Classifications of Twin Star Solutions for a Constant Speed of Sound Parameterized Equation of State

We explore the possible mass radius relation of compact stars for the equation of states with a first order phase transition. The low density matter is described by a nuclear matter equation of state resulting from fits to nuclear properties. A constant speed of sound parametrization is used to describe the high density matter phase with the speed of sound $c_s^2=1$. A classification scheme of four distinct categories including twin star solutions, i. e. solutions with the same mass but differing radii, is found which are compatible with the $M \ge 2M_\odot$ pulsar mass constraint. We show the dependence of the mass and radius differences on the transition parameters and delineate that higher twin star masses are more likely to be accompanied by large radius differences. These massive twin stars are generated by high values of the discontinuity in the energy density and the lowest possible values of the transition pressure that still result in masses of $M \geq 2M_\odot$ at the maximum of the hadronic branch.