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Hybrid hadron-quark equations of state that give rise a third family ofstable compact stars have been shown to be compatible with the LIGO-Virgo eventGW170817. Stable configurations in the third family are called hybridhadron-quark stars. The equilibrium stable hybrid hadron-quark star branch isseparated by the stable neutron star branch with a branch of unstable hybridhadron-quark stars. The end-state of these unstable configurations has not beenstudied, yet, and it could have implications for the formation and existence oftwin stars -- hybrid stars with the same mass as neutron stars but differentradii. We modify existing hybrid hadron-quark equations of state with afirst-order phase transition in order to guarantee a well-posed initial valueproblem of the equations of general relativistic hydrodynamics, and study thedynamics of non-rotating or rotating unstable twin stars via 3-dimensionalsimulations in full general relativity. We find that unstable twin starsnaturally migrate toward the hadronic branch. Before settling into the hadronicregime, these stars undergo (quasi)radial oscillations on a dynamical timescalewhile the core bounces between the two phases. Our study suggests that it maybe difficult to form stable twin stars if the phase transition is sustainedover a large jump in energy density, and hence it may be more likely thatastrophysical hybrid hadron-quark stars have masses above the twin star regime.We also study the minimum-mass instability for hybrid stars, and find thatthese configurations do not explode, unlike the minimum-mass instability forneutron stars. Additionally, our results suggest that oscillations between thetwo Quantum Chromodynamic phases could provide gravitational wave signalsassociated with such phase transitions in core-collapse supernovae and whitedwarf-neutron star mergers.

The fate of twin stars on the unstable branch: implications for the formation of twin stars