Excursion set peaks: a self-consistent model of dark halo abundances and clustering

Abstract

We describe how to extend the excursion set peaks framework so that its\npredictions of dark halo abundances and clustering can be compared directly\nwith simulations. These extensions include: a halo mass definition which uses\nthe TopHat filter in real space; the mean dependence of the critical density\nfor collapse delta_c on halo mass m; and the scatter around this mean value.\nAll three of these are motivated by the physics of triaxial rather than\nspherical collapse. A comparison of the resulting mass function with N-body\nresults shows that, if one uses delta_c(m) and its scatter as determined from\nsimulations, then all three are necessary ingredients for obtaining ~10%\naccuracy. E.g., assuming a constant value of delta_c with no scatter, as\nmotivated by the physics of spherical collapse, leads to many more massive\nhalos than seen in simulations. The same model is also in excellent agreement\nwith N-body results for the linear halo bias, especially at the high mass end\nwhere the traditional peak-background split argument applied to the mass\nfunction fit is known to underpredict the measured bias by ~10%. In the\nexcursion set language, our model is about walks centered on special positions\n(peaks) in the initial conditions -- we discuss what it implies for the usual\ncalculation in which all walks contribute to the statistics.\n