Statistically Efficient Testing of the Hubble and Lundmark Laws on IRAS Galaxy Samples
Abstract
The local redshiftdistance (zr) power laws, z is proportional to r^p^, of exponents p = 1, 2, which are predicted respectively by generic big bang cosmology and chronometric cosmology, are tested on flux and redshiftlimited subsamples of the sample of Strauss et al. (1992). The completeness of this sample at 60 microns makes possible statistically optimal nonparametric estimates of the corresponding luminosity functions, which are used for the tests. The present analysis is basically free of assumptions regarding the spatial distribution of the galaxies; only the absence of selection on flux down to its limiting value, at each given redshift, is used. The Hubble law (p= 1) predicts values for (i) dispersion in log flux and (ii) the slope of the regression of log flux on log redshift that almost invariably exceed their actual values, by amounts typically of the order of 30% in the case of the dispersion in log flux. Since ancillary perturbative hypotheses would further increase the excess of the prediction over observation, this inconsistency appears irreconcilable. The Hubble law prediction for (iii) the correlation of log luminosity with redshift also almost invariably exceeds the observed value. The mean prediction errors for (i)(iii) are, in this order, approximately 10 σ, 6 σ, and 9 σ, for the subsample in the range 500 km s^1^ < cz < = 30,000 km s^1^. The Lundmark law (p= 2) predictions for these quantities are in strikingly close agreement with their directly observed values, having deviations of less than ~0.5% or less than 1 σ. In addition, this law predicts that the Hubble law predictions will deviate from observation in the manner observed. For example, the Lundmark law prediction for the correlation of the Hubble law luminosity with log redshift is correct within less than 0.5%, or 1/20 or the error in the prediction of the Hubble law itself for this quantity. Corrections for possible peculiar motions of the Galaxy of a realistic order of magnitude have no qualitative impact on these results. Bright subsamples, inclusive of approximately onehalf or onefourth of this number of galaxies, give comparable results. So also do subsamples in more limited redshift ranges, e.g., 500 km s^1^ < cz <= 20,000 km s^1^ or 2000 km s^1^ < cz <= 10,000 km s^1^. The rms error in the Lundmark law prediction for log flux at the observed redshift is less than the observed dispersion in log flux by ~9%, but the corresponding rms error in the Hubble law predictions exceeds the observed dispersion by ~4%, in the case of the cited sample of 2551 galaxies.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 1993
 DOI:
 10.1086/172849
 Bibcode:
 1993ApJ...411..465S
 Keywords:

 Big Bang Cosmology;
 Hubble Constant;
 Infrared Astronomy Satellite;
 Milky Way Galaxy;
 Red Shift;
 Statistical Tests;
 Interstellar Matter;
 Probability Theory;
 Spatial Distribution;
 Astrophysics;
 COSMOLOGY: OBSERVATIONS;
 GALAXIES: DISTANCES AND REDSHIFTS