Nuclear Matter Equation Of State Research Articles

Nuclear Matter Equation of State in the Brueckner–Hartree–Fock Approach and Standard Skyrme Energy Density Functionals

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin–isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon–nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy density functional, and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Exploring the Distribution and Impact of Bosonic Dark Matter in Neutron Stars

The presence of dark matter (DM) within neutron stars (NSs) can be introduced by different accumulation scenarios in which DM and baryonic matter (BM) may interact only through the gravitational force. In this work, we consider asymmetric self-interacting bosonic DM, which can reside as a dense core inside the NS or form an extended halo around it. It is seen that depending on the boson mass (mχ), self-coupling constant (λ) and DM fraction (Fχ), the maximum mass, radius and tidal deformability of NSs with DM admixture will be altered significantly. The impact of DM causes some modifications in the observable features induced solely by the BM component. Here, we focus on the widely used nuclear matter equation of state (EoS) called DD2 for describing NS matter. We show that by involving DM in NSs, the corresponding observational parameters will be changed to be consistent with the latest multi-messenger observations of NSs. It is seen that for mχ≳200 MeV and λ≲2π, DM-admixed NSs with 4%≲Fχ≲20% are consistent with the maximum mass and tidal deformability constraints.

Quasi-monoenergetic heavy ion acceleration driven by sub-100 PW linearly polarized laser pulses in the radiation-dominated QED regime

Heavy ion acceleration from an ultrathin foil target irradiated by a p-polarized and spatially Gaussian laser pulse at intensity of 1023 W/cm2 is studied by using two-dimensional particle-in-cell simulations. We find that, in the extremely intense laser fields, the radiation reaction force from bright γ-rays radiated by radially oscillating electrons is large enough to match the Coulomb explosive force of foil electrons. The undesirable transverse expansion of the foil from the electron heating and inhomogeneous radial profile of the laser intensity is effectively suppressed. The foil maintains relatively good opacity in its central region stabilizing localized acceleration of heavy ions. With a laser of intensity 3.4 × 1023 W/cm2, duration of 33 fs, and power of 96 PW, a dense monoenergetic Au79+ ion bunch with a peak energy of ∼160 GeV can be obtained in the radiation-dominated QED regime. Such a high-quality heavy ion beam is useful for investigating nuclear matter equation of state and quantum chromodynamic phase transition in intermediate-energy heavy ion collisions.

Nuclear matter equation of state and stability of charged compact stars embedded in f(T) modified gravity, under cosmic acceleration

This work mainly focuses on modeling the charged compact stars and investigating their properties in the framework of [Formula: see text] modified gravity, under the accelerated phase of the universe. In this study, we have introduced the modified gravity and dark matter to culture the evolution of the charged neutron stars by considering the present situation. True knowledge and proper study on the macroscopic parameters of the compact stars are very much needed to realize the microscopic properties and behavior of the core nuclear matter at very high density and pressure. The existence of modified Chaplygin gas as an exotic fluid inside the core of these stars in [Formula: see text] gravity plays a very important role inside the stars. We have found out that exotic fluid has a great impact on the equation of state of the core nuclear matter and even on the stability of the compact stars. Pressure anisotropy reduces the tidal deformability of the charged stars in an appreciable amount and helps to get a more compact structure. But surprisingly, the compact stars are still able to maintain their spherically stable and equilibrium configuration. Further, we can put constraints on several macroscopic parameters of the compact stars and can investigate their evolution from our present investigation.

The Interrelated Roles of Correlations in the Nuclear Equation of State and in Response Functions: Application to a Chiral Confining Theory

We study the role of short-range correlations, as well as pion and rho loops governing long-range RPA correlations, in nuclear matter properties and response functions. We use an adapted formulation of the Brueckner G-matrix approach to generate a pair correlation function satisfying the Beg–Agassi–Gal theorem, providing a natural cutoff to the loop integrals. We present results for the case of a relativistic chiral theory, including the effects of quark confinement and of the chirally broken vacuum in a version where parameters are directly connected to QCD observables or constrained by well-established hadron phenomenology. This provides a unified and coherent view of the nuclear matter equation of state and the effect of correlations on neutrino–nucleus scattering.

Bayesian inference of neutron-star observables based on effective nuclear interactions

Based on the Skyrme-Hartree-Fock model (SHF) as well as its extension [the Korea-IBS-Daegu-SKKU (KIDS) model] and the relativistic mean-field (RMF) model, we have studied the constraints on the parameters of the nuclear matter equation of state (EOS) from adopted astrophysical observables using a Bayesian approach. While the masses and radii of neutron stars generally favor a stiff isoscalar EOS and a moderately soft nuclear symmetry energy, model dependence on the constraints is observed and mostly originates from the incorporation of higher-order EOS parameters and differences between relativistic and nonrelativistic models. At twice saturation density, the value of the symmetry energy is constrained to be ${48}_{\ensuremath{-}11}^{+15}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the standard SHF model, ${48}_{\ensuremath{-}15}^{+8}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the KIDS model, and ${48}_{\ensuremath{-}6}^{+5}\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ in the RMF model, around their maximum a posteriori values within $68%$ confidence intervals. Our study helps to obtain a robust constraint on nuclear matter EOS, and, meanwhile, to understand the model dependence of the results.

Rapidly rotating neutron stars with realistic nuclear matter equation of state

AbstractWe performed the comparison of three different numerical codes for constructing equilibrium models; (I) a code for static equilibrium configurations, (II) an implementation of the Hartle–Thorne slow‐rotation approximation, (III) a numerical solution of the full Einstein equations by LORENE. We aimed to construct sequences of uniformly rotating configurations at various rotation frequencies up to the Keplerian frequency for a hybrid hadronic–quark matter EOS where a smooth transition is provided between two separate phases. We investigated the difference between the results computed by the implementation of Hartle–Thorne slow‐rotation approximation and by LORENE/nrotstar, respectively. We have concluded that the codes can increase the difference between the slow‐rotating and the fast‐rotating approach exponentially, reaching 6.67% for the maximal mass configuration rotating at the Keplerian frequency.

Constraining scalarization in scalar-Gauss-Bonnet gravity through binary pulsars

In the present paper we derive strong constrains on scalarization in scalar-Gauss-Bonnet (SGB) gravity using observations of pulsars in close binary systems. Since scalarized neutron stars carry a nonzero scalar change, they emit scalar dipole radiation while inspiraling which speeds up the orbital decay. The observations support the conjecture that such radiation is either absent or very small for the observed binary pulsars. Using this, we determine the allowed range of parameters for SGB gravity. We also transfer the derived constraints to black holes in SGB gravity. It turns out that the maximum mass of a scalarized black hole cannot exceed roughly 10 to 20 solar masses, depending on the initial assumptions we make for the nuclear matter equations of state. The black hole scalar charge on the other hand can reach relatively large values that are potentially observable.

I-Love-Q relations in Hořava-Lifshitz gravity

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars.

Sensitivity of neutron star observations to three-nucleon forces

Astrophysical observations of neutron stars have been widely used to infer the properties of the nuclear matter equation of state. Beside being a source of information on average properties of dense matter, the data provided by electromagnetic and gravitational wave (GW) facilities are reaching the accuracy needed to constrain, for the first time, the underlying nuclear dynamics. In this work, we assess the sensitivity of current and future neutron star observations to directly infer the strength of repulsive three-nucleon forces, which are key to determine the stiffness of the equation of state. Using a Bayesian approach, we focus on the constraints that can be derived on three-body interactions from binary neutron star mergers observed by second- and third-generations of gravitational wave interferometers. We consider both single and multiple observations. For current detectors at design sensitivity, the analysis suggests that only low mass systems, with large signal-to-noise ratios, allow one to reliably constrain the three-body forces. However, our results show that a single observation with a third-generation interferometer, such as the Einstein Telescope or Cosmic Explorer, will constrain the strength of the repulsive three-nucleon potential with exquisite accuracy, turning third-generation GW detectors into new laboratories to investigate the properties of nucleon interactions.

Embedding short-range correlations in relativistic density functionals through quasi-deuterons

The formation of clusters at sub-saturation densities, as a result of many-body correlations, constitutes an essential feature for a reliable modelization of the nuclear matter equation of state (EoS). Phenomenological models that make use of energy density functionals (EDFs) offer a convenient approach to account for the presence of these bound states of nucleons when introduced as additional degrees of freedom. However, in these models clusters dissolve, by construction, when the nuclear saturation density is approached from below, revealing inconsistencies with recent findings that evidence the existence of short-range correlations (SRCs) even at larger densities. The idea of this work is to incorporate SRCs in established models for the EoS, in light of the importance of these features for the description of heavy-ion collisions, nuclear structure and in the astrophysical context. Our aim is to describe SRCs at supra-saturation densities by using effective quasi-clusters immersed in dense matter as a surrogate for correlations, in a regime where cluster dissolution is usually predicted in phenomenological models. Within the EDF framework, we explore a novel approach to embed SRCs within a relativistic mean-field model with density dependent couplings through the introduction of suitable in-medium modifications of the cluster properties, in particular their binding energy shifts, which are responsible for describing the cluster dissolution. As a first exploratory step, the example of a quasi-deuteron within the generalized relativistic density functional approach is investigated. The zero temperature case is examined, where the deuteron fraction is given by the density of a boson condensate. For the first time, suitable parameterizations of the cluster mass shift at zero temperature are derived for all baryon densities. They are constrained by experimental results for the effective deuteron fraction in nuclear matter near saturation and by microscopic many-body calculations in the low-density limit. A proper description of well-constrained nuclear matter quantities at saturation is kept through a refit of the nucleon meson coupling strengths. The proposed parameterizations allow to also determine the density dependence of the quasi-deuteron mass fraction at arbitrary isospin asymmetries. The strength of the deuteron-meson couplings is assessed to be of crucial importance. Novel effects on some thermodynamic quantities, such as the matter incompressibility, the symmetry energy and its slope, are finally discerned and discussed. The findings of the present study represent a first step to improve the description of nuclear matter and its EoS at supra-saturation densities in EDFs by considering correlations in an effective way. In a next step, the single-particle momentum distributions in nuclear matter can be explored using proper wave functions of the quasi-deuteron in the medium. The momentum distributions are expected to exhibit a high-momentum tail, as observed in the experimental study of SRCs by nucleon knockout with high-energy electrons. This will be studied in a forthcoming publication with an extensive presentation of the theoretical method and the results.

Thinking Outside the Box: Numerical Relativity with Particles

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of compact binary mergers. To date, essentially all simulation codes that solve the full set of Einstein’s equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves the commonly used BSSN formulation of the Einstein equations on a structured mesh and the matter equations via Lagrangian particles. We show here, for the first time, SPHINCS_BSSN neutron star merger simulations with piecewise polytropic approximations to four nuclear matter equations of state. In this set of neutron star merger simulations, we focus on perfectly symmetric binary systems that are irrotational and have 1.3 M⊙ masses. We introduce some further methodological refinements (a new way of steering dissipation, an improved particle–mesh mapping), and we explore the impact of the exponent that enters in the calculation of the thermal pressure contribution. We find that it leaves a noticeable imprint on the gravitational wave amplitude (calculated via both quadrupole approximation and the Ψ4 formalism) and has a noticeable impact on the amount of dynamic ejecta. Consistent with earlier findings, we only find a few times 10−3M⊙ as dynamic ejecta in the studied equal mass binary systems, with softer equations of state (which are more prone to shock formation) ejecting larger amounts of matter. In all of the cases, we see a credible high-velocity (∼0.5…0.7c) ejecta component of ∼10−4M⊙ that is launched at contact from the interface between the two neutron stars. Such a high-velocity component has been suggested to produce an early, blue precursor to the main kilonova emission, and it could also potentially cause a kilonova afterglow.

Neutron stars and phase diagram in a hard-wall AdS/QCD model

We study the phase diagram of (large-${N}_{c}$) QCD using a simplistic holographic hard-wall model with a dynamical scalar field and a homogeneous Ansatz representing a smeared instanton/baryon density. The resulting phase diagram is qualitatively consistent with expectations, including a mesonic, baryonic, quarkyonic, and quark-gluon plasma phase. As in other holographic models, we also find a baryonic popcorn transition, which appears at large chemical potential as a crossover. We then evaluate the nuclear matter equation of state, which turns out to be rather stiff with a large peaked sound velocity above the conformal limit, construct corresponding neutron stars using the Tolman-Oppenheimer-Volkov equations, and finally use a full numerical gravity/hydrodynamics computation to extract the gravitational wave signal of neutron star mergers.

Unified nuclear matter equations of state constrained by the in-medium balance in density-dependent covariant density functionals

Considering the effects of charge screening, we propose a new numerical recipe within the framework of Thomas-Fermi approximation, where the properties of nuclear matter throughout a vast density range can be obtained self-consistently. Assuming spherical and cylindrical approximations for the Wigner-Seitz cell, typical nuclear matter structures (droplet, rod, slab, tube, bubble, and uniform) are observed. We then investigate the EOSs and microscopic structures of nuclear matter with both fixed proton fractions and $\beta$-equilibration, where two covariant density functionals DD-LZ1 and DD-ME2 are adopted. Despite the smaller slope $L$ of symmetry energy obtained with the functional DD-LZ1, the curvature parameter $K_\mathrm{sym}$ is much larger than that of DD-ME2, which is attributed to the peculiar density-dependent behavior of meson-nucleon couplings guided by the restoration of pseudo-spin symmetry around the Fermi levels in finite nuclei. Consequently, different mass-radius relations of neutron stars are predicted by the two functionals. Different microscopic structures of nonuniform nuclear matter are obtained as well, which are expected to affect various physical processes in neutron star properties and evolutions.

Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI

High-energy heavy-ion collisions offer the unique possibility to study fundamental properties of nuclear matter in the laboratory, which are relevant for our understanding of the structure of compact stellar objects and the dynamics of neutron star mergers. Of particular interest are the nuclear matter equation of state (EOS), the in-medium modifications of hadrons and the degrees of freedom of matter at high densities and temperatures. Pioneering experiments exploring the EOS for symmetric matter were performed at the SIS18 accelerator of GSI, measuring, as function of beam energy, the collective flow of protons and of light fragments and subthreshold strangeness production. These data were reproduced by various microscopic transport model calculations, providing, up to date, the best constraint for the EOS of symmetric matter with an incompressibility of about 200 MeV for densities up to twice the saturation density. This article reviews the experimental results on subthreshold kaon production together with the theoretical interpretation and gives a brief outlook towards future experiments at higher densities.

Inferring the dense nuclear matter equation of state with neutron star tides

During the late stages of a neutron star binary inspiral finite-size effects come into play, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817—the first direct detection of gravitational waves from a neutron star binary—this can lead to strong constraints on the neutron star equation of state. As detectors become more sensitive, effects which may have a smaller influence on the neutron star tidal deformability need to be taken into consideration. Dynamical effects, such as oscillation mode resonances triggered by the orbital motion, have been shown to contribute to the tidal deformability, especially close to the neutron star coalesence, where current detectors are most sensitive. We calculate the contribution of the various stellar oscillation modes to the tidal deformability and demonstrate the (anticipated) dominance of the fundamental mode. We show what the impact of the matter composition is on the tidal deformability, as well as the changes induced by more realistic additions to the problem, e.g. the presence of an elastic crust. Finally, based on this formulation, we develop a simple phenomenological model describing the effective tidal deformability of neutron stars and show that it provides a surprisingly accurate representation of the dynamical tide close to merger.

Hybrid stars from a constrained equation of state

We determine, within a meta-model, the properties of the nuclear matter equation of state (EoS) that allow for a phase transition to deconfinement matter. It is shown that the properties that define the isoscalar channel are the ones that are affected, in particular, a phase transition implies much larger values of the skewness and kurtosis. The effect of multi-quark interaction channels in the description of the quark phase in hybrid stars is also studied. NS properties, such as the mass and radius of the quark core, show an interplay dependence between the 8-quark vector and the 4-quark isovector-vector interactions. We show that low mass NS, M ~ 1.4M⊙, may already contain a quark core, and satisfy all existing NS observational constraints. We discuss the strangeness content of the quark core and its influence on the speed of sound.

Study of strange matter in STAR with express analysis

The STAR experiment provides a perfect machinery for studying strange matter for more than two decades. Recently, we developed the express procedure, which allows online monitoring of the collected physics data. The high quality of express calibration and reconstruction provides a unique possibility to run the express production and observe almost in real time strange particles including mesons, hyperons, resonances and even hypernuclei. The STAR Beam Energy Scan II program, including fixed target Au+Au collisions taken in 2018–2021, is particularly suited to study hypernuclei. Light hypernuclei are expected to be abundantly produced in low energy heavy-ion collisions. Measurements of hypernuclei production and their properties will provide information on the hyperon-nucleon interactions, which are essential ingredients for understanding nuclear matter equation of state at high net-baryon densities, such as inside neutron stars. With the heavy fragment trigger introduced for the 2021 data taking, we were able to run the express production at the STAR High Level Trigger farm. The collected data were suffcient to observe the decay process of Λ5He →4Hepπ− with more than 11σ significance, measure binding energy as a function of hypernuclei mass, and study hypernuclei decay properties with the Dalitz plot technique.

Thermal properties of hot and dense medium in interacting hadron resonance gas model

The meson exchange interaction based on relativistic mean-field (RMF) theory has been introduced in the hadron resonance gas (HRG) model, called interacting HRG (iHRG) model. This model can be used to explain the experimental data both at finite temperature (T) with finite chemical potential (μB) and finite temperature at vanishing chemical potential. The nuclear matter equation of state also can be explained at zero temperature with finite baryon density (finite chemical potential) due to the presence of attractive and repulsive interactions between the hadrons in the iHRG model. Similarly, the lattice equation of state is well described at μB = 0 and finite temperature by the iHRG model. In the present study, we have calculated the thermodynamical quantities as a function of temperature and chemical potential using both HRG and iHRG models. Also, we have presented the isothermal compressibility (kT), specific heat (CV), and speed of sound (cs2) as a function of μB, T, and center of mass energies. The effect of kinematic acceptance on these quantities are also presented as a function of μ and T. Results from this study on kT are compared with results from other heavy-ion transport models and experimental data up to LHC energies.

Chiral Effective Field Theory’s Impact on Advancing Quantum Monte Carlo Methods

Thirty years ago, Steven Weinberg published his seminal paper on "Nuclear Forces from chiral Lagrangians" which has revolutionized the field of theoretical nuclear physics. Nowadays, interactions derived from chiral effective field theory are routinely used to describe nuclear systems ranging from atomic nuclei to the dense matter explored in the core of neutron stars with theoretical uncertainty estimates. In our contribution to the special issue "Celebrating 30 years of Steven Weinberg's paper Nuclear Forces from Chiral Lagrangians", we focus on the impact that chiral effective field theory interactions have played in advancing microscopic studies of atomic nuclei and the nuclear-matter equation of state using quantum Monte Carlo methods.