Hybrid stars with reactive interfaces: Analysis within the Nambu–Jona-Lasinio model

Abstract

It has been shown recently that quark-hadron conversions at the interface of a hybrid star may have a key role on the dynamic stability of the compact object. In this work we perform a systematic study of hybrid stars with reactive interfaces using a model-agnostic piecewise-polytropic hadronic equation of state and the Nambu--Jona-Lasinio (NJL) model for three-flavor quark matter. For the hadronic phase we use a soft, an intermediate and a stiff parametrization that match at $1.1{n}_{0}$ with predictions based on chiral effective field theory (cEFT) interactions. In the NJL Lagrangian we include scalar, vector and 't Hooft interactions. The vector coupling constant ${g}_{v}$ is treated as a free parameter. We also consider that there is a split between the deconfinement and the chiral phase transitions which is controlled by changing the conventional value of the vacuum pressure $\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{0}$ in the NJL thermodynamic potential by $\ensuremath{-}({\mathrm{\ensuremath{\Omega}}}_{0}+\ensuremath{\delta}{\mathrm{\ensuremath{\Omega}}}_{0})$, being $\ensuremath{\delta}{\mathrm{\ensuremath{\Omega}}}_{0}$ a free parameter. We analyze the mass-radius ($M\text{\ensuremath{-}}R$) relation in the case of rapid ($\ensuremath{\tau}\ensuremath{\ll}1\text{ }\text{ }\mathrm{ms}$) and slow ($\ensuremath{\tau}\ensuremath{\gg}1\text{ }\text{ }\mathrm{ms}$) conversions, being $\ensuremath{\tau}$ the reaction timescale. In the case of slow interface reactions we find $M\text{\ensuremath{-}}R$ curves with a cusp at the maximum mass point where a pure hadronic branch and a slow-stable hybrid star (SSHS) branch coincide. We find that the length of the slow-stable branch grows with the increase of the transition density and the energy density jump at the hadron-quark interface. We calculate the tidal deformabilities of SSHSs and analyze them in the light of the GW170817 event.