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.

We consider the precession of isolated neutron stars in which superfluid is not pinned to the stellar crust perfectly. In the case of perfect pinning, Shaham (1977) showed that there are no slowly oscillatory, long-lived modes. When the assumption of perfect pinning is relaxed, new modes are found that can be long-lived, but are expected to be damped rather than oscillatory, unless the drag force on moving superfluid vortex lines has a substantial component perpendicular to the direction of relative motion. The response of a neutron star to external torques, such as the spindown torque, is also treated. We find that when computing the response of a star to perturbations, assuming perfect coupling of superfluid to normal matter from the start can miss some effects.

The ∆-isobar degrees of freedom are included in the covariant density functional (CDF) theory to study the equation of state (EoS) and composition of dense matter in compact stars. In addition to ∆'s we include the full octet of baryons, which allows us to study the interplay between the onset of delta isobars and hyperonic degrees of freedom. Using both the Hartree and Hartree-Fock approximation we find that ∆'s appear already at densities slightly above the saturation density of nuclear matter for a wide range of the meson-∆ coupling constants. This delays the appearance of hyperons and significantly affects the gross properties of compact stars. Specifically, ∆'s soften the EoS at low densities but stiffen it at high densities. This softening reduces the radius of a canonical 1.4M star by up to 2 km for a reasonably attractive ∆ potential in matter, while the stiffening results in larger maximum masses of compact stars. We conclude that the hypernuclear CDF parametrizations that satisfy the 2M maximum mass constraint remain valid when ∆ isobars are included, with the important consequence that the resulting stellar radii are shifted toward lower values, which is in agreement with the analysis of neutron star radii.

We study the equation of state and composition of hypernuclear matter within a relativistic density functional theory with density-dependent couplings. The parameter space of hyperon-scalar-meson couplings is explored by allowing for mixing and breaking of SU(6) symmetry, while keeping the nucleonic coupling constants fixed. The subset of equations of state, which corresponds to small values of hyperon-scalar-meson couplings, allows for massive M 2.25M compact stars; the radii of hypernuclear stars are within the range 12-14 km. We also study the equation of state of hot neutrino-rich and neutrinoless hypernuclear matter and confirm that neutrinos stiffen the equation of state and dramatically change the composition of matter by keeping the fractions of charged leptons nearly independent of the density prior to the onset of neutrino transparency. We provide piecewise polytropic fits to six representative equations of state of hypernuclear matter, which are suitable for applications in numerical astrophysics.