Dense hadronic matter in neutron stars

The existence of stars with masses up to 2M and the hints of the existence of stars with radii smaller than 11 km seem to require, at the same time, a stiff and a soft hadronic equation of state at large densities. We argue that these two, apparently contradicting, constraints are actually an indication of the existence of two families of compact stars: hadronic stars which could be very compact and quark stars which could be vary massive. In this respect, a crucial role is played, in the hadronic equation of state, by the delta isobars whose early appearance shifts to large densities the formation of hyperons. We also discuss how recent experimental information on the symmetry energy of nuclear matter at saturation indicates, indirectly, an early appearance of delta isobars in neutron star matter.