Neutron Star Core Research Articles

Dependence of the tidal deformability of neutron stars on the nuclear equation of state* *Supported by the Shanxi Provincial Foundation for Returned Overseas Scholars (20220037), the Natural Science Foundation of Shanxi Province (20210302123085), the discipline construction project of Yuncheng university, and the National Natural Science Foundation of China (12075327)

Within the Bayesian framework, using an explicitly isospin-dependent parametric equation of state (EOS) for the core of neutron stars (NSs), we studied how the NS EOS behaves when we confront it with the tidal deformabilities of canonical NSs with different error and different lower boundaries, and with the tidal deformabilities of massive NSs. We found that it does not significantly improve the constraints on the NS EOS but has a weak effect on narrowing down the slope parameter of the symmetry energy by decreasing the measurement errors of . Both the isospin-dependent and isospin-independent parts of the NS EOS were significantly constrained and raised as the tidal deformabilities of massive NSs were adopted in the calculations, especially in high-density regions. We also found that is more competent to limit the curvature parameter than the slope parameter of the symmetry energy, whereas the opposite occurs for the radius of canonical NSs . The tidal deformability of an NS with two times the solar mass is more sensitive to skewness than the curvature parameter of the symmetry energy, and and have no correlation with the former.

Impacts of the Direct Urca and Superfluidity inside a Neutron Star on Type I X-Ray Bursts and X-Ray Superbursts

We investigate the impacts of the neutrino cooling mechanism inside the neutron star (NS) core on the light curves of type I X-ray bursts and X-ray superbursts. From several observations of NS thermal evolution, physical processes of fast neutrino cooling, such as the direct Urca (DU) process, are indicated. They significantly decrease the surface temperature of NSs, though the cooling effect could be suppressed by nucleon superfluidity. In the present study, focusing on the DU process and nucleon superfluidity, we investigate the effects of NS cooling on the X-ray bursts using a general-relativistic stellar-evolution code. We find that the DU process leads to a longer recurrence time and higher peak luminosity, which could be obstructed by the neutrons’ superfluidity. We also apply our burst models to the comparison with Clocked burster GS 1826−24, and to the recurrence time of a superburst triggered by carbon ignition. These effects are significant within a certain range of binary parameters and the uncertainty of the NS equation of state.

Fast Neutrino Cooling in the Accreting Neutron Star MXB 1659-29

Modeling of crust heating and cooling across multiple accretion outbursts of the low mass X-ray binary MXB 1659-29 indicates that the neutrino luminosity of the neutron star core is consistent with direct Urca (dUrca) reactions occurring in ∼1% of the core volume. We investigate this scenario with neutron star models that include a detailed equation of state parametrized by the slope of the nuclear symmetry energy L, and a range of neutron and proton superfluid gaps. We find that the predicted neutron star mass depends sensitively on L and the assumed gaps. We discuss which combinations of superfluid gaps reproduce the inferred neutrino luminosity. Larger values of L ≳ 80 MeV require superfluidity to suppress dUrca reactions in low mass neutron stars, i.e., the proton or neutron gap is sufficiently strong and extends to high enough density. However, the largest gaps give masses near the maximum mass, making it difficult to accommodate colder neutron stars. The heat capacities of our models span the range from fully paired to fully unpaired nucleons meaning that long-term observations of core cooling could distinguish between models. As a route to solutions with a larger emitting volume, which could provide a more natural explanation for the inferred neutrino luminosity, we discuss the possibility of alternative, less efficient, fast cooling processes in exotic cores. To be consistent with the inferred neutrino luminosity, such processes must be within a factor of ∼1000 of dUrca. We discuss the impact of future constraints on neutron star mass, radius, and the density dependence of the symmetry energy.

Equation of state for hot hyperonic neutron star matter

Abstract The FSU2H equation-of-state model, originally developed to describe cold neutron star matter with hyperonic cores, is extended to finite temperature. Results are presented for a wide range of temperatures and lepton fractions, which cover the conditions met in protoneutron star matter, neutron star mergers, and supernova explosions. It is found that the temperature effects on the thermodynamical observables and the composition of the neutron star core are stronger when the hyperonic degrees of freedom are considered. An evaluation of the temperature and density dependence of the thermal index leads to the observation that the so-called Γ law, widely used in neutron star merger simulations, is not appropriate to reproduce the true thermal effects, specially when hyperons start to be abundant in the neutron star core. To make finite temperature equations of state easily accessible, simple parametrizations of the thermal index for nucleonic and hyperonic β-stable neutrino-free matter are provided.

Neutron-Mirror-Neutron Oscillation and Neutron Star Cooling.

It was pointed out in a recent paper that the observed cooling rate of old, cold neutron stars (NS) can provide an upper limit on the transition rate of neutron to mirror neutron (n-n^{'}). This limit is so stringent that it would preclude any discovery of n→n^{'} oscillation in the current round of terrestrial searches for the process. Motivated by this crucially important conclusion, we critically analyze this suggestion and note an interesting new effect present in nearly exact mirror models for n→n^{'} oscillation, which significantly affects this bound. The new element is the β decay n^{'}→p^{'}+e^{'}+ν[over ¯]_{e}^{'}, which creates a cloud of mirror particles n^{'}, p^{'}, e^{'}, and D^{'} inside the NS core. The e^{'} can "rob" the energy generated by the n→n^{'} transition via e-e^{'} scattering enabled by the presence of a (minute) millicharge in mirror particles. This energy is emitted as unobserved mirror photons via fast mirror bremsstrahlung leading to a relaxation of this upper limit.

Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

ABSTRACT The main contribution to the effective shear modulus of neutron star crust can be calculated within Coulomb solid model and can be approximated by simple analytical expression for arbitrary (even multicomponent) composition. Here I consider correction associated with electron screening within Thomas–Fermi approximation. In particular, I demonstrate that for relativistic electrons (density ρ > 106 g cm−3) this correction can be estimated as $\delta \mu _\mathrm{eff}^\mathrm{V}= -9.4\times 10^{-4}\sum _Z n_Z Z^{7/3} e^2/a_\mathrm{e},$ where summation is taken over ion species, nZ is number density of ions with charge Ze, kTF is Thomas–Fermi screening wavenumber. Finally, ae = (4πne/3)−1/3 is electron sphere radius. Quasi-neutrality condition ne = ∑ZZnZ is assumed. This result holds true for arbitrary (even multicomponent and amorphous) matter and can be applied for neutron star crust and (dense) cores of white dwarfs. For example, the screening correction reduces shear modulus by ∼9 per cent for Z ∼ 40, which is typical for inner layers of neutron star crust.

Probing dark gauge boson with observations from neutron stars

We present an investigation on the production of light dark gauge bosons by the nucleon bremsstrahlung processes in the core of neutron stars. The dark vector is assumed to be a $U(1{)}_{B\ensuremath{-}L}$ gauge boson with a mass much below keV. We calculate the emission rate of the dark vector produced by the nucleon bremsstrahlung in the degenerate nuclear matter. In addition, we take into account the photon-dark vector conversion for the photon luminosity observed at infinity. Combining with the observation of J1856 surface luminosity, we find that a recently discovered excess of J1856 hard x-ray emission in the 2--8 keV energy range by X-ray Multi-Mirror Mission-Newton and Chandra x-ray telescopes could be consistently explained by a dark vector with gauge coupling ${e}^{\ensuremath{'}}=5.56\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, mixing angle $ϵ=1.29\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$, and mass ${m}_{{\ensuremath{\gamma}}^{\ensuremath{'}}}\ensuremath{\lesssim}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$. We also show that the mixing angle $ϵ>7.97\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for ${m}_{{\ensuremath{\gamma}}^{\ensuremath{'}}}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$ and the gauge coupling ${e}^{\ensuremath{'}}>4.13\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ for ${m}_{{\ensuremath{\gamma}}^{\ensuremath{'}}}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{keV}$ have been excluded at 95% confidence level by the J1856 surface luminosity observation. Our best-fit dark vector model satisfies the current limits on hard x-ray intensities from the Swift and INTEGRAL hard x-ray surveys. Future hard x-ray experiments such as the Nuclear Spectroscopic Telescope Array may give a further test on our model.

Quarkyonic matter state of neutron stars

This work extends our previous study of isospin symmetric quarkyonic matter to quarkyonic neutron matter which might be relevant to the inner cores of neutron stars. The vector-isovector $\rho$ mesons are introduced to the model mainly to account for isospin density interactions, just like $\omega$ meson for baryon density interactions. The modified Lagrangian still preserves approximate chiral symmetry which could be significantly broken at lower density. And new free parameters are fixed by adopting the experimental constraints on the symmetry energy and its slope at saturation density. Eventually, the pressure, mass-radius relation, and tidal deformability are explored in advance for the quarkyonic neutron stars. While the pressure and tidal deformability are well consistent with experimental and observational restrictions, the mass-radius relation is unable to reproduce the observed two solar mass of PSR J0740+6620.

Constraining neutron-star matter with microscopic and macroscopic collisions

Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not probed only in astrophysical observations, but also in terrestrial heavy-ion collision experiments. Here we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars1–9 and from heavy-ion collisions of gold nuclei at relativistic energies10,11 with microscopic nuclear theory calculations12–17 to improve our understanding of dense matter. We find that the inclusion of heavy-ion collision data indicates an increase in the pressure in dense matter relative to previous analyses, shifting neutron-star radii towards larger values, consistent with recent observations by the Neutron Star Interior Composition Explorer mission5–8,18. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities. This work combines nuclear theory, nuclear experiment and astrophysical observations, and shows how joint analyses can shed light on the properties of neutron-rich supranuclear matter over the density range probed in neutron stars.

Neutron star properties with careful parametrization in the vector and axial-vector meson extended linear sigma model

The existence of quark matter inside the cores of heavy neutron stars is a possibility which can be probed with modern astrophysical observations. We use a vector and axial-vector meson extended quark-meson model to describe quark matter in the core of neutron stars. We discover that an additional parameter constraint is necessary in the quark model to ensure chiral restoration at high densities. By investigating hybrid star sequences with various parameter sets, we show that low sigma meson masses are needed to fulfill the upper radius constraints and that the maximum mass of stable hybrid stars is only slightly dependent on the parameters of the crossover-type phase transition. Using this observation and results from recent astrophysical measurements, a constraint of $2.5<{g}_{V}<4.3$ is set for the constituent quark--vector meson coupling. The effect of a nonzero bag constant is also investigated, and we observe that its effect is small for values adopted in previous works.

Exploring terra incognita in the phase diagram of strongly interacting matter—experiments at FAIR and NICA

The fundamental properties of dense nuclear matter, as it exists in the core of massive stellar objects, are still largely unknown. The investigation of the high-density equation of state (EOS), which determines mass and radii of neutron stars and the dynamics of neutron star mergers, is in the focus of astronomical observations and of laboratory experiments with heavy-ion collisions. Moreover, the microscopic degrees-of-freedom of strongly interacting matter at high baryon densities are also unknown. While Quantum-Chromo-Dynamics (QCD) calculations on the lattice find a smooth chiral crossover between hadronic matter and the quark-gluon plasma for high temperatures at zero baryon chemical potential, effective models predict a 1st order chiral transition with a critical endpoint for matter at large baryon chemical potentials. Up to date, experimental data both on the high-density EOS and on a possible phase transition in dense baryonic matter are very scarce. In order to explore this terra incognita, dedicated experimental programs are planned at future heavy-ion research centres: the CBM experiment at FAIR, and the MPD and BM@N experiments at NICA. The research programs and the layout of these experiments will be presented. The future results of these laboratory experiments will complement astronomical observations concerning the EOS, and, in addition, will shed light on the microscopic degrees of freedom of QCD matter at neutron star core densities.

Chiral symmetry restoration and Δ matter formation in neutron stars

We analyze the effects of chiral symmetry restoration in hadronic matter, including the lowest-lying baryonic resonance $\Delta$ based on the parity doublet model. We study the role of $\Delta$ and its chiral partner on the equation of state (EoS) of dense matter under neutron star (NS) conditions of $\beta$-equilibrium and charge neutrality. We find that the softening of the EoS driven by the early onset of $\Delta$ matter due to partial restoration of chiral symmetry allows accommodating the modern multi-messenger astrophysical constraints on the mass, radius, and tidal deformability. The softening above the saturation density is accompanied by subsequent stiffening at high densities. We also find that the matter composition in the NS cores may be different upon variations of the repulsive interactions of $\Delta$ baryons in hadronic matter.

Number spectra of nonequilibrium neutrinos from neutron stars: Impact of realistic nuclear interactions and free hyperons

The number spectrum of nonequilibrium neutrinos resulting from neutron star matter deviation from beta equilibrium is calculated. For this purpose, the chemical potential gap ($\ensuremath{\delta}\ensuremath{\mu}$) in a typical density change and in the high degeneracy regime (${k}_{B}T\ensuremath{\le}0.1\phantom{\rule{0.28em}{0ex}}\text{MeV}$) is estimated. This is done under the application of realistic descriptions of nuclear matter and the assumption of the presence of free hyperons (${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}, {\mathrm{\ensuremath{\Lambda}}}^{0}$) in the neutron star core. Realistic nuclear interactions are taken into account by a microscopic many-body approach---the lowest order constrained variational (LOCV) method---for asymmetric nuclear matter. We find that addition of a three-body force interaction leads to a dramatic change in the trend of the symmetry energy at high densities and consequently the change in the sign of $\ensuremath{\delta}\ensuremath{\mu}$. This, as a result, changes the dominant flavor of the nonequilibrium neutrinos. By accounting for the hyperons' presence, we see that apart from the sign change of $\ensuremath{\delta}\ensuremath{\mu}$ its value can change noticeably. In hypernuclear matter, the effect of particle fractions is also very important. We have also investigated the effect of deviation from beta equilibrium on the dynamic part of the number spectra of nonequilibrium neutrinos produced in the neutron branch of the modified Urca process. It is shown that this part of the number spectra is not affected significantly by the nonequilibrium process and can be replaced by its equilibrium value.

Can we decipher the composition of the core of a neutron star?

General relativity guarantees a unique one-to-one correspondence between static observables of neutron stars (NSs) accessible by multimessenger astronomy, such as mass-radius or tidal deformability, and the equation of state (EoS) of beta equilibrated matter. It is well known that these static properties are not enough to discern conventional NSs from hybrid stars. However, if one assumes that hadrons present in the neutron star core are only neutrons and protons, the lepton fraction is expected to be determined unequivocally by the condition of chemical equilibrium. Using a simple analytical method based on a polynomial expansion of the EoS, we show that multiple solutions are possible to the beta-equilibrium equation, leading to a characteristic indetermination on the composition of the interiors of NSs, even in the purely nucleonic hypothesis. We further show that additional empirical information on symmetric matter at high densities are not very efficient to pin down the composition, if uncertainties on measurements are accounted for. We conclude that constraints on the symmetry energy at high densities only, can make meaningful impact to decipher the composition of neutron star core. Our results give a lower limit to the uncertainty on the NS core composition that can be obtained with astrophysical and terrestrial experiments.

Superconducting Phases in Neutron Star Cores

Using a phenomenological Ginzburg–Landau model that includes entrainment, we identify the possible ground states for the neutron and proton condensates in the core of a neutron star, as a function of magnetic field strength. Combining analytical and numerical techniques, we find that much of the outer core is likely to be a “type-1.5” superconductor (instead of a type-II superconductor as often assumed), in which magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide an approximate criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core. We also show that bundles of fluxtubes can coexist with non-superconducting regions, but only in a small part of the parameter space.

Impact of massive neutron star radii on the nature of phase transitions in dense matter

The last few years have seen tremendous progress in the observation of the global properties of neutron stars (NSs), e.g., masses, radii and tidal deformabilities. Such properties provide information about possible phase transitions in the inner cores of NSs, provided the connection between observed masses and radii and the equation of state (EoS) is well understood. We focus the present study on first-order phase transition, which often softens the EoS and consequently reduces the maximum mass as well as the radii of NSs. Here, we challenge this conventional expectation by constructing explicit examples of EoSs undergoing a first-order phase transition, but which are much stiffer that their purely hadronic counterparts. We also provide comparisons with the recently proposed quarkyonic EoS which suggests a strong repulsion in the core of NSs, and we show that their stiffness can be realistically masqueraded by stiff first-order phase transitions to exotic matter.

Ensembles of unified crust and core equations of state in a nuclear-multimessenger astrophysics environment

We present an ensemble of unified neutron star crust and core equations of state, constructed using an extended Skyrme energy density functional through the crust and outer core, and appended by two piecewise polytropes at higher densities. The equations of state are parameterized by the first three coefficients in the density expansion of the symmetry energy J, L and \(K_{\mathrm{sym}}\), the moment of inertia of a 1.338 M\(_{\odot }\) star \(I_{1.338}\) and the maximum neutron star mass \(M_{\mathrm{max}}\). We construct an ensemble with uniform priors on all five parameters, and then apply data filters to the ensemble to explore the effect of combining neutron skin data from PREX with astrophysical measurements of radii and tidal deformabilities from NICER and LIGO/VIRGO. Neutron skins are calculated directly using the EDFs. We demonstrate that both the nuclear data and astrophysical data play a role in constraining crust properties such as the mass, thickness and moment of inertia of the crust and the nuclear pasta layers therein, and that astrophysical data better constrains \(K_{\mathrm{sym}}\) than PREX data.

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Multi-Physics Constraints at Different Densities to Probe Nuclear Symmetry Energy in Hyperonic Neutron Stars

The appearance of strangeness in the form of hyperons within the inner core of neutron stars is expected to affect its detectable properties, such as its global structure or gravitational wave emission. This work explores the parameter space of hyperonic stars within the framework of the Relativistic Mean Field model allowed by the present uncertainties in the state-of-the-art nuclear and hypernuclear experimental data. We impose multi-physics constraints at different density regimes to restrict the parameter space: Chiral effective field theory, heavy-ion collision data, and multi-messenger astrophysical observations of neutron stars. We investigate possible correlations between empirical nuclear and hypernuclear parameters, particularly the symmetry energy and its slope, with observable properties of neutron stars. We do not find a correlation for the hyperon parameters and the astrophysical data. However, the inclusion of hyperons generates a tension between the astrophysical and heavy-ion data constraining considerably the available parameter space.

Core structures of vortices in Ginzburg-Landau theory for neutron P23 superfluids

We investigate vortex solutions in the Ginzburg-Landau theory for neutron $^3P_2$ superfluids relevant for neutron star cores in which neutron pairs possess the total angular momentum $J=2$ with spin-triplet and $P$ wave, in the presence of the magnetic field parallel to the angular momentum of vortices. The ground state is known to be in the uniaxial nematic (UN) phase in the absence of magnetic field, while it is in the $D_2$ ($D_4$) biaxial nematic (BN) phase in the presence of the magnetic field below (above) the critical value. We find that a singly quantized vortex always splits into two half-quantized non-Abelian vortices connected by soliton(s) as a vortex molecule with any strength of the magnetic field. In the UN phase, two half-quantized vortices with ferromagnetic cores are connected by a linear soliton with the $D_4$ BN order. In the $D_2$ ($D_4$) BN phase, two half-quantized vortices with cyclic cores are connected by three linear solitons with the $D_4$ ($D_2$) BN order. The energy of the vortex molecule monotonically increases and the distance between the two half-quantized vortices decreases with the magnetic field increases, except for a discontinuously increasing jump of the distance at the critical magnetic field. We also construct an isolated half-quantized non-Abelian vortex in the $D_4$ BN phase.