  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.
