The Determination of the Deceleration Parameter and the Cosmological Constant from the Redshift-Magnitude Relation

Abstract

Sandage's photoelectric photometry of brightest cluster galaxies has been used with published photometry by Baum for a redetermination of the deceleration parameter qo in cosmological models both with and without a cosmological constant A. It is found that the observations are adequate only for setting upper and lower bounds on this constant, 2 X 10- > A > -2 X l0- . Solutions for qo have been computed for a number of combinations of the data and are given in the paper. For A = 0, the thirty-eight galaxies of Sandage with <0.2 give q = 0.6 + 0.4 (p.e.); combined with Baum's data, they give q0 = 1.5 j 0.4 (p.e.). An evolutionary correction of = 0.00 + 0.05 mag per 10 years increases the uncertainty and gives qo = 1.5 + 0.9. The Friedmann age of such a model is 7 X 10 years, and the mean density is 3 X 10-29 g . Uncertainties in the values of these parameters are discussed, and it is concluded that there is no irreconcilable discrepancy with ages determined for particular objects, or with mean densities obtained in other ways.