Quark phases in neutron stars consistent with implications of NICER

The analyses for the NICER data imply $R_{2.0M_\odot}=12.41^{+1.00}_{-1.10}$ km and $R_{1.4M_\odot}=12.56^{+1.00}_{-1.07}$ km, indicating the lack of significant variation of the radii from $1.4 M_\odot$ to $2.0 M_\odot$. This feature cannot be reproduced by the hadronic matter due to the softening of equation of state (EoS) by hyperon mixing, indicating the possible existence of quark phases in neutron-star interiors. % Two models are used for quark phases: In the quark-hadron transition (QHT) model, quark deconfinement phase transitions from a hadronic-matter EoS are taken into account so as to give reasonable mass-radius ($MR$) curves by adjusting the quark-quark repulsions and the density dependence of effective quark mass. % In the quarkyonic model, the degrees of freedom inside the Fermi sea are treated as quarks and neutrons exist at the surface of the Fermi sea, where $MR$ curves are controlled mainly by the thickness of neutron Fermi layer. % The QHT and quarkyonic EoSs can be adjusted so as to reproduce radii, tidal deformabilities, pressure and central densities inferred from the NICER analysis better than the nucleonic matter EoS, demonstrating the clear impacts of quark phases. Then, the maximum mass for the quakyonic-matter EoS is considerably larger than that for the QHT-matter EoS.