The detection of GW170817 and its electromagnetic counterparts allows to constrain the equation of state of dense matter in new and complementary ways. Very stiff equations of state are ruled out by the upper limit on the average tidal deformability,Λ 800, imposed by the detected gravitational wave signal. A lower limit, Λ 400, can also be extracted by considering the large amount of ejected matter which powers the kilonova AT2017gfo. By using several microscopic nucleonic equations of state, we first confirm the existence of a monotonic relation between R 1.5 (the radius of the 1.5M ⊙ configuration) andΛ. This translates the limits oñ Λ into limits on the radius: 11.8 km R 1.5 13.1 km. We then show that the monotonic relation is violated, if a second branch of compact stars composed of quark matter exists, as in the two-families or the twin-stars scenarios. In particular, it is possible to fulfill the limits onΛ while having R 1.5 significantly smaller than 12 km. In both those scenarios the event GW170817/AT2017gfo originates from the merger of a hadronic star and a star containing quark matter.

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We study cold dense quark matter and hybrid neutron stars with a Dyson-Schwinger quark model and various choices of the quark-gluon vertex. We obtain the equation of state of quark matter in beta equilibrium and investigate the hadron-quark phase transition in combination with a hadronic equation of state derived within the Brueckner-Hartree-Fock many-body theory. Comparing with the results for quark matter with the rainbow approximation, the Ball-Chiu ansatz and the 1BC ansatz for the quark-gluon vertex lead to a reduction of the effective interaction at finite chemical potential, qualitatively similar to the effect of our gluon propagator. We find that the phase transition and the equation of state of the quark or mixed phase and consequently the resulting hybrid star mass and radius depend mainly on a global reduction of the effective interaction due to effects of both the quark-gluon vertex and gluon propagator, but are not sensitive to the vertex ansatz.

We calculate neutron star's moment of inertia and deformabilities using various microscopic equations of state for nuclear and hybrid star configurations. We confirm several universal relations between the various observables in these cases. We focus in particular on the constraints for the neutron star radii imposed by a determination of the average tidal deformability of the binary neutron star system GW170817. We find compatible radii between 12 and 13 kilometers and identify the suitable equations of state.

We calculate the equation of state of strange quark matter and the interior structure of strange quark stars in a Dyson-Schwinger quark model within rainbow or Ball-Chiu vertex approximation. We emphasize constraints on the parameter space of the model due to stability conditions of ordinary nuclear matter. Respecting these constraints, we find that the maximum mass of strange quark stars is about 1.9 solar masses, and typical radii are 9-11 km. We obtain an energy release as large as 3.6 × 10 53 erg from conversion of neutron stars into strange quark stars.