The Angular Size — Redshift Relation as a Cosmological Tool

Abstract

The angular size — redshift (θ − z) relation can in principle be used to discriminate between world models because the angular size subtended by a rigid rod is quite a sensitive function of cosmology, specially at z ≳ 0.5. The test is simpler to apply to objects for which a metric diameter is measured than to objects with isophotal diameters (Sandage 1961). It was first suggested by Hoyle (1938) at the Paris symposium on Radio Astronomy, that the separation between the two lobes of extragalactic radio sources such as Cyg-A, could be used for performing such a test. In an Einstein-de Sitter Universe sources like Cyg-A cannot have angular sizes ≲ 15 arcsec (the minimum occuring at z = 1.25) whereas in the Steady State Universe their sizes should asymptotically approach a value near 4 arcsec at large redshifts. It was not until the early seventies that the test was actually applied to samples of radio quasars with redshifts of upto ~ 2 (Legg 1970; Wiley 1971; Wardle & Wiley 1974). The angular sizes were found to show a large scatter due to a wide distribution of physical sizes and the projection effects associated with the essentially linear radio structures. The upper envelope to the θ -values (which would be expected to show much less scatter) nevertheless appeared to fall off monotonically with increasing z, more or less like the Euclidean relation θ ∝ z^-1. The θ − z test thus appeared to be incompatible with the predictions of uniform world models in which the linear sizes of quasars are independent of epoch.