Effects of color superconductivity on the nucleation of quark matter in neutron stars

Abstract

We study the nucleation of quark matter drops at the center of cold deleptonized neutron stars. This is relevant in the determination of the critical mass $M_{cr}$ of hadronic stars above which it is possible a transition to a quark star (strange or hybrid). We investigate the dependence of $M_{cr}$ upon the parameters of the quark model (the Bag constant $B$, the pairing gap $\Delta$, and the surface tension $\sigma$ of the quark-hadron interphase) and for different parametrization of the hadronic equations of state. The dependence of $M_{cr}$ on $B$, $\Delta$ and $\sigma$ is mild if the parameters of the quark model correspond to hybrid stars, and strong if they correspond to strange stars. For a large part of the parameter space corresponding to hybrid stars, the critical mass is very close (but smaller than) the maximum mass of hadronic stars, and therefore compatible with a "mixed" population of compact stars (pure hadronic up to the critical mass and hybrid above the critical mass). For very large $B$ the critical mass is never smaller than the maximum mass of hadronic stars, implying that quark stars cannot form through the here studied mechanism. The energy released in the conversion is $3 \times 10^{52}$ erg - $4 \times 10^{53}$ erg, i.e. sufficient to power a gamma ray burst.