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 Brückner-Hartree-Fock equation of state with the realistic Bonn-B potential for the hadronic phase and a covariant nonlocal 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 $2M_{\odot }$ and a maximum mass above $2.17M_{\odot }$ 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.

The effect of pasta phases on the quark-hadron phase transition is investigated for a set of relativistic mean-field equations of state for both hadron and quark matter. The results of the full numerical solution with pasta phases are compared with those of an interpolating construction used in previous works, for which we demonstrate an adequate description of the numerical results. A one-to-one mapping of the free parameter of the construction to the physical surface tension of the quark-hadron interface is obtained for which a fit formula is given. For each pair of quark and hadron matter models the critical value of the surface tension is determined, above which the phase transition becomes close to the Maxwell construction. This result agrees well with earlier theoretical estimates. The study is extended to neutron star matter in beta equilibrium with electrons and muons and is applied to investigate the effect of pasta phases on the structure of hybrid compact stars and the robustness of a possible third family solution.

We study the interface effects of a quark-hadron mixed phase in compact stars. The properties of nuclear matter are obtained based on the relativistic-mean-field model. For the quark phase, we adopt a perturbation model with running quark masses and coupling constant. At certain choices of parameter sets, it is found that varying the quark-hadron interface tension will have sizable effects on the radii ($\mathrm{\Delta }R\approx 600\mathrm{m}$) and tidal deformabilities ($\mathrm{\Delta }\mathrm{\Lambda }/\mathrm{\Lambda }\approx 50\%$) of 1.36 solar mass hybrid stars. These provide possibilities for us to constrain the quark-hadron interface tension with future gravitational wave observations as well as the ongoing NICER mission.

We investigate systematically the quark-hadron mixed phase in dense stellar matter and its influence on compact star structures. The properties of quark matter and hadronic matter are fixed based on various model predictions. Beside adopting constant values, the surface tension $\mathrm{\Sigma }$ for the quark-hadron interface is estimated with the multiple reflection expansion method and equivparticle model. To fix the structures of quark-hadron pasta phases, a continuous dimensionality of the structure is adopted as proposed by Ravenhall et al. The corresponding properties of hybrid stars are then obtained and confronted with pulsar observations. It is found that the correlation between radius and tidal deformability in traditional neutron stars preserves in hybrid stars. For those permitted by pulsar observations, in almost all cases, the quark phase persists inside the most massive compact stars. The quark-hadron interface plays an important role in hybrid star structures once quark matter emerges. The surface tension $\mathrm{\Sigma }$ estimated with various methods increases with density, which predicts stiffer equation of states (EOSs) for the quark-hadron mixed phase and increases the maximum mass of hybrid stars. With or without the emergence of quark matter, the obtained EOSs of hybrid star matter are close to each other at densities $n\lesssim 0.8{\mathrm{fm}}^{-3}$, while larger uncertainty is expected at higher densities.

In the framework of the relativistic mean-field model with Thomas-Fermi approximation, we study the structures of low-density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $\beta$ equilibration. It is found that the properties of droplets and bubbles are similar in body-centered cubic (bcc) and face-centered cubic (fcc) lattices, where the fcc lattice generally becomes more stable than bcc lattice as density increases. For the rod and tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $\omega \text{−}\rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L=41.34$ MeV, which predicts larger onset densities for core-crust transition and nonspherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.

We study the hadron-quark phase transition, taking into account the finite-size effects for neutron star matter. For the hadron phase, we adopt a realistic equation of state within the framework of the Brueckner-Hartree-Fock theory. For the quark phase, we apply the Dyson-Schwinger method. The properties of the mixed phase are clarified by considering the finite-size effects. We find that, if the surface tension is strong enough, the equation of state becomes to be close the one with the Maxwell condition, though we properly adopt the Gibbs conditions. This result is qualitatively the same with the one by the use of the simple bag model. We also find that the mass-radius relation by the EoS is consistent with the observations of massive neutron stars.