The contributions of matter inside and outside of haloes to the matter power spectrum

Halo-based models have been successful in predicting the clustering of matter. However, the validity of the postulate that the clustering is fully determined by matter inside haloes remains largely untested, and it is not clear a priori whether non-virialized matter might contribute significantly to the non-linear clustering signal. Here, we investigate the contribution of haloes to the matter power spectrum as a function of both scale and halo mass by combining a set of cosmological N-body simulations to calculate the contributions of different spherical overdensity regions, Friends-of-Friends (FoF) groups and matter outside haloes to the power spectrum. We find that matter inside spherical overdensity regions of size R_{200, mean} cannot account for all power for 1 ≲ k ≲ 100 h Mpc^{- 1}, regardless of the minimum halo mass. At most, it accounts for 95 per cent of the power (k ≳ 20 h Mpc^{- 1}). For 2 ≲ k ≲ 10 h Mpc^{- 1}, haloes with mass M_200,mean ≲ 10^{11} h^{-1} M_{⊙} contribute negligibly to the power spectrum, and our results appear to be converged with decreasing halo mass. When haloes are taken to be regions of size R_{200, crit}, the amount of power unaccounted for is larger on all scales. Accounting also for matter inside FoF groups but outside R_{200, mean} increases the contribution of halo matter on most scales probed here by 5-15 per cent. Matter inside FoF groups with M_{200, mean} > 10⁹ h^-1 M_⊙ accounts for essentially all power for 3 < k < 100 h Mpc^-1. We therefore expect halo models that ignore the contribution of matter outside R_{200, mean} to overestimate the contribution of haloes of any mass to the power on small scales (k ≳ 1 h Mpc^{- 1}).