COLD DARK-MATTER .1. THE FORMATION OF DARK HALOS

We use numerical simulations of critically closed cold dark matter (CD M) models to study the effects of numerical resolution on observable q uantities. We study simulations with up to 256(3) particles using the particle-mesh (PM) method and with up to 144(3) particles using the ad aptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifyi ng halos, including a new algorithm that finds all particles within cl osed contours of the smoothed density field surrounding a peak. The si mulated halos show more substructure than predicted by the Press-Schec hter theory. We are able to rule out all Omega = 1 CDM models for line ar amplitude a,greater than or similar to 0.5 because the simulations produce too many massive halos compared with the observations. The sim ulations also produce too many low-mass halos. The distribution of hal os characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km s(-1) less than or similar to V-circ less than or equal to 350 km s(-1).