Universal merger histories of dark-matter haloes

We study merger histories of dark-matter haloes in a suite of N-body simulations that span different cosmological models. The simulated cases include the up-to-date Wilkinson Microwave Anisotropy Probe 5 cosmology and other test cases based on the Einstein-deSitter cosmology with different power spectra. We provide a robust fitting function for the conditional mass function of progenitor haloes of a given halo. This fit is valid for the different cosmological models and for different halo masses and redshifts, and it is a significant improvement over earlier estimates. Based on this fit, we develop a simple and accurate technique for transforming the merger history of a given simulated halo into haloes of different mass, redshift and cosmology. Other statistics such as main-progenitor history and merger rates are accurately transformed as well. This method can serve as a useful tool for studying galaxy formation. It is less sensitive to the low accuracy of the fit at small time-steps, and it can thus replace the more elaborate task of construction Monte Carlo realizations. As an alternative approach, we confirm the earlier finding by Neistein & Dekel that the main-progenitor follows a log-normal distribution. This property of merger trees allows us to better capture their behaviour as a function of time and descendant mass, but a broader suite of simulations is required for evaluating the dependence of the log-normal parameters on the cosmological model.