We study the structure and substructure of halos obtained in N-body simulations for a ΛCDM cosmology with non-Gaussian initial conditions. The initial statistics are lognormal in the gravitational potential field with positive (LN_p) and negative (LN_n) skewness; the sign of the skewness is conserved by the density field, and the power spectrum is the same for all the simulations. Our aim is not to test a given non-Gaussian statistics but to explore the generic effect of positive- and negative-skew statistics on halo properties. From our low-resolution simulations, we find that LN_p (LN_n) halos are systematically more (less) concentrated than their Gaussian counterparts. This result is confirmed by our Milky Way- and cluster-sized halos resimulated with high resolution. In addition, they show inner density profiles that depend on the statistics: the innermost slopes of LN_p (LN_n) halos are steeper (shallower) than those obtained from the corresponding Gaussian halos. A subhalo population embedded in LN_p halos is more susceptible to destruction than its counterpart inside Gaussian halos. On the other hand, subhalos in LN_n halos tend to survive longer than subhalos in Gaussian halos. The spin parameter probability distribution of LN_p (LN_n) halos is skewed to smaller (larger) values with respect to the Gaussian case. Our results show how the statistics of the primordial density field can influence some halo properties, opening the possibility of constraining, albeit indirectly, the primordial statistics at small scales.
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