Finite-size effects at the hadron-quark transition and heavy hybrid   stars
  We study the role of finite-size effects at the hadron-quark phase transition in a new hybrid equation of state constructed from an ab-initio Br\"uckner-Hartree-Fock equation of state with the realistic Bonn-B potential for the hadronic phase and a covariant non-local Nambu--Jona-Lasinio model for the quark phase. We construct static hybrid star sequences and find that our model can support stable hybrid stars with an onset of quark matter below $2 M_\odot$ and a maximum mass above $2.17 M_\odot$ in agreement with recent observations. If the finite-size effects are taken into account the core is composed of pure quark matter. Provided that the quark vector channel interaction is small, and the finite size effects are taken into account, quark matter appears at densities 2-3 times the nuclear saturation density. In that case the proton fraction in the hadronic phase remains below the value required by the onset of the direct URCA process, so that the early onset of quark matter shall affect on the rapid cooling of the star. 
N. Yasutake, R. Lastowiecki, S. Benic, D. Blaschke, T. Maruyama and T.   Tatsumi
astro-ph.HE hep-ph nucl-th