The Mass Function of Galaxy Systems from Local Density Maxima: Groups and Clusters of Galaxies

The mass function of galaxy systems in a cold dark matter cosmogony is considered with the peak constraint that proto-objects form around local density maxima. Different possible definitions of peak mass are analyzed to test their reliability down to the low-mass tail. The effects of non-Gaussian features on the distribution of primordial fluctuations are also discussed. A prediction of the model is the time evolution of the luminosity function and the characteristic mass: a self-similar evolution provides a fairly accurate description even at moderate redshifts. The resulting mass multiplicity, within a biased cold dark matter model with Gaussian, scale-invariant (n = 1), adiabatic primordial perturbations, provides a fit of the existing data on the optical luminosity function for groups and clusters of galaxies.