Excursion set peaks in energy as a model for haloes

Abstract

ABSTRACT The simplest models of dark matter halo formation rely on the heuristic assumption, motivated by spherical collapse, that virialized haloes originate from initial regions that are maxima of the smoothed matter density field. Here, we replace this notion with the dynamical requirement that protohaloes be regions where the local gravitational flow converges to a point. For this purpose, we look for spheres whose acceleration at the boundary – relative to their centre of mass – points towards their geometric centre: that is, spheres with null dipole moment. We show that these configurations are minima of the energy, corresponding to the most energetically bound spheres. Therefore, we study peaks of the smoothed energy overdensity field. This significant conceptual change is technically trivial to implement: to change from density to energy one need only modify the standard top-hat smoothing filter. However, this comes with the important benefit that, for power spectra of cosmological interest, the model is no longer plagued by divergences: improving the physics mends the mathematics. In addition, the ‘excursion set’ requirement that the smoothed matter density crosses a critical value can be naturally replaced by a threshold in energy. Measurements in simulations of haloes more massive than 1013h−1M⊙ show very good agreement with a number of generic predictions of our model.