A new class of equations of state (EoS) for strongly interacting matter is presented which is characterized by a density-dependent stiffening of the hadronic phase due to the quark substructure of baryons (Pauli blocking on the quark level between baryons) and by a density-dependent stiffening in the quark matter phase after the chiral/deconfinement transition due to higher order (8-quark) interactions in the scalar and vector current channels.
It is demonstrated that such an EoS can describe high-mass twin compact stars as a unique feature of identifying a strong first-order phase transition in mass and radius observations of compact stars, thus supporting the existence of a critical endpoint in the QCD phase diagram.
Furthermore, rotating compact star configurations are considered which reveal a unique feature of this new hybrid EoS for scenarios of hybrid star formation in either accreting LMXBs or spinning-down isolated pulsars.
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