THE EFFECTS OF SPATIAL CORRELATIONS ON MERGER TREES OF DARK-MATTER HALOES

The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called 'merger trees') are analyse d. We compare the mass functions of dark haloes derived by a new metho d for calculating merger trees, that proposed by Rodrigues & Thomas (R T), with those given by other methods such as the Block model, the Pre ss-Schechter formula and our own formula in which the mass functions a re analytically expressed in a way that takes into consideration the s patial correlations. It is found that the mass functions given by the new method are well fitted by those given by our formula. We believe t hat the new method (RT) naturally and correctly takes into account the spatial correlations of the density fluctuations due to a calculated, grid-based realization of the density fluctuations and so is very use ful for estimating the merger tree accurately in a way that takes into consideration spatial correlations. Moreover, by applying our formula , we present an analytic expression which reproduces the mass function derived by the Block model. We therefore show clearly why and how the mass functions given by the new method and the Block model are differ ent from each other. Furthermore, we note that the construction of mer ger trees is sensitive to the criterion of collapse and merging of ove rlapped haloes in cases in which two or more haloes happen to overlap. In fact, it is shown that the mass function is very much affected whe n the criterion of overlapping is changed.