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

Abstract: 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 $2.05~M_\odot$ and $1.48~M_\odot$ having radius differences between 3.2 km 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 $(P_Q-P_H)_{\rm max} \approx P_c$ 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.