Hybrid equation of state with pasta phases and third family of compact stars I: Pasta phases and effective mixed phase model

We investigate the effect of the pasta phases formation on the quark-hadron phase transition for a set of relativistic mean-field equations of state for both, hadron and quark matter. The results are compared with a mimicking construction, which was used in a recent study of the robustness of the third family solution instead of the full numerical solution with pasta phases. We demonstrate, that the construction allows for describing the numerical results well and obtain a one-to-one map of the parameter of the construction to the physical surface tension. For each pair of the models we determined the critical value of the surface tension, above which the phase transition becomes close to the Maxwell construction. It agrees qualitatively with earlier theoretical estimates.