  The structure and dark matter halo core properties of dwarf spheroidal
galaxies (dSphs) are investigated. A double-isothermal model of an isothermal
stellar system, embedded in an isothermal dark halo core provides an excellent
fit to the various observed stellar surface density distributions. The stellar
system can be well characterised by King profiles with a broad distribution of
concentration parameters c. The core scale length of the stellar system a_* is
sensitive to the central dark matter density rho_0. In contrast to
single-component systems, the cut-off radius of the stellar system, rs_t,
however does not trace the tidal radius but the core radius r_c of its dark
matter halo. c is therefore sensitive to the ratio of the stellar to the dark
matter velocity dispersion, sigma_*/sigma_0. Simple empirical relationships are
derived that allow to calculate the dark halo core parameters rho_0, r_c and
sigma_0, given the observable quantities sigma_*, a_* and c. The DIS model is
applied to the Milky Way's dSphs. Their halo velocity dispersions lie in a
narrow range of 10km/s <= sigma_0 <= 18km/s with halo core radii of 280pc <=
r_c <= 1.3kpc and r_c=2a_*. All dSphs follow closely the same universal dark
halo core scaling relation rho_0*r_c=75 Msolar/pc^2 that characterises the
cores of more massive galaxies over several orders of magnitude in mass. The
dark matter core mass is a strong function of core radius. Inside a fixed
radius r_u, with r_u the logarithmic mean of the dSph's core radii, the total
enclosed mass M_u is however roughly constant, although outliers should exist.
For our dSphs we find r_u=400pc and M_u=2.6*10^7 Msolar. The core densities of
the Galaxy's dSphs are very high, with rho_0=0.2 Msolar/pc^3. They should
therefore be tidally undisturbed. Observational evidence for tidal effects
might then provide a serious challenge for the cold dark matter scenario.
