An analytic model for the epoch of halo creation

In this paper we describe the Bayesian link between the cosmological mass f unction and the distribution of times at which isolated haloes of a given m ass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the dist ribution of 'creation' times of the haloes. This monotonic growth is an ine vitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse . This gives the prior for the creation time given no information about hal o mass. Applying Bayes' theorem then allows any mass function to be convert ed into a distribution of times at which haloes of a given mass are created . This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can b e combined to give a joint density function, and discuss the relation betwe en the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N-body simu lations, and compare the link between the mass function and creation rate w ith the analytic theory.