Merger trees and the multiplicity function of haloes

We present a new method for calculating the merger history of matter halos inhierarchical clustering cosmologies. The linear density field is smoothed on arange of scales, these are then ordered in decreasing density and a merger treeconstructed. The method is similar in many respects to the block model of Cole\& Kaiser but has a number of advantages: (i) it retains information about thespatial correlations between halos, (ii) it uses a series of overlapping gridsand is thereby much better at finding rare, high-mass halos, (iii) it is notlimited to halos whose mass ratios are powers of two, and (iv) it is based onan actual realization of the density field and so can be tested against N-bodysimulations. The major disadvantages are (i) the minimum halo mass is eighttimes the unit cell with a corresponding loss of dynamic range, and (ii)occasionally the relative location of halos in the tree does not reflect thecorrect ordering of their collapse times, as computed from the mean halodensity. We show that our model exhibits the required scaling behaviour whentested on power-law spectra of density perturbations, but that it predicts farmore massive halos than does the Press-Schechter formalism for flat spectra. Wesuggest reasons why this should be so.Comment: plain tex, 10 pages; figures (all Postscript) in a uuencoded compressed tar file; submitted to M.N.R.A.