Statistical analysis of catalogs of extragalactic objects. VII. Two and threepoint correlation functions for the highresolution ShaneWirtanen catalog of galaxies.
Abstract
We present estimates of the two and threepoint angular correlation functions for the highresolution (10') ShaneWirtanen catalog of galaxies. Special attention is given to statistical corrections for platetoplate variations of limiting magnitude, counting error, and the effect of the 10' x 10' counting cell. The twopoint function is well approximated by a power law for o < 2?5, corresponding to a projected distance of 9h' Mpc (H = IOOh km s Mpc1), 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, ShaneWirtanen, and Jagellonian samples. Corrections for redshift effects are about 207o for scaling between the Zwicky and ShaneWirtanen catalogs, and including them improves the agreement among the estimates. The twopoint 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 threepoint function shows little or no evidence of a preference for linear features in the galaxy distribution. Subject headings: galaxies: clusters of
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1977
 DOI:
 10.1086/155588
 Bibcode:
 1977ApJ...217..385G
 Keywords:

 Astronomical Catalogs;
 Galactic Clusters;
 Statistical Correlation;
 Astronomical Photography;
 Autocorrelation;
 Cosmology;
 Error Analysis;
 Photographic Plates;
 Red Shift;
 Relativity;
 Scaling Laws;
 Astrophysics