We present a comparison of halo properties in cosmological simulations of collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM) for a range of dark matter cross sections. We find, in agreement with various authors, that CDM yields cuspy halos that are too centrally concentrated as compared to observations. Conversely, SIDM simulations using a Monte Carlo N-body technique produce halos with significantly reduced central densities and flatter cores. We introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally and present predictions for SIDM and CDM. SIDM also produces more spherical halos than CDM, providing possibly the strongest observational constraint on SIDM. In our simulations with SIDM cross sections σDM ≈ 10-23 to 10-25 cm2 GeV-1, collisions reduce the central density in galaxy halos, with larger cross sections producing lower densities. Simulations in the upper end of this range best match current observations of galaxy properties but are disfavored by cluster simulations of Yoshida and colleagues. This problem would be alleviated in models in which the cross section is velocity dependent.
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