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 and allows for a redefinition of the halo boundary in a flexible way. We assume that haloes 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 ξ_hm and ξ_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 $\approx 2{{\ \rm per\ cent}}$ residuals over the radial range 0.1 h^-1 Mpc < r < 80 h^-1 Mpc, and for halo masses in the range 10¹³ h^-1 M_⊙ < M < 10¹⁵ h^-1 M_⊙. 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_t/R_sp ≈ 1.3. Surprisingly, our proposed definition results in halo abundances that are well described by the Press-Schechter mass function with δ_sc = 1.449 ± 0.004. The clustering bias parameter is offset from the standard background-split prediction by $\approx 10{{\ \rm per\ cent}}\!-\!15{{\ \rm per\ cent}}$. This level of agreement is comparable to that achieved with more standard halo definitions.