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

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 the by 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 $\approx 2%$residualsovertheradialrange$0.1\ h^{-1}{\rm Mpc} < r < 80\ h^{-1}{\rm Mpc}$,andforhalomassesintherange$10^{13}\ h^{-1}{\rm M}{\odot} < M < 10^{15}\ h^{-1}{\rm M}{\odot}$. Our proposed halo boundary is related to the splashback radius by a roughly constant multiplicative factor. Taking the 87-percentile as reference we find $r_{\mathrm{t}}\mathrm{/}{R}_{\mathrm{s}\mathrm{p}}\approx 1.3$. 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 $\approx 10\mathrm{\%}-15\mathrm{\%}$. This level of agreement is comparable to that achieved with more standard halo definitions.