Do Distinct Cosmological Models Predict Degenerate Halo Populations?

Abstract

Using cosmological N-body simulations, we investigate the influence of the matter density parameter Ωm and the linear theory power spectrum P(k) on statistical properties of the dark matter halo population—the mass function n(M), two-point correlation function ξ(r), and pairwise velocity statistics v12(r) and σ12(r). For fixed linear theory P(k), the effect of changing Ωm is simple: the halo mass scale M* shifts in proportion to Ωm, pairwise velocities (at fixed M/M*) are proportional to Ω, and halo clustering at fixed M/M* is unchanged. If one simultaneously changes the power spectrum amplitude σ8 to maintain the normalization condition σ8Ω = const, then n(M) stays approximately constant near M ~ 5 × 1014 h-1 M☉, and halo clustering and pairwise velocities are similar at fixed M. However, the shape of n(M) changes, with a decrease of Ωm from 0.3 to 0.2, producing a ~30% drop in the number of low-mass halos. One can preserve the shape of n(M) over a large dynamic range by changing the spectral tilt ns or shape parameter Γ, but the required changes are substantial—e.g., masking a decrease of Ωm from 0.3 to 0.2 requires Δns ≈ 0.3 or ΔΓ ≈ 0.15. These changes to P(k) significantly alter the halo clustering and halo velocities. The sensitivity of the dark halo population to cosmological model parameters has encouraging implications for efforts to constrain cosmology and galaxy bias with observed galaxy clustering, since the predicted changes in the halo population cannot easily be masked by altering the way that galaxies occupy halos. A shift in Ωm alone would be detected by any dynamically sensitive clustering statistic; a cluster normalized change to σ8 and Ωm would require a change in galaxy occupation as a function of M/M*, which would alter galaxy clustering; and a simultaneous change to P(k) that preserves the halo mass function would change the clustering of the halos themselves.