Color superconducting quark matter core in the third family of compact stars

We investigate first order phase transitions from $\beta$-equilibrated hadronic matter to color flavor locked quark matter in compact star interior. The hadronic phase including hyperons and Bose-Einstein condensate of $K^-$ mesons is described by the relativistic field theoretical model with density dependent meson-baryon couplings. The early appearance of hyperons and/or Bose-Einstein condensate of $K^-$ mesons delays the onset of phase transition to higher density. In the presence of hyperons and/or $K^-$ condensate, the overall equations of state become softer resulting in smaller maximum masses than the cases without hyperons and $K^-$ condensate. We find that the maximum mass neutron stars may contain a mixed phase core of hyperons, $K^-$ condensate and color superconducting quark matter. Depending on the parameter space, we also observe that there is a stable branch of superdense stars called the third family branch beyond the neutron star branch. Compact stars in the third family branch may contain pure color superconducting core and have radii smaller than those of the neutron star branch. Our results are compared with the recent observations on RX J185635-3754 and the recently measured mass-radius relationship by X-ray Multi Mirror-Newton Observatory.