A physical and concise halo model based on the depletion radius

Abstract

We develop a self-consistent and accurate halo model by partitioning matter according to the depletion radii of haloes. Unlike conventional models that define haloes with the virial radius while relying on a separate exclusion radius or ad-hoc fixes to account for halo exclusion, our model distributes mass across all scales self-consistently. Using a cosmological simulation, we show that our halo definition leads to very simple and intuitive model components, with the one-halo term given by the Einasto profile with no truncation needed, and the halo-halo correlation function following a universal power-law form down to the halo boundary. The universal halo-halo correlation also allows us to easily model the distribution of unresolved haloes as well as diffuse matter. Convolving the halo profile with the halo-halo correlation function, we obtain a complete description of the halo-matter correlation across all scales, which self-consistently accounts for halo exclusion on the transition scale. Mass conservation is explicitly maintained in our model, and the scale dependence of the classical halo bias is easily reproduced. Our model can successfully reconstruct the halo-matter correlation function with percent level accuracy for halo virial masses in the range of 10 11.5 ℎ −1 M < 𝑀 vir < 10 15.35 ℎ −1 M at 𝑧 = 0, and covers the radial range of 0.01ℎ −1 Mpc < 𝑟 < 20ℎ −1 Mpc. We also show that our model profile can accurately predict the characteristic depletion radius at the minimum bias and the splash-back radius at the steepest density slope locations.

Physical Evolution of Dark Matter Halo around the Depletion Boundary

“…Moreover, it is worth mentioning that the r id is an excellent match to the optimal halo exclusion radius proposed by García et al (2021) in a halo model of the correlation function. This further supports that the depletion radius can be used as a physical halo boundary that self-consistently decomposes the cosmic density field into different halos, as recently implemented in Zhou & Han (2023).…”

“…These results illustrate the great potential of using the depletion radii as new probes for halo evolution. In a companion work (Zhou & Han 2023), we will also show that a more concise halo model can be built using these radii, which consists of a simple one-halo profile in the Einasto form and an intuitively scale-free halo−halo correlation. Along with further theoretical understanding of them in analytical models, we expect that many more applications of them can be found that can boost our understanding of halo evolution and structure formation in general.…”