Signals in the tidal deformability for phase transitions in compact stars with constraints from GW170817

We compute the tidal deformabilities for neutron star merger for equations of state with a strong first order phase transition producing a new separate branch in the mass-radius diagram. A case is found where all three possible pairs of combinations between these two neutron star branches are present for the total mass of $M=2.7M_{\odot }$ of the observed merger event GW170817. It is demonstrated that the plot of the two tidal deformabilities ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ of the binary neutron star can show up to three separate branches. We propose that the future detections of neutron star merger events with the same value for ${\mathrm{\Lambda }}_1$ but different values of ${\mathrm{\Lambda }}_2$ serve as a signal for the existence of a strong first order phase transition in neutron star matter.