A Redefinition of the Halo Boundary Leads to a Simple yet Accurate Halo Model of Large Scale Structure

Abstract: We present a model for the halo--mass correlation function that explicitly incorporates halo exclusion. We assume that halos trace mass in a way that can be described using a single scale-independent bias parameter. However, our model exhibits scale dependent biasing due to the impact of halo-exclusion, the use of a soft'' (i.e. not infinitely sharp) halo boundary, and differences in the one halo term contributions to $\xi_{\rm hm}$ and $\xi_{\rm mm}$. These features naturally lead us to a redefinition of the halo boundary that lies at theby eye'' transition radius from the one--halo to the two--halo term in the halo--mass correlation function. When adopting our proposed definition, our model succeeds in describing the halo--mass correlation function with $\approx 2\%$ residuals over the radial range $0.1\ h^{-1}{\rm Mpc} < r < 80\ h^{-1}{\rm Mpc}$, and for halo masses in the range $10^{13}\ h^{-1}{\rm M}{\odot} < M < 10^{15}\ h^{-1}{\rm M}{\odot}$. Our proposed halo boundary is related to the splashback radius by a roughly constant multiplicative factor. Taking the 87-percentile as reference we find $r_{\rm t}/R_{\rm sp} \approx 1.3$. Surprisingly, our proposed definition results in halo abundances that are well described by the Press-Schechter mass function with $\delta_{\rm sc}=1.449\pm 0.004$. The clustering bias parameter is offset from the standard background-split prediction by $\approx 10\%-15\%$. This level of agreement is comparable to that achieved with more standard halo definitions.