A model for infall around virialized haloes

Motivated by the recent direct detection of cosmological gas infall, we develop an analytical model for calculating the mean density profile around an initial overdensity that later forms a dark matter halo. We account for the problem of peaks within peaks; when considering a halo of a given mass we ensure that this halo is not a part of a larger virialized halo. For haloes that represent high-sigma fluctuations we recover the usual result that such haloes preferentially lie within highly overdense regions; in the limit of very low-sigma fluctuations, on the other hand, we show that haloes tend to lie within voids. Combined with spherical collapse, our results yield the typical density and velocity profiles of the gas and dark matter that surround virialized haloes.