Environmental dependence of cold dark matter halo formation

We use a high-resolution N-body simulation to study how the formation of cold dark matter haloes is affected by their environments, and how such environmental effects produce the age dependence of halo clustering observed in recent N-body simulations. We estimate, for each halo selected at redshift z = 0, an 'initial' mass M-i defined to be the mass enclosed by the largest sphere which contains the initial barycentre of the halo particles and within which the mean linear density is equal to the critical value for spherical collapse at z = 0. For haloes of a given final mass, M-h, the ratio M-i/M-h has large scatter, and the scatter is larger for haloes of lower final masses. Haloes that form earlier on average have larger M-i/M-h, and so correspond to higher peaks in the initial density field than their final masses imply. Old haloes are more strongly clustered than younger ones of the same mass because their initial masses are larger. The age dependence of clustering for low-mass haloes is entirely due to the difference in the initial/final mass ratio. Low-mass old haloes are almost always located in the vicinity of big structures, and their old ages are largely due to the fact that their mass accretions are suppressed by the hot environments produced by the tidal fields of the larger structure. The age dependence of clustering is weaker for more massive haloes because the heating by large-scale tidal fields is less important.