High-mass twin stars with a multi-polytrope EoS

We show that in the 3-polytropes model of Hebeler et al. \cite{Hebeler:2013nza} for the neutron star equation of state at supersaturation densities a third family of compact stars can be obtained which confirms the possibility of high-mass twin stars that have coincident masses $M_1=M_2\approx 2~M_\odot$ and significantly different radii $|R_1-R_2|>2-3$ km. We show that the causality constraint puts severe limitations on the maximum mass of the third family sequence which can be relaxed when this scheme is extended to four polytropes thus mimicking a realistic high-density matter EoS.