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DOE OSTI2025

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius (M–R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M–R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Bayesian statistics↗

DOE OSTI2026

Neutrino flavor instabilities in neutron star mergers with moment transport: Slow, fast, and collisional modes

Determining where, when, and how neutrino flavor oscillations must be included in large-scale simulations of hot and dense astrophysical environments is an enduring challenge that must be tackled to obtain accurate predictions. Here, using an angular moment-based linear stability analysis framework, we examine the different kinds of flavor instabilities that can take place in the context of the postprocessing of a neutron star merger simulation, with a particular focus on the collisional flavor instability and a careful assessment of several commonly used approximations. First, neglecting anisotropies of the neutrino field, we investigate the extent to which commonly used monoenergetic growth rates reproduce the results obtained from a full multienergy treatment. Contrary to the large discrepancies found in core-collapse supernova environments, we propose a simple combination of energy-averaged estimates that reproduces the multienergy growth rates in our representative simulation snapshot. We then quantify the impact of additional physical effects, including nuclear many-body corrections, scattering opacities, and the inclusion of the vacuum term in the neutrino Hamiltonian. Finally, we include the neutrino distribution anisotropies, which allows us to explore, for the first time in a multienergy setting, the interplay between collisional, fast, and slow modes in a moment-based neutron star merger simulation. We find that, despite a dominance of the fast instability in most of the simulation volume, certain regions exhibit only a collisional instability, while others, especially at large distances, exhibit a slow instability that is largely underestimated if anisotropic effects are neglected.

neutrino oscillations↗

DOE OSTI2025

Impact of neutrino flavor conversions on neutron star merger dynamics, ejecta, nucleosynthesis, and multimessenger signals

We present numerical relativity simulations of binary neutron star mergers incorporating neutrino flavor transformations triggered by fast flavor instability, quantum many-body effects, or potential beyond standard model physics. In both long-lived and short-lived remnant scenarios, neutrino flavor conversions modify species-dependent neutrino luminosities and mean energies, and drive the matter towards more neutron rich conditions. They produce up to more neutron rich ejecta and significantly boost the r-process yields, especially in low-density, near-equatorial outflows. We identify regions unstable to fast flavor instabilities and find that these instabilities persist despite flavor conversions. We further test the sensitivity to the equilibration timescale of the flavor conversions, finding that slower flavor conversions can interact with thermodynamic equilibration, and increase the neutron richness of the ejecta. Flavor conversions may also contribute to stronger gravitational wave and neutrino emissions, pointing to a correlation between neutrino transport and merger dynamics. Furthermore, these results highlight the potential impact of flavor conversions while motivating future work to improve on theoretical understanding of flavor instabilities in global simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Binary neutron star mergers as potential sources for ultrahigh-energy cosmic rays and high-energy neutrinos

Recent studies suggest that the most energetic cosmic rays, exceeding 100 EeV, may primarily consist of 𝑟-process nuclei. This highlights binary neutron star mergers and collapsars as promising sources of ultrahigh-energy cosmic rays (UHECRs). Building on these insights, we examine the conditions that facilitate the efficient production of UHE 𝑟-process nuclei during the prompt radiation (PR), extended emission (EE), and plateau emission phases of short gamma-ray bursts (sGRBs) following neutron star mergers. Our study reveals that jets associated with the PR phase, characterized by typical bulk Lorentz factors (≳ 400–500), dissipation radii, and magnetic field strengths, can accelerate 𝑟-process nuclei to energies ≳ 100 EeV, while preserving them during propagation within the source. Additionally, we investigate the production of HE neutrinos from photomeson and hadronic interactions, as well as from the 𝛽 decay of accelerated 𝑟-process nuclei. We find that the HE neutrino fluxes from sGRBs, mainly produced via photomeson interactions, are significantly limited to preserve the accelerated heavy nuclei, leading to lower fluxes than the predictions without allowing for contributions to UHECRs. Our results suggest that sGRBs may potentially contribute to UHECRs during the PR phase and to HE neutrinos during the EE phase—a scenario that can be tested by future neutrino observatories.

Cosmic ray sources↗

DOE OSTI2024

Compiled properties of nucleonic matter and nuclear and neutron star models from nonrelativistic and relativistic interactions

Here, this paper compiles the model parameters and zero-temperature properties of an extensive collection of published theoretical nuclear interactions, including 255 nonrelativistic (Skyrme-like) forces, 270 relativistic mean field (RMF) and point-coupling (RMF-PC) forces, and 13 Gogny-like forces. This forms the most exhaustive tabulation of model parameters to date. The properties of uniform symmetric matter and pure neutron matter at the saturation density are determined. Symmetry properties found from the second-order term of a Taylor expansion in neutron excess are compared with the energy difference of pure neutron and symmetric nuclear matter at the saturation density. Selected liquid-droplet model parameters, including the surface tension and surface symmetry energy, are determined for semi-infinite surfaces. Theoretical liquid droplet model neutron skin thicknesses of the neutron-rich closed-shell nuclei 48 Ca and 208 Pb are compared with published theoretical Hartree-Fock and experimental results. A similar comparison is made between theoretical liquid-droplet and experimental values of dipole polarizabilities. In addition, radii, binding energies, moments of inertia and tidal deformabilities of 1.2⁢M ⊙ , 1.4⁢M ⊙ and 1.6⁢M ⊙ neutron stars are computed. An extensive correlation analysis of bulk matter, nuclear structure, and low-mass neutron star properties is performed and compared with nuclear experiments and astrophysical observations.

nuclear astrophysics↗

DOE OSTI2024

Interpreting Mass and Radius Measurements of Neutron Stars with Dark Matter Halos

Abstract The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate. Depending on the DM model, these DM admixed NSs (DANSs) could have significantly different properties than pure baryonic NSs, accessible through X-ray observations of rotation-powered pulsars. We adopt the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction. The distribution of DM in the DANS as a halo affects the path of X-rays emitted from hot spots on the visible baryonic surface, causing notable changes in the pulse profile observed by telescopes such as NICER, compared to pure baryonic NSs. We explore how various DM models affect the DM mass distribution, leading to different types of dark halos. We quantify the deviation in observed X-ray flux from stars with each of these halos. We identify the pitfalls in interpreting mass and radius measurements of NSs inferred from electromagnetic radiation and constraining the baryonic matter EOS if these dark halos exist.

Shawqi, Shafayat (ORCID:0000000210956183)↗

DOE OSTI2024

Bayesian inference of fine features of the nuclear equation of state from future neutron star radius measurements to 0.1 km 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 metamodel 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 sym , and skewness J sym characterizing the density dependence of nuclear symmetry energy E sym ⁡(ρ), respectively, from mean values of NS radii consistent with existing observations and an expected accuracy Δ⁢R ranging from about 1.0 to 0.1 km. Here, we found that (1) the Δ⁢R has little effect on inferring the stiffness of SNM at suprasaturation densities, (2) smaller Δ⁢R reveals more accurately not only the PDFs but also pairwise correlations among parameters characterizing high-density E sym ⁡(ρ), (3) a double-peak feature of the PDF(K sym ) corresponding to the strong K sym – J sym and K sym – L anticorrelations is revealed when Δ⁢R is less than about 0.2 km, and the locations of the two peaks are sensitive to the maximum value of J sym reflecting the stiffness of E sym ⁡(ρ) above about 3 times the saturation density ρ 0 of SNM, and (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 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

r -process Nucleosynthesis from Hyperaccreting Neutron Stars in Common Envelopes

We investigate nuclear reactions and feedback in hyperaccreting neutron star environments, considering accretion rates in the range 0.3–3 × 10 4 M ⊙ yr −1 , typical of short-period compact-object binaries in common envelopes. Our models account for weak reactions, neutrino energy loss, nuclear energy release, pair production, degenerate equations of state, and general relativistic hydrodynamics. Depending on the accretion rates, these systems can develop both proton- and neutron-rich atmospheres with strong convective instabilities linking the neutrino sphere to the outgoing accretion shock inside the radiation trapping zone. Convection drives nucleons through multiple heating and cooling cycles, with photodisintegration dominating during the heating phase and heavy element synthesis during the cooling phase, ejecting material with abundances that depend on the accretion rate and depth of the final decompression trajectory. The turbulent nature of convective currents is conducive to creating a wide range of nuclear products through a variety of effects, including nuclear statistical equilibrium freeze-out and the r-, p-, and γ-processes. We also observe a novel multistep process in reheated trajectories, consisting of proton-capture and photodissociation reactions operating on r-process seeds, producing overall neutron-deficient isotopes. A significant amount of infalling gas experiences high entropy and short (millisecond) freeze-out timescales capable of making r-process elements with high overabundances through a disequilibrium effect between neutrons and α-particles that does not require an excess of neutrons.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Neutrino Flavor Transformation in Neutron Star Mergers

Here, we present the first numerical relativity simulations including neutrino flavor transformations that could result from flavor instabilities, quantum many-body effects, or potential beyond standard model physics in neutron star mergers. We find that neutrino flavor transformations impact the composition and structure of the remnant, potentially leaving an imprint on the postmerger gravitational-wave signal. They also have a significant impact on the composition and nucleosynthesis yields of the ejecta.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Angle-dependent in Situ Fast Flavor Transformations in Post-neutron-star-merger Disks

Abstract The remnant black hole–accretion disk system resulting from binary neutron star mergers has proven to be a promising site for synthesizing the heaviest elements via rapid neutron capture ( r -process). A critical factor in determining the full r -process pattern in these environments is the neutron richness of the ejecta, which is strongly influenced by neutrino interactions. One key ingredient shaping these interactions is fast neutrino flavor conversions (FFCs), which arise due to angular crossings in neutrino distributions and occur on nanosecond timescales. We present the first three-dimensional in situ angle-dependent modeling of FFCs in postmerger disks, implemented within general relativistic magnetohydrodynamics with Monte Carlo neutrino transport. Our results reveal that, by suppressing electron neutrinos, FFCs more efficiently cool the disk and weaken the early thermally driven wind. Less releptonization due to electron neutrino absorption makes this cooler wind more neutron rich, producing a more robust r -process at higher latitudes of the outflow. This study underscores the necessity of incorporating FFCs in realistic simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

2D end-to-end modelling of kilonovae from binary neutron star merger remnants

We investigate the kilonova emission resulting from outflows produced in a 3D general-relativistic magnetohydrodynamic (GRMHD) simulation of a hypermassive neutron star (HMNS) remnant. We map the outflows into the flash hydrodynamics code to model their expansion in axisymmetry, and study the effects of employing different r-process heating rates. Except for the highest heating rate prescription, we find no significant differences with respect to overall ejecta dynamics and morphology compared to the simulation without heating. Once homologous expansion is attained, typically after ~2s for these ejecta, we map the outflows to the sedona radiative transfer code and compute the spectral evolution of the kilonova and broad-band light curves in various Legacy Survey of Space and Time (LSST) bands. The kilonova properties depend on the remnant lifetime, with peak luminosities and peak time-scales increasing for longer lived remnants that produce more massive ejecta. For all models, there is a strong dependence of both the bolometric and broad-band light curves on the viewing angle. While the short-lived (12 ms) remnant produces higher luminosities when viewed from angles closer to the pole, longer lived remnants (240 ms and 2.5 s) are more luminous when viewed from angles closer to the equator. Our results highlight the importance of self-consistent, long-term modelling of merger ejecta, and taking viewing-angle dependence into account when interpreting observed kilonova light curves. We find that magnetized outflows from an HMNS – if it survives long enough – could explain blue kilonovae, such as the blue emission seen in AT2017gfo.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Imprints of High-Density Nuclear Symmetry Energy on Crustal Fraction of Neutron Star Moment of Inertia

The density dependence of nuclear symmetry energy E sym (ρ) remains the most uncertain aspect of the equation of state (EOS) of supradense neutron-rich nucleonic matter. Utilizing an isospin-dependent parameterization of the nuclear EOS, we investigate the implications of the observational crustal fraction of the neutron star (NS) moment of inertia ΔI/I for the E sym (ρ). We find that symmetry energy parameters significantly influence the ΔI/I, while the EOS of symmetric nuclear matter has a negligible effect. In particular, an increase in the slope L and skewness J sym of symmetry energy results in a larger ΔI/I, whereas an increase in the curvature K sym leads to a reduction in ΔI/I. Moreover, the ΔI/I is shown to have the potential for setting a lower limit of symmetry energy at densities exceeding 3 ρ 0 , particularly when L is constrained to values less than 60 MeV, thereby enhancing our understanding of supradense NS matter.

equation of state↗

DOE OSTI2024

Asymptotic-state prediction for fast flavor transformation in neutron star mergers

Neutrino flavor instabilities appear to be omnipresent in dense astrophysical environments, thus presenting a challenge to large-scale simulations of core-collapse supernovae and neutron star mergers (NSMs). Subgrid models offer a path forward, but require an accurate determination of the local outcome of such conversion phenomena. Focusing on “fast” instabilities, related to the existence of a crossing between neutrino and antineutrino angular distributions, we consider a range of analytical mixing schemes, including a new, fully three-dimensional one, and also introduce a new machine learning (ML) model. We compare the accuracy of these models with the results of several thousands of local dynamical calculations of neutrino evolution from the conditions extracted from classical NSM simulations. Our ML model shows good overall performance, but struggles to generalize to conditions from a NSM simulation not used for training. The multidimensional analytic model performs and generalizes even better, while other analytic models (which assume axisymmetric neutrino distributions) do not have reliably high performances, as they notably fail as expected to account for effects resulting from strong anisotropies. As a result, the ML and analytic subgrid models extensively tested here are both promising, with different computational requirements and sources of systematic errors.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Afterglows from Binary Neutron Star Postmerger Systems Embedded in Active Galactic Nuclei Disks

Abstract The observability of afterglows from binary neutron star mergers occurring within active galactic nuclei (AGN) disks is investigated. We perform 3D GRMHD simulations of a postmerger system and follow the jet launched from the compact object. We use semianalytic techniques to study the propagation of the blast wave powered by the jet through an AGN disk-like external environment, extending to distances beyond the disk scale height. The synchrotron emission produced by the jet-driven forward shock is calculated to obtain the afterglow emission. The observability of this emission at different frequencies is assessed by comparing it to the quiescent AGN emission. In the scenarios where the afterglow could temporarily outshine the AGN, we find that detection will be more feasible at higher frequencies (≳10 14 Hz) and the electromagnetic counterpart could manifest as a fast variability in the AGN emission, on timescales less than a day.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Unraveling trace anomaly of supradense matter via neutron star compactness scaling

The trace anomaly Δ ≡ 1/3 −𝑃/𝜖 =1/3 −𝜙 quantifies the possibly broken conformal symmetry in supradense matter under pressure 𝑃 at energy density 𝜖. Perturbative QCD (pQCD) predicts a vanishing Δ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) is still very uncertain. The extraction of Δ from NS observations strongly depends on the employed model for nuclear equation of state (EOS). Using the IPAD-TOV method based on an intrinsic and perturbative analysis of the dimensionless (IPAD) Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using 10 5 EOSs generated randomly with a metamodel in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness 𝜉 ≡ 𝐺⁡𝑀 NS /𝑅⁢𝑐 2 ≡ 𝑀 NS /𝑅 of a NS with mass 𝑀 NS and radius 𝑅 scales very accurately with $\bar{Π}$ c ≡ $Π$ c · (1 +18⁢X/25) ≡ X/(1 +3⁢X 2 +4⁢X) · (1 +18⁢X/25) where X ≡ 𝜙 c = 𝑃 c /𝜖 c is the ratio of pressure over energy density at NS centers. The scaling of NS compactness thus enables one to readily read off the central trace anomaly Δ c = 1/3 −X directly from the observational data of either the mass-radius or red-shift measurements. Finally, we then demonstrate indeed that the available NS data themselves from recent X-ray and gravitational wave observations can determine model insensitively the trace anomaly as a function of energy density in NS cores, providing a stringent test of existing NS models and a clear guidance in a new direction for further understanding the nature and EOS of supradense matter.

nuclear astrophysics↗

DOE OSTI2025

A Unified Model of Kilonovae and Gamma-Ray Bursts in Binary Mergers Establishes Neutron Stars as the Central Engines of Short GRBs

We expand the theoretical framework by O. Gottlieb et al., which connects binary merger populations with long and short binary gamma-ray bursts (lbGRBs and sbGRBs, respectively), incorporating kilonovae (KNe) as a key diagnostic tool. We show that lbGRBs, powered by massive accretion disks around black holes (BHs), should be accompanied by bright, red KNe. In contrast, sbGRBs—if also powered by BHs—would produce fainter, red KNe, potentially biasing against their detection. However, magnetized hypermassive neutron star (HMNS) remnants that precede BH formation can produce jets with power (P NS ≈ 10 51 erg s –1 ) and Lorentz factor (Γ > 10) likely compatible with sbGRB observations, and would result in distinctly bluer KNe, offering a pathway to identifying the sbGRB central engine. Recent modeling by J. C. Rastinejad et al. found luminous red KNe consistently accompany lbGRBs, supporting their origin in BH-massive disk systems, likely following a short-lived HMNS phase. The preferential association of sbGRBs with comparably luminous KNe argues against the BH engine hypothesis for sbGRBs, while the bluer hue of these KNe provides additional support for an HMNS-driven mechanism. Within this framework, BH–NS mergers likely contribute exclusively to the lbGRB population with red KNe. Our findings suggest that GW170817 may, in fact, have been an lbGRB to on-axis observers. Finally, we discuss major challenges faced by alternative lbGRB progenitor models, such as white dwarf–NS or white dwarf–BH mergers and accretion-induced collapse forming magnetars, which fail to align with observed GRB timescales, energies, and KN properties.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Investigating the crust of neutron stars with neural-network quantum states

An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm −3 and 0.1 fm −3 , matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter.

Nuclear astrophysics↗

DOE OSTI2025

Influence of neutrino-electron scattering and neutrino-pair annihilation on hypermassive neutron star

Here, we investigate the influence of inelastic neutrino microphysics in general-relativistic magnetohydrodynamics simulations of a hypermassive neutron star. In particular, we include species/energy groups coupled neutrino-matter interactions, such as inelastic neutrino-electron scattering and electron-positron annihilation kernels, into simulations up to 50 ms. Neutrino-electron inelastic scattering is known to have effective neutrino-matter energy exchange. We show that, with neutrino-electron inelastic scattering, simulations predict 75% higher disc mass with slightly different mass-averaged compositions, and 18% more ejected mass with similar distributions. The enhancement of the mass of the disc and the ejecta results in stronger baryon pollution, leading to less favorable jet launching environments. Furthermore, neutrino luminosities are about 50%, 40%, and 30% higher for electron neutrino, electron antineutrino, and heavy-lepton neutrinos. In contrast, we do not see any significant impacts due to electron-positron annihilation.

79 ASTRONOMY AND ASTROPHYSICS↗