Nuclear Saturation Density Research Articles

Anisotropic neutron stars modelling: constraints in Krori\u2013Barua spacetime

Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfluidity, strong magnetic fields, hyperons, pion-condensation. Therefore an anisotropic neutron star core seems more realistic than an ideally isotropic one. We model anisotropic neutron stars working in the Krori–Barua (KB) ansatz without preassuming an equation of state. We show that the physics of general KB solutions is encapsulated in the compactness. Imposing physical and stability requirements yields a maximum allowed compactness 2GM/Rc^2 < 0.71 for a KB-spacetime. We further input observational data from numerous pulsars and calculate the boundary density. We focus especially on data from the LIGO/Virgo collaboration as well as recent independent measurements of mass and radius of miilisecond pulsars with white dwarf companions by the Neutron Star Interior Composition Explorer (NICER). For these data the KB-spacetime gives the same boundary density which surprisingly equals the nuclear saturation density within the data precision. Since this value designates the boundary of a neutron core, the KB-spacetime applies naturally to neutron stars. For this boundary condition we calculate a maximum mass of 4.1 solar masses.

Confronting GW190814 with hyperonization in dense matter and hypernuclear compact stars

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.

Quarkyonic matter equation of state in beta-equilibrium

Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasiparticles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass ($\ensuremath{\gtrsim}2\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) and the radius of a $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ star (${R}_{1.4}\ensuremath{\lesssim}13.5\text{ }\text{ }\mathrm{km}$). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. We propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.

Adding crust to BPS Skyrme neutron stars

The Skyrme model and its generalisations provide a conceptually appealing field-theory basis for the description of nuclear matter and, after its coupling to gravity, also of neutron stars. In particular, a specific Skyrme submodel, the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model, allows both for an exact field-theoretic and a mean-field treatment of neutron stars, as a consequence of its perfect fluid property. A pure BPS Skyrme model description of neutron stars, however, only describes the neutron star core, by construction. Here we consider different possibilities to extrapolate a BPS Skyrme neutron star at high baryon density to a description valid at lower densities. In the exact field-theoretic case, a simple effective description of the neutron star crust can be used, because the exact BPS Skyrme neutron star solutions formally extend to sufficiently low densities. In the mean-field case, on the other hand, the BPS Skyrme neutron star solutions always remain above the nuclear saturation density and, therefore, must be joined to a different nuclear physics equation of state already for the outer core. We study the resulting neutron stars in both cases, facilitating an even more complete comparison between Skyrmionic neutron stars and neutron stars obtained from other approaches, as well as with observations.

Axions in neutron star mergers

Supernovae and cooling neutron stars have long been used to constrain the properties of axions, such as their mass and interactions with nucleons and other Standard Model particles. We investigate the prospects of using neutron star mergers as a similar location where axions can be probed in the future. We examine the impact axions would have on mergers, considering both the possibility that they free-stream through the dense nuclear matter and the case where they are trapped. We calculate the mean free path of axions in merger conditions, and find that they would free-stream through the merger in all thermodynamic conditions. In contrast to previous calculations, we integrate over the entire phase space while using a relativistic treatment of the nucleons, assuming the matrix element is momentum-independent. In particular, we use a relativistic mean field theory to describe the nucleons, taking into account the precipitous decrease in the effective mass of the nucleons as density increases above nuclear saturation density. We find that within current constraints on the axion-neutron coupling, axions could cool nuclear matter on timescales relevant to neutron star mergers. Our results may be regarded as first steps aimed at understanding how axions affect merger simulations and potentially interface with observations.

The QCD axion at finite density

We show how the properties of the QCD axion change in systems at finite baryonic density, such as neutron stars. At nuclear saturation densities, where corrections can be reliably computed, we find a mild reduction of the axion mass and up to an order of magnitude enhancement in the model-independent axion coupling to neutrons. At moderately higher densities, if realized, meson (kaon) condensation can trigger axion condensation. We also study the axion potential at asymptotically large densities, where the color-superconducting phase of QCD potentially leads to axion condensation, and the mass of the axion is generically several orders of magnitude smaller than in vacuum due to the suppressed instantons. Several phenomenological consequences of the axion being sourced by neutron stars are discussed, such as its contribution to their total mass, the presence of an axionic brane, or axion-photon conversion in the magnetosphere.

Nucleon effective mass in hot dense matter

Nucleon effective masses are studied in the framework of the Brueckner-Hartree-Fock many-body approach at finite temperature. Self-consistent calculations using the Argonne $V_{18}$ interaction including microscopic three-body forces are reported for varying temperature and proton fraction up to several times the nuclear saturation density. Our calculations are based on the exact treatment of the center-of-mass momentum instead of the average-momentum approximation employed in previous works. We discuss in detail the effects of the temperature together with those of the three-body forces, the density, and the isospin asymmetry. We also provide an analytical fit of the effective mass taking these dependencies into account. The temperature effects on the cooling of neutron stars are briefly discussed based on the results for betastable matter.

Nonparametric constraints on neutron star matter with existing and upcoming gravitational wave and pulsar observations

Observations of neutron stars, whether in binaries or in isolation, provide information about the internal structure of the most extreme material objects in the Universe. In this work, we combine information from recent observations to place joint constraints on the properties of neutron star matter. We use (i) lower limits on the maximum mass of neutron stars obtained through radio observations of heavy pulsars, (ii) constraints on tidal properties inferred through the gravitational waves neutron star binaries emit as they coalesce, and (iii) information about neutron stars' masses and radii obtained through X-ray emission from surface hot spots. In order to combine information from such distinct messengers while avoiding the kind of modeling systematics intrinsic to parametric inference schemes, we employ a nonparametric representation of the neutron-star equation of state based on Gaussian processes conditioned on nuclear theory models. We find that existing astronomical observations imply $R_{1.4}=12.32^{+1.09}_{-1.47}\,\mathrm{km}$ for the radius of a $1.4\,M_{\odot}$ neutron star and $p(2\rho_\mathrm{nuc})=3.8^{+2.7}_{-2.9}\times10^{34}\,\mathrm{dyn}/\mathrm{cm}^2$ for the pressure at twice nuclear saturation density at the 90% credible level. The upper bounds are driven by the gravitational wave observations, while X-ray and heavy pulsar observations drive the lower bounds. Additionally, we compute expected constraints from potential future astronomical observations and find that they can jointly determine $R_{1.4}$ to ${\cal{O}}(1)\,\mathrm{km}$ and $p(2\rho_\mathrm{nuc})$ to 80% relative uncertainty in the next five years.

Analytic I-Love-C relations for realistic neutron stars

Recent observations of neutron stars (NS) with radio, X-rays and gravitational waves have begun to constrain the equation of state (EoS) for nuclear matter beyond the nuclear saturation density. To one's surprise, there exist approximate universal relations connecting certain bulk properties of NSs that are insensitive to the underlying EoS and having important applications on probing fundamental physics including nuclear and gravitational physics. To date, analytic works on universal relations for realistic NSs are lacking, which may lead to a better understanding of the origin of the universality. Here, we focus on the universal relations between the compactness(C), moment of inertia (I), and tidal deformability(related to the Love number), and derive analytic, approximate I-Love-C relations. To achieve this, we construct slowly-rotating/ tidally-deformed NS solutions analytically starting from an extended Tolman VII model that accurately describes non-rotating realistic NSs, allowing us to extract the moment of inertia and the tidal deformability on top of the compactness. We solve the field equations analytically by expanding them about the Newtonian limit and keeping up to 6th order in the stellar compactness. Based on these analytic solutions, we can mathematically demonstrate the O(10%) EoS variation in the I-C and Love-C relations and the O(1%) variation in the I-Love relation that have previously been found numerically. Our new analytic relations agree more accurately with numerical results for realistic NSs(especially the I-C and Love-C ones) than the analytic relations for constant density stars derived in previous work. Based on these analytic findings, we attribute a possible origin of the universality for the I-C and Love-C relations to the fact that the energy density of realistic NSs can be approximated as a quadratic function, as is the case for the Tolman VII solution.

Postmerger Gravitational-Wave Signatures of Phase Transitions in Binary Mergers.

With the first detection of gravitational waves from a binary system of neutron stars GW170817, a new window was opened to study the properties of matter at and above nuclear-saturation density. Reaching densities a few times that of nuclear matter and temperatures up to 100MeV, such mergers also represent potential sites for a phase transition (PT) from confined hadronic matter to deconfined quark matter. While the lack of a postmerger signal in GW170817 has prevented us from assessing experimentally this scenario, two theoretical studies have explored the postmerger gravitational-wave signatures of PTs in mergers of a binary system of neutron stars. We here extend and complete the picture by presenting a novel signature of the occurrence of a PT. More specifically, using fully general-relativistic hydrodynamic simulations and employing a suitably constructed equation of state that includes a PT, we present the occurrence of a "delayed PT," i.e., a PT that develops only some time after the merger and produces a metastable object with a quark-matter core, i.e., a hypermassive hybrid star. Because in this scenario, the postmerger signal exhibits two distinct fundamental gravitational-wave frequencies-before and after the PT-the associated signature promises to be the strongest and cleanest among those considered so far, and one of the best signatures of the production of quark matter in the present Universe.

Equation of State and Progenitor Dependence of Stellar-mass Black Hole Formation

Abstract The core collapse of a massive star results in the formation of a proto-neutron star (PNS). If enough material is accreted onto a PNS, it will become gravitationally unstable and further collapse into a black hole (BH). We perform a systematic study of failing core-collapse supernovae in spherical symmetry for a wide range of pre-supernova progenitor stars and equations of state (EOSs) of nuclear matter. We analyze how variations in progenitor structure and the EOS of dense matter above nuclear saturation density affect the PNS evolution and subsequent BH formation. Comparisons of core collapse for a given progenitor star and different EOSs show that the path traced by the PNS in mass-specific entropy phase space is well correlated with the progenitor compactness and is almost EOS independent, apart from the final end point. Furthermore, BH formation occurs, to a very good approximation, soon after the PNS overcomes the maximum gravitational mass supported by a hot NS with constant specific entropy equal to . These results show a path to constraining the temperature dependence of the EOS through the detection of neutrinos from a failed galactic supernova.

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

We report benchmark calculations of the energy per particle of pure neutron matter as a function of the baryon density using three independent many-body methods: Brueckner-Bethe-Goldstone, Fermi hypernetted chain/single-operator chain, and auxiliary-field diffusion Monte Carlo. Significant technical improvements are implemented in the latter two methods. The calculations are made for two distinct families of realistic coordinate-space nucleon-nucleon potentials fit to scattering data, including the standard Argonne $v_{18}$ interaction and two of its simplified versions, and four of the new Norfolk $\Delta$-full chiral effective field theory potentials. The results up to twice nuclear matter saturation density show some divergence among the methods, but improved agreement compared to earlier work. We find that the potentials fit to higher-energy nucleon-nucleon scattering data exhibit a much smaller spread of energies.

Effects of symmetry energy on the radius and tidal deformability of neutron stars in the relativistic mean-field model

Abstract The radii and tidal deformabilities of neutron stars are investigated in the framework of the relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, $\omega$ meson and $\rho$ meson coupling terms are included in a popular RMF Lagrangian, i.e., the TM1 parameter set, which is adopted for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector–isovector meson, $\rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii in the intermediate-mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number, which is related to the quadrupole deformation of the star in a static external tidal field and can be extracted from the observation of a gravitational wave generated by a binary star merger. We find that its value at $1.4 \mathrm{M}_\odot$ has a linear correlation to the slope of symmetry energy, unlike that previously studied. With the latest constraints of tidal deformabilities from the GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of a lower symmetry energy slope for the updated supernova EoS, which is applicable to simulations of neutron star mergers. Furthermore, an analogous analysis is also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 \mathrm{M}_\odot$ have very similar linear relations in these RMF models.

PSR J0030+0451, GW170817, and the Nuclear Data: Joint Constraints on Equation of State and Bulk Properties of Neutron Stars

Abstract Very recently the NICER collaboration published the first-ever accurate measurement of mass and radius together for PSR J0030+0451, a nearby isolated quickly rotating neutron star (NS). In this work we set the joint constraints on the equation of state (EoS) and some bulk properties of NSs with the data of PSR J0030+0451, GW170817, and some nuclear experiments. The piecewise polytropic expansion method and the spectral decomposition method have been adopted to parameterize the EoS. The resulting constraints are consistent with each other. Assuming the maximal gravitational mass of nonrotating NS M TOV lies between 2.04M ⊙ and 2.4M ⊙, with the piecewise method the pressure at twice nuclear saturation density is measured to be at the 90% level. For an NS with canonical mass of 1.4M ⊙, we have the moment of inertia , tidal deformability , radius , and binding energy at the 90% level, which are improved in comparison to the constraints with the sole data of GW170817. These conclusions are drawn for the mass/radius measurements of PSR J0030+0451 by Riley et al. For the measurements of Miller et al., the results are rather similar.

Empirical constraints on the high-density equation of state from multimessenger observables

We search for possible correlations between neutron star observables and thermodynamic quantities that characterize high density nuclear matter. We generate a set of model-independent equations of state describing stellar matter from a Taylor expansion around saturation density. Each equation of state which is a functional of the nuclear matter parameters is thermodynamically consistent, causal and compatible with astrophysical observations. We find that the neutron star tidal deformability and radius are strongly correlated with the pressure, the energy density and the sound velocity at different densities. Similar correlations are also exhibited by a large set of mean-field models based on non-relativistic and relativistic nuclear energy density functionals. These model independent correlations can be employed to constrain the equation of state at different densities above saturation from measurements of NS properties with multi-messenger observations. In particular, precise constraints on the radius of PSR J0030+0451 thanks to NICER observations would allow to better infer the properties of matter around two times the nuclear saturation density.

Constraining the Equation of State of High-density Cold Matter Using Nuclear and Astronomical Measurements

Abstract The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imposing a cut on the maximum mass or other quantities. Our method can be used with any parameterization of the equation of state (EOS). We use both a spectral parameterization and a piecewise polytropic parameterization with variable transition densities to illustrate the implications of current measurements and show how future measurements in many domains could improve our understanding of cold catalyzed matter. We find that different types of measurements will play distinct roles in constraining the EOS in different density ranges. For example, better symmetry energy measurements will have a major influence on our understanding of matter somewhat below nuclear saturation density but little influence above that density. In contrast, precise radius measurements or multiple tidal deformability measurements of the quality of those from GW170817 or better will improve our knowledge of the EOS over a broader density range.

PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter

Abstract Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state (EoS) of this dense matter is to measure both a star’s equatorial circumferential radius R e and its gravitational mass M. Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Explorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are km and (68%). The independent analysis reported in the companion paper by Riley et al. explores different emitting spot models, but finds spot shapes and locations and estimates of R e and M that are consistent with those found in this work. We show that our measurements of R e and M for PSR J0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.

A NICER View of PSR J0030+0451: Implications for the Dense Matter Equation of State

Abstract Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASA’s Neutron Star Interior Composition Explorer (NICER) mission. In this Letter we study the implications of the mass–radius inference reported for this source by Riley et al. for the dense matter equation of state (EoS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EoS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EoS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EoS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass–radius likelihood function derived by Riley et al. using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSR J0030+0451.

Possibility of $ \rho$ meson condensation in neutron stars: Unified approach of chiral SU(3) model and QCD sum rules

In the present work the conjunction of chiral SU(3) model with QCD sum rules is employed to explore the possibility of $ \rho$ meson condensation in neutron stars. The quark and gluon condensates in terms of which the in-medium masses of $ \rho$ mesons can be expressed are calculated using the chiral SU(3) model in the charge neutral matter which is relevant for neutron stars. We observe that the condition of $ \rho$ meson condensation is satisfied for the density of about 7$ \rho_{{0}}^{}$ , where $ \rho_{{0}}^{}$ is the nuclear saturation density. We also observe that the medium modified mass of $ \rho$ meson is found to have a considerable effect on the mass-radius relationship of neutron star. In the end, a brief qualitative discussion of the magnetic field is also involved to search for further possibilities of $ \rho$ meson condensation.

Bulk viscosity of baryonic matter with trapped neutrinos

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.