The effects of spatial correlations on merger trees of dark matter haloes

The effects of spatial correlations of density fluctuations on mergerhistories of dark matter haloes (so-called `{\it merger trees}') are analysed.We compare the mass functions of dark haloes derived by a new method forcalculating merger trees, that proposed by Rodrigues \& Thomas (RT), with thosegiven by other methods such as the Block model, the Press-Schechter formula andour own formula in which the mass functions are analytically expressed in a waythat takes into consideration the spatial correlations. It is found that themass functions given by the new method are well fit by those given by ourformula. We believe that new method (RT) {\it naturally} and correctly takesinto account the spatial correlations of the density fluctuations due to acalculated, grid-based realisation of the density fluctuations and so is veryuseful for estimating the merger tree accurately in a way that takes intoconsideration spatial correlations. Moreover, by applying our formula, we present an analytic expression whichreproduces the mass function derived by the Block model. We therefore showclearly why and how the mass functions given by the new method and the Blockmodel are different from each other. Furthermore, we note that the constructionof merger trees is sensitive to the criterion of collapse and merging ofoverlapped haloes in cases in which two or more haloes happen to overlap. Infact, it is shown that the mass function is very much affected when thecriterion of overlapping is changed.Comment: Submitted to MNRAS; 10 pages MN latex file, including 5 figures (epsf