arXiv subjects

Bao-An Li

Publications and source records attributed to Bao-An Li.

At least 19 recordsLinked to original sources

arXiv2026

Spin transport in intermediate-energy heavy-ion collisions

In this mini-review, we provide a brief status report on investigating spin transport phenomena in intermediate-energy heavy-ion collisions by simulating solutions of the spin- and isospin-dependent Boltzmann-Uehling-Uhlenbeck (SIBUU) transport equation using the test-particle method. We outline the physics foundation and technical approach, summarize our main results and identify key challenges in further studying spin transport within the SIBUU framework. As examples, we show how the global and local spin polarizations of nucleons, the spin splitting of nucleon collective flows as well as flows of light clusters at different spin states can be used to explore interesting new physics associated with the nuclear spin-orbit potential in dense neutron-rich medium. The spin-orbit potential and the rigorous angular momentum conservation are also shown to affect spin-averaged observables. Hopefully the new findings and challenges identified here will stimulate further studies both theoretically and experimentally on spin transport in intermediate-energy heavy-ion collisions.

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arXiv2026

Symbolic Regression for Interpretable Emulation of Proton Collective Flow in Intermediate-Energy Heavy-Ion Collisions

Symbolic regression provides an interpretable machine-learning approach for constructing explicit analytic relations between physical inputs and observables. In this work, we develop symbolic-regression emulators for the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model and compare their performance with deep neural network (DNN) emulators. Using the same transport-model data employed in our previous emulator studies, we show that symbolic regression can reproduce the proton mid-rapidity slope $F_1$ of transverse flow $v_1$ and elliptic flow $v_2$ with accuracy comparable to that of DNNs, while providing explicit analytic expressions and substantially faster prediction once trained. We further demonstrate the use of symbolic regression in the reverse direction by constructing analytic relations that predict the in-medium nucleon-nucleon cross-section modification factor $X$ from the flow observables. Although the symbolic-regression models require substantially longer training times and exhibit greater run-to-run variation than DNNs, their analytic form and rapid evaluation make them promising tools for future transport-model sensitivity and uncertainty analyses.

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arXiv2026

How Neutron Star Radii Encode the Dense-Matter Equation of State and Hadron-Quark Transition

We investigate how future high-precision neutron star (NS) radius measurements encode microscopic information about the dense-matter equation of state (EOS), focusing on a possible first-order hadron--quark phase transition and the resulting mass--radius topology. Within a Bayesian framework using meta-model EOSs with nine microscopic parameters, we analyze mock radius measurements $R_{1.4}=11.9\pm\sigma_R$ km with $\sigma_R=0.9$ and $0.1$ km for canonical NSs. We introduce inverse EOS--radius mappings that give the posterior mean of each EOS parameter as a function of $R_{1.4}$. Their slope measures radius sensitivity, while their curvature determines the leading precision dependence of the posterior mean through the Jensen expansion. Resolving the mappings into four mass--radius topologies, Connected, Disconnected, Both, and No-Quark-Matter, reveals a clear hierarchy of information. The symmetry-energy parameters $L$ (slope) and $K_{\rm sym}$ (curvature) are strongly encoded in $R_{1.4}$ and their posterior means shift appreciably with improved radius precision, whereas the higher-order hadronic parameters show stronger topology dependence. Among the transition parameters, the transition density $\rho_t$ is the most strongly encoded in $R_{1.4}$, while the energy-density jump and quark-matter sound speed are more strongly associated with the topology of the full mass--radius sequence. Since the different topologies have strongly overlapping $R_{1.4}$ distributions, even precise radius measurements cannot by themselves identify the topology or uniquely determine the high-density transition properties. These results provide a parameter-dependent hierarchy for assessing the scientific return of future high-precision radius measurements and complementary probes of high-density

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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

Quantifying the Information Gain from Future High-Precision Radius Measurements for Identifying Twin Neutron Stars

Twin neutron stars (NSs), characterized by identical gravitational masses but different radii, are among the most promising astrophysical signatures of a strong first-order hadron--quark phase transition in supradense matter. We investigate how increasingly precise NS radius measurements improve the Bayesian inference of twin-star observability using mock radius data for a canonical $1.4\,M_\odot$ NS. Radius uncertainties are varied from the current level of about $0.9$ km to the $\approx 0.1$ km precision anticipated from future X-ray and gravitational-wave observations. We quantify the information gained using the posterior distribution of the maximum twin-star radius separation $\Delta R$ together with an analytical model of branch distinguishability and complementary information-theoretic measures based on the branch observational efficiency and the Shannon entropy. The combined analyses reveal three inference regimes: a prior-dominated regime for $\sigma_R \gtrsim 0.6$ km, a rapid information-gain regime for $0.2 \lesssim \sigma_R \lesssim 0.6$ km, and an information-saturation regime for $\sigma_R \lesssim 0.2$ km. These complementary analyses consistently indicate that radius measurements with a precision of about $0.2$ km already extract most of the information available for identifying twin NSs within the present Bayesian framework. Beyond establishing a quantitative observational benchmark for future high-precision radius measurements, this work provides a general Bayesian framework for quantifying the information gain from progressively more precise observations and identifying the point of diminishing scientific returns.

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arXiv2026

Universal EOS-Radius Inverse Mappings Govern Precision-Dependent Inference of the Neutron Star Equation of State

Bayesian inference of the neutron star (NS) equation of state (EOS) generally assumes that improved observations primarily reduce posterior uncertainties while leaving inferred EOS parameters unchanged. Using mock measurements of the radius of a canonical $1.4\,M_\odot$ NS with identical central values but varying observational precisions, we show that the inferred posterior means of EOS parameters can shift systematically as the measurement uncertainty changes. We demonstrate that this behavior originates from previously unidentified nearly universal inverse mappings between the NS radius $R_{1.4}$ and empirical EOS parameters. Across a broad range of observational precisions, posterior samples collapse onto nearly unique functions. These mappings are largely independent of observational precision and define a low-dimensional EOS manifold underlying Bayesian inference. We show that the precision dependence of inferred EOS parameters arises from nonlinear filtering of the posterior radius distribution through these mappings. In the narrow-distribution limit this effect reduces to a Jensen-type correction proportional to the local curvature of the inverse mapping, while for presently realistic uncertainties the full nonlinear-filtering relation accurately reproduces the posterior means. Our results reveal a geometric origin of precision-dependent inference in NS EOS studies and provide a new framework for connecting astrophysical observations directly to microscopic nuclear many-body theories.

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arXiv2026

A New Scaling of Neutron Star Tidal Deformability for Directly Probing the Core Equation of State

The dimensionless tidal deformability, $\Lambda$, of neutron stars (NSs), inferred from gravitational-wave (GW) observations, has thus far been used primarily to constrain the pressure of dense matter near twice nuclear saturation density, leaving the core equation of state (EOS) largely inaccessible to inspiral-phase GW observations. We show that the core EOS can be probed directly through $\Lambda$ using a perturbative analysis of the dimensionless stellar-structure and tidal-response equations formulated in terms of scaled intrinsic variables, without invoking any specific EOS model. We uncover a remarkable EOS-insensitive scaling relation between $\Lambda$ and the central EOS parameter $\mathrm{X}\equiv P_{\rm c}/\varepsilon_{\rm c}$, where $P_{\rm c}$ and $\varepsilon_{\rm c}$ denote the central pressure and energy density, respectively. The relation is validated against a broad ensemble of physically viable EOSs. Applying it to tidal deformabilities inferred from events such as GW170817 enables a direct determination of $\mathrm{X}$. We further derive a tight lower bound, $\Lambda_{\rm{TOV}}\gtrsim 9.2^{+1.2}_{-1.2}$, for maximum-mass NSs along stable mass-radius sequences, quantitatively demonstrating that even the most compact stable NSs remain distinctly separated from black holes, for which $\Lambda_{\rm{BH}}=0$. These findings reveal a previously unrecognized connection between inspiral-phase tidal deformability and the core EOS, establishing a direct link between GW observables and the microphysics of ultradense matter in the strong-gravity regime. The resulting scaling establishes inspiral-phase tidal deformability as a direct and largely model-insensitive probe of the EOS of NS cores.

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arXiv2026

Bayesian Constraints on the Neutron Star Equation of State with a Smooth Hadron-Quark Crossover

We perform a Bayesian inference of the dense-matter equation of state (EOS) within a unified framework that incorporates hadronic matter, quark matter, and a smooth hadron-to-quark crossover. The EOS is constrained using physical consistency conditions, gravitational wave data from GW170817, NICER mass versus radius measurements, and hypothetical future high-precision radius observations. In contrast to most previous studies that assume a sharp first-order phase transition or fix part of the EOS, we simultaneously infer hadronic, quark, and crossover parameters within a single statistical framework. We find that current observations strongly constrain the density dependence of the nuclear symmetry energy, particularly its slope and curvature. In contrast, the highest density hadronic parameters and quark-matter properties remain only weakly constrained. We further show that the trace anomaly exhibits a remarkably universal behavior across the accepted EOS ensemble and remains largely insensitive to current observational constraints. This indicates that the present data primarily probe the low to intermediate density EOS. At the same time, robust inference of quark matter and genuinely high-density physics will require next-generation precision radius measurements or complementary observables.

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arXiv2026

Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter

Nucleon short-range correlations (SRCs) and their high-momentum tails (HMTs) encode key short-range dynamics in nuclei and dense matter. This review provides a concise overview of SRC features relevant to the Equation of State (EOS) of isospin-asymmetric nuclear matter. We summarize empirical and theoretical properties of the single-nucleon momentum distribution $n(k)$, emphasizing the role of the neutron--proton tensor force, the dominance of correlated np pairs, and the enhancement of minority-species HMTs. Links to nucleon effective E-masses, quasi-deuteron components, and orbital entanglement are briefly noted. We examine how SRC-induced HMTs modify kinetic and potential contributions to the EOS in both non-relativistic and relativistic frameworks, including the softening of the kinetic symmetry energy and departures from the isospin parabolic approximation of asymmetric nuclear EOS. Sensitivity to high-momentum components and generalizations to arbitrary dimensions are also highlighted. Implications for heavy-ion reactions are summarized, including effects on particle yields, collective flows, deeply sub-threshold particle production and hard photon emission, driven by modified initial nucleon momentum distributions and abundant high relative-momentum np pairs during the reaction. Finally, we outline SRC-HMT consequences for neutron-star matter, covering proton fractions, tidal deformabilities, $Z$-factors, cooling, and the core--crust transition, as well as possible connections to dark-matter interactions in dense environments.

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arXiv2026

Trace Anomaly of Cold Dense Matter Constrained by Collective Flow

The trace anomaly of dense matter, $\Delta \equiv 1/3 - P/\varepsilon$, defined through the ratio $w \equiv P/\varepsilon$ of pressure $P$ to energy density $\varepsilon$, quantifies deviations from conformal symmetry and provides a dimensionless measure of the stiffness of the equation of state (EOS) relevant for both neutron stars and heavy-ion collisions. While $\Delta(\varepsilon)$ has recently been inferred from neutron star observations, we report the first Bayesian extraction of the trace anomaly from collective flow observables in intermediate-energy heavy-ion collisions. By employing transport-model simulations that explicitly decouple the cold matter mean-field potential from thermal effects, we directly constrain the EOS of cold dense matter. Remarkably, the trace anomaly inferred from laboratory flow data agrees quantitatively, within $68\%$ credible intervals, with independent astrophysical posterior bands. This nontrivial agreement demonstrates that heavy-ion collisions and neutron star observations probe the same macroscopic properties in a mutually consistent way, establishing the dense-matter trace anomaly as a composition-insensitive macroscopic bridge observable across widely different physical environments.

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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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arXiv2026

An Effective Upper Bound on the Pressure-to-Energy Density Ratio in Neutron Stars

The equation-of-state (EOS) parameter $\phi \equiv P/\varepsilon$, defined as the ratio of pressure to energy density, encapsulates the fundamental response of matter under extreme compression. Its value at the center of the most massive neutron star (NS), $\x \equiv P_{\rm c}/\varepsilon_{\rm c}$, provides an upper bound on the maximum attainable central EOS parameter of cold visible matter. Remarkably, owing to the intrinsically nonlinear structure of the EOS in General Relativity (GR), this bound lies far below the naive Special Relativity (SR) limit of unity. In this work, we refine the theoretical upper bound on $\x$ in a self-consistent manner by incorporating, in addition to the causality constraint from SR, the mass-sphere stability condition associated with the mass evolution pattern in the vicinity of the NS center. This condition is formulated within the intrinsic and perturbative analysis of the dimensionless Tolman--Oppenheimer--Volkoff equations (IPAD-TOV) framework. The combined constraints yield an improved bound, $\x \lesssim 0.385$, which is slightly above but fully consistent with the previously derived causal-only limit, $\x \lesssim 0.374$. We further derive an improved scaling relation for NS compactness and demonstrate its robustness across a broad set of 284 realistic EOSs, including models with first-order phase transitions, exotic degrees of freedom, continuous crossover behavior, and deconfined quark cores. Within the IPAD-TOV framework, the resulting bound on $\x$ provides a new EOS-insensitive probe of the microphysics of cold superdense matter compressed by strong-field gravity in GR.

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arXiv2026

Beyond $ρ^{2/3}$ Scaling: Microscopic Origins and Multimessengers of High-Density Nuclear Symmetry Energy

Nuclear symmetry energy $E_{\mathrm{sym}}(ρ)$ encoding the cost to make nuclear matter more neutron rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It affects significantly the radii, tidal deformations, cooling rates and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\mathrm{sym}}(ρ)$ scales as $(ρ/ρ_0)^{2/3}$ near the saturation density $ρ_0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density dependent. After examining many empirical evidences and understanding theoretical findings in the literature we conclude that: (1) Siemens' $ρ^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2ρ_0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\mathrm{sym}}(ρ)$ up to $2ρ_0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\mathrm{sym}}$ and higher-order parameters, (3) Above $2ρ_0$, uncertainties grow due to poorly constrained spin-isospin dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining multimessengers from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining precisely the high-density $E_{\mathrm{sym}}(ρ)$ and the EOS of supradense neutron-rich matter.

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arXiv2025

Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues

Nucleon short-range correlations (SRCs) and the associated high-momentum tail (HMT) in its momentum distribution $n(k)$ represent a universal feature of strongly interacting Fermi systems. In nuclear matter, SRCs arise primarily from the spin-isospin dependence of the tensor and short-range components of the nucleon-nucleon interaction, leading to a substantial depletion of its Fermi sea and a characteristic $k^{-4}$ tail populated predominantly by isosinglet neutron-proton pairs. These microscopic structures modify both the kinetic and interaction contributions to the Equation of State (EOS) of dense matter and thereby influence a broad range of neutron-star (NS) properties. This short review provides a streamlined overview of how SRC-induced changes in $n(k)$ reshape the kinetic EOS, including its symmetry energy part and how these effects propagate into macroscopic NS observables, including mass-radius relations, tidal deformabilities, direct Urca thresholds and core-crust transition. We summarize key existing results, highlight current observational constraints relevant for testing SRC-HMT effects, and outline open questions for future theoretical, experimental, and multimessenger studies of dense nucleonic matter.

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arXiv2025

Is The Trace Anomaly at its Minimum Value at Neutron Star Centers?

While the equation of state (EOS) $P(\varepsilon)$ of neutron star (NS) matter has been extensively studied, the EOS-parameter $ϕ= P/\varepsilon$ or equivalently the dimensionless trace anomaly $Δ= 1/3 - ϕ$, which quantifies the balance between pressure $P$ and energy density $\varepsilon$, remains far less explored, especially in NS cores. Its bounds and density profile carry crucial information about the nature of superdense matter. Physically, the EOS-parameter $ϕ$ represents the mean stiffness of matter accumulated from the stellar surface up to a given density. Based on the intrinsic structure of the Tolman--Oppenheimer--Volkoff equations, we show that $ϕ$ decreases monotonically outward from the NS center, independent of any specific input NS EOS model. Furthermore, observational evidence of a peak in the speed-of-sound squared (SSS) density-profile near the center effectively rules out a valley and a subsequent peak in the radial profile of $ϕ$ at similar densities, reinforcing its monotonic decrease. These model-independent relations impose strong constraints on the near-center behavior of the EOS-parameter $ϕ$, particularly demonstrating that the mean stiffness (or equivalently $Δ$) reaches a local maximum (minimum) at the center.

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arXiv2025

Revisiting the Possibility of a Sharp Phase Transition in Cold Neutron Stars

First-order phase transitions (FOPTs) in cold neutron stars (NSs) have been extensively studied and have provided valuable insights into the behavior of the densest matter visible in our Universe, although a strong consensus has yet to emerge. Revisiting the possibility of a hadron-quark FOPT from a new perspective, we examine the interplay between the coupled nature of gravity and microscopic interactions in Tolman--Oppenheimer--Volkoff (TOV) equations and the fundamental requirements of thermodynamic consistency in NSs. We demonstrate that a sharp FOPT manifested as a plateau in the equation of state (EOS) $P(\varepsilon)$, i.e., pressure $P$ versus energy density $\varepsilon$, is intrinsically incompatible with the regularity conditions of the TOV solutions. Although numerical integrations of the TOV equations with EOSs incorporating FOPTs may yield seemingly reasonable mass-radius relations consistent with current observations, such results can mask underlying inconsistencies. Our analysis thus establishes a structural consistency criterion for constraining dense-matter EOSs using NS observables, complementing existing studies of possible phase transitions in NS interiors.

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arXiv2025

Bayesian Quantification of Observability and Equation of State of Twin Stars

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equation of state (EOS) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a meta-model with 9-parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12-18\% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. We show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared $c_{\rm qm}^2$ has two peaks, one below and another above the conformal limit $c_{\rm qm}^2=1/3$ predicted by perturbative QCD.

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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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