Angular diameter distances in clumpy Friedmann universes

Solving null-geodesic equations, behavior of angular diameter distances is studied in inhomogeneous cosmological models, which are given by performing N-body simulations with the CDM spectrum. The distances depend on the separation angle theta of ray pairs, the mass m and the radius r(s) of particles consisting of galaxies and dark matter balls, and cosmological model parameters. The calculated distances are compared with the Dyer-Roeder angular diameter distance with the clumpiness parameter alpha (= 0 - 1), and for each ray pair the corresponding alpha is determined. Shooting many ray pairs, we derive statistical quantities such as the average value (<(alpha)over bar>), the dispersion (a,), and the distribution of alpha. It is found in four cosmological models with (Omega(0), lambda(0)) = (1,0): (0.2, 0), (0.4, 0), (0.2, 0.8) for the particle parameters m similar or equal to. 2 x 10(11) M-. and r(s) = (10 - 40)h(-1) kpc that (1) <(alpha)over bar> is nearly equal to 1 or the Friedmann distance is best fitted, (2) a, decreases with the increase of the redshift z and radius r(s), (3) for theta much greater than 1 arcsec, sigma(alpha) is very small, but for theta < 1 arcsec it is so large that the use of only the the Friedmann distance (cu = 1) may cause some errors for quantitative analysis of cosmological leasing, (4) the distribution of a is symmetric and asymmetric for a, < 0.5 and > 0.8; respectively, and (5) sigma(alpha) is smallest and largest in models with (1, 0) and (0.2, 0), respectively. The cosmological constant has the role of decreasing sigma(alpha).