Context. Hadronic matter undergoes a deconfinement transition to quark matter at high temperature and/or high density. It would be realized in collapsing cores of massive stars. Aims. In the framework of the MIT bag model, the ambiguities of the interaction are encapsulated in the bag constant. Some progenitor stars that invoke the core collapses explode as supernovae, and other ones become black holes. The fates of core collapses are investigated for various cases. Methods. Equations of state including the hadron-quark phase transition are constructed for the cases of the bag constant B = 90, 150, and 250 MeV fm-3. To describe the mixed phase, the Gibbs condition is used. Adopting the equations of state with different bag constants, the core collapse simulations are performed for the progenitor models with 15 and 40 MâŠ™. Results. If the bag constant is small, for example B = 90 MeV fm-3, the interval between the bounce and black hole formation is shortened drastically for the model with 40 M âŠ™, and the second bounce revives the shock wave leading to explosion for the model with 15 MâŠ™.
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