Self-consistent theory of halo mergers

The rate of merging of dark matter haloes is an absolutely essential ingredient for studies of both structure and galaxy formation. Remarkably, however, our quantitative understanding of the halo merger rate is still quite limited, and current analytic descriptions based upon the extended Press-Schechter formalism are fundamentally flawed. We show that a mathematically self-consistent merger rate must be consistent with the evolution of the halo abundance in the following sense. The merger rate must, when inserted into the Smoluchowski coagulation equation, yield the correct evolution of the halo abundance. We then describe a numerical technique to find merger rates that are consistent with this evolution. We present results from a preliminary study in which we find merger rates that reproduce the evolution of the halo abundance according to the Press-Schechter formalism for power-law power spectra. We discuss the limitations of the current approach and outline the questions that must still be answered before we have a fully consistent and correct theory of halo merger rates.