Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at more moderate densities, to describe its physical properties. At lower densities the CFL phase may be disfavored by stresses that seek to separate the Fermi surfaces of the different flavors, and comparison with the competing alternative phases, which may break translation and/or rotation invariance, is done using phenomenological models. We review the calculations that underlie these results and then discuss transport properties of several color-superconducting phases and their consequences for signatures of color superconductivity in neutron stars.

In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor (β-)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.

We calculate the bulk-viscous dissipation time for adiabatic density oscillations in nuclear matter at densities of one to seven times the nuclear saturation density and at temperatures ranging from 1 MeV, where corrections to previous low-temperature calculations become important, up to 10 MeV, where the assumption of neutrino transparency is no longer valid. Under these conditions, which are expected to occur in neutron star mergers, damping of density oscillations arises from $\beta$ equilibration via weak interactions. We find that for 1-kHz oscillations the shortest dissipation times are in the 5- to 20-ms range, depending on the equation of state, which means that bulk viscous damping could affect the dynamics of a neutron star merger. For higher frequencies, the dissipation time can be even shorter.

We compute the mass, radius and tidal deformability of stars containing phase transitions from hadronic to quark phase(s). These quantities are computed for three types of hadronic envelopes: purely nuclear, hyperonic, and $\mathrm{\Delta }$-resonance–hyperon admixed matter. We consider either a single first-order phase transition to a quark phase with a maximally stiff equation of state (EOS) or two sequential first-order phase transitions mimicking a transition from hadronic (H) to a quark matter phase followed by a second phase transition to another quark phase. Such a construct emulates the results of the computations of the EOS, which include two-flavor color-superconducting and color-flavor-locked superconducting phases at low and high density. We explore the parameter space which produces low-mass twin and triplet configurations where equal-mass stars have substantially different radii and tidal deformabilities. We demonstrate that while for purely hadronic stiff EOS the obtained maximum mass is inconsistent with the upper limit on this quantity placed by GW170817, the inclusion of the hyperonic and $\mathrm{\Delta }$-resonance degrees of freedom, as well as the deconfinement phase transition at sufficiently low density, produces a configuration of stars consistent with this limit. The obtained hybrid star configurations are in the mass range relevant for the interpretation of the GW170817 event. We compare our results for the tidal deformability with the limits inferred from GW170817 showing that the onset of non-nucleonic phases, such as $\mathrm{\Delta }$-resonance–hyperon admixed phase and/or the quark phase(s), are favored by these data if the nuclear EOS is stiff. Also, we show that low-mass twins and especially triplets proliferate the number of combinations of possible types of stars that can undergo a merger event, the maximal number being six in the case of triplets. The prospects for uncovering the first-order phase transition(s) to and in quark matter via measurements of tidal deformabilities in merger events are discussed.

We explore the implications of the recent radius determination of PSR $\mathrm{J}0740+6620$ by the NICER experiment, combined with the neutron skin measurement by the PREX-II experiment and the associated inference of the slope of symmetry energy, for the structure of hybrid stars with a strong first-order phase transition from nucleonic to quark matter. We combine a covariant density-functional nucleonic equation of state (EOS) with a constant-speed-of-sound EOS for quark matter. We show that the radius and tidal deformability ranges obtained from GW170817 can be reconciled with the implication of the PREX-II experiment if there is a phase transition to quark matter in the low-mass compact star. In the high-mass segment, the EOS needs to be stiff to comply with the large-radius inference for PSR $\mathrm{J}0740+6620$ and $\mathrm{J}0030+0451$ with masses $M\simeq 2M_{\odot }$ and $M\simeq 1.4M_{\odot }$. We show that twin stars are not excluded, but the mass and radius ranges (with $M\ge M_{\odot }$) are restricted to narrow domains $\mathrm{\Delta }{M}_{\mathrm{twin}}\lesssim 0.05M_{\odot }$ and $\mathrm{\Delta }{R}_{\mathrm{twin}}\sim 1.0\mathrm{km}$. We also show that the existence of twin configurations is compatible with the light companion in the GW190814 event being a hybrid star in the case of values of the sound-speed square $s=0.6$ and $s=1/3$.