While various codes exist to systematically and robustly find haloes and subhaloes in cosmological simulations (Knebe et al., 2011, Onions et al., 2012), this is the first work to introduce and rigorously test codes that find tidal debris (streams an
d other unbound substructure) in fully cosmological simulations of structure formation. We use one tracking and three non-tracking codes to identify substructure (bound and unbound) in a Milky Way type simulation from the Aquarius suite (Springel et al., 2008) and post-process their output with a common pipeline to determine the properties of these substructures in a uniform way. By using output from a fully cosmological simulation, we also take a step beyond previous studies of tidal debris that have used simple toy models. We find that both tracking and non-tracking codes agree well on the identification of subhaloes and more importantly, the {em unbound tidal features} associated with them. The distributions of basic properties of the total substructure distribution (mass, velocity dispersion, position) are recovered with a scatter of $sim20%$. Using the tracking code as our reference, we show that the non-tracking codes identify complex tidal debris with purities of $sim40%$. Analysing the results of the substructure finders, we find that the general distribution of {em substructures} differ significantly from the distribution of bound {em subhaloes}. Most importantly, both bound and unbound {em substructures} together constitute $sim18%$ of the host halo mass, which is a factor of $sim2$ higher than the fraction in self-bound {em subhaloes}. However, this result is restricted by the remaining challenge to cleanly define when an unbound structure has become part of the host halo. Nevertheless, the more general substructure distribution provides a more complete picture of a halos accretion history.
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 n=-2.5. We carefully consider finite volume effects that may call into qu
estion 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 LCDM 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>=-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 alpha=-1.0 may greatly overestimate the number of subhaloes at the smallest scales in the CDM hierarchy.
