Nuclear Equation Of State Research Articles

Effects of Different Closure Choices in Core-collapse Supernova Simulations

The two-moment method is widely used to approximate the full neutrino transport equation in core-collapse supernova (CCSN) simulations, and different closures lead to subtle differences in the simulation results. In this paper, we compare the effects of closure choices on various physical quantities in 1D and 2D time-dependent CCSN simulations with our multigroup radiation hydrodynamics code Fornax. We find that choices of the third-order closure relations influence the time-dependent simulations only slightly. Choices of the second-order closure relation have larger consequences than choices of the third-order closure, but these are still small compared to the remaining variations due to ambiguities in some physical inputs such as the nuclear equation of state. We also find that deviations in Eddington factors are not monotonically related to deviations in physical quantities, which means that simply comparing the Eddington factors does not inform one concerning which closure is better.

NArCoS: The new hodoscope for neutrons and charged particles

Proper detection of neutrons and charged particles is motivated by the recent efforts to construct new facilities for radioactive ion beams (RIBs) worldwide. Detection of neutrons is an important opportunity to improve our understanding of nuclear spectroscopy and reaction dynamics, with the possibility of constraining theoretical models of the nuclear equation of state (NEoS) and investigating in-medium nuclear interactions. This topic also has important implications in the study of astrophysical objects, such as neutron stars. In this work, the state-of-the-art of Neutron Array for Correlation Studies (NArCoS), a new hodoscope for neutron and charged particles under construction in Catania (INFN), is briefly reviewed.

Nuclear Equation of State from Nuclear Collective Excited State Properties

Nuclear Equation of State from Nuclear Collective Excited State Properties

Impacts of the U(1)A anomaly on nuclear and neutron star equation of state based on a parity doublet model

We examine the role of the $\mathrm{U}{(1)}_{A}$ anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the $\mathrm{U}{(1)}_{A}$ anomaly by the Kobayashi-Maskawa-'t Hooft (KMT) interaction in the mesonic sector. After examining the roles of the KMT term in vacuum, we discuss its impacts on nuclear equations of state (EOS). The $\mathrm{U}{(1)}_{A}$ anomaly increases the masses of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\sigma}$ mesons and enhances the chiral symmetry breaking. Also, the $\mathrm{U}{(1)}_{A}$ anomaly enlarges the energy difference between chiral symmetric and symmetry broken vacuum; in turn, the chiral restoration at high density adds a larger energy density (often referred as a bag constant) to EOSs than in the case without the anomaly, leading to softer EOSs. Including these $\mathrm{U}{(1)}_{A}$ effects, we update the previously constructed unified equations of state that interpolate the nucleonic EOS at ${n}_{B}\ensuremath{\le}2{n}_{0}$ (${n}_{0}=0.16\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$; nuclear saturation density) and quark EOS at ${n}_{B}\ensuremath{\ge}5{n}_{0}$. The unified EOS is confronted with the observational constraints on the masses and radii of neutron stars. The softening of EOSs associated with the $U$(1) anomaly reduces the overall radii, relaxing the previous constraint on the chiral invariant mass ${m}_{0}$. Including the attractive nonlinear $\ensuremath{\rho}\text{\ensuremath{-}}\ensuremath{\omega}$ coupling for the reduced slope parameter in the symmetry energy, our new estimate is $400\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}\ensuremath{\le}{m}_{0}\ensuremath{\le}700\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, with ${m}_{0}$ smaller than our previous estimate by $\ensuremath{\approx}$200 MeV.

Isospin symmetry breaking in the charge radius difference of mirror nuclei

Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of $^{48}\mathrm{Ca}$ and $^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

Effects of nuclear matter and composition in core-collapse supernovae and long-term proto-neutron star cooling

Abstract We study the influence of hot and dense matter in core-collapse supernovae by adopting an up-to-date nuclear equation of state (EOS) based on the microscopic nuclear many-body frameworks. We explore effects of the EOS based on the Dirac–Brückner–Hartree–Fock theory through comparisons with those based on the variational method. We also examine effects of the differences in the composition of nuclei and nucleons by using the same EOS as the variational method but employing two different treatments in computations of nuclear abundances. We perform numerical simulations of core-collapse supernovae adopting the three EOSs. We also perform numerical simulations of the long-term evolution over 70 s of the proto-neutron star cooling. We show that the impacts of different modeling of the composition are remarkable as in those due to different treatments of uniform matter in the gravitational collapse, bounce and shock propagation. The cooling of a proto-neutron star and the resulting neutrino emission are also affected by the compositional difference even if the same treatment is used in computing uniform matter of the EOS.

Determining the Core Structure and Nuclear Equation of State of Rotating Core-collapse Supernovae with Gravitational Waves by Convolutional Neural Networks

Detecting gravitational waves from a nearby core-collapse supernova would place meaningful constraints on the supernova engine and nuclear equation of state. Here we use convolutional neural network models to identify the core rotational rates, rotation length scales, and the nuclear equation of state (EoS), using the 1824 waveforms from Richers et al. for a 12 solar mass progenitor. A high prediction accuracy for the classifications of the rotation length scales (93%) and the rotational rates (95%) can be achieved using the gravitational-wave signals from −10 to 6 ms core bounce. By including an additional 48 ms signal during the prompt convection phase, we could achieve an accuracy of 96% in the classification of the four main EoS groups. By combining the three models above, we could correctly predict the core rotational rates, rotation length scales, and the EoS at the same time with an accuracy of more than 85%. Finally, applying a transfer-learning method for an additional 74 waveforms from FLASH simulations, we show that our model using Richers’ waveforms could successfully predict the rotational rates from Pan’s waveforms even for a continuous value with mean absolute errors of 0.32 rad s−1 only. These results demonstrate the much broader parameter regimes to which our model can be applied to identify core-collapse supernova events through gravitational-wave signals.

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.

Hubble constant and nuclear equation of state from kilonova spectro-photometric light curves

The merger of two compact objects of which at least one is a neutron star is signalled by transient electromagnetic emission in a kilonova (KN). This event is accompanied by gravitational waves and possibly other radiation messengers such as neutrinos or cosmic rays. The electromagnetic emission arises from the radioactive decay of heavy r-process elements synthesized in the material ejected during and after the merger. In this paper we show that the analysis of KNe light curves can provide cosmological distance measurements and constrain the properties of the ejecta. In this respect, MAAT, the new Integral Field Unit in the OSIRIS spectrograph on the 10.4 m Gran Telescopio CANARIAS (GTC), is well suited for the study of KNe by performing absolute spectro-photometry over the entire 3600 − 10 000 Å spectral range. Here, we study the most representative cases regarding the scientific interest of KNe from binary neutron stars, and we evaluate the observational prospects and performance of MAAT on the GTC to do the following: (a) study the impact of the equation of state on the KN light curve, and determine to what extent bounds on neutron star (NS) radii or compactness deriving from KN peak magnitudes can be identified and (b) measure the Hubble constant, H0, with precision improved by up to 40%, when both gravitational wave data and photometric-light curves are used. In this context we discuss how the equation of state, the viewing angle, and the distance affect the precision and estimated value of H0.

The essential character of the neutrino mechanism of core-collapse supernova explosions

Abstract Calibrating with detailed 2D core-collapse supernova (CCSN) simulations, we derive a simple CCSN explosion condition based solely upon the terminal density profiles of state-of-the-art stellar evolution calculations of the progenitor massive stars. This condition captures the vast majority of the behaviour of the one hundred 2D state-of-the-art models we performed to gauge its usefulness. The goal is to predict, without resort to detailed simulation, the explodability of a given massive star. We find that the simple maximum fractional ram pressure jump discriminant we define works well ∼90 per cent of the time and we speculate on the origin of the few false positives and false negatives we witness. The maximum ram pressure jump generally occurs at the time of accretion of the silicon/oxygen interface, but not always. Our results depend upon the fidelity with which the current implementation of our code F ornax adheres to Nature and issues concerning the neutrino–matter interaction, the nuclear equation of state, the possible effects of neutrino oscillations, grid resolution, the possible role of rotation and magnetic fields, and the accuracy of the numerical algorithms employed remain to be resolved. Nevertheless, the explodability condition we obtain is simple to implement, shows promise that it might be further generalized while still employing data from only the unstable Chandrasekhar progenitors, and is a more credible and robust simple explosion predictor than can currently be found in the literature.

Exploring the Fate of Stellar Core Collapse with Supernova Relic Neutrinos

Core collapse of massive stars leads to different fates for various physical factors, which gives different spectra of the emitted neutrinos. We focus on the supernova relic neutrinos (SRNs) as a probe to investigate the stellar collapse fate. We present the SRN fluxes and event rate spectra at a detector for three resultant states after stellar core collapse, the typical mass neutron star, the higher mass neutron star, or the failed supernova forming a black hole, based on different nuclear equations of state. Then possible SRN fluxes are formed as mixtures of the three components. We also show the expected sensitivities at the next-generation water-based Cherenkov detectors, SK-Gd and Hyper-Kamiokande, as constraining the mixture fractions. This study provides a practical example of extracting astrophysical constraints through SRN measurement.

Investigation of the inner edge of neutron star crusts: Temperature dependence and related effects

The mutual correlation between the nuclear equation of state (EOS) and the bulk properties of neutron stars (NS) is crucial in probing both of them. Here, we use EOSs of hot $npe$ ($npe\ensuremath{\mu}$) nuclear matter, based on the density-dependent CDM3Y-Paris nucleon-nucleon interaction in the nonrelativistic Hartree-Fock scheme, to investigate the temperature dependence of the core-crust transition properties under $\ensuremath{\beta}$ equilibrium, at the inner edge of NS. We use four EOSs that provide symmetric nuclear matter saturation incompressibility of 218 and 252 MeV, with two parametrizations of the density dependence of the isovector part of the M3Y force. We found that the softer EOS estimates larger proton fraction in the NS matter and indicates a wider range for direct Urca (DU) cooling process within the core center of NSs. Increasing the temperature decreases the density corresponding to the threshold proton fraction for DU process, increasing the region for the DU process inside NSs. The muons decrease the isospin asymmetry of the $npe\ensuremath{\mu}$ NS matter at its core center, its thermal pressure, and the DU threshold density. The muon fraction slightly changes with temperature. A value of about half the proton fraction is inferred for the $\ensuremath{\beta}$-stable muon fraction of hot $npe\ensuremath{\mu}$ matter, around the core center. Based on the four considered EOSs, the liquid core-solid crust transition density, pressure, and proton fraction are estimated to increase from $(0.54\ifmmode\pm\else\textpm\fi{}0.02){\ensuremath{\rho}}_{0}, 0.36\ifmmode\pm\else\textpm\fi{}0.12\phantom{\rule{4pt}{0ex}}\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, and 0.03, respectively at $T=0\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, to $(0.85\ifmmode\pm\else\textpm\fi{}0.04){\ensuremath{\rho}}_{0}, 7.36\ifmmode\pm\else\textpm\fi{}0.52\phantom{\rule{4pt}{0ex}}\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, and 0.14, respectively at $T=50\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$.

Exploring the NΛ–NΣ coupled system with high precision correlation techniques at the LHC

The interaction of Λ and Σ hyperons (Y) with nucleons (N) is strongly influenced by the coupled-channel dynamics. Due to the small mass difference of the NΛ and NΣ systems, the sizable coupling strength of the NΣ↔NΛ processes constitutes a crucial element in the determination of the NΛ interaction. In this letter we present the most precise measurements on the interaction of pΛ pairs, from zero relative momentum up to the opening of the NΣ channel. The correlation function in the relative momentum space for pΛ⊕p‾Λ‾ pairs measured in high-multiplicity triggered pp collisions at s=13 TeV at the LHC is reported. The opening of the inelastic NΣ channels is visible in the extracted correlation function as a cusp-like structure occurring at relative momentum k⁎=289MeV/c. This represents the first direct experimental observation of the NΣ↔NΛ coupled channel in the pΛ system. The correlation function is compared with recent chiral effective field theory calculations, based on different strengths of the NΣ↔NΛ transition potential. A weaker coupling, as possibly supported by the present measurement, would require a more repulsive three-body NNΛ interaction for a proper description of the Λ in-medium properties, which has implications on the nuclear equation of state and for the presence of hyperons inside neutron stars.

Dark Matter Capture by Neutron Stars with Modern Nuclear Equations of State

Dark Matter Capture by Neutron Stars with Modern Nuclear Equations of State

Neutrino emission from binary neutron star mergers: characterising light curves and mean energies

Neutrinos are copiously emitted by neutron star mergers, due to the high temperatures reached by dense matter during the merger and its aftermath. Neutrinos influence the merger dynamics and shape the properties of the ejecta, including the resulting r-process nucleosynthesis and kilonova emission. In this work, we analyse neutrino emission from a large sample of binary neutron star merger simulations in Numerical Relativity, covering a broad range of initial masses, nuclear equation of state and viscosity treatments. We extract neutrino luminosities and mean energies, and compute quantities of interest such as the peak values, peak broadnesses, time averages and decrease time scales. We provide a systematic description of such quantities, including their dependence on the initial parameters of the system. We find that for equal-mass systems the total neutrino luminosity (several 10^{53}{hbox {erg}~{hbox {s}}^{-1}}) decreases as the reduced tidal deformability increases, as a consequence of the less violent merger dynamics. Similarly, tidal disruption in asymmetric mergers leads to systematically smaller luminosities. Peak luminosities can be twice as large as the average ones. Electron antineutrino luminosities dominate (initially by a factor of 2-3) over electron neutrino ones, while electron neutrinos and heavy flavour neutrinos have similar luminosities. Mean energies are nearly constant in time and independent on the binary parameters. Their values reflect the different decoupling temperature inside the merger remnant. Despite present uncertainties in neutrino modelling, our results provide a broad and physically grounded characterisation of neutrino emission, and they can serve as a reference point to develop more sophisticated neutrino transport schemes.

Jet launching from binary neutron star mergers: Incorporating neutrino transport and magnetic fields

We perform general relativistic, magnetohydrodynamic simulations of merging binary neutron stars incorporating neutrino transport and magnetic fields. Our new radiative transport module for neutrinos adopts a general relativistic, truncated-moment formalism. The binaries consist of two identical, irrotational stars modeled by the Skyrme Lyon (SLy) nuclear equation of state. They are initially in quasicircular orbit and threaded with a poloidal magnetic field that extends from the stellar interior into the exterior, as in typical pulsars. We insert neutrino processes shortly after the merger and focus on the role of neutrinos in launching a jet following the collapse of the hypermassive neutron star (HMNS) remnant to a spinning black hole (BH). We treat two microphysical versions: one (a ``warm-up'') evolving a single neutrino species and considering only charged-current processes and the other evolving three species $({\ensuremath{\nu}}_{e},{\overline{\ensuremath{\nu}}}_{e},{\ensuremath{\nu}}_{\mathrm{x}})$ and related processes. We trace the evolution until the system reaches a quasiequilibrium state after BH formation. We find that the $\mathrm{BH}+\text{disk}$ remnant eventually launches an incipient jet. The electromagnetic Poynting luminosity is $\ensuremath{\sim}{10}^{53}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, consistent with that of typical short gamma-ray bursts. The effect of neutrino cooling shortens the lifetime of the HMNS and lowers the amplitude of the major peak of the gravitational wave power spectrum somewhat. After BH formation, neutrinos help clear out the matter near the BH poles, resulting in lower baryon-loaded surrounding debris. The neutrino luminosity resides in the range $\ensuremath{\sim}{10}^{52\ensuremath{-}53}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ once quasiequilibrium is achieved. Comparing with the neutrino-free models, we observe that the inclusion of neutrinos yields similar ejecta masses and is inefficient in carrying off additional angular momentum.

Wave-optical Effects in the Microlensing of Continuous Gravitational Waves by Star Clusters

Rapidly rotating neutron stars are promising sources for existing and upcoming gravitational-wave interferometers. While relatively dim, these systems are expected to emit continuously, allowing for signal to be accumulated through persistent monitoring over year-long timescales. If, at some point during the observational window, the source comes to lie behind a dense collection of stars, transient gravitational lensing may occur. Such events, though rare, would modulate the waveform, induce phase drifts, and ultimately affect parameter inferences concerning the nuclear equation of state and/or magnetic field structure of the neutron star. Importantly, the radiation wavelength will typically exceed the Schwarzschild radius of the individual perturbers in this scenario, implying that (micro)lensing occurs in the diffractive regime, where geometric optics does not apply. In this paper, we make use of numerical tools that borrow from Picard–Lefschetz theory to efficiently evaluate the relevant Fresnel–Kirchhoff integrals for n ≳ 102 microlenses. Modulated strain profiles are constructed both in general and for particular neutron star trajectories relative to some simulated macrolenses.

Constraining equation-of-state groups from g-mode asteroseismology

ABSTRACT Buoyancy-restored modes inside neutron stars depend sensitively on both the microphysical (e.g. composition and entropy gradients) and macrophysical (e.g. stellar mass and radius) properties of the star. Asteroseismology efforts for g modes are therefore particularly promising avenues for recovering information concerning the nuclear equation of state. In this work, it is shown that the overall low-temperature g-space consists of multiple groups corresponding to different classes of equation of state (e.g. hadronic versus hybrid). This is in contrast to the case of pressure-driven modes, for example, which tend to follow a universal relation regardless of microphysical considerations. Using a wide library of currently viable equations of state, perturbations of static, stratified stars are calculated in general relativity to demonstrate in particular how g-space groupings can be classified according to the mean mass density, temperature, central speed of sound, and tidal deformability. Considering present and future observations regarding gravitational waves, accretion outbursts, quasi-periodic oscillations, and precursor flashes from gamma-ray bursts, it is shown how one might determine which group the g modes belong to.

PUSHing Core-collapse Supernovae to Explosions in Spherical Symmetry. V. Equation of State Dependency of Explosion Properties, Nucleosynthesis Yields, and Compact Remnants

Abstract In this fifth paper of the series, we use the parameterized, spherically symmetric explosion method PUSH to investigate the impact of eight different nuclear equations of state (EOS). We present and discuss the explosion properties and the detailed nucleosynthesis yields, and predict the remnant (neutron star or black hole) for all our simulations. For this, we perform two sets of simulations. First, a complete study of nonrotating stars from 11 to 40 M ⊙ at three different metallicities using the SFHo EOS; and, second, a suite of simulations for four progenitors (16 M ⊙ at three metallicities and 25 M ⊙ at solar metallicity) for eight different nuclear EOS. We compare our predicted explosion energies and yields to observed supernovae and to the metal-poor star HD 84937. We find EOS-dependent differences in the explosion properties and the nucleosynthesis yields. However, when comparing to observations, these differences are not large enough to rule out any EOS considered in this work.

Tidal deformation of dynamical horizons in binary black hole mergers

An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal deformation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late stages of the inspiral phase when the black holes get close to each other, the source multipole moments might be more relevant in probing their properties and the No-Hair conjecture; contrastingly, these Love numbers do not vanish. In this paper, we track the source multipole moments in simulations of several binary black hole mergers and calculate these Love numbers. We present evidence that, at least for modest mass ratios, the behavior of the source multipole moments is universal.