Exploring the bottom of the CDM hierarchy using scale-free simulations

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Many numerical studies show that dark matter halos have a plethora of substructure, down to the smallest resolved scales. However, the very bottom of the Cold Dark Matter (CDM) hierarchy at a few earth masses, where the spectral index n approaches -3 and structure begins to form simultaneously on a variety of scales, remains relatively unexplored. It is possible that the subhalo mass distribution, which appears to be described by a simple power-law down to mass scales 10^6 solar masses, remains unchanged and independent of scale and n. A few studies have indicated that this appears to be the case, which is surprising considering all other statistical indicators, such as the halo mass function, as well as the internal properties of halos, such as concentration, show a dependence on n. To explore the effect of the spectral index on the subhalo mass function we ran two large, scale-free simulations, P(k)=Ak^n with n=-1 and -2.5. We find that the subhalo mass function does depend on the spectral index, with the power-law becoming shallower as n->-3.