Predicting the number, spatial distribution, and merging history of dark matter halos

We present a new algorithm (PINOCCHIO: pinpointing orbit-crossing collapsed hierarchical objects) to accurately predict the formation and evolution of individual dark matter halos in a given realization of an initial linear density field. Compared with the halo population formed in a large (3603 particles) collisionless simulation of a cold dark matter (CDM) universe, our method is able to predict to better than 10% statistical quantities such as the mass function, two-point correlation function, and progenitor mass function of the halos. Masses of individual halos are estimated accurately as well, with errors typically of order 30% in the mass range well resolved by the numerical simulation. These results show that the hierarchical formation of dark matter halos can be accurately predicted using local approximations to the dynamics when the correlations in the initial density field are properly taken into account. The approach allows one to automatically generate a large ensemble of accurate merging histories of halos with complete knowledge of their spatial distribution. The construction of the full merger tree for a 2563 realization requires a few hours of CPU time on a personal computer, orders of magnitude faster than the corresponding N-body simulation would take, and does not need any extensive postprocessing. The technique can be efficiently used, for instance, for generating the input for galaxy formation modeling.