A two-phase description of the quark-nuclear matter hybrid equation of state that takes into account the effect of excluded volume in both the hadronic and the quark matter phases is introduced.
The nuclear phase manifests a reduction of the available volume as density increases, leading to a stiffening of the matter. The quark matter phase displays a reduction of the effective string tension in the confining density functional from available volume contributions. The nuclear equation of state is based upon the relativistic density functional model DD2 with excluded volume. The quark matter is based upon a mean-field modification to the free fermi gas and will be discussed in greater detail. The interactions are decomposed into mean scalar and vector components. The scalar interaction is motivated by a string potential between quarks, whereas the vector interaction potential is motivated by higher order interactions of quarks leading to an increased stiffening at high densities. As an application, we consider matter under compact star constraints of electric neutrality and $β$-equilibrium. We obtain mass-radius relations for hybrid stars that form a third family, disconnected from the purely hadronic star branch, and fulfill the $2M_\odot$ constraint.
In this contribution, we outline a new 2-phase description of the quark-nuclear matter hybrid equation of state that takes into account effects of phase space occupation (excluded volume) in both, the hadronic and the quark matter phases. For the nuclear matter phase, the reduction of the available volume at increasing density leads to a stiffening, while for the quark matter phase a reduction of the effective string tension in the confining density functional is obtained. The deconfinement phase transition in the resulting hybrid equation of state is sensitive to both excluded volume effects.…
In this article the role of the supersaturation density equation of state (EOS) is explored in simulations of failed core-collapse supernova explosions. Therefore the nuclear EOS is extended via a one-parameter excluded volume description for baryons, taking into account their finite and increasing volume with increasing density in excess of saturation density. Parameters are selected such that the resulting supernova EOS represent extreme cases, with high pressure variations at supersaturation density which feature extreme stiff and soft EOS variants of the reference case, i.e. without exclud…
Nuclear equation of state (EoS) plays an important role in understanding the formation of compact objects such as neutron stars and black holes. The true nature of the EoS has been a matter of debate at any density range not only in the nuclear physics but also in the astronomy and astrophysics. We have constructed a database of EoSs by compiling data from the literature. Our database contains the basic properties of the nuclear EoS of symmetric nuclear matter and of pure neutron matter. It also includes the detailed information about the theoretical models, for example the adopted methods and…
We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and there-body nuclear forces. We utilize an extended liquid drop model of heavy nuclei and a quantum-theoretical mass evaluation for light nuclei. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOS's for supernova s…
Strongly interacting matter with criticality induced by modified excluded volume in core-collapse supernova simulations
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；University of Wroclaw（弗罗茨瓦夫大学）；Silesian University in Opava（奥帕瓦西里西亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung（德国重离子研究中心）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）；Universitat de Valéncia（瓦伦西亚大学）；Observatori Astronòmic, Universitat de València（瓦伦西亚大学天文台）
The equation of state (EOS) for hot asymmetric nuclear matter which is constructed with the variational method starting from the Argonne v18 and Urbana IX nuclear forces is applied to spherically symmetric core-collapse supernovae (SNe). We first investigate the EOS of isentropic beta-stable SN matter, and find that the matter with the variational EOS is more neutron-rich than that with the Shen EOS. Using the variational EOS for uniform matter supplemented by the Shen EOS of non-uniform matter at low densities, we perform general-relativistic spherically symmetric simulations of core-collapse…
A new table of the nuclear equation of state (EOS) based on realistic nuclear potentials is constructed for core-collapse supernova numerical simulations. Adopting the EOS of uniform nuclear matter constructed by two of the present authors with the cluster variational method starting from the Argonne v18 and Urbana IX nuclear potentials, the Thomas-Fermi calculation is performed to obtain the minimized free energy of a Wigner-Seitz cell in non-uniform nuclear matter. As a preparation for the Thomas-Fermi calculation, the EOS of uniform nuclear matter is modified so as to remove the effects of …
We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and $β$-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the $Δ(1232)$ isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for $β$-stable nuclear matter to compute various structural proper…
In this contribution, we have made use of the contemporary equation of states (EOSs) for the complete neutron star structure, and confronted them with one particular glitch constrain for the crustal moment of inertia (MOI). We find that with these EOSs, the radii of three millisecond pulsars selected by NICER: PSR J0437-4715, PSR J1614-2230, PSR J0751+1807, are all around 12.5 km. Also, a star with $M \lesssim 1.55 M_{\odot}$ would fulfill the MOI calculation for glitch constrain with the latest neutron superfluidity density, and the glitch crisis might not be present.
Multi-messenger observations of neutron star (NS) mergers have the potential to revolutionize nuclear astrophysics. They will improve our understanding of nucleosynthesis, provide insights about the equation of state (EOS) of strongly-interacting matter at high densities, and enable tests of the theory of gravity and of dark matter. Here, we focus on the EOS, where both gravitational waves (GWs) from neutron-star mergers and X-ray observations from space-based detectors such as NICER will provide more stringent constraints on the structure of neutron stars. Furthermore, recent advances in nucl…
We present a review of a broad selection of nuclear matter equations of state (EOSs) applicable in core-collapse supernova studies. The large variety of nuclear matter properties, such as the symmetry energy, which are covered by these EOSs leads to distinct outcomes in supernova simulations. Many of the currently used EOS models can be ruled out by nuclear experiments, nuclear many-body calculations, and observations of neutron stars. In particular the two classical supernova EOS describe neutron matter poorly. Nevertheless, we explore their impact in supernova simulations since they are comm…
We study the effects of nuclear symmetry energy on the mass-radius relation and tidal deformability of neutron stars, considering the self-consistency of the equation of state (EOS). We first construct a set of unified EOSs based on relativistic mean-field models with different density dependence of the symmetry energy. For the description of pasta phases appearing in the inner crust of neutron stars, we perform a self-consistent Thomas-Fermi calculation using the same nuclear interaction as that for the uniform matter in the core. To examine possible effects from the self-consistency of the E…
A precise understanding of the equation of state (EOS) of dense and hot matter is key to modeling relativistic astrophysical environments, including core-collapse supernovae (CCSNe), protoneutron star (PNSs) evolution, and compact binary mergers. In this paper, we extend the microscopic zero-temperature BL (Bombaci and Logoteta) %nuclear equation of state nuclear EOS %derived by Bombaci and Logoteta to finite temperature and arbitrary nuclear composition. We employ this new EOS to describe hot $β$-stable nuclear matter and to compute various structural properties of nonrotating PNS. %protoneut…
We perform an extensive study of the influence of nuclear weak interactions on core-collapse supernovae (CCSNe), paying particular attention to consistency between nuclear abundances in the equation of state (EOS) and nuclear weak interactions. We compute properties of uniform matter based on the variational method. For inhomogeneous nuclear matter, we take a full ensemble of nuclei into account with various finite-density and thermal effects and directly use the nuclear abundances to compute nuclear weak interaction rates. To quantify the impact of a consistent treatment of nuclear abundances…
We present an updated general purpose nuclear equation of state (EoS) for use in simulations of core-collapse supernovae, neutron star mergers and black hole collapse. This EoS is formulated in the context of Density Functional Theory (DFT) and is generalized to include all DFT EoSs consistent with known nuclear and astrophysical constraints. This EoS also allows for the possibility of the formation of material with a net proton excess ($Y_p > 0.5$) and has an improved treatment of the nuclear statistical equilibrium and the transition to heavy nuclei as the density approaches nuclear matter d…
Ab initio methods using weakly interacting nucleons give a good description of condensed nuclear matter up to densities comparable to the nuclear saturation density. At higher densities palpable strong interactions between overlapping nucleons become important; we propose that the interactions will continuously switch over to follow a holographic model in this region. In order to implement this, we construct hybrid equations of state (EoSs) where various models are used for low density nuclear matter, and the holographic V-QCD model is used for non-perturbative high density nuclear matter as w…
Using a extended version of the Quantum Hadrodynamics (QHD), I propose a new microscopic equation of state (EoS) able to correctly reproduce the main properties of symmetric nuclear matter at the saturation density, as well produce massive neutron stars and satisfactory results for the radius and the tidal parameter $Λ$. I show that even when hyperons are present, this EoS is able to reproduce at least 2.00 solar masses neutron star. The constraints about the radius of a $2.00M_\odot$ and the minimum mass that enable direct Urca effect are also checked.
We study the influence of hot and dense matter in core-collapse supernovae by adopting up-to-date nuclear equation of state (EOS) based on the microscopic nuclear many-body frameworks. We explore effects of EOS based on the Dirac Brueckner 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 by the variational method but employing two different treatments in computations of nuclear abundances. We perform numerical simulations of core-collapse supernovae adop…
Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multi-messenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in …
We perform a Bayesian analysis in the basis of a recently developed two-parameter class of hybrid equations of state that allow for high-mass compact star twins. While recently a wide range of radii, from 9 - 15 km, has been inferred for different neutron stars using different techniques, we perform our analysis under the supposition that the radii are towards the large end ($13-15$ km). We use this radius constraint together with the undebated statistically independent constraint for high masses ($\sim 2~M_\odot$) as priors in selecting the most probable hybrid equations of state from a famil…
Taking into account the terrestrial experiments and the recent astrophysical observations of neutron stars and gravitational-wave signals, we impose restrictions on the equation of state (EoS) for isospin-asymmetric nuclear matter. Using the relativistic mean-field model with SU(3) flavor symmetry, we investigate the impacts of effective nucleon mass, nuclear incompressibility, and slope parameter of nuclear symmetry energy on the nuclear and neutron-star properties. It is found that the astrophysical information of massive neutron stars and tidal deformabilities as well as the nuclear experim…
We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the wide…
Exploiting a very large library of physically plausible equations of state (EOSs) containing more than $10^{7}$ members and yielding more than $10^{9}$ stellar models, we conduct a survey of the impact that a neutron-star radius measurement via electromagnetic observations can have on the EOS of nuclear matter. Such measurements are soon to be expected from the ongoing \textit{Neutron Star Interior Composition Explorer} mission and will complement the constraints on the EOS from gravitational-wave detections. Thanks to the large statistical range of our EOS library, we can obtain a first quant…
Binary neutron star mergers (NSMs) have been confirmed as one source of the heaviest observable elements made by the rapid neutron-capture (r-) process. However, modeling NSM outflows -- from the total ejecta masses to their elemental yields -- depends on the unknown nuclear equation of state (EOS) that governs neutron-star structure. In this work, we derive a phenomenological EOS by assuming that NSMs are the dominant sources of the heavy element material in metal-poor stars with r-process abundance patterns. We start with a population synthesis model to obtain a population of merging neutron…
We examine the influence of the density dependence of the symmetry energy on several properties of neutron stars. In particular, we study the constraints set on the nuclear matter equation of state by the values of the tidal deformability and neutron star radius, using a diverse set of relativistic and non-relativistic mean field models consistent with bulk properties of finite nuclei and the observed lower bound on the maximum mass of neutron star. The tidal deformability and radius show a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter param…
Pure hadronic compact stars, above a limiting value ($\approx$1.6 M$_\odot$) of their gravitational masses, to which predictions of most of other equations of state (EoSs) are restricted, can be reached from the equation of state (EoS) obtained using DDM3Y effective interaction. This effective interaction is found to be quite successful in providing unified description of elastic and inelastic scattering, various radioactivities and nuclear matter properties. We present a systematic study of the properties of pure hadronic compact stars. The $β$-equilibrated neutron star matter using this EoS …
The equation of state (EoS) of hot and dense matter is a fundamental input to describe static and dynamical properties of neutron stars, core-collapse supernovae and binary compact-star mergers. We review the current status of the EoS for compact objects, that have been studied with both ab-initio many-body approaches and phenomenological models. We limit ourselves to the description of EoSs with purely nucleonic degrees of freedom, disregarding the appearance of strange baryonic matter and/or quark matter. We compare the theoretical predictions with different data coming from both nuclear phy…
Core-collapse simulations of massive stars are performed using the equation of state (EOS) based on the microscopic variational calculation with realistic nuclear forces. The progenitor models with the initial masses of $15M_\odot$, $9.6M_\odot$, and $30M_\odot$ are adopted as examples of the ordinary core-collapse supernova with a shock stall, the low-mass supernova with a successful explosion, and the black hole formation, respectively. Moreover, the neutrinos emitted from the stellar collapse are assessed. Then, the variational EOS is confirmed to work well in all cases. The EOS dependences…
The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of core-collapse supernovae and neutron star mergers. The properties of matter near and above nuclear saturation density are uncertain, which translates into uncertainties in astrophysical simulations and their multi-messenger signatures. Therefore, a wide range of EOSs spanning the allowed range of nuclear interactions are necessary for determining the sensitivity of these astrophysical phenomena and their signatures to variations in input microphysics. We present a new set of finite temperature E…
The formation of clusters in nuclear matter is investigated, which occurs e.g. in low energy heavy ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean field model. All three models contain bound states of nuclei with mass number A <= 4. It is explored to which extent the complex medium effects can be mimicked by the simpler exclud…
A quantitative knowledge of the nuclear Equation of State (EoS) requires an accurate estimation of the uncertainties on the EoS parameters and their mutual correlations. Such correlations are empirically observed in a large set of EoS models by different authors, but they are not always fully understood. We show that some of these correlations can be interpreted from basic physical constraints imposed on a simple Taylor expansion of the binding energy around saturation density. In particular, we investigate the correlations among the following empirical parameters: the symmetry energy $E_{sym}…
We show how observations of gravitational waves from binary neutron star (BNS) mergers over the next few years can be combined with insights from nuclear physics to obtain useful constraints on the equation of state (EoS) of dense matter, in particular, constraining the neutron-matter EoS to within 20% between one and two times the nuclear saturation density $n_0\approx 0.16\ {\text{fm}^{-3}}$. Using Fisher information methods, we combine observational constraints from simulated BNS merger events drawn from various population models with independent measurements of the neutron star radii expec…
The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. In this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a…
An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayer's condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so t…
Recent observations of neutron stars with gravitational waves and X-ray timing provide unprecedented access to the equation of state (EoS) of cold dense matter at densities difficult to realize in terrestrial experiments. At the same time, predictions for the EoS with reliable uncertainty estimates from chiral effective field theory ($χ$EFT) bound our theoretical ignorance. In this work, we analyze astrophysical data using a nonparametric representation of the neutron-star EoS conditioned on $χ$EFT to directly constrain the underlying physical properties of the compact objects. We discuss how …
Transition of a compact star into the third family for an equation of state (EoS) featuring mass twins is considered. The energy released at a baryon number conserving transition for static compact stars configurations is computed for two sets of models for comparison. The EoS of choice is the density dependent functional DD2 EoS with excluded model correction for hadronic matter which suffers a phase transition into deconfined quark matter described by a constant speed of sound approach. The two sets of EoS models feature different compact star mass onsets that maximize the energy and radius …
We present an updated and improved equation of state (which we call the NDL EoS) for use in neutron-star structure and supernova simulations. This EoS is based upon a framework originally developed by Bowers & Wilson, but there are numerous changes. Among them are: (1) a reformulation in the context of density functional theory; (2) the possibility of the formation of material with a net proton excess (Ye > 0.5); (3) an improved treatment of the nuclear statistical equilibrium and the transition to heavy nuclei as the density approaches nuclear matter density; (4) an improved treatment of the …
Neutron stars are compact objects of large interest in the nuclear astrophysics community. The extreme conditions present in such systems impose big challenges to our current microscopic models of nuclear structure. Equation of states (EoS) are frequently derived from sophisticated quantum mechanical models, such as: relativistic, non-relativistic and many mean-field approaches. Every single model, in general, contains many parameters such as the NN interaction strength, particle compositions, etc. These are particular features of each model and can be represented by numbers and categories in …
Gravitational waves (GWs) generated by axisymmetric rotating collapse, bounce, and early postbounce phases of a galactic core-collapse supernova will be detectable by current-generation gravitational wave observatories. Since these GWs are emitted from the quadrupole-deformed nuclear-density core, they may encode information on the uncertain nuclear equation of state (EOS). We examine the effects of the nuclear EOS on GWs from rotating core collapse and carry out 1824 axisymmetric general-relativistic hydrodynamic simulations that cover a parameter space of 98 different rotation profiles and 1…
The observations of optical and near-infrared counterparts of binary neutron star mergers not only enrich our knowledge about the abundance of heavy elements in the Universe, or help reveal the remnant object just after the merger as generally known, but also can effectively constrain dense nuclear matter properties and the equation of state (EOS) in the interior of the merging stars. Following the relativistic mean-field description of nuclear matter, we perform the Bayesian inference of the EOS and the nuclear matter properties using the first multi-messenger event GW170817/AT2017gfo, togeth…
Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $\pm 15\%$ between 1.4 M$_{\odot}$ and 2.0 M$_{\odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases …
We explore constraints on the equation of state (EOS) of neutron-rich matter based on microscopic calculations up to nuclear densities and observations of neutron stars. In a previous work we showed that predictions based on modern nuclear interactions derived within chiral effective field theory and the observation of two-solar-mass neutron stars result in a robust uncertainty range for neutron star radii and the EOS over a wide range of densities. In this work we extend this study, employing both the piecewise polytrope extension from Hebeler et al. as well as the speed of sound model of Gre…
We investigate the fundamental mode of non-radial oscillations of non-rotating compact stars in general relativity using a set of equations of state (EOS) connecting state-of-the-art calculations at low and high densities. Specifically, a low density model based on the chiral effective field theory (EFT) and high density results based on perturbative Quantum Chromodynamics (QCD) are matched through different interpolating polytropes fulfilling thermodynamic stability and subluminality of the speed of sound, together with the additional requirement that the equations of state support a two sola…
