Hadronic Stars versus Hybrid stars: how can we identify them?

The properties of high-density hadronic matter have been investigated for some time to predict properties of neutron stars including mass/radius and the maximum mass of a neutron star. Recent results indicate the properties of dense hadronic matter up to several times saturation density may be strongly constrained by properties of three-nucleon interactions and hyperon-nucleon interactions. We review some of these results and their comparison to observations. At high pressure, nuclear matter will undergo a transition to quark matter, so sufficiently heavy neutron stars may really be ``hybrid stars'' with quark matter cores. We will discuss the ``Constant Sound Speed'' (CSS) parameterization of the quark matter EoS, and show how it provides a generic way of understanding the topology of the mass-radius relation, as well as more specific features like the maximum mass and typical radius. CSS provides a fairly general framework or language for comparing different quark matter models with each other and with data, and for expressing experimental constraints in model-independent terms.