Testing the Hubble Law from Magnitude-Redshift Data of Field Galaxies: The Effect of the Shape of the Luminosity Function
The calibration of the redshift-distance relation cz = Hr P , with z the redshift, r the distance and H and p two parameters, from (m,z)-data requires an initial guess on the luminosity function (LF) of the sample. The simplest assumption is that the LF is a Dirac function, that means that all considered objects have the same absolute magnitude M 0 (“standard candles”). Once the relation is calibrated it may then be used to determine vice versa the distance of a particular object or the LF of a total sample of objects. This is obviously a circular approach since a wrong initial assumption on the LF may have biased the calibration. Almost 20 years ago Segal and his co-workers have started a debate with their statement that, if the LF is only a function of M (no evolutionary effects), it is possible to determine the LF and the exponent p galaxy data.