Subhaloes in scale-free cosmologies

We explore the dependence of the subhalo mass function on the spectral index n of the linear matter power spectrum using scale-free Einstein-de Sitter simulations with n = -1 and -2.5. We carefully consider finite volume effects that may call into question previous simulations of n < -2 power spectra. Subhaloes are found using a 6D friends-of-friends algorithm in all haloes originating from high-σ peaks. For n = -1, we find that the cumulative subhalo mass function is independent of the parameters used in the subhalo finding algorithm and is consistent with the subhalo mass function found in Λ cold dark matter (ΛCDM) simulations. In particular, the subhalo mass function is well fit by a power-law with an index of α = -0.9, that is the mass function has roughly equal mass in subhaloes per logarithmic interval in subhalo mass. Conversely, for n = -2.5, the algorithm parameters affect the subhalo mass function since subhaloes are more triaxial with less well-defined boundaries. We find that the index α is generally larger with α ≳ -0.75. We infer that although the subhalo mass function appears to be independent of n so long as n ≳ -2, it begins to flatten as n → -3. Thus, the common practice of using α ≈ -1.0 may greatly overestimate the number of subhaloes at the smallest scales in the CDM hierarchy.