arXiv subjects

Nai-Bo Zhang

Publications and source records attributed to Nai-Bo Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Inference of fine-features of dense matter EOS from future high-precision data of neutron star radii

Future high-precision X-ray and gravitational wave observatories are expected to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects of the Equation of State (EOS) and to what precision they will be better constrained. Within a Bayesian framework using a meta-model EOS and mock high-precision NS data, the posterior probability distribution functions (PDFs) of NS matter EOS parameters for both hadronic and quark phases and the transition between them were recently studied. We report here a few highlights of these studies.

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arXiv2026

Bayesian Inference of Hybrid Star Properties from Future High-Precision Measurements of Their Radii

Future high-precision X-ray and gravitational-wave observations of neutron stars (NSs) are expected to constrain NS radii with uncertainties as small as $σ\simeq 0.1$~km. Such unprecedented precision offers a unique opportunity to extract new information about the nature and equation of state (EOS) of supradense matter in NS cores. Using mock radius data with uncertainties ranging from $σ= 1.0$ to $0.1$~km, together with a flexible meta-model NS EOS that allows for a first-order hadron-quark phase transition, we perform a Bayesian statistical analysis to assess the impact of radius measurements on EOS constraints. We find that high-precision radius measurements, particularly for massive NSs, significantly tighten constraints on the hadron-quark transition density $ρ_t$, the quark matter mass fraction in NS cores, and several parameters characterizing the EOS of supranuclear hadronic matter, although the degree of improvement depends on the assumed prior range of $ρ_t$. In contrast, even with the highest precision considered, NS radii -- including those of massive stars -- remain largely insensitive to the stiffness of quark matter, independent of the measurement accuracy or the prior range adopted for $ρ_t$.

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arXiv2025

Illuminating dark matter admixed in neutron stars with simultaneous mass-radius constraints

We investigate how simultaneous mass and radius measurements of massive neutron stars (NSs) can help constrain properties of dark matter (DM) possibly admixed in them. Within a fermionic DM model that interacts only through gravitation, along with a well-constrained nuclear matter equation of state, we show that the simultaneous mass and radius measurement of PSRJ0740+6620 reduces the uncertainty of DM central energy density by more than 50\% compared to the results obtained from using the two observables independently, while other DM parameters remain unconstrained. Additionally, we find that the DM fraction $f_D$ should be smaller than 2\% when constrained by the observed NS maximum mass alone, and it could be even smaller than 0.3\% with the simultaneous measurement of mass and radius, supporting the conclusion that only a small amount of DM exists in DM admixed neutron stars (DANS).

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arXiv2025

Imprints of high-density nuclear symmetry energy on the crustal fraction of neutron star moment of inertia

The density dependence of nuclear symmetry energy $E_{\rm sym}(ρ)$ remains the most uncertain aspect of the equation of state (EOS) of supradense neutron-rich nucleonic matter. Implications of observational crustal fraction of neutron star (NS) moment of inertia $ΔI/I$ on the $E_{\rm sym}(ρ)$ are examined in the present work, utilizing an isospin-dependent parameterization of NS EOS. We find that symmetry energy parameters significantly influence the $ΔI/I$, while the EOS of symmetric nuclear matter has a negligible effect. An increase in the slope $L$ and skewness $J_{\rm sym}$ of symmetry energy results in a larger $ΔI/I$, whereas an increase in the curvature $K_{\rm sym}$ leads to a reduction in $ΔI/I$. Additionally, we discuss the imprints of observational $ΔI/I$ on the symmetry energy for NSs with masses of 1.0 M$_\odot$ or 1.4 M$_\odot$. Our results indicate that the $ΔI/I$ has the potential to set a lower limit of symmetry energy at densities exceeding $3ρ_0$, particularly when $L$ is constrained to values less than $60$ MeV, thereby enhancing our understanding of supradense NS matter.

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arXiv2025

Impact of the nuclear equation of state on the formation of twin stars

Twin stars-two stable neutron stars (NSs) with the same mass but different radii have long been proposed to appear as a consequence of a possible first-order phase transition in NS matter. Within a meta-model for the EOS of hybrid stars, we revisit the viability of twin stars and its dependence on numerous parameters characterizing the EOS of nuclear matter, quark matter, and the phase transition between them. While essentially no experimental constraint exists for the last two, parameters characterizing the EOS of neutron-rich nucleonic matter have been constrained within various ranges by terrestrial experiments and astrophysical observations. Within these ranges, the impact of nuclear EOS and crust-core transition density on the formation of twin stars is studied. It is found that the symmetry energy of neutron-rich nucleonic matter notably influences the formation of twin stars, particularly through its slope $L$ and curvature $K_{\rm sym}$. Conversely, varying the EOS of symmetric nuclear matter within their currently known uncertainty ranges shows minimal influence on the formation of twin stars.

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arXiv2024

Bayesian Inference of Fine-Features of Nuclear Equation of State from Future Neutron Star Radius Measurements to 0.1km Accuracy

To more precisely constrain the Equation of State (EOS) of supradense neutron-rich nuclear matter, future high-precision X-ray and gravitational wave observatories are proposed to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects (other than the stiffness generally spoken of in the literature) of the EOS and to what precision they will be better constrained. In this work, within a Bayesian framework using a meta-model EOS for NSs, we infer the posterior probability distribution functions (PDFs) of incompressibility $K_{0}$ and skewness $J_{0}$ of symmetric nuclear matter (SNM) as well as the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ characterizing the density dependence of nuclear symmetry energy $E_{\rm{sym}}(ρ)$, respectively, from mean values of NS radii consistent with existing observations and an expected accuracy $ΔR$ ranging from about 1.0 km to 0.1 km. We found that (1) the $ΔR$ has little effect on inferring the stiffness of SNM at suprasaturation densities, (2) smaller $ΔR$ reveals more accurately not only the PDFs but also pairwise correlations among parameters characterizing high-density $E_{\rm{sym}}(ρ)$, (3) a double-peak feature of the PDF($K_{\rm{sym}}$) corresponding to the strong $K_{\rm{sym}}-J_{\rm{sym}}$ and $K_{\rm{sym}}-L$ anti-correlations is revealed when $ΔR$ is less than about 0.2 km, and the locations of the two peaks are sensitive to the maximum value of $J_{\rm{sym}}$ reflecting the stiffness of $E_{\rm{sym}}(ρ)$ above about 3 times the saturation density $ρ_0$ of SNM, (4) the high-precision radius measurement for canonical NSs is more useful than that for massive ones for constraining the EOS of nucleonic matter around $(2-3)ρ_0$.

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arXiv2024

Impact of The Newly Revised Gravitational Redshift of X-ray Burster GS 1826-24 on The Equation of State of Supradense Neutron-Rich Matter

Thanks to the recent advancement in producing rare isotopes and measuring their masses with unprecedented precision, the updated nuclear masses around the waiting-point nucleus $^{64}$Ge in the rapid-proton capture process have led to a significant revision of the surface gravitational redshift of the neutron star (NS) in GS 1826-24 by re-fitting its X-ray burst light curve ({\it X. Zhou et al., Nature Physics {\bf 19}, 1091 (2023)}) using Modules for Experiments in Stellar Astrophysics (MESA). The resulting NS compactness $ξ$ is between 0.244 and 0.342 at 95\% confidence level and its upper boundary is significantly smaller than the maximum $ξ$ previously known. Incorporating this new data within a comprehensive Bayesian statistical framework, we investigate its impact on the Equation of State (EOS) of supradense neutron-rich matter and the required spin frequency for GW190814's minor $m_2$ with mass $2.59\pm 0.05$M$_{\odot}$ to be a rotationally stable pulsar. We found that the EOS of high-density symmetric nuclear matter (SNM) has to be softened significantly while the symmetry energy at supersaturation densities stiffened compared to our prior knowledge from earlier analyses using data from both astrophysical observations and terrestrial nuclear experiments. In particular, the skewness $J_0$ characterizing the stiffness of high-density SNM decreases significantly, while the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ of nuclear symmetry energy all increase appreciably compared to their fiducial values. We also found that the most probable spin rate for the $m_2$ to be a stable pulsar is very close to its mass-shedding limit once the revised redshift data from GS 1826-24 is considered, making the $m_2$ unlikely the most massive NS observed so far.

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arXiv2023

Properties of First-Order Hadron-Quark Phase Transition from Inverting Neutron Star Observables

By inverting the observational data of several neutron star observables in the three dimensional parameter space of the constant speed of sound (CSS) model while fixing all hadronic Equation of State parameters at their currently known most probable values, we constrain the three parameters of the CSS model and their correlations. Using two lower radius limits of $R_{2.01}=11.41$ km and $R_{2.01}=12.2$ km for PSR J0740+6620 obtained from two independent analyses using different approaches by the Neutron Star Interior Composition Explorer (NICER) Collaboration, the speed of sound squared $c_{\rm QM}^2$ in quark matter is found to have a lower limit of $0.35$ and $0.43$ in unit of $c^2$, respectively, above its conformal limit of $c_{\rm QM}^2<1/3$. An approximately linear correlation between the first-order hadron-quark transition density $ρ_t$ and its strength $Δ\varepsilon$ is found. Moreover, the presence of twin star is deemed improbable by the present work.

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arXiv2023

Impact of Symmetry Energy on Sound Speed and Spinodal Decomposition in Dense Neutron-Rich Matter

Using a meta model for nuclear Equation of State (EOS) with its parameters constrained by astrophysical observations and terrestrial nuclear experiments, we examine effects of nuclear EOS especially its symmetry energy \esym term on the speed of sound squared $C^2_s(ρ)$ and the critical density $ρ_t$ where $C^2_s(ρ_t)$ vanishes (indicating the onset of spinodal decomposition) in both dense neutron-rich nucleonic matter relevant for relativistic heavy-ion collisions and the cold $n+p+e+μ$ matter in neutron stars at $β$-equilibrium. Unlike in nucleonic matter with fixed values of the isospin asymmetry $δ$, in neutron stars with a density dependent isospin profile $δ(ρ)$ determined consistently by the $β$ equilibrium and charge neutrality conditions, the $C^2_s(ρ)$ almost always show a peak and then vanishes at $ρ_t$. The latter strongly depends on the high-density behavior of \esym if the skewness parameter $J_0$ characterizing the stiffness of high-density symmetric nuclear matter (SNM) EOS is not too far above its currently known most probable value of about $-190$ MeV inferred from recent Bayesian analyses of neutron star observables. Moreover, in the case of having a super-soft \esym that is decreasing with increasing density above about twice the saturation density of nuclear matter, the $ρ_t$ is significantly lower than the density where the \esym vanishes (indicating the onset of isospin-separation instability and pure neutron matter formation) in neutron star cores.

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arXiv2022

A theoretical overview of isospin and EOS effects in heavy-ion reactions at intermediate energies

The isospin dependence of in-medium nuclear effective interactions is a fundamental issue in nuclear physics and has broad ramifications in astrophysics. Its uncertainties, especially the difference of neutron-proton interactions in the isosinglet and isotriplet channels, affect significantly the density and momentum dependence of the isovector single-nucleon potential and nucleon-nucleon short-range correlation in neutron-rich matter. Consequently, the neutron-proton effective mass splitting and the density dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion reactions especially those involving rare isotopes is a useful tool for probing the isospin dependence of nuclear effective interactions through (1) the neutron-skin in coordinate and proton-skin in momentum of the initial state of colliding nuclei, (2) the density and momentum dependence of especially the isovector nuclear mean-field as well as (3) the isospin dependence of in-medium nucleon-nucleon cross sections. Observations of neutron stars especially since GW1710817 have also helped us significantly in understanding the isospin dependence of nuclear effective interactions. {\it We summarize here a review talk on these issues given at the 2021 International Workshop on multi-facets of EOS and Clustering. For details we refer the readers to the original publications and references therein}.

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arXiv2021

Impact of NICER's Radius Measurement of PSR J0740+6620 on Nuclear Symmetry Energy at Suprasaturation Densities

By directly inverting several neutron star observables in the three-dimensional parameter space for the Equation of State of super-dense neutron-rich nuclear matter, we show that the lower radius limit for PSR J0740+6620 of mass $2.08\pm 0.07~M_{\odot}$ from Neutron Star Interior Composition Explorer (NICER)'s very recent observation sets a much tighter lower boundary than previously known for nuclear symmetry energy in the density range of $(1.0\sim 3.0)$ times the saturation density $ρ_0$ of nuclear matter. The super-soft symmetry energy leading to the formation of proton polarons in this density region of neutron stars is clearly disfavoured by the first radius measurement for the most massive neutron star observed reliably so far.

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arXiv2021

Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817

New observational data of neutron stars since GW170817 have helped improve our knowledge about nuclear symmetry energy especially at high densities. We have learned particularly: (1) The slope parameter $L$ of nuclear symmetry energy at saturation density $ρ_0$ of nuclear matter from 24 new analyses is about $L\approx 57.7\pm 19$ MeV at 68\% confidence level consistent with its fiducial value, (2) The curvature $K_{\rm{sym}}$ from 16 new analyses is about $K_{\rm{sym}}\approx -107\pm 88$ MeV, (3) The magnitude of nuclear symmetry energy at $2ρ_0$, i.e. $E_{\rm{sym}}(2ρ_0)\approx 51\pm 13$ MeV at 68\% confidence level, has been extracted from 9 new analyses of neutron star observables consistent with results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories, (4) while the available data from canonical neutron stars do not provide tight constraints on nuclear symmetry energy at densities above about $2ρ_0$, the lower radius boundary $R_{2.01}=12.2$ km from NICER's very recent observation of PSR J0740+6620 of mass $2.08\pm 0.07$ $M_{\odot}$ and radius $R=12.2-16.3$ km at 68\% confidence level sets a tight lower limit for nuclear symmetry energy at densities above $2ρ_0$, (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars indicate that the phase transition shift appreciably both the $L$ and $K_{\rm{sym}}$ to higher values but with larger uncertaintie , (6) The high-density behavior of nuclear symmetry energy affects significantly the minimum frequency necessary to rotationally support GW190814's secondary component of mass (2.50-2.67) $M_{\odot}$ as the fastest and most massive pulsar discovered so far.

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arXiv2020

GW190814's secondary component with mass $(2.50-2.67)$ M$_{\odot}$ as a super-fast pulsar

Using Stergioulas's RNS code for investigating fast pulsars with Equation of States (EOSs) on the causality surface (where the speed of sound equals that of light) of the high-density EOS parameter space satisfying all known constraints from both nuclear physics and astrophysics, we show that one possible explanation for the GW190814's secondary component of mass $(2.50-2.67)$ M$_{\odot}$ is that it is a super-fast pulsar spinning faster than 971 Hz about 42\% below its Kepler frequency. If confirmed, it would be the fastest pulsar with the highest mass observed presently. There is a large and physically allowed EOS parameter space below the causality surface where pulsars heavier than 2.50 M$_{\odot}$ are supported if they can rotate even faster with critical frequencies depending strongly on the high-density behavior of nuclear symmetry energy.

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arXiv2020

Constraints on the muon fraction and density profile in neutron stars

Muons in neutron stars (NSs) play especially important roles in addressing several interesting new physics questions associated with detecting as well as understanding interactions and astrophysical effects of muonphilic dark matter particles. The key model inputs for studying the latter are the total muon mass $M_μ$, the muon mass fraction $M_μ/M_{\rm NS}$ over the NS mass $M_{\rm NS}$ and the muon radial density profile $ρ_μ(r)$ in NSs of varying masses. We investigate these quantities within a minimum model for the core of NSs consisting of neutrons, protons, electrons, and muons using an explicitly isospin-dependent parametric Equation of State (EOS) constrained by available nuclear laboratory experiments and the latest astrophysical observations of NS masses, radii and tidal deformabilities. We found that the absolutely maximum muon mass $M_μ$ and its mass fraction $M_μ/M_{\rm NS}$ in the most massive NSs allowed by causality are about 0.025 $M_\odot$ and 1.1\%, respectively. For the most massive NS of mass 2.14 $M_\odot$ observed so far, they reduce to about 0.020 $M_\odot$ and 0.9\%, respectively. We also study respective effects of individual parameters describing the EOS of high-density neutron-rich nucleonic matter on the muon contents in NSs with varying masses. We found that the most important but uncertain nuclear physics ingredient for determining the muon contents in NSs is the high-density nuclear symmetry energy.

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arXiv2019

The key factor to determine the relation between radius and tidal deformability of neutron stars: slope of symmetry energy

The constraints on tidal deformability $Λ$ of neutron stars are first extracted from GW170817 by LIGO and Virgo Collaborations but the relation between radius $R$ and tidal deformability $Λ$ is still nuder debate. Using an isospin-dependent parameterized equation of state (EOS), we study the relation between $R$ and $Λ$ of neutron stars and its dependence on parameters of symmetry energy $E_{\rm sym}$ and EOS of symmetric nuclear matter $E_0$ when the mass is fixed as $1.4$ $M_\odot$, $1.0$ $M_\odot$, and $1.8$ $M_\odot$, respectively. We find that, though the changes of high order parameters of $E_{\rm sym}$ and $E_0$ can shift the individual values of $R_{1.4}$ and $Λ_{1.4}$ to different values, the $R_{1.4}\simΛ_{1.4}$ relation approximately locates at the same fitted curve. The slope of symmetry energy $L$ plays the dominated role in determining the $R_{1.4}\simΛ_{1.4}$ relation. By checking the mass dependence of $R\simΛ$ relation, the well fitted $R\simΛ$ relation for 1.4 $M_\odot$ is broken for massive neutron stars.

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arXiv2019

Towards Understanding Astrophysical Effects of Nuclear Symmetry Energy

Determining the Equation of State (EOS) of dense neutron-rich nuclear matter is a shared goal of both nuclear physics and astrophysics. Except possible phase transitions, the density dependence of nuclear symmetry \esym is the most uncertain part of the EOS of neutron-rich nucleonic matter especially at supra-saturation densities. Much progresses have been made in recent years in predicting the symmetry energy and understanding why it is still very uncertain using various microscopic nuclear many-body theories and phenomenological models. Simultaneously, significant progresses have also been made in probing the symmetry energy in both terrestrial nuclear laboratories and astrophysical observatories. In light of the GW170817 event as well as ongoing or planned nuclear experiments and astrophysical observations probing the EOS of dense neutron-rich matter, we review recent progresses and identify new challenges to the best knowledge we have on several selected topics critical for understanding astrophysical effects of the nuclear symmetry energy.

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arXiv2019

Implications of the mass $M=2.17^{+0.11}_{-0.10}$M$_\odot$ of PSR~J0740+6620 on the Equation of State of Super-Dense Neutron-Rich Nuclear Matter

We study implications of the very recently reported mass $M=2.17^{+0.11}_{-0.10}$M$_\odot$ of PSR~J0740+6620 on the Equation of State (EOS) of super-dense neutron-rich nuclear matter with respect to existing constraints on the EOS based on the mass $M=2.01\pm 0.04$M$_\odot$ of PSR~J0348+0432, the maximum tidal deformability of GW170817 and earlier results of various terrestrial nuclear laboratory experiments. The lower limit of the skewness $J_0$ measuring the stiffness of super-dense isospin-symmetric nuclear matter is raised raised from about -220 MeV to -150 MeV, reducing significantly its current uncertainty range. The lower bound of the high-density symmetry energy also increases appreciably leading to a rise of the minimum proton fraction in neutron stars at $β$-equilibrium from about 0 to 5\% around three times the saturation density of nuclear matter. The difficulties for some of the most widely used and previously well tested model EOSs to predict simultaneously both a maximum mass higher than 2.17 M$_\odot$ and a pressure consistent with that extracted from GW170817 present some interesting new challenges for nuclear theories.

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arXiv2019

Relation between gravitational mass and baryonic mass for non-rotating and rapidly rotating neutron stars

With a selected sample of neutron star (NS) equation-of-states (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass $M_g$ and baryonic mass $M_b$, and the relations between the maximum NS mass supported through uniform rotation ($M_{\rm max}$) and that of nonrotating NSs ($M_{\rm TOV}$). We find that if one intends to apply an EOS-independent quadratic, universal transformation formula ($M_b=M_g+A\times M_{g}^2$) to all EOSs, the best fit $A$ value is 0.080 for non-rotating NSs only and 0.073 when different spin periods are considered. The residual error of the transformation is as large as $\sim0.1M_{\odot}$. For different EOSs, we find that the parameter $A$ for non-rotating NSs is proportional to $R_{1.4}^{-1}$ (where $R_{1.4}$ is NS radius for 1.4$M_\odot$ in unit of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01$M_\odot$ for the quadratic form and less than 0.01$M_\odot$ for the cubic form ($M_b=M_g+A_1\times M_{g}^2+A_2\times M_{g}^3$). We also find a very tight and general correlation between the normalized mass gain due to spin $Δm\equiv(M_{\rm max}-M_{\rm TOV})/M_{\rm TOV}$ and the spin period normalized to the Keplerian period ${\cal P}$, i.e. ${\rm log_{10}}Δm = (-2.74\pm0.05){\rm log_{10}}{\cal P}+{\rm log_{10}}(0.20\pm 0.01)$, which is independent of EOS models. Applications of our results to GW170817 is discussed.

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