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Several global parameters of compact stars are related via empirical relations, which are (nearly) independent of the underlying equation of state (EoS) of dense matter and, therefore, are said to be universal. We investigate the universality of relations that express the maximum mass and the radius of non-rotating and maximally rapidly rotating configurations, as well as their moment of inertia, in terms of the compactness of the star. For this, we first utilize a collection of cold (zero-temperature) and hot (isentropic) nucleonic EoS and confirm that the universal relations are holding for our collection of EoS. We then go on, to add to our collection and test for the same universality models of EoS that admit a strong first-order phase transition from nucleonic to deconfined quark matter. Also in this case we find that the universal relations hold, in particular for hot, isentropic hybrid stars. By fitting the universal relations to our computed data, we determine the coefficients entering these relations and the accuracy to which they hold., Comment: 16 pages, 8 figures, published in MNRAS, Vol. 515, p. 3539 (2022)

We study compact stars with hybrid equations of state consisting of a nuclear outer region and two nested quark phases, each separated from the lower density phase by a strong first-order phase transition. The stability of these models is determined by calculating their radial oscillation modes with different conversion rates between adjacent phases and hence junction conditions for the modes at the phase separation interface between them. In the case when the timescale of transition is faster than the period of oscillations, we recover the traditional stability criterion implying that $\partial M/\partial\rho_c>0$ on the stable branch(es), where $M$ is the mass and $\rho_c$ is the central density. In the opposite limit of slow conversion, we find stable stellar multiplets beyond triplets consisting of stars that are stable by the usual criterion plus slow-conversion (denoted by $s$) hybrid stars with $\partial M/\partial\rho_c, Comment: 11 pages, 14 figures

We review the physics of hyperons and $\Delta$-resonances in dense matter in compact stars. The covariant density functional approach to the equation of state and composition of dense nuclear matter in the mean-field Hartree and Hartree-Fock approximation is presented, with regimes covering cold $\beta$-equilibrated matter, hot and dense matter with and without neutrinos relevant for the description of supernovas and binary neutron star mergers, as well as dilute expanding nuclear matter in collision experiments. We discuss the static properties of compact stars with hyperons and $\Delta$-resonances in light of constraints placed in recent years by the multimessenger astrophysics of compact stars on the compact stars' masses, radii, and tidal deformabilities. The effects of kaon condensation and strong magnetic fields on the composition of hypernuclear stars are also discussed. The properties of rapidly rotating compact hypernuclear stars are discussed and confronted with the observations of 2.5-2.8 solar mass compact objects in gravitational wave events. We further discuss the cooling of hypernuclear stars, the neutrino emission reactions, hyperonic pairing, and the mass hierarchy in the cooling curves that arises due to the onset of hyperons. The effects of hyperons and $\Delta$-resonances on the equation of state of hot nuclear matter in the dense regime, relevant for the transient astrophysical event and in the dilute regime relevant to the collider physics is discussed. The review closes with a discussion of universal relations among the integral parameters of hot and cold hypernuclear stars and their implications for the analysis of binary neutron star merger events., Comment: v3 and v2: 79 pages, 26 figures, final version (minor changes and additions, typos corrected). v1: 76 pages, 26 figures. arXiv admin note: text overlap with arXiv:2105.14050

We construct a new equation of state for the baryonic matter under an intense magnetic field within the framework of covariant density functional theory. The composition of matter includes hyperons as well as &Delta, resonances. The extension of the nucleonic functional to the hypernuclear sector is constrained by the experimental data on &Lambda, and &Xi, hypernuclei. We find that the equation of state stiffens with the inclusion of the magnetic field, which increases the maximum mass of neutron star compared to the non-magnetic case. In addition, the strangeness fraction in the matter is enhanced. Several observables, like the Dirac effective mass, particle abundances, etc. show typical oscillatory behavior as a function of the magnetic field and/or density which is traced back to the occupation pattern of Landau levels.

In this work, we consider the consequences of phase transition in dense QCD on the properties of compact stars and implications for the observational program in gravitational wave and X-ray astrophysics. The key underlying assumption of our modeling is a strong first-order phase transition past the point where the hadronic branch of compact stars reaches the two-solar mass limit. Our analysis predicts ultracompact stars with very small radii - in the range of 6-9 km - living on compact star sequences that are entirely consistent with the current multimessenger data. We show that sequences featuring two-solar mass hadronic stars consistent with radio-pulsar observations are also consistent with the inferences of large radii for massive neutron stars by NICER X-ray observations of neutron stars and the small radii predicted by gravitational waves analysis of the binary neutron star inspiral event GW170817 for our models that feature a strong first-order QCD phase transition., Comment: v2: matches published version, 6 pages, 5 figures

We discuss the bulk viscosity of hot and dense $npe\mu$ matter arising from weak-interaction direct Urca processes. We consider two regimes of interest: (a) the neutrino-transparent regime with $T\leq T_{\rm tr}$ ($T_{\rm tr}\simeq 5\div 10$ MeV is the neutrino-trapping temperature); and (b) the neutrino-trapped regime with $T\geq T_{\rm tr}$. Nuclear matter is modeled in relativistic density functional approach with density-dependent parametrization DDME2. The maximum of the bulk viscosity is achieved at temperatures $T \simeq 5\div 6$ MeV in the neutrino-transparent regime, then it drops rapidly at higher temperatures where neutrino-trapping occurs. As an astrophysical application, we estimate the damping timescales of density oscillations by the bulk viscosity in neutron star mergers and find that, e.g., at the oscillation frequency $f=10$ kHz, the damping will be very efficient at temperatures $4\leq T\leq 7$ MeV where the bulk viscosity might affect the evolution of the post-merger object., Comment: 16 pages, 9 figures, matches published version

In this work, we extend our previous study of the bulk viscosity of hot and dense $npe$ matter induced by the Urca processes in the neutrino trapped regime to $npe\mu$ matter by adding the muonic Urca processes as well as the purely leptonic electroweak processes involving electron-muon transition. The nuclear matter is modeled in a relativistic density functional approach with two different parametrizations which predict neutrino dominated matter (DDME2 model) and antineutrino dominated matter (NL3 model) at temperatures for which neutrinos/antineutrinos are trapped. In the case of neutrino-dominated matter, the main equilibration mechanism is lepton capture, whereas in the case of antineutrino-dominated matter this is due to neutron decay. We find that the equilibration rates of Urca processes are higher than that of the pure leptonic processes, which implies that the Urca-process-driven bulk viscosity can be computed with the leptonic reactions assumed to be frozen. We find that the bulk viscosity decreases with temperature as $\zeta\sim T^{-2}$ at moderate temperatures. At high temperatures this scaling breaks down by sharp drops of the bulk viscosity close to the temperature where the proton fraction is density-independent and the matter becomes scale-invariant. This occurs also when the matter undergoes a transition from the antineutrino-dominated regime to the neutrino-dominated regime where the bulk viscosity attains a local maximum. We also estimate the bulk viscous dissipation timescales and find that these are in the range $\gtrsim$ 1 s for temperatures above the neutrino trapping temperature. These timescales would be relevant only for long-lived objects formed in binary neutron star mergers and hot proto-neutron stars formed in core-collapse supernovas., Comment: 26 pages, 13 figures

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy-momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients., 54 pages

Finite-temperature equation of state (EoS) and the composition of dense nuclear and hypernuclear matter under conditions characteristic of neutron star binary merger remnants and supernovas are discussed. We consider both neutrino free-streaming and trapped regimes which are separated by a temperature of a few MeV. The formalism is based on covariant density functional (CDF) theory for the full baryon octet with density-dependent couplings, suitably adjusted in the hypernuclear sector. The softening of the EoS with the introduction of the hyperons is quantified under various conditions of lepton fractions and temperatures. We find that $\Lambda$, $\Xi^-$, and $\Xi^0$ hyperons appear in the given order with a sharp density increase at zero temperature at the threshold being replaced by an extended increment over a wide density range at high temperatures. The $\Lambda$ hyperon survives in the deep subnuclear regime. The triplet of $\Sigma$s is suppressed in cold hypernuclear matter up to around seven times the nuclear saturation density, but appears in significant fractions at higher temperatures, $T\geq 20$ MeV, in both supernova and merger remnant matter. We point out that a special isospin degeneracy point exists where the baryon abundances within each of the three isospin multiplets are equal to each other as a result of (approximate) isospin symmetry. At that point, the charge chemical potential of the system vanishes. We find that under the merger remnant conditions, the fractions of electron and $\mu$-on neutrinos are close and are about 1\%, whereas in the supernova case, we only find a significant fraction ($\sim$10\%) of electron neutrinos, given that in this case, the $\mu$-on lepton number is zero., Comment: v2: 16 pages, 7 figure, minor clarifications, matches published version. v1: 17 pages, 6 figures, submitted to "Universe"

In this work, we study the effect of (anti)kaon condensation on the properties of compact stars that develop hypernuclear cores with and without an admixture of $\Delta$-resonances. We work within the covariant density functional theory with the parameters adjusted to $K$-atomic and kaon-nucleon scattering data in the kaonic sector. The density-dependent parameters in the hyperonic sector are adjusted to the data on $\Lambda$ and $\Xi^-$ hypernuclei data. The $\Delta$-resonance couplings are tuned to the data obtained from their scattering off nuclei and heavy-ion collision experiments. We find that (anti)kaon condensate leads to a softening of the equation of state and lower maximum masses of compact stars than in the absence of the condensate. Both the $K^-$ and $\bar K^0$-condensations occur through a second-order phase transition, which implies no mixed-phase formation. For large values of (anti)kaon and $\Delta$-resonance potentials in symmetric nuclear matter, we observe that condensation leads to an extinction of $ \Xi^{-,0}$ hyperons. We also investigate the influence of inclusion of additional hidden-strangeness $\sigma^{*}$ meson in the functional and find that it leads to a substantial softening of the equation of state and delay in the onset of (anti)kaons., Comment: 14 pages, 11 figures, accepted for publication in Phys. Rev. D

We study the oscillations modes of differential rotating remnants of binary neutron star inspirals by modeling them as incompressible Riemann ellipsoids parametrized by the ratio $f$ of their internal circulation to the rotation frequency. The effects of viscosity and gravitational wave radiation on the modes are studied and it is shown that these bodies exhibit generic instabilities towards gravitational wave radiation akin to the Chandrasekhar--Friedman--Schutz instabilities for uniformly rotating stars. The odd-parity modes are unstable for all values of $f$ (except for the spherical model) and deformations, whereas the even parity unstable modes appear only in highly eccentric ellipsoids. We quantify the modification of the modes with varying mass of the model and the magnitude of the viscosity. The modes are weakly dependent on the range of the masses relevant to the binary neutron star mergers. Large turbulent viscosity can lead to a suppression of the gravitational wave instabilities, whereas kinematical viscosity has a negligible influence on the modes and their damping timescales., Comment: 16 pages, 11 figures. Submitted to MNRAS

We conjecture and verify a set of universal relations between global parameters of hot and fast-rotating compact stars, including a relation connecting the masses of the mass-shedding (Kepler) and static configurations. We apply these relations to the GW170817 event by adopting the scenario in which a hypermassive compact star remnant formed in a merger evolves into a supramassive compact star that collapses into a black hole once the stability line for such stars is crossed. We deduce an upper limit on the maximum mass of static, cold neutron stars $ 2.15^{+0.10}_{-0.07}\le M^\star_{\mathrm{TOV}} \le 2.24^{+0.12}_{-0.10} $ for the typical range of entropy per baryon $2 \le S/A \le 3$ and electron fraction $Y_e = 0.1$ characterizing the hot hypermassive star. Our result implies that accounting for the finite temperature of the merger remnant relaxes previously derived constraints on the value of the maximum mass of a cold, static compact star., Comment: 17 pages, 11 figures

Binary neutron star mergers, such as the multimessenger GW170817 event, may produce hypermassive compact objects which are supported against collapse by the internal circulation of the fluid within the star. We compute their unstable modes of oscillations driven by gravitational wave radiation and shear viscosity, modeling them as triaxial Riemann ellipsoids. We work in a perturbative regime, where the gravitational radiation reaction force is taken into account at 2.5-post-Newtonian order and find unstable modes with dissipation timescales $\gtrsim 1$ ms which are relevant to the transient state of a hypermassive remnant of a merger. We show that the secular instabilities are dominated by gravitational wave radiation. If the shear viscosity is included, it can increase the growth times or even stabilize the unstable modes, but it must have values several orders of magnitude larger than predicted for cold neutron stars., 7 pages, 3 figures, 1 table. Accepted by ApJ Letters

We study the composition of nuclear matter at sub-saturation densities, non-zero temperatures, and isospin asymmetry, under the conditions characteristic of binary neutron star mergers, stellar collapse, and low-energy heavy-ion collisions. The composition includes light clusters with mass number $A\le 4$, a heavy nucleus ($\isotope[56]{Fe}$), the $\Delta$-resonances, the isotriplet of pions, as well as the $\Lambda$ hyperon. The nucleonic mean-fields are computed from a zero-range density functional, whereas the pion-nucleon interactions are treated to leading order in chiral perturbation theory. We show that with increasing temperature and/or density the composition of matter shifts from light-cluster to heavy baryon dominated one, the transition taking place nearly independent of the magnitude of the isospin. Our findings highlight the importance of simultaneous treatment of light clusters and heavy baryons in the astrophysical and heavy-ion physics contexts., Comment: v3: matches published version; v2: version in print, some clarifications, corrections, and additional references, 8 page, 4 figures. v1: 6 pages, 4 figures

We use covariant density functional theory to obtain the equation of state (EoS) of matter in compact stars at non-zero temperature, including the full baryon octet as well as the $\Delta(1232)$ resonance states. Global properties of hot $\Delta$-admixed hypernuclear stars are computed for fixed values of entropy per baryon ($S/A$) and lepton fraction ($Y_L$). Universal relations between the moment of inertia, quadrupole moment, tidal deformability, and compactness of compact stars are established for fixed values of $S/A$ and $Y_L$ that are analogous to those known for cold catalyzed compact stars. We also verify that the $I$-Love-$Q$ relations hold at finite temperature for constant values of $S/A$ and $Y_L$., Comment: 20 pages, 15 figures

We examine the possibility that the light companion in the highly asymmetric binary compact object coalescence event GW190814 is a hypernuclear star. We use density functional theory with functionals that have been tuned to the properties of $\Lambda$ hypernuclei as well as astrophysical constraints placed by the masses of the most massive millisecond pulsars, the mass-radius range inferred from the NICER experiment, and the binary neutron star merger event GW170817. We compute general-relativistic static and maximally rotating Keplerian configurations of purely nucleonic and hypernuclear stars. We find that while nucleonic stars are broadly consistent with a neutron star being involved in GW190814, this would imply no new degrees of freedom in the dense matter up to 6.5 times the nuclear saturation density. Allowing for hyperonization of dense matter, we find that the maximal masses of hypernuclear stars, even for maximal rapidly rotating configurations, are inconsistent with a stellar nature interpretation of the light companion in GW190814, implying that this event involved two black holes rather than a neutron star and a black hole., Comment: 5 pages, 4 figures; v2: minor editorial improvements, matches published version

The $\Delta$-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 $\Delta$'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 $\Delta$'s appear already at densities slightly above the saturation density of nuclear matter for a wide range of the meson-$\Delta$ coupling constants. This delays the appearance of hyperons and significantly affects the gross properties of compact stars. Specifically, $\Delta$'s soften the EoS at low densities but stiffen it at high densities. This softening reduces the radius of a canonical $1.4 M_\odot$ star by up to 2~km for a reasonably attractive $\Delta$ potential in matter, while the stiffening results in larger maximum masses of compact stars. We conclude that the hypernuclear CDF parametrizations that satisfy the 2$M_\odot$ maximum mass constraint remain valid when $\Delta$ 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., Comment: 7 pages, 4 figures; v2: minor changes, matches published version

We study bulk viscosity arising from weak current Urca processes in dense baryonic matter at and beyond nuclear saturation density. We consider the temperature regime where neutrinos are trapped and therefore have nonzero chemical potential. We model the nuclear matter in a relativistic density functional approach, taking into account the trapped neutrino component. We find that the resonant maximum of the bulk viscosity would occur at or below the neutrino trapping temperature, so in the neutrino trapped regime the bulk viscosity decreases with temperature as $T^{-2}$, this decrease being interrupted by a drop to zero at a special temperature where the proton fraction becomes density-independent and the material scale-invariant. The bulk viscosity is larger for matter with lower lepton fraction, i.e., larger isospin asymmetry. We find that bulk viscosity in the neutrino-trapped regime is smaller by several orders of magnitude than in the neutrino-transparent regime, which implies that bulk viscosity in neutrino-trapped matter is probably not strong enough to affect significantly the evolution of neutron star mergers. This also implies weak damping of gravitational waves emitted by the oscillations of the postmerger remnant in the high-temperature, neutrino-trapped phase of evolution., Comment: v2: matches published version, 27 pages, 21 figures, uses RevTex

The thermal evolution of hypernuclear compact stars is studied for stellar models constructed on the basis of covariant density functional theory in Hartree and Hartree-Fock approximation. Parametrizations of both types are consistent with the astrophysical mass constraints on compact stars and available hypernuclear data. We discuss the differences of these density functionals and highlight the effects they have on the composition and on the cooling of hypernuclear stars. It is shown that hypernuclear stars computed with density functional models that have a low symmetry energy slope, $L$, are fairly consistent with the cooling data of observed compact stars. The class of stellar models based on larger $L$ values gives rise to the direct Urca process at low densities, which leads to significantly faster cooling. We conjecture high-density pairing for protons and $\Lambda$'s in the $P$-wave channel and provide simple scaling arguments to obtain these gaps. As a consequence the most massive stellar models with masses $1.8 \le M/M_{\odot} \le2$ experience slower cooling by hyperonic dUrca processes which involve $\Lambda$'s and protons., Comment: 15 pages, 8 figures

We study the axion cooling of neutron stars within the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model, which allows for tree level coupling of electrons to the axion {and locks the Peccei-Quinn charges of fermions via an angle parameter}. This extends our previous study [Phys. Rev. D 93, 065044 (2016)] limited to hadronic models of axions. We explore the two-dimensional space of axion parameters within the DFSZ model by comparing the theoretical cooling models with the surface temperatures of a few stars with measured surface temperatures. It is found that axions masses $m_a\ge 0.06$ to 0.12 eV can be excluded by x-ray observations of thermal emission of neutron stars (in particular by those of Cas A), the precise limiting value depending on the angle parameter of the DFSZ model. It is also found that axion emission by electron bremsstrahlung in neutron star crusts is negligible except for the special case where neutron Peccei-Quinn charge is small enough, so that the coupling of neutrons to axions can be neglected., v2: Extended discussion and results, matches published version, 10 pages, 9 figures; v1: 8 pages, 7 figures, uses RevTex

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 $\Delta$-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 to a quark matter phase followed by a second phase transition to another quark phase. 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 $\Delta$-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 $\Delta$-resonance--hyperon admixed phase and/or the quark phase(s), are favored by this 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., Comment: 11 pages, 9 figures, 5 tables; minor corrections, matches published version

A set of hadronic equations of state (EoSs) derived from relativistic density functional theory and constrained by terrestrial experiments, astrophysical observations, in particular by the GW170817 event, and chiral effective field theory ($\chi$EFT) of neutron matter is used to explore the sensitivity of the EoS parameterization on the few nuclear matter characteristics defined at the saturation density. We find that the gross properties of compact stars are most sensitive to the isoscalar skewness coefficient $Q_{\text{sat}}$ and the isovector slope coefficient $L_{\text{sym}}$ around saturation density, since the higher order coefficients, such as $K_{\text{sym}}$, are fixed by our model. More specifically, (i) among these $Q_{\text{sat}}$ is the dominant parameter controlling both the maximum mass and the radii of compact stars while $L_{\rm sym}$ is constrained somewhat by $\chi$EFT of neutron matter; (ii) massive enough ($M\sim 2.0~M_{\odot})$ compact stars featuring both hyperons and $\Delta$ resonances can be obtained if the value of $Q_{\text{sat}}$ is large enough; (iii) the emergence of $\Delta$'s reduces the radius of a canonical mass ($M\sim 1.4~M_{\odot})$ compact star thus easing the tension between the predictions of the relativistic density functionals and the inferences from the X-ray observation of nearby isolated neutron stars., Comment: 13 pages, 11 figures, 3 tables. Discussions and references added. Phys. Rev. C in press

We use a set of hadronic equations of state derived from covariant density functional theory to study the impact of their high-density behavior on the properties of rapidly rotating $\Delta$-resonance-admixed hyperonic compact stars. In particular, we explore systematically the effects of variations of the bulk energy isoscalar skewness, $Q_{\mathrm{sat}}$, and the symmetry energy slope, $L_{\mathrm{sym}}$, on the masses of rapidly rotating compact stars. With models for equation of state satisfying all the modern astrophysical constraints, excessively large gravitational masses of around $2.5 \, M_{\odot}$ are only obtained under three conditions: (a) strongly attractive $\Delta$-resonance potential in nuclear matter, (b) maximally fast (Keplerian) rotation, and (c) parameter ranges $Q_{\mathrm{sat}}\gtrsim500$ MeV and $L_{\mathrm{sym}}\lesssim50$ MeV. These values of $Q_{\mathrm{sat}}$ and $L_{\mathrm{sym}}$ have a rather small overlap with a large sample (total of about 260) parametrizations of covariant nucleonic density functionals. The extreme nature of requirements (a)-(c) reinforces the theoretical expectation that the secondary object involved in the GW190814 event is likely to be a low-mass black hole rather than a supramassive neutron star., Comment: 8 pages with 5 figures, matches published version

We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev's formalism for the non-equilibrium statistical operator. In particular, we discuss the shear-stress tensor to second order in gradients and argue that the relaxation terms for the dissipative quantities arise from memory effects contained in the statistical operator. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing Kubo-type formulae for the second-order transport coefficients., v2: 11 pages, no figures, references added, matches published version. v1: 10 pages

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 $\sim 3\%$ 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., 8 pages, 4 figures, 2 tables; matches published version, updated fig. 2

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet $S$-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-$S$ proton pairing and triplet coupled $P$-$F$-wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors., Review article, 63 pages, 28 figures, v4 matches journal version. [v2 and v3: 58 pages, 28 figures, v1: 50 pages, 27 figures]