The discovery of pulsars PSR J1614-2230 and PSR J0348+0432 with masses of around 2Mʘ imposes strong constraints on the equations of state of cold, ultradense matter. If a phase transition from hadronic matter to quark matter were to occur in the inner cores of such massive neutron stars, the energetically favorable state of quark matter would be a color superconductor. In this study, we analyze the stability and maximum mass of such neutron stars. The hadronic phase is described by nonlinear relativistic mean-field models, and the local Nambu-Jona Lasinio model is used to describe quark matter in the 2SC+s quark phase. The phase transition is treated as a Maxwell transition, assuming a sharp hadron-quark interface, and the "constant-sound-speed" (CSS) parametrization is employed to discuss the existence of stellar twin configurations. We find that massive neutron stars such as J1614-2230 and J0348+0432 can only exist on the connected stellar branch but not on the disconnected twin-star branch. The latter can only support stars with masses that are strictly below 2Mʘ.Facultad de Ciencias Astronómicas y Geofísica
