In this work we consider strange stars formed by quark matter in the color-flavor-locked (CFL) phase of color superconductivity. The CFL phase is described by a Nambu-Jona-Lasinio model with four-fermion vector and diquark interaction channels. The effect of the color superconducting medium on the gluons are incorporated into the model by including the gluon self-energy in the thermodynamic potential. We construct parametrizations of the model by varying the vector coupling $G_V$ and comparing the results to the data on tidal deformability from the GW170817 event, the observational data on maximum masses from massive pulsars such as the MSP $\mathrm{J}0740+6620$, and the mass/radius fits to NICER data for PSR $\mathrm{J}003+0451$. Our results point out to windows for the $G_V$ parameter space of the model, with and without gluon effects included, that are compatible with all these astrophysical constraints, namely, $0.21<G_V/G_S<0.4$, and $0.02<G_V/G_S<0.1$, respectively. We also observe a strong correlation between the tidal deformabilites of the GW170817 event and $G_V$. Our results indicate that strange stars cannot be ruled out in collisions of compact binaries from the structural point of view.

We investigate the stability of the magnetic dual chiral density wave (MDCDW) phase of cold and dense QCD against collective low-energy fluctuations of the order parameter. The appearance of additional structures in the system free energy due to the explicit breaking of the rotational and isospin symmetries by the external magnetic field play a crucial role in the analysis. The new structures stiffen the spectrum of the thermal fluctuations in the transverse direction, thereby avoiding the Landau-Peierls instability that affects single-modulated phases at arbitrarily low temperatures. The lack of Landau-Peierls instabilities in the MDCDW phase makes this inhomogeneous phase of dense quark matter of particular interest for the physics of neutron stars.

In this review, we discuss the physical characteristics of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and argue why it is a promising candidate for the interior matter phase of neutron stars. The MDCDW condensate occurs in the presence of a magnetic field. It is a single-modulated chiral density wave characterized by two dynamically generated parameters: the fermion quasiparticle mass m and the condensate spatial modulation q. The lowest-Landau-level quasiparticle modes in the MDCDW system are asymmetric about the zero energy, a fact that leads to the topological properties and anomalous electric transport exhibited by this phase. The topology makes the MDCDW phase robust against thermal phonon fluctuations, and as such, it does not display the Landau–Peierls instability, a staple feature of single-modulated inhomogeneous chiral condensates in three dimensions. The topology is also reflected in the presence of the electromagnetic chiral anomaly in the effective action and in the formation of hybridized propagating modes known as axion-polaritons. Taking into account that one of the axion-polaritons of this quark phase is gapped, we argue how incident $\gamma$-ray photons can be converted into gapped axion-polaritons in the interior of a magnetar star in the MDCDW phase leading the star to collapse, a phenomenon that can serve to explain the so-called missing pulsar problem in the galactic center.

In this paper, we find the heat capacity of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and use it to explore the feasibility of this phase for a neutron star interior. MDCDW is a spatially inhomogeneous phase of quark matter known to be favored at intermediate densities over the chirally symmetric phase and the color-flavor-locked superconducting phase. By comparing our result to the lower limit of the core heat capacity established from observations of transiently accreting neutron stars, we show that the heat capacity of MDCDW quark matter is well above that lower limit and hence cannot be ruled out. This result adds to a wealth of complementary investigations, all of which has served to strengthen the viability of a neutron star interior made of MDCDW quark matter. For completeness, we review the contributions to the heat capacity of the main neutron star ingredients at low, high, and intermediate densities, with and without the presence of a magnetic field.