TESTS OF LOCAL REDSHIFT-DISTANCE LAWS ON THE BASIS OF A COMPLETE OPTICAL-SAMPLE

The linear and square (homogeneous quadratic) redshift-distance laws a re tested statistically at redshifts less than or similar to 0.01, on the basis of the whole-sky complete sample of elliptical type galaxies of Visvanathan and conservative subsamples. Objective estimates are m ade of the probabilities of deviations as large as the actual ones bet ween the prediction and direct observation, by statistically efficient and equitable methods. Luminosity functions are also estimated and te sted for consistency. Sample statistics corrected for the observationa l magnitude cutoff, on the basis of the estimated luminosty functions, are reported. As in the case of the infrared and X-ray wave bands, th e predictions of the linear law appear to be significantly deviant fro m the observations, by 7 sigma at the reported completeness level of 1 2.4 mag (290 galaxies), or by 4 sigma for the subsample brighter than 11.6 mag (205 galaxies). The square law predictions are in close agree ment with direct observation. The linear law predictions for the dispe rsion in apparent magnitude are overestimates, while any material loca l perturbations or irregularities would be expected to result in an un derestimate. The physical reality of exculpatory perturbations or poss ible evolution is questioned further by the fact that the deviations i n the linear law predictions are statistically just as predicted by th e square law.