation functions estimated for the Zwicky, Shane-Wirtanen, and Jagellonian samples. Corrections for redshift effects are about 207o for scaling between the Zwicky and Shane-Wirtanen catalogs, and including them improves the agreement among the estimates. The two-point spatial function is estimated to be r) = (r0/r) , with r0 = 4.7h-' Mpc, 0.05 Mpc < hr < 9 Mpc. The threepoint function at 0 < 30 is well represented by the model (l, 2, 3) = Q[ (l) (2) + 2) (3) + (3) (l)] for the spatial function, with Q = 1.29 + 0.21. The three-point function shows little or no evidence of a preference for linear features in the galaxy distribution. Subject headings: galaxies: clusters of