  In an attempt to place an explicit constraint on dark matter models, we
define and estimate a mean surface density of a dark halo within a radius of
maximum circular velocity, which is derivable for various galaxies with any
dark-matter density profiles. We find that this surface density is generally
constant across a wide range of maximum circular velocities of $\sim$ 10 to 400
km s$^{-1}$, irrespective of different density distribution in each of the
galaxies. This common surface density at high halo-mass scales is found to be
naturally reproduced by both cold and warm dark matter (CDM and WDM) models,
even without employing any fitting procedures. However, the common surface
density at dwarf-galaxy scales, for which we have derived from the Milky Way
and Andromeda dwarf satellites, is reproduced only in a massive range of WDM
particle masses, whereas CDM provides a reasonable agreement with the observed
constancy. This is due to the striking difference between mass-concentration
relations for CDM and WDM halos at low halo-mass scales. In order to explain
the universal surface density of dwarf-galaxy scales in WDM models, we suggest
that WDM particles need to be heavier than 3 keV.
