Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.
Proc Natl Acad Sci U S A. 1982 Jun;79(12):3913-7. doi: 10.1073/pnas.79.12.3913.
Spatial homogeneity in the radial direction of low-redshift galaxies is subjected to Kafka-Schmidt V/V(m) tests using well-documented samples. Homogeneity is consistent with the assumption of the Lundmark (quadratic redshift-distance) law, but large deviations from homogeneity are implied by the assumption of the Hubble (linear redshift-distance) law. These deviations are similar to what would be expected on the basis of the Lundmark law. Luminosity functions are obtained for each law by a nonparametric statistically optimal method that removes the observational cutoff bias in complete samples. Although the Hubble law correlation of absolute magnitude with redshift is reduced considerably by elimination of the bias, computer simulations show that its bias-free value is nevertheless at a satistically quite significant level, indicating the self-inconsistency of the law. The corresponding Lundmark law correlations are quite satisfactory satistically. The regression of redshift on magnitude also involves radial spatial homogeneity and, according to R. Soneira, has slope determining the redshift-magnitude exponent independently of the luminosity function. We have, however, rigorously proved the material dependence of the regression on this function and here exemplify our treatment by using the bias-free functions indicated, with results consistent with the foregoing argument.
运用有详细记录的样本，对低红移星系的径向各向同性进行卡夫卡-施密特 V/V(m)检验。同伦德马克（二次红移-距离）定律的假设一致，星系的同质性与哈勃（线性红移-距离）定律的假设相悖。这些与根据伦德马克定律所预期的相悖。对于每种定律，我们都采用非参数统计最优方法来获取光度函数，该方法可以消除完整样本中的观测截止偏差。尽管消除偏差会大大降低哈勃定律与红移的绝对星等之间的相关性，但计算机模拟表明，其无偏差值仍然具有相当显著的统计学水平，这表明该定律存在自相矛盾。相应的伦德马克定律相关性在统计学上非常令人满意。根据 R. Soneira 的说法，红移与星等的回归也涉及到径向空间同质性，并且其斜率可以独立于光度函数来确定红移-星等指数。然而，我们已经严格证明了这种回归与该函数的物质依赖性，并且在这里我们通过使用无偏差函数进行了示例说明，结果与前面的论证一致。
