  We study mass-radius relations for compact stars employing an equation of
state (EOS) of dense matter based on a Skyrme fluid. The zero-temperature
mean-field model is based on mesonic excitations, incorporates the scale
breaking of QCD, and accommodates baryons (nucleons) which arise as a solitonic
configuration of mesonic fields. Stable configurations are obtained for central
densities $\rho_c/\rho_n\leq 5.0$ where $\rho_n=2.575\times 10^{14}$ g/cc is
the nuclear saturation density. These {\it Skyrmion Stars} are mostly fluid,
with a crust which we describe by the EOS of Baym, Pethick and Sutherland.
Their masses and radii are in the range $0.4 \le M/M_{\odot} \le 3.6$ and $13
{\rm km} \le R \le 23 {\rm km}$, respectively. The minimum spin period is
computed to be between $0.7 {\rm ms}\le P \le 2.1 {\rm ms}$. They appear to
have a mass-radius curve quite different from either neutron or quark stars,
and provide a suitable description of the heavier mass neutron stars discovered
recently due to the inherently stiff EOS. Within the same model, we compute the
dominant neutrino emissivity in neutron-rich $\beta$-equilibrated matter, and
determine the cooling behaviour of Skyrmion stars.
