Outskirts of dark matter haloes

Halo models of large scale structure provide powerful and indispensable tools for phenomenological understanding of the clustering of matter in the Universe. While the halo model builds structures out of the superposition of haloes, defining halo profiles in their outskirts-beyond their virial radii-becomes increasingly ambiguous, as one cannot assign matter to individual haloes in a clear way. In this paper, we address this issue by finding a systematic definition of mean halo profile that can be extended to large distances-beyond the virial radius of the halo-and matched to simulation results. These halo profiles are compensated and are the key ingredients for the computation of cosmological correlation functions in an amended halo model. The latter, introduced in our earlier work [A. Y. Chen and N. Afshordi, Phys. Rev. D 101, 103522 (2020)], provides a more physically accurate phenomenological description of nonlinear structure formation, which respects conservation laws on large scales. Here, we show that this model can be extended from the matter auto-power spectrum to the halo-matter cross-power spectra by using data from N-body simulations. Furthermore, we find that this (dimensionless) definition of the compensated halo profile, r3 x rho or thorn /M200c, has a near-universal maximum in the small range of 0.03-0.04 around the virial radius, r similar or equal to r200c, nearly independent of the halo mass. The profiles cross zero into negative values in the halo outskirts-beyond 2-3 x r200c-consistent with our previous results. We provide a preliminary fitting function for the compensated halo profiles (extensions of Navarro-Frenk-White profiles), which can be used to compute more physical observables in large scale structure.