Equation Of State Research Articles

The interior of Uranus

We present improved empirical density profiles of Uranus and interpret them in terms of their temperature and composition using a new random algorithm. The algorithm to determine the temperature and composition is agnostic with respect to the temperature gradient in non-isentropic regions and chooses amongst all possible gradients randomly that are stable against convection and correspond to an Equation of State (EoS) compatible composition. Our empirical models are based on an efficient implementation of the Theory of Figures (ToF) up to tenth order including a proper treatment of the atmosphere. The accuracy of tenth order ToF enables us to present accurate calculations of the gravitational moments of Uranus up to J14: J6 = (5.3078 ± 0.3312) 10−7, J8 = (−1.1114 ± 0.1391) 10−8, J10 = (2.8616 ± 0.5466) 10−10, J12 = (−8.4684 ± 2.0889) 10−12, and J14 = (2.7508 ± 0.7944) 10−13. We consider two interior models of Uranus that differ with respect to the maximal number of materials allowed per layer of Uranus (three versus four composition components). The case with three materials does not allow Hydrogen and Helium (H-He) in deeper parts of Uranus and results in a higher water (H2O) abundance which leads to lower central temperatures. On the other hand, the models with four materials allow H-He to be mixed into the deeper interior and lead to rock-dominated solutions. We find that these four composition components’ models are less reliable due to the underlying empirical models’ incompatibility with realistic Brunt frequencies. Most of our models are found to be either purely convective with the exception of boundary layers, or only convective in the outermost region above ~80% of the planets’ radius rU. Almost all of our models possess a region ranging between ~(0.75–0.9) rU that is convective and consists of ionic H2O which could explain the generation of Uranus’ magnetic field.

Cosmological model with linear equation of state parameter in f(R,Lm) gravity

In this paper, we examine the universe's expansion in f(R,Lm) gravity for a particular form of f(R,Lm)=R2+Lmn. The field equations for flat FLRW metric with matter Lagrangian Lm=ρ are derived. Hubble parameter in terms of red-shift(z) are derived using the linear form of Equation of State (EoS) parameter ω=w0+w1z. By using Bayesian statistical techniques based on χ2-minimization technique, we have obtained the best fit values of the model parameters of this model for cosmic chronometer and supernovae Pantheon datasets. The evolution of the equation of state parameter(ω), energy density (ρ), pressure (p), cosmographic parameters, and the impact of the energy conditions with best-fit values of the model parameters are all thoroughly examined. We have also analyze Om diagnostic's behaviour and determine the present age of universe for this model.

Tolman VII (TVII) Solution with Theory of Energy-Momentum Squared Gravity (EMSG) in Neutron Stars

Abstract We study the Tolman VII (TVII) solution for the Energy-Momentum Squared Gravity (EMSG) as well as the solution’s compatibility with stars properties. We perform a systematic analysis of the suitability of the equation of state (EoS) for energy density and pressure profiles. In calculations, for convenience, all physical quantities are expressed in the form of dimensionless quantities by introducing the quantity ζ = r/R. This dimensionless quantity will be used to determine the ratio between a star’s mass and its radius. The TVII solution provides limits on compactness C ∈ [0.01, 0.27] and neutron star’s mass 2.60M ⊙. Having α as a free parameter of the EMSG model gives the new range compactness C ∈ [0.01, 0.386] for ζ[0, 1] with α ∈ [0.01, ∞] and shows a star mass of 2.97M⊙. The metric eλ effective and the metric eν effective produce the range of α ∈ [0.1, 0.6], which represents both metric to be physical.

A pulsed power facility for studying the warm dense matter regime.

A pulsed power facility has been designed for studying the warm dense matter regime. It is based on the pulsed Joule heating technique, originally proposed by Korobenko and Rakhel [Int. J. Thermophy. 20, 1257 (1999)], where a 3.96µF capacitor bench is used for inducing a solid to plasma phase transition to metallic foils confined into a sapphire cell. The first experiments have been conducted on pure aluminum. Experimental data have been collected using electrical and optical diagnostics. Direct measurements of tension, current, pressure, and particle velocity allow us to evaluate the equation of state (EOS) and the DC conductivity of expanded aluminum. The results are compared to hydrodynamic simulations performed with various EOS models. As a result, collected data on aluminum highlight the relevance of our experimental procedure for improving EOS modeling in the warm dense matter regime.

Indication of Sharp and Strong Phase Transitions from NICER Observations

In this Letter, we present a new, weakly model-dependent test for “standard” equation-of-state (EoS) models that disfavor sharp and strong phase transitions by using NS mass and radius observations. We show the radii of two NSs observed by NICER (PSR J0740+6620 and PSR 0030+0451) are correlated if these two NSs are built upon standard EoS models. The radii of NSs with different masses are sensitive to the pressures at different densities, and the pressures at different densities are strongly correlated in standard EoS models. We further show that the correlation of the NS radii can be significantly weakened when additional degrees of freedom concerning the first-order phase transitions are added into the EoSs. We propose a new quantity, D L, which measures the extent to which the linear correlation of the radii of two NSs is weakened. Our method gives a 48% identification probability (with a 5% false alarm rate) of finding beyond-standard EoS models in NICER observations. Future observations with higher measurement accuracy can confirm or rule out this identification. Our method is generalizable to any pair of NS masses and can be employed with other sets of observations in the future.

Dependence of the reconstructed core-collapse supernova gravitational wave high-frequency feature on the nuclear equation of state in real interferometric data

Dependence of the reconstructed core-collapse supernova gravitational wave high-frequency feature on the nuclear equation of state in real interferometric data

Sound velocity measurement based on laser-induced micro-flyers

The measurement of high-pressure sound velocity in solid materials is crucial for developing constitutive equations and equations of state for materials in extreme stress–strain rate conditions. In this study, we propose a novel method for high-pressure sound velocity measurement using laser-induced micro-flyer technology. By optimizing laser driving conditions and target structure design, we measure high-pressure sound velocity using the “reverse-impact geometry” approach. The well-established Photon Doppler Velocimetry system allows for high-precision, single-shot measurements of both flyer velocity and particle velocity histories. A systematic error analysis shows that the longitudinal sound velocity of aluminum obtained in this experiment is consistent with data from traditional devices, such as gas guns, within the error margin. Finally, we analyze the potential application value of this method in laser technology as well as high-pressure dynamic responses of materials, and conclude the current shortcomings and possible improvements of this method.

Equation of state of the relativistic electron–positron–photon plasma at arbitrary temperature and degeneracy

We consider the plasma made of relativistic electrons and positrons in thermodynamic equilibrium with photons at arbitrary temperature and degeneracy. We establish various thermodynamic identities as a function of the electron and positron chemical potentials and temperature. The high-temperature regime in which the electrons and positrons are ultrarelativistic is recovered. The excess of electrons with respect to positrons or the excess of positrons with respect to electrons depends on the thermodynamic conditions. Doing so, we go beyond what is usually found in the literature where only the high temperature regime is usually tackled.

Estimation of gas diffusion coefficient for gas/oil-saturated porous media systems by use of early-time pressure-decay data: An experimental/numerical approach

This paper presented a novel numerical method for estimating the gas diffusion coefficient based on the early-time pressure-decay data. Experimentally, “flooding–soaking” procedures were developed to perform the gas diffusion in an oil-saturated tight core under different gas phase volume conditions. After flooding, the capillary bundle model was used to calculate the oil–gas contact area. The early-time pressure-decay data of the gas phase were monitored and recorded during the soaking process. Theoretically, a non-equilibrium inner boundary condition coupled with the characteristics of experimental early-time pressure had been incorporated to develop a diffusion model for a gas/oil-saturated tight core system. Based on gas-phase mass balance equations and gas equation of state, the diffusion coefficients were optimized once the discrepancy between experimental data and numerical solutions was minimized. According to the estimated results in this study, the CH4 diffusion coefficients were 3.74 × 10−11 and 3.86 × 10−11 m2/s in tight core saturated with crude oil, respectively. Moreover, the oil–gas contact area significantly impacts the diffusion flux in oil-saturated porous media. Specifically, an additional 10% contact area results in a 75% increase in CH4 diffusion mass. In addition, with the application of our proposed model to CH4/bitumen and CO2/bitumen systems, the diffusion coefficients were in close agreement with the results reported in previous literature, indicating that the proposed model was applicable to both gas/liquid and gas/liquid-saturated porous media systems.

Numerical study on cavitation generation induced by the high-speed jet impact on the water surface

The complex interaction between shock waves and two-phase interfaces can generate cavitation. In this study, the cavitation induced by the high-speed jet impact on the water surface was investigated. The mixture fluid is modeled using the barotropic equation of state under the framework of the two-phase flow model, which can describe the mixture of air, water, and vapor with any proportion. Through constructing a 1D Riemann problem for the impact-induced cavitation phase transition, it indicates that the coupling effect of multiple rarefaction waves emitted from the two-phase interface is responsible for the cavitation phase transition inside the liquid. Then, a 3D (three-dimensional) simulation regarding the impact of a high-speed jet on the water surface was conducted and validated against previous experiments that captured the cavitation phase transition phenomenon in the central region after the jet impact. The 3D simulation results revealed the spatial structure and development process of shock waves in detail. The coupling effects of shock waves and two-phase interfaces generate a ring-shaped rarefaction wave, which develops radially inward and superimposes, resulting in the formation of acorn-shaped cavitation bubble nuclei inside the water. The 3D simulation can provide spatial shock/rarefaction wave structures and internal flow details that have never been obtained in experiments, such as shock generation and propagation, rarefaction wave generation and center convergence, and the internal structure of acorn-shaped cavitation nucleation. Furthermore, the influence of the jet velocity on the cavitation intensity was analyzed, and a quantitative relationship was provided.

Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations

We investigate the formation and decay of oscillons during the post-inflationary reheating epoch from inflaton oscillations around asymptotically flat potentials V(φ) in the presence of an external coupling of the form 1/2 g 2 φ 2 χ 2. It is well-known that in the absence of such an external coupling, the attractive self-interaction term in the potential leads to the formation of copious amounts of long-lived oscillons both for symmetric and asymmetric plateau potentials. We perform a detailed numerical analysis to study the formation of oscillons in the α-attractor E- and T-model potentials using the publicly available lattice simulation codeCosmoLattice. We observe the formation of nonlinear oscillon-like structures with the average equation of state ⟨wφ ⟩ ≃ 0 for a range of values of the inflaton self-coupling λ and the external coupling g 2. Our results demonstrate that oscillons form even in the presence of an external coupling and we determine the upper bound on g 2 which facilitates oscillon formation. We also find that eventually, these oscillons decay into the scalar inflaton radiation as well as into the quanta of the offspring field χ. Thus, we establish the possibility that reheating could have proceeded through the channel of oscillon decay, along with the usual decay of the oscillating inflaton condensate into χ particles. For a given value of the self-coupling λ, we notice that the lifetime of a population of oscillons decreases with an increase in the strength of the external coupling, following an (approximately) inverse power-law dependence on g 2.

Multipolar Electromagnetic Emission of Newborn Magnetars

It is generally recognized that the electromagnetic multipolar emission from magnetars can be used to explain radiation from soft gamma repeaters or anomalous X-ray pulsars, but they have little impact on the spin-down of magnetars. We here present an analytical solution for the neutron star multipolar electromagnetic fields and their associated expected luminosities. We find that for newborn millisecond magnetars, the spin-down luminosity from higher multipolar components can match or even exceed that from the dipole component. Such high-intensity radiation will undoubtedly affect related astrophysical phenomena at the birth of a magnetar. We show that the spin-down luminosity from multipoles can well explain the majority of gamma-ray burst (GRB) afterglows, from the plateau starting at several hundred seconds until the normal decay phase lasting for many years. The fitted magnetar parameters for GRB afterglows are all typical values, with spins in the millisecond range and magnetic field strengths on the order of 1014–1015 G. Our results, in turn, provide support for the hypothesis that GRBs originate from the birth of magnetars with a period of a few milliseconds, thus deepening our understanding of the complex magnetic field structure and the equation of state of magnetars.

A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data

PSR J0740+6620 is the neutron star with the highest precisely determined mass, inferred from radio observations to be 2.08 ± 0.07 M ⊙. Measurements of its radius therefore hold promise to constrain the properties of the cold, catalyzed, high-density matter in neutron star cores. Previously, Miller et al. and Riley et al. reported measurements of the radius of PSR J0740+6620 based on Neutron Star Interior Composition Explorer (NICER) observations accumulated through 2020 April 17, and an exploratory analysis utilizing NICER background estimates and a data set accumulated through 2021 December 28 was presented in Salmi et al. Here we report an updated radius measurement, derived by fitting models of X-ray emission from the neutron star surface to NICER data accumulated through 2022 April 21, totaling ∼1.1 Ms additional exposure compared to the data set analyzed in Miller et al. and Riley et al., and to data from XMM-Newton observations. We find that the equatorial circumferential radius of PSR J0740+6620 is 12.92−1.13+2.09 km (68% credibility), a fractional uncertainty ∼83% the width of that reported in Miller et al., in line with statistical expectations given the additional data. If we were to require the radius to be less than 16 km, as was done in Salmi et al., then our 68% credible region would become R=12.76−1.02+1.49 km, which is close to the headline result of Salmi et al. Our updated measurements, along with other laboratory and astrophysical constraints, imply a slightly softer equation of state than that inferred from our previous measurements.

Ice Formation, Exsolution, and Multiphase Equilibria in the Methane–Ethane–Nitrogen System at Titan Surface Conditions

Titan is unique among the icy satellites in that it has a thick atmosphere, stable surficial bodies of liquid, and a precipitation system that promotes interactions between the two. Although Titan’s surface conditions are typically assumed to be above the freezing point temperatures of the major constituent species of the climate system (methane, ethane, and nitrogen), conditions may be sufficiently cool across parts of Titan to allow for ice formation alongside known liquid-vapor phases. In this study, we used Raman spectroscopy, visual inspection, and the CRYOCHEM 2.0 equation of state to map the appearance of first ice and to quantify the amount of nitrogen dissolution into liquid in the methane–ethane–nitrogen system along a 1.5 bar isobaric cooling path in the temperature range 80–95 K. This was with the intent of (1) determining the effects nitrogen has on the phase behaviors of the methane–ethane binary system, and (2) establishing the temperatures and ternary mixing ratios needed for ice formation on Titan’s surface. We found that ethane-rich mixtures enter a three-phase solid–liquid–vapor equilibrium and are characterized by nitrogen-rich exsolution upon freezing and ice that form at the bottom of the sample. With sufficient methane content, the mixtures cross a univariant four-phase solid–liquid–liquid–vapor boundary, which contributes to a distinct isothermal freezing point profile and ice that forms starting at the liquid–liquid interface. Our results generally agree with findings from previous studies of the methane–ethane–nitrogen system and are intended to add to our current understanding of Titan’s geochemical processes.

Sunyaev–Zeldovich Signals from L* Galaxies: Observations, Analytics, and Simulations

We analyze measurements of the thermal Sunyaev–Zeldovich (tSZ) effect arising in the circumgalactic medium (CGM) of L* galaxies, reported by J. N. Bregman et al. (B+22) and S. Das et al. (D+23). In our analysis, we use the Y. Faerman et al. CGM models, a new power-law model (PLM), and the TNG100 simulation. For a given M vir, our PLM has four parameters: the fraction, f hCGM, of the halo baryon mass in hot CGM gas, the ratio, ϕ T , of the actual gas temperature at the virial radius to the virial temperature, and the power-law indices, a P,th and a n for the thermal electron pressure and the hydrogen nucleon density. The B+22 Compton-y profile implies steep electron pressure slopes (a P,th ≃ 2). For isothermal conditions, the temperature is at least 1.1 × 106 K, with a hot CGM gas mass of up to 3.5 × 1011 M ⊙ for a virial mass of 2.75 × 1012 M ⊙. However, if isothermal, the gas must be expanding out of the halos. An isentropic equation of state is favored for which hydrostatic equilibrium is possible. The B+22 and D+23 results are consistent with each other and with recent (0.5–2 keV) CGM X-ray observations of Milky Way mass systems. For M vir ≃ 3 × 1012 M ⊙, the scaled Compton pressure integrals, E(z)−2/3Y500/Mvir,125/3 , lie in the narrow range, 2.5 × 10−4–5.0 × 10−4 kpc2, for all three sets of observations. TNG100 underpredicts the tSZ parameters by factors ∼0.5 dex for the L* galaxies, suggesting that the feedback strengths and CGM gas losses are overestimated in the simulated halos at these mass scales.

The Radius of the High-mass Pulsar PSR J0740+6620 with 3.6 yr of NICER Data

We report an updated analysis of the radius, mass, and heated surface regions of the massive pulsar PSR J0740+6620 using Neutron Star Interior Composition Explorer (NICER) data from 2018 September 21 to 2022 April 21, a substantial increase in data set size compared to previous analyses. Using a tight mass prior from radio-timing measurements and jointly modeling the new NICER data with XMM-Newton data, the inferred equatorial radius and gravitational mass are 12.49−0.88+1.28 km and 2.073−0.069+0.069 M ⊙, respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, with an estimated systematic error ≲ 0.1 km. This result was obtained using the best computationally feasible sampler settings providing a strong radius lower limit but a slightly more uncertain radius upper limit. The inferred radius interval is also close to the R=12.76−1.02+1.49 km obtained by Dittmann et al., when they require the radius to be less than 16 km as we do. The results continue to disfavor very soft equations of state for dense matter, with R < 11.15 km for this high-mass pulsar excluded at the 95% probability. The results do not depend significantly on the assumed cross-calibration uncertainty between NICER and XMM-Newton. Using simulated data that resemble the actual observations, we also show that our pipeline is capable of recovering parameters for the inferred models reported in this paper.

Evaluating extensions to LCDM: an application of Bayesian model averaging and selection

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter ΩK, a spectral index ns = 1 and a varying n run, a constant dark energy equation of state (EOS) w 0CDM and a time-dependent one w 0 w aCDM. We also assess cosmological data against a varying effective number of neutrino species N eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results.We reinforce the standard ΛCDM model statistical preference when combining CMB data withCMB lensing, BAO, and Bicep-KECK 2018 data against the K-ΛCDM model anddns /d ln k-ΛCDM with a probability > 80%. Whenevaluating the dark energy EOS, we find that this dataset does not exhibit a strong preferencebetween the standard ΛCDM model and the constant dark energy EOS model w 0CDM,with a model posterior probability distribution of approximately ≈ 40%:60% in favour of w 0CDM, while the time-varying dark energy EOS model only holds below 1%probability. We find a similar result also when considering the N eff-ΛCDM model, with asplit probability almost 50%-50% from both our datasets.Overall, our application of BMA reveals that including model uncertainty in these cases does notsignificantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmologicalmodel evaluation.

Upper Limit of Sound Speed in Nuclear Matter: A Harmonious Interplay of Transport Calculation and Perturbative Quantum Chromodynamic Constraint

Very recently, it has been shown that there is an upper bound on the squared sound speed of nuclear matter from the transport, which reads cs2≤0.781 . In this work, we demonstrate that this upper bound is corroborated by the reconstructed equation of state (EOS; modeled with a nonparametric method) for ultradense matter. The reconstruction integrates multimessenger observation for neutron stars, in particular, the latest radius measurements for PSR J0437–4715 ( 11.36−0.63+0.95 km), PSR J0030+0451 ( 11.71−0.83+0.88 km, in the ST+PDT model), and PSR J0740+6620 ( 12.49−0.88+1.28 km) by NICER have been adopted. The result shows in all cases, the cs2≤0.781 upper limit for EOS will naturally yield the properties of matter near the center of the massive neutron star consistent with the causality-driven constraint from pQCD, where, in practice, the density in implementing the pQCD likelihood (n L) is applied at 10ns (where ns is the nuclear saturation density). We also note that there is a strong correlation for the maximum c s 2 with n L, and cs2≤0.781 is somehow violated when n L = n c,TOV. The result indicates that a higher n L, even considering the uncertainties from statistics, is more natural. Moreover, the remarkable agreement between the outcomes derived from these two distinct and independent constraints (i.e., the transport calculation and pQCD boundary) lends strong support to their validity. In addition, the latest joint constraint for R 1.4, R 2.0, R 1.4 − R 2.0, and M TOV are 11.94−0.68+0.77 km, 11.99−0.67+0.88 km, −0.1−0.27+0.42 km, and 2.24−0.10+0.13M⊙ (at 90% credible level), respectively.

Concentration and cavitation in the Riemann solutions to the Umami Chaplygin Euler equations

The concentration phenomena in fluid dynamics can be mathematically described by delta-shocks. With the introduction of flux-function, the Riemann problem for the Euler system with Umami Chaplygin gas equation of state is discussed. What Umami Chaplygin gas means is that the fluid obeys the pressure–density relation where the pressure is negative and is a new generalization of Chaplygin gas. The solutions with six kinds of structures are constructed. Unlike the Chaplygin gas, the delta-shock occurs in solutions, even though the system is strictly hyperbolic and two characteristic fields are genuinely nonlinear. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Additionally, the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions are identified and analyzed as the Umami Chaplygin gas pressure and flux-function vanish simultaneously. It is proved that as the pressure and flux-function drop to zero, any solution consisting of two shocks tends to the delta-shock solution of the pressureless Euler system, and any solution consisting of two rarefaction waves tends to the vacuum Riemann solution of the pressureless Euler system. Finally, some numerical results exhibiting the processes of formation of delta-shocks and vacuum states are presented.

Effects of dark matter on the spontaneous scalarization in neutron stars

Dark matter, an important portion of compact objects, can influence different phenomena in neutron stars. The spontaneous scalarization in the scalar-tensor gravity has been proposed for neutron stars. Here, we investigate the spontaneous scalarization in dark matter admixed neutron stars. Applying the dark matter equations of state, we calculate the structure of scalarized neutron stars containing dark matter. The dark matter equations of state are based on observational data from the rotational curves of galaxies and the fermionic self-interacting dark matter. Our results verify that the spontaneous scalarization is affected by the dark matter pressure in neutron stars. Depending on the central density of scalarized dark matter admixed neutron stars, the dark matter pressure alters the central scalar field. The increase of dark matter pressure in low-density scalarized stars amplifies the central scalar field. However, the pressure of dark matter in high-density scalarized stars suppresses the central scalar field. Our calculations confirm that the stars in the merger event GW170817 and in the low-mass X-ray binary 4U 1820-30 can be scalarized dark matter admixed neutron stars.