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 ${\xi }_{\mathrm{hm}}$ and ${\xi }_{\mathrm{mm}}$. 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 $\approx 2\%$ residuals over the radial range $0.1h^{-1}\mathrm{Mpc}<r<80h^{-1}\mathrm{Mpc}$, and for halo masses in the range $10^{13}{h}^{-1}{\mathrm{M}}_{\odot }<M<10^{15}{h}^{-1}{\mathrm{M}}_{\odot }$. Our proposed halo boundary is related to the splashback radius by a roughly constant multiplicative factor. Taking the 87-percentile as reference we find $r_{\mathrm{t}}/R_{\mathrm{sp}}\approx 1.3$. Surprisingly, our proposed definition results in halo abundances that are well described by the Press-Schechter mass function with ${\delta }_{\mathrm{sc}}=1.449\pm 0.004$. 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.

12 pages, 5 figures

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