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-sigma 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 Lambda cold dark matter (Lambda CDM) simulations. In particular, the subhalo mass function is well fit by a power-law with an index of alpha = -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 alpha is generally larger with alpha greater than or similar to -0.75. We infer that although the subhalo mass function appears to be independent of n so long as n greater than or similar to -2, it begins to flatten as n -> -3. Thus, the common practice of using alpha approximate to -1.0 may greatly overestimate the number of subhaloes at the smallest scales in the CDM hierarchy.