Transition from Clumpy to Smooth Angular Diameter Distances

Abstract

Distance relations in a locally inhomogeneous universe are expected to behave like the Dyer-Roeder solution on small angular scales and the Friedmann-Robertson-Walker solution on large angular scales. Within a simple compact clump model the transition between these asymptotic behaviors is demonstrated and quantified. The redshift dependent transition scale is of order a few arcseconds; this implies it should have little influence on large angular scale cosmological tests such as the volume-redshift relation but possibly significant effects on arcsecond angular diameter measurements of radio galaxies and AGNs. For example, at $z=2$ on arcsecond scales a clumpy flat universe mimics the angular diameter distance of a smooth $\Omega =0.27$ model.

10 pages, 3 figures, AAS LaTeX (aaspp4.sty), accepted by ApJ. Revised version contains additional text and figure on observational consequences for cosmological tests

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