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.