  We consider the problem of determining the structure of the dark halo of
nearby dwarf spheroidal galaxies (dSphs) from the spherical Jeans equations.
Whether the dark halos are cusped or cored at the centre is an important
strategic problem in modern astronomy. The observational data comprise the
line-of-sight velocity dispersion of a luminous tracer population. We show that
when such data are analysed to find the dark matter density with the spherical
Poisson and Jeans equations, then the generic solution is a dark halo density
that is cusped like an isothermal. Although milder cusps (like the
Navarro-Frenk-White 1/r cusp and even cores are possible, they are not generic.
Such solutions exist only if the anisotropy parameter beta and the logarithmic
slope of the stellar density gamma satisfy the constraint gamma = 2 x beta at
the centre or if the radial velocity dispersion falls to zero at the centre.
This surprisingly strong statement is really a consequence of the assumption of
spherical symmetry, and the consequent coordinate singularity at the origin.
So, for example, a dSph with an exponential light profile can exist in
Navarro-Frenk- White halo and have a flat velocity dispersion, but anisotropy
in general drives the dark halo solution to an isothermal cusp. The identified
cusp or core is therefore a consequence of the assumptions (particularly of
spherical symmetry and isotropy), and not the data.
