Splashback radius in a spherical collapse model

It has been shown some years ago that dark matter haloes outskirts are characterized by very steep density profiles in a very small radial range. This feature has been interpreted as a pile up of at a similar location of different particle orbits, namely splashback material at half an orbit after collapse. Adhikari et al. (2014), obtained the location of the splashback radius through a very simple model, namely calculating a dark matter shell trajectory in the secondary infall model while it crosses a growing, NFW profile shaped, dark matter halo. Since they imposed a halo profile instead of calculating it from the trajectories of the shells of dark matter, they were not able to find the dark matter profile around the splashback radius. In the present paper, we use an improved spherical infall model taking into shell crossing, and several physical effects like ordered, and random angular momentum, dynamical friction, adiabatic contraction, etc. This allow us to determine the density profile from the inner to outer region, and study the behavior of the outer density profile. We will compare the density profiles, and the logarithmic slope of the density profile with the results of Diemer \& Kravtsov (2014) simulations, finding a good agreement between the prediction of the model and the simulations.