MAGNITUDE-NUMBER COUNT RELATION OF GALAXIES IN AN INHOMOGENEOUS UNIVERSE

The magnitude-number count (m-N) relation of galaxies is investigated by taking into account the amplification of fluxes due to inhomogeneities. On the basis of relativistic optical equations, the amplification probability function, which was first derived by Futamase and Sasaki in the case of the flat dust-filled background universe, is generalized to the flat and open background models which can have a non-vanishing cosmological term. The validity and limitation of the probability function are investigated by comparing it with the corresponding results of the numerical simulation, where the relativistic optical equations are solved in a model universe. The validity of basic assumptions for distances in the m-N formula of Omote and Yoshida is examined, and by adopting our new probability function, the realistic m-N relation in an inhomogeneous universe is calculated. The possible test for surveying the cosmological inhomogeneities on large scales is also briefly discussed.