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

摘要

The linear and square (homogeneous quadratic) redshift-distance laws are tested statistically at red-shifts approx < 0.01, on the basis of the whole-sky complete sample of elliptical type galaxies of Visvanathan and conservative subsamples. Objective estimates are made of the probabilities of deviations as large as the actual ones between the prediction and direct observation, by statistically efficient and equitable methods. Luminosity functions are also estimated and tested for consistency. Sample statistics corrected for the observational magnitude cutoff, on the basis of the estimated luminosty functions, are reported. As in the case of the infrared and X-ray wave bands, the predictions of the linear law appear to be significantly deviant from the observations, by 7 σ at the reported completeness level of 12.4 mag (290 galaxies), or by 4 σ for the subsample brighter than 11.6 mag (205 galaxies). The square law predictions are in close agreement with direct observation. The linear law predictions for the dispersion in apparent magnitude are overestimates, while any material local perturbations or irregularities would be expected to result in an underestimate. The physical reality of exculpatory perturbations or possible evolution is questioned further by the fact that the deviations in the linear law predictions are statistically just as predicted by the square law.