Robustness of third family solutions for hybrid stars against mixed phase effects

We investigate the robustness of third family solutions for hybrid compact stars with a quark matter core that correspond to the occurrence of high-mass twin stars against a softening of the phase transition by means of a construction that mimics the effects of pasta structures in the mixed phase. We consider a class of hybrid equations of state that exploits a relativistic mean-field model for the hadronic as well as for the quark matter phase. We present parametrizations that correspond to branches of high-mass twin star pairs with maximum masses between 2.05 M_⊙ and 1.48 M_⊙ having radius differences between 3.2 and 1.5 km, respectively. When compared to a Maxwell construction with a fixed value of critical pressure P_c, the effect of the mixed phase construction consists in the occurrence of a region of pressures around P_c belonging to the coexistence of hadronic and quark matter phases between the onset pressure at P_H and the end of the transition at P_Q. The maximum broadening which would still allow mass-twin compact stars is found to be (P_Q-PH)max≈P_c for all parametrizations within the present class of models. At least the heavier of the neutron stars of the binary merger GW170817 could have been a member of the third family of hybrid stars. We present the example of another class of hybrid star equations of state for which the appearance of the third family branch is not as robust against mixed phase effects as that of the present work.