Thermodynamic instabilities in dense asymmetric nuclear matter and in compact stars

We investigate the presence of thermodynamic instabilities in compressed asymmetric baryonic matter, reachable in high energy heavy ion collisions, and in the cold β-stable compact stars. To this end we study the relativistic nuclear equation of state with the inclusion of Δ-isobars and require the global conservation of baryon and electric charge numbers. Similarly to the low density nuclear liquid-gas phase transition, we show that a phase transition can occur in dense asymmetric nuclear matter and it is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the electric charge concentration). Such thermodynamic instabilities can imply a very different electric charge fraction Z/A in the coexisting phases during the phase transition and favoring an early formation of Δ− particles with relevant phenomenological consequences in the physics of the protoneutron stars and compact stars. Finally, we discuss the possible co-existence of very compact and very massive compact stars in terms of two separate families: compact hadronic stars and very massive quark stars.