In this work, we explore how astronomical observations (specifically measurements of masses and radii) can constrain the presence of quark matter inside neutron stars, namely the phase transition from nuclear matter to deconfined quark matter. Our approach employs Bayesian analysis to study this constraint. In this sense to model Hadronic matter we used the relativistic mean-field approximation, for which we have selected two parameter sets: $NL{3}^{*}\omega \rho$, representing hadronic matter with nucleons only, and $EL3\omega \rho$ with nucleons only and $EL3\omega \rho Y$, which includes hyperons. On the other hand deconfined quark matter is modeled using the vector-MIT bag model. Also, for our purpose, the first order phase transition is implemented using the Maxwell construction. Bayesian inference is performed by optimizing three parameters: the bag constant (i.e. $B^{1/4}$), the vector coupling constant $(G_v)$, and the Dirac sea contribution ($b_4$). We found that a phase transition could exist at densities below $2.0n_0$ for both the $EL3\omega \rho$ and $NL{3}^{*}\omega \rho$ parametrizations. As a consequence, the inferred parameters of the vector MIT bag model, based on our likelihood function, imply hybrid stars with large quark cores.

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• Neutron stars & pulsars