The equation of state of dense matter: Stiff, soft, or both?

We review the constraints on the equation of state (EoS) of dense matter that have been obtained with the detection of GW170817 and its electromagnetic counterparts. While extremely stiff EoSs are ruled out by the gravitational wave signal, also extremely soft EoSs seem disfavored because they are unable to provide massive enough accretion disks. In this respect, the two-families scenario, in which hadronic stars (HSs) and quark stars (QSs) coexist, could offer a viable solution: the hadronic matter EoS is very soft and leads to very small radii, whereas the quark matter EoS is stiff and leads to large masses. In this scenario, GW170817 could be interpreted as due to the merger of an HS and a QS. We present a parametric study of the two-families scenario in which the quark matter EoS is computed by a constant-speed-of-sound (c s ) model and study the astrophysical constraints on the free parameters of the model. For this study, we fix c 2s = 1/3, which holds true at asymptotically high densities (the conformal limit). If quark matter is absolutely stable, its baryon density at zero pressure must be smaller than twice the nuclear saturation density and its energy per baryon is a few tens of MeV smaller than that of iron.