Shallow cores in the dark matter halos: self-interaction in action?

Using observational data for a sample of dark matter dominated galaxies and two cluster of galaxies, we have found that the central halo density does not depend on its mass, and the core radius is roughly proportional to the maximum rotation velocity. A good agreement with these scaling laws is obtained for CDM halos whose dense inner parts were expanded by gravothermal instabilities if the particles efficiently self-interact only in these parts. We find that the particle cross-section is inversely proportional to the velocity dispersion.