The velocity field of bright nearby galaxies. I - The variation of mean absolute magnitude with redshift for galaxies in a magnitude-limited sample

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Abstract

The sample of all E and SO galaxies in the magnitude-limited Revised Shapley-Ames Catalog (RSA) shows a strong and highly significant correlation of absolute magnitude with redshift. As an example, catalog galaxies with V0 = 6000 km s - are 2.6 mag brighter in MB, in the mean, than galaxies with V0 = 1000 km s - . We show that this observed effect must exist in any magnitude-limited catalog of objects which have a broad luminosity function. In such a catalog, the concept of a fixed mean absolute magnitude (a standard candle) does not apply, and neglect of the variation of M with V0 will cause photometric distances to be progressively incorrect with increasing redshifl. Clearly, erroneous conclusions would be made concerning the linearity of the local Hubble expansion field if M had been assumed to be constant. In this paper we calculate the maximum likelihood distribution of M for E and SO galaxies in the RSA [i.e., the luminosity function M)], and the completeness function f(m) of the catalog itself at various apparent magnitudes. We then show that the shapes of these distributions agree with the great cluster (M) function and with the direct data on the completeness of the RSA. The two calculated functions are then used to show that the expected variation of M with V0 agrees with the observed correlation, provided that the underlying local velocity field is linear. No such agreement would have been obtained for a nonlinear velocity field, using the great cluster luminosity function. We also show that the calculated luminosity functions for E and SO galaxies differ significantly from each other. If the functions are normalized at MnT = - 21, then the bright end of T(M) for SO galaxies is 0.7 mag fainter than for E systems. The wide scatter of the RSA E and SO galaxies in the Hubble (m, v0)-diagram is shown to be understood using the calculated (M) and f(m) distributions and a linear Hubble expansion. The slope of 5 in the Rubble m 5 log v0 equation, which is valid only if a particular sample of galaxies has a very narrow luminosity function, is, as expected, unrecognizable in these field galaxy data. Subject headings: cosmology - galaxies: redshifis - luminosity function

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