Scaling relations of the slightly self-interacting cold dark matter in
  galaxies and clusters
  Recent observations in galaxies and clusters indicate dark matter density
profiles exhibit core-like structures which contradict to the numerical
simulation results of collisionless cold dark matter. The idea of
self-interacting cold dark matter (SICDM) has been invoked to solve the
discrepancies between the observations and numerical simulations. In this
article, I derive some important scaling relations in galaxies and clusters by
using the long-range SICDM model. These scaling relations give good agreements
with the empirical fittings from observational data in galaxies and clusters if
the dark matter particles are only slightly self-interacting. Also, there may
exist a universal critical optical depth $\tau_c$ that characterizes the
core-like structures. These results generally support the idea of SICDM to
tackle the long-lasting dark matter problem.
