Proving the CEP with compact stars?

We present a model for hybrid compact stars composed of a quark core and a hadronic mantle with an abrupt first order phase transition at the interface and in accordance with the latest astrophysical measurements of two 2 M_sun pulsars. We demonstrate the possibility of a disconnected mass-radius sequence (third family) of high-mass pulsars as a distinct feature due to a large jump $\Delta \epsilon$ in the energy density of the first order phase transition setting in at $\epsilon_{\rm crit}\approx 500$ MeV/fm$^3$ and fulfilling $\Delta \epsilon/\epsilon_{\rm crit} > 0.6$. We conclude that the measurement of so called \textit{twin} compact stars at high mass (~ 2 M_sun) would support the existence of a first order phase transition in symmetric matter at zero temperature entailing the existence of a critical end point (CEP) in the QCD phase diagram.