The recent measurement of a 1.97 ± 0.04 solar-mass pulsar places a stringent lower bound on the maximum mass of compact stars and therefore challenges the existence of any agents that soften the equation of state of ultra-dense matter. We investigate whether hyperons and/or quark matter can be accommodated in massive compact stars by constructing an equation of state based on a combination of phenomenological relativistic hyper-nuclear density functional and an effective model of quantum chromodynamics (the Nambu-Jona-Lasinio model). Stable configurations are obtained with M ≥ 1.97 M featuring hyper-nuclear and quark matter in color superconducting state if the equation of state of nuclear matter is stiff above the saturation density, the transition to quark matter takes place at a few times the nuclear saturation density, and the repulsive vector interactions in quark matter are substantial.

Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, that give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within ∼ 3% for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.

Magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev's non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of the equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green's functions defined with respect to the equilibrium statistical operator.

Compact stars may contain quark matter in their interiors at densities exceeding several times the nuclear saturation density. We explore models of such compact stars where there are two first-order phase transitions: the first from nuclear matter to a quark-matter phase, followed at a higher density by another first-order transition to a different quark-matter phase [e.g., from the two-flavor color-superconducting (2SC) to the color-flavor-locked (CFL) phase]. We show that this can give rise to two separate branches of hybrid stars, separated from each other and from the nuclear branch by instability regions, and, therefore, to a new family of compact stars, denser than the ordinary hybrid stars. In a range of parameters, one may obtain twin hybrid stars (hybrid stars with the same masses but different radii) and even triplets where three stars, with inner cores of nuclear matter, 2SC matter, and CFL matter, respectively, all have the same mass but different radii.

In strong magnetic fields the transport coefficients of strange quark matter become anisotropic. We determine the general form of the complete set of transport coefficients in the presence of a strong magnetic field. By using a local linear response method, we calculate explicitly the bulk viscosities ζ ⊥ and ζ transverse and parallel to the B-field respectively, which arise due to the non-leptonic weak processes u + s ↔ u + d. We find that for magnetic fields B < 10 17 G, the dependence of ζ ⊥ and ζ on the field is weak, and they can be approximated by the bulk viscosity for zero magnetic field. For fields B > 10 18 G, the dependence of both ζ ⊥ and ζ on the field is strong, and they exhibit de Haas-van Alphen-type oscillations. With increasing magnetic field, the amplitude of these oscillations increases, which eventually leads to negative ζ ⊥ in some regions of parameter space. We show that the change of sign of ζ ⊥ signals a hydrodynamic instability. As an application, we discuss the effects of the new bulk viscosities on the r-mode instability in rotating strange quark stars. We find that the instability region in strange quark stars is affected when the magnetic fields exceeds the value B = 10 17 G. For fields which are larger by an order of magnitude, the instability region is significantly enlarged, making magnetized strange stars more susceptible to r-mode instability than their unmagnetized counterparts.