Ie. Segal et Jf. Nicoll, TESTS OF LOCAL REDSHIFT-DISTANCE LAWS ON THE BASIS OF A COMPLETE OPTICAL-SAMPLE, The Astrophysical journal, 465(2), 1996, pp. 578-594
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.