Merging history trees for dark matter haloes: tests of the Merging Cell Model in a CDM cosmology

The merging history of dark matter haloes is computed with the Merging Cell Model proposed by Rodrigues & Thomas. While originally discussed in the ca se of scale-free power spectra, it is developed and tested here in the fram ework of the cold dark matter cosmology. The halo mass function, the mass d istribution of progenitors and child haloes, as well as the probability dis tribution of formation times, have been computed and compared with the avai lable analytic predictions. The halo autocorrelation function has also been obtained (a first for a semi-analytic merging tree), and tested against an alytic formulae. An overall good agreement is found between results of the model, and the predictions derived from the Press & Schechter theory and it s extensions. More severe discrepancies appear when formulae that better de scribe N-body simulations are used for comparison. In many instances, the m odel can be a useful tool for following the hierarchical growth of structur es. In particular, it is suitable for addressing the issue of the formation and evolution of galaxy clusters, as well as the population of Lyman-break galaxies at high redshift, and their clustering properties.