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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

First-principles equations of state and structures of liquid metals in multi-megabar conditions

Liquid metals at extreme pressures and temperatures are widely interested in the high-pressure community. Based on density functional theory molecular dynamics, we conduct first-principles investigations on the equation of state ( EOS) and structures of four metals (Cu, Fe, Pb, and Sn) at 1.5–5 megabar conditions and 5 × 10 3 –4 × 10 4 K. Our first-principles EOS data enable evaluating the performance of four EOS models in predicting Hugoniot densities and temperatures of the four systems. We find the melting temperature of Cu is 1000–2000 K higher and shows a similar Clapeyron slope, in comparison to those of Fe. Our structure, coordination number, and diffusivity analysis indicates all the four liquid metals form similar simple close-packed structures. Our results set theoretical benchmarks for EOS development and structures of metals in their liquid states and under dynamic compression.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accuracy of Kohn–Sham density functional theory for warm- and hot-dense matter equation of state

We study the accuracy of Kohn–Sham density functional theory (DFT) for warm- and hot-dense matter (WDM and HDM). Specifically, considering a wide range of systems, we perform accurate ab initio molecular dynamics simulations with temperature-independent local/semilocal density functionals to determine the equations of state at compression ratios of 3x–7x and temperatures near 1 MK. We find very good agreement with path integral Monte Carlo benchmarks, while having significantly smaller error bars and smoother data, demonstrating the accuracy of DFT for the study of WDM and HDM at such conditions. In addition, using a Δ-machine learned force field scheme, we confirm that the DFT results are insensitive to the choice of exchange-correlation functional, whether local, semilocal, or nonlocal.

Suryanarayana, Phanish (ORCID:0000000151720049)↗
DOE OSTI2023

Deducing neutron star equation of state parameters directly from telescope spectra with uncertainty-aware machine learning

Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of the superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method which relies on certain theoretical assumptions and simplifications about the uncertainties. It first infers the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. Here we demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and a path towards circumventing the need for theoretical assumptions to infer physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2020

Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo Measurements

The Neutron Star Interior Composition Explorer collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars (NSs). In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of NSs from the gravitational wave signal of the compact binary merger GW170817. Further, we compare the constraints on the EOS to those set by the recent measurement of a 2.14 Me pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a NS–black hole merger, which yields weaker constraints on the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2 + 1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge ( B , S ) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of T c ( μ B , μ S ) = T c ( 1 − ( κ 2 B μ ^ B 2 + κ 2 S μ ^ S 2 + 2 κ 11 B S μ ^ B μ ^ S ) ) along different lines in the ( μ B , μ S ) plane. On lattices with fixed cutoff in units of temperature, a T = 1 / 8 , we find κ 2 B = 0.015 ( 1 ) , κ 2 S = 0.0124 ( 5 ) and κ 11 B S = − 0.0050 ( 7 ) . We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μ s = 0 . We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, T c ( m s ) = T c ( m s phy ) ( 1 − 0.097 ( 2 ) ( m s − m s phys ) / m s phy + O ( ( Δ m s ) 2 ) . Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Implications of an improved water equation of state for water-rich planets

Water (H 2 O), in all forms, is an important constituent in planetary bodies, controlling habitability and influencing geological activity. Under conditions found in the interior of many planets, as the pressure increases, the H-bonds in water gradually weaken and are replaced by ionic bonds. Recent experimental measurements of the water equation of state (EOS) showed both a new phase of H-bonded water ice, ice-VIIt, and a relatively low transition pressure just above 30 GPa to ionic bonded ice-X, which has a bulk modulus 2.5 times larger. The higher bulk modulus of ice-X produces larger planets for a given mass, thereby either reducing the atmospheric contribution to the volume of many exoplanets or limiting their water content. We investigate the impact of the new EOS measurements on the planetary mass–radius relation and interior structure for water-rich planets. We find that the change in the planet mass–radius relation caused by the systematic differences between previous and new experimental EOS measurements is comparable to the observational uncertainties in some planet sizes – an issue that will become more important as observations continue to improve.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2021

Future Physics Perspectives on the Equation of State from Heavy Ion Collisions to Neutron Stars

With the computational power and algorithmic improvements available today, the ongoing STAR/RHIC and HADES/GSI experiments, the future FAIR and NICA facilities becoming operational, and the new precise measurements from NICER and LIGO/VIRGO, the high-energy nuclear physics and astrophysics communities are in the unique position to set very stringent constraints on the equation of state of strongly interacting matter. Here, we review the state-of-the-art of different approaches used in the description of hot and ultradense baryonic matter in and out of equilibrium, and discuss the regions in the phase diagram where heavy-ion collisions and neutron star mergers can overlap. Future perspectives are discussed to help define a comprehensive, multi-disciplinary strategy to map out the phase diagram of strongly interacting matter from heavy ion collisions to neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Thermal Equations of State of Magnesite: Implication for the Complex Mid‐Lower Mantle Seismic Scatterers

Abstract Magnesite (MgCO 3 ) entering the lower mantle together with the subducted oceanic crust is an important carbon carrier. The reaction between magnesite and mantle minerals has been documented, but its influence on the density and velocity profiles of lower mantle remains unexplored. To decipher the deep carbon transportation and its associated effect, here we determined the thermal equations of state of magnesite up to 120 GPa and 2600 K using X‐ray diffraction in laser‐heated diamond anvil cells. The obtained thermal elastic parameters of magnesite facilitated a comprehensive understanding on the influence of magnesite‐SiO 2 reaction, variation of carbon and SiO 2 content, and temperature on the origin of lower‐mantle scatterers at 1,000–1,800 km depth. Our modeling revealed that the depth of the lower‐mantleV S scatterers is mainly controlled by the Al 2 O 3 content in SiO 2 , while its magnitude depends on the SiO 2 content. Along normal geotherm, the magnesite‐SiO 2 reaction would occur before the post‐stishovite transition, consuming substantial SiO 2 in the subducted oceanic crust. Depending on the amount of residual SiO 2 , the post‐stishovite transition can produce a 2.5–5.2 (2)%V S reduction, compatible with the observed seismic scatterers in Izu‐Bonin and Mariana subduction zones. Along slab geotherm, this reaction occurs after the post‐stishovite transition, generating a greaterV S reduction of 4.4–6.4 (4)%. We thus propose that the reaction between sinking MgCO 3 and SiO 2 in the slab is one of the potential factors influencing the magnitude of the lower‐Vs scatterers at 1,000–1,900 km depth. Our results provide new insights into the deep‐mantle carbonate transportation influencing regional geophysics.

Geochemistry & Geophysics↗
DOE OSTI2020

Equation of State and Progenitor Dependence of Stellar-mass Black Hole Formation

The core collapse of a massive star results in the formation of a proto-neutron star (PNS). If enough material is accreted onto a PNS, it will become gravitationally unstable and further collapse into a black hole (BH). We perform a systematic study of failing core-collapse supernovae in spherical symmetry for a wide range of pre-supernova progenitor stars and equations of state (EOSs) of nuclear matter. We analyze how variations in progenitor structure and the EOS of dense matter above nuclear saturation density affect the PNS evolution and subsequent BH formation. Comparisons of core collapse for a given progenitor star and different EOSs show that the path traced by the PNS in mass-specific entropy phase space ${M}_{\mathrm{grav}}^{\mathrm{PNS}}-\tilde{s}$ is well correlated with the progenitor compactness and is almost EOS independent, apart from the final end point. Furthermore, BH formation occurs, to a very good approximation, soon after the PNS overcomes the maximum gravitational mass supported by a hot NS with constant specific entropy equal to $\tilde{s}$. These results show a path to constraining the temperature dependence of the EOS through the detection of neutrinos from a failed galactic supernova.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Constraining the Dense Matter Equation of State with New NICER Mass–Radius Measurements and New Chiral Effective Field Theory Inputs

Pulse profile modeling of X-ray data from the Neutron Star Interior Composition Explorer is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory (χEFT), and masses and tidal deformabilities inferred from gravitational-wave detections of binary neutron star mergers, this has led to a steady improvement in our understanding of the dense matter equation of state (EOS). Here, we consider the impact of several new results: the radius measurement for the 1.42 M ⊙ pulsar PSR J0437−4715 presented by Choudhury et al., updates to the masses and radii of PSR J0740+6620 and PSR J0030+0451, and new χEFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions—a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS)—we find the radius of a 1.4 M ⊙ (2.0 M ⊙ ) neutron star to be constrained to the 95% credible ranges ${12.28}_{-0.76}^{+0.50}$ km (${12.33}_{-1.34}^{+0.70}$ km) for the PP model and ${12.01}_{-0.75}^{+0.56}$ km (${11.55}_{-1.09}^{+0.94}$ km) for the CS model. The maximum neutron star mass is predicted to be ${2.15}_{-0.16}^{+0.14}$M ⊙ and ${2.08}_{-0.16}^{+0.28}$M ⊙ for the PP and CS models, respectively. We explore the sensitivity of our results to different orders and different densities up to which χEFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference R 2.0 − R 1.4 of the radius of 2 M ⊙ and 1.4 M ⊙ neutron stars within our EOS inference.

gravitational wave sources↗
DOE OSTI2023

Equation of State and Spin Crossover of (Al, Fe)–Phase H

The transport of hydrogen into Earth's deep interior may have an impact on lower mantle dynamics as well as on the seismic signature of subducted material. Due to the stability of the hydrous phases δ-AlOOH (delta phase), MgSiO 2 (OH) 2 (phase H), and ε-FeOOH at high temperatures and pressures, their solid solutions may transport significant amounts of hydrogen as deep as the core-mantle boundary. Here we have constrained the equation of state, including the effects of a spin crossover in the Fe 3+ atoms, of (Al, Fe)-phase H: Al 0.84 Fe 3+ 0.07 Mg 0.02 Si 0.06 OOH, using powder X-ray diffraction measurements to 125 GPa, supported by synchrotron Mössbauer spectroscopy measurements on (Al, Fe)-phase H and δ-(Al, Fe)OOH. The changes in spin state of Fe 3+ in (Al, Fe)-phase H results in a significant decrease in bulk sound velocity and occurs over a different pressure range (48–62 GPa) compared with δ-(Al, Fe)OOH (32–40 GPa). Changes in axial compressibilities indicate a decrease in the compressibility of hydrogen bonds in (Al, Fe)-phase H near 30 GPa, which may be associated with hydrogen bond symmetrization. The formation of (Al, Fe)-phase H in subducted oceanic crust may contribute to scattering of seismic waves in the mid-lower mantle (~1,100–1,550 km). Accumulation of 1–4 wt.% (Al, Fe)-phase H could reproduce some of the seismic signatures of large, low seismic-velocity provinces. Our results suggest that changes in the electronic structure of phases in the (δ-AlOOH)-(MgSiO 2 (OH) 2 )-(ε-FeOOH) solid solution are sensitive to composition and that the presence of these phases in subducted oceanic crust could be seismically detectable throughout the lower mantle.

58 GEOSCIENCES↗
DOE OSTI2023

Deducing neutron star equation of state from telescope spectra with machine-learning-derived likelihoods

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Lattice QCD constraints on the critical point from an improved precision equation of state

In this paper we employ lattice simulations to search for the critical point of QCD. We search for the onset of a first-order QCD transition on the phase diagram by following contours of constant entropy density from imaginary to real chemical potentials under conditions of strangeness neutrality. We scan the phase diagram and investigate whether these contours meet to determine the probability that the critical point is located in a certain region on the 𝑇−𝜇 𝐵 plane. To achieve this we introduce a new, continuum extrapolated equation of state at zero density with improved precision using lattices with 𝑁 𝜏 =8, 10, 12, 16 time slices, and supplement it with new data at imaginary chemical potential. The current precision allows us to exclude, at the 2⁢𝜎 level, the existence of a critical point at 𝜇 𝐵 <450 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equations of state

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equations of state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when $\gamma$ > 2 or it weakens them when $\gamma$ < 2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1 + $\sqrt{2}$. Finally, results have been validated with numerical simulations performed with the FLASH code.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Constraints on initial baryon stopping and equation of state from directed flow

Our investigation focuses on the rapidity-dependent directed flow, v 1 (y), of identified hadrons in Au+Au collisions across a broad range of √S NN from 7.7 to 200 GeV. Employing a (3+1)-dimensional hybrid framework, our study successfully reproduces the characteristic features of the measured v 1 (y) for both mesons and baryons across the considered beam energies. Notably, our analysis reveals the constraining power of baryonic v 1 (y) on the initial baryon stopping mechanism. Together with mesonic v 1 (y), the directed flow serves as a crucial tool for probing the equation of state governing dense nuclear matter at finite chemical potentials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕ ). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕ ), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕ ) and larger planets (>2 × R ⊕ ) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕ ), when viewed from the perspective of planet equilibrium temperature (T eq ), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

79 ASTRONOMY AND ASTROPHYSICS↗