Different Equations Of State Research Articles

Pressure-volume relationships of some solids based on double potential energy functions

We present an analysis for the pressure-volume relationship of substances viz. Neon, Argon, Aluminum, Copper, Lithium Hydride, and Magnesium Oxide using interatomic potential functions due to Morse, Rydberg, and Davydov. The formulations for P-V relationship have been obtained using these potential functions. The results for pressure as a function of volume are determined up to a range of V/(V_0=0.5) for each solid. The results are mapped with the values obtained from the Shanker equation and the Hama-SuitoEOS. The relationship between P and V through different equations of state(EOS) for different solids depends on the values of K_(0 )as well as K_0^’. A material would be more incompressible if both K_(0)and 〖K〗_0^’are high. For example in case of Cu, K_(0 )is somewhat less than that for MgO but 〖K〗_0^’ is larger for Cu than that for MgO. This makes Cu to be more incompressible than MgO. This is evident from the results which reveal P = 620GPa for Cu, and P = 430GPa for MgO both at V/V_0 = 0.5, the maximum compressions.

Stable and self-consistent charged gravastar model within the framework of f(R,,T) gravity

In this work, we discuss the configuration of a gravastar (gravitational vacuum stars) in the context of f(R, ,T ) gravity by employing the Mazur–Mottola conjecture (Mazur and Mottola in Report No. LA-UR-01-5067, 2001; Mazur and Mottola, Proc Natl Acad Sci USA 101:9545, 2004). The gravastar is conceptually a substitute for a black hole theory as available in the literature and it has three regions with different equation of states. By assuming that the gravastar geometry admits a conformal Killing vector, the Einstein–Maxwell field equations have been solved in different regions of the gravastar by taking a specific equation of state as proposed by Mazur and Mottola. We match our interior spacetime to the exterior spherical region which is completely vacuum and described by the Reissner–Nordström geometry. For the particular choice of f(R,,T) of f(R, ,T )=R+2gamma T, here we analyze various physical properties of the thin shell and also present our results graphically for these properties. The stability analysis of our present model is also studied by introducing a new parameter eta and we explore the stability regions. Our proposed gravastar model in the presence of charge might be treated as a successful stable alternative of the charged black hole in the context of this version of gravity.

Process Simulation Modelling of the Catalytic Hydrodeoxygenation of 4-Propylguaiacol in Microreactors

A process simulation model was created using Aspen Plus to investigate the hydrodeoxygenation of 4-propylguaiacol, a model component in lignin-derived pyrolysis oil, over a presulphided NiMo/Al2O3 solid catalyst. Process simulation modelling methods were used to develop the pseudo-homogeneous packed bed microreactor. The reaction was conducted at 400 °C and an operating pressure of 300 psig with a 4-propylguaiacol liquid flow rate of 0.03 mL·min−1 and a hydrogen gas flow rate of 0.09 mL·min−1. Various operational parameters were investigated and compared to the experimental results in order to establish their effect on the conversion of 4-propylguaiacol. The parameters studied included reaction temperature, pressure, and residence time. Further changes to the simulation were made to study additional effects. In doing so, the operation of the same reactor was studied adiabatically, rather than isothermally. Moreover, different equations of state were used. It was observed that the conversion was enhanced with increasing temperature, pressure, and residence time. The results obtained demonstrated a good model validation when compared to the experimental results, thereby confirming that the model is suitable to predict the hydrodeoxygenation of pyrolysis oil.

Charged gravastars in f(R,T,RμνTμν) gravity

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

Critical properties of calibrated relativistic mean-field models for the transition to warm, nonhomogeneous nuclear and stellar matter

The critical properties for the transition to warm, asymmetric, non-homogeneous nuclear matter are analysed within a thermodynamical spinodal approach for a set of well calibrated equations of state. It is shown that even though different equations of state are constrained by the same experimental, theoretical and observational data, and the properties of symmetric nuclear matter are similar within the models, the properties of very asymmetric nuclear matter, such as the one found inside of neutron stars, differ a lot for various models. Some models predict larger transition densities to homogeneous matter for beta-equilibrated matter than for symmetric nuclear matter. Since one expects that such properties have a noticeable impact on the the evolution of either a supernova or neutron star merger, this different behavior should be understood in more detail.

Thermal evolution of relativistic hyperonic compact stars with calibrated equations of state

A set of unified relativistic mean-field equations of state for hyperonic compact stars recently built in [M. Fortin, Ad. R. Raduta, S. Avancini, and C. Providencia, Phys. Rev. D {\bf 101}, 034017 (2020)] is used to study the thermal evolution of non-magnetized and non-rotating spherically-symmetric isolated and accreting neutron stars under different hypothesis concerning proton $S$-wave superfluidity. These equations of state have been obtained in the following way: the slope of the symmetry energy is in agreement with experimental data; the coupling constants of $\Lambda$ and $\Xi$-hyperons are determined from experimental hypernuclear data; uncertainties in the nucleon-$\Sigma$ interaction potential are accounted for; current constraints on the lower bound of the maximum neutron star mass are satisfied. Within the considered set of equations of state, the presence of hyperons is essential for the description of the cooling/heating curves. One of the conclusions we reach is that the criterion of best agreement with observational data leads to different equations of states and proton $S$-wave superfluidity gaps when applied separately for isolated neutron stars and accreting neutron stars in quiescence. This means that at least in one situation the traditional simulation framework that we employ is not complete and/or the equations of state are inappropriate. Another result is that, considering equations of state which do not allow for nucleonic dUrca or allow for it only in very massive NS, the low luminosity of SAX J1808 requires a repulsive $\Sigma$-hyperon potential in symmetric nuclear matter in the range $U_\Sigma^{(N)}\approx 10-30$ MeV. This range of values for $U_\Sigma^{(N)} $ is also supported by the criterion of best agreement with all available data from INS and XRT.

Static spherically symmetric three-form stars

We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field A_{alpha beta gamma }, which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5 M_{odot } mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory.

Detecting resonant tidal excitations of Rossby modes in coalescing neutron-star binaries with third-generation gravitational-wave detectors

Rossby modes ($r$-modes) of rotating neutron stars can be excited by the gravitomagnetic forces in coalescing binary systems. A previous study by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)] showed that this kind of dynamical tide (DT) can induce phase shifts of $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{rad}$ on gravitational waveforms, which is detectable by third-generation (3G) detectors. We study the impact of this DT on measuring neutron-star parameters in the era of 3G detectors. We incorporate two universal relations among neutron-star properties predicted by different equations of state: (i) the well-known I-Love relation between momentum of inertia and ($f$-mode) tidal Love number, and (ii) a relation between the $r$-mode overlap and tidal Love number, which we newly explore. We find that $r$-mode DT will provide rich information about slowly rotating neutron stars with frequency 10--100 Hz and spin inclination angle 18\ifmmode^\circ\else\textdegree\fi{}--110\ifmmode^\circ\else\textdegree\fi{}. For a binary neutron-star system (with a signal-to-noise ratio $\ensuremath{\sim}1500$ in the Cosmic Explorer), the spin frequency of each individual neutron star can be constrained to 6% (fractional error) in the best-case scenario. The degeneracy between the Love numbers of individual neutron stars is dramatically reduced: each individual Love number can be constrained to around 20% in the best case, while the fractional error for both symmetric and antisymmetric Love numbers are reduced by factors of around 300. Furthermore, DT also allows us to measure the spin inclination angles of the neutron stars, to 0.09 rad in the best case, and thus place constraints on neutron-star natal kicks and supernova explosion models. In addition to parameter estimation, we also develop a semianalytic method that accurately describes detailed features of the binary evolution that arise due to the DT.

Axisymmetric models for neutron star merger remnants with realistic thermal and rotational profiles

Merging neutron stars are expected to produce hot, metastable remnants in rapid differential rotation, which subsequently cool and evolve into rigidly rotating neutron stars or collapse to black holes. Studying this metastable phase and its further evolution is essential for the prediction and interpretation of the electromagnetic, neutrino, and gravitational signals from such a merger. In this work, we model binary neutron star merger remnants and propose new rotation and thermal laws that describe post-merger remnants. Our framework is capable to reproduce quasi-equilibrium configurations for generic equations of state, rotation and temperature profiles, including nonbarotropic ones. We demonstrate that our results are in agreement with numerical relativity simulations concerning bulk remnant properties like the mass, angular momentum, and the formation of a massive accretion disk. Because of the low computational cost for our axisymmetric code compared to full 3+1-dimensional simulations, we can perform an extensive exploration of the binary neutron star remnant parameter space studying several hundred thousand configurations for different equation of states.

Quiescent luminosities of accreting neutron stars with different equation of states

We model the quiescent luminosity of accreting neutron stars with several equation of states (EOSs), including the effect of pion condensation and superfluidity. As a consequence of comparison with the observations, we show that the results with Togashi EoS (the strong direct Urca process is forbidden) and TM1e EoS (mass at direct Urca process is $2.06 M_\odot$) can explain the observations well by considering pion condensation and the effect of superfluidity, while LS220 EoS and TM1 EoS can explain the observations well by considering the baryon direct Urca process and the effect of superfluidity. Besides, we compare the results with the observations of a neutron star RX J0812.4-3114 which has the low average mass accretion rate ($\langle\dot{M}\rangle\sim(4-15)\times 10^{-12}~M_\odot ~\rm yr^{-1}$) but high thermal luminosity ($L_q^\infty\sim(0.6-3)\times10^{33}~\rm erg ~ s^{-1}$), and we suggest that a low-mass neutron star ($<1M_\odot$) with minimum cooling can explain the lower limit of the observation of thermal luminosity of RX J0812.4-3114, which is qualitatively consistent with the previous work~\cite{Zhao2019}. However, to explain its upper limit, some other heating mechanisms besides standard deep crustal heating may be needed.

Inference of protoneutron star properties from gravitational-wave data in core-collapse supernovae

The eventual detection of gravitational waves from core-collapse supernovae (CCSN) will help improve our current understanding of the explosion mechanism of massive stars. The stochastic nature of the late post-bounce gravitational wave signal due to the non-linear dynamics of the matter involved and the large number of degrees of freedom of the phenomenon make the source parameter inference problem very challenging. In this paper we take a step towards that goal and present a parameter estimation approach which is based on the gravitational waves associated with oscillations of proto-neutron stars (PNS). Numerical simulations of CCSN have shown that buoyancy-driven g-modes are responsible for a significant fraction of the gravitational wave signal and their time-frequency evolution is linked to the physical properties of the compact remnant through universal relations, as demonstrated in [1]. We use a set of 1D CCSN simulations to build a model that relates the evolution of the PNS properties with the frequency of the dominant g-mode, which is extracted from the gravitational-wave data using a new algorithm we have developed for our study. The model is used to infer the time evolution of a combination of the mass and the radius of the PNS. The performance of the method is estimated employing simulations of 2D CCSN waveforms covering a progenitor mass range between 11 and 40 solar masses and different equations of state. Considering signals embedded in Gaussian gravitational wave detector noise, we show that it is possible to infer PNS properties for a galactic source using Advanced LIGO and Advanced Virgo data at design sensitivities. Third generation detectors such as Einstein Telescope and Cosmic Explorer will allow to test distances of ${\cal O}(100\, {\rm kpc})$.

Probing the boundary of phase transition of nuclear matter using proton flows in heavy-ion collisions at 2-8 GeV/nucleon

Based on the relativistic transport model ART with the hadronic equation of state extended to have a phase transition via the use of the MIT bag model, properties of phase transition of dense nuclear matter formed in relativistic heavy-ion collisions are investigated. Proton sideward and directed flows are calculated with different equation of states in Au + Au collisions at beam energies of 2, 4, 6 and 8 GeV/nucleon. Compared with AGS experimental data in existence, the boundary of first-order phase transition is roughly confined, i.e., in the range of 2.5-4 times saturation density with temperature about 64-94 MeV. Such constraints are useful for ongoing RHIC Beam Energy Scan-II program to study the QCD matter phase diagram.

High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any solution of any system of hyperbolic balance laws in multiple spatial dimensions and not only time independent solutions. The solution has to be known a priori, either as an analytical expression or as discrete data. The proposed framework modifies the standard finite volume approach such that the well-balancing property is obtained and in case the method is high order accurate, this is maintained under our modification. We present numerical tests for the compressible Euler equations with and without gravity source term and with different equations of state, and for the equations of compressible ideal magnetohydrodynamics.

Measurement of gas contents in shale reservoirs – impact of gas density and implications for gas resource estimates

Gas shale reservoirs pose unique measurement challenges due to their ultra-low petrophysical properties and complicated pore structures. A small variation in an experimental parameter, under high-pressure conditions, may result in huge discrepancies in gas contents and the resource estimates derived from such data. This study illustrates the impact of the equation of state on the gas content determined for a shale sample. The gas content was determined from laboratory-measured high-pressure methane adsorption isotherms and theoretically described by a hybrid type model. The modelling involved the use of the Dubinin–Radushkevich isotherm to obtain the adsorbed phase density followed by the Langmuir isotherm to describe the resultant absolute adsorptions. Significant variations were observed in measured adsorption isotherms due to the variations in gas densities calculated from different equations of states. The model parameters and the gas in-place volumes estimated from those parameters also varied significantly.

Reflecting laser-driven shocks in diamond in the megabar pressure range

AbstractIn this work we present experimental results on the behavior of diamond at megabar pressure. The experiment was performed using the PHELIX facility at GSI in Germany to launch a planar shock into solid multi-layered diamond samples. The target design allows shock velocity in diamond and in two metal layers to be measured as well as the free surface velocity after shock breakout. As diagnostics, we used two velocity interferometry systems for any reflector (VISARs). Our measurements show that for the pressures obtained in diamond (between 3 and 9 Mbar), the propagation of the shock induces a reflecting state of the material. Finally, the experimental results are compared with hydrodynamical simulations in which we used different equations of state, showing compatibility with dedicated SESAME tables for diamond.

Shock Hugoniot Data for Water up to 5 Mbar Obtained with Quartz Standard at High-Energy Laser Facilities

In this work, we present experimental results on the behavior of liquid water at megabar pressure. The experiment was performed using the HIPER (High-Intensity Plasma Experimental Research) laser facility, a uniaxial irradiation chamber of GEKKO XII (GXII) at the Institute of Laser Engineering (ILE), and the PHELIX at GSI (GSI Helmholtz Centre for Heavy Ion Research), a single-beam high-power laser facility, to launch a planar shock into solid multilayered water samples. Equation-of-state data of water (H2O are obtained in the pressure range 0.50–4.6 Mbar by tuning the laser-drive parameters. The Hugoniot parameters (pressure, density, etc.) and the shock temperature were simultaneously determined by using VISAR and SOP as diagnostic tools and quartz as the standard material for impedance mismatch experiments. Finally, our experimental results are compared with hydrodynamic simulations tested with different equations of state, showing good compatibility with tabulated SESAME tables for water.

Migration jumps of planets in transition discs

Context. Transition discs form a special class of protoplanetary discs that are characterised by a deficiency of disc material close to the star. In a subgroup, inner holes in these discs can stretch out to a few tens of au while there is still mass accretion onto the central star observed at the same time. Aims. We analyse the proposition that this type of wide transition disc is generated by the interaction of the disc with a system of embedded planets. Methods. We performed two-dimensional hydrodynamics simulations of a flat disc. Different equations of state were used including locally isothermal models and more realistic cases that consider viscous heating, radiative cooling, and stellar heating. Two massive planets (with masses of between three and nine Jupiter masses) were embedded in the disc and their dynamical evolution due to disc–planet interaction was followed for over 100 000 yr. The simulations account for mass accretion onto the star and planets. We included models with parameters reminiscent of the system PDS 70. To assess the observability of features in our models we performed synthetic ALMA observations. Results. For systems with a more massive inner planet, there are phases where both planets migrate outward engaged in a 2:1 mean motion resonance via the Masset-Snellgrove mechanism. In sufficiently massive discs, the resulting formation of a vortex and the interaction with it can trigger rapid outward migration of the outer planet where its distance can increase by tens of au in a few thousand years. After another few thousand years, the outer planet rapidly migrates back inwards into resonance with the inner planet. We call this emerging composite phenomenon a migration jump. Outward migration and the migration jumps are accompanied by a high mass accretion rate onto the star. The synthetic images reveal numerous substructures depending on the type of dynamical behaviour. Conclusions. Our results suggest that the outward migration of two embedded planets is a prime candidate for the explanation of the observed high stellar mass accretion rate in wide transition discs. The models for PDS 70 indicate it is not currently undergoing a migration jump but might very well be in a phase of outward migration.

Theoretical versus Observational Uncertainties: Composition of Giant Exoplanets

Abstract In order to characterize giant exoplanets and better understand their origin, knowledge of how the planet’s composition depends on its mass and stellar environment is required. In this work, we simulate the thermal evolution of gaseous planets and explore how various common model assumptions such as different equations of state, opacities, and heavy-element distributions affect the inferred radius and metallicity. We examine how the theoretical uncertainties translate into uncertainties in the inferred planetary radius and bulk metallicity. While we confirm the mass–metallicity trend previously reported in the literature, this correlation disappears when removing a 20 M ⊕ heavy-element core from all the planets. We also show that using an updated hydrogen–helium equation of state leads to more compact planets. As a result, we present six planets that should be classified as inflated warm Jupiters. We next demonstrate that including the opacity enhancement due to metal-rich envelopes of irradiated planets changes the planetary radius significantly, which can have large effects on the inferred metallicity. Even though there are other model assumptions that have not been considered in this work, we could show that the calculated theoretical uncertainties can already be comparable or even larger than the observational ones. Therefore, theoretical uncertainties are likely to be even larger. We therefore conclude that progress in theoretical models of giant planets is essential in order to take full advantage of current and future exoplanetary data.

Seismic solar models from Ledoux discriminant inversions

Context. The Sun constitutes an excellent laboratory of fundamental physics. With the advent of helioseismology, we were able to probe its internal layers with unprecendented precision and thoroughness. However, the current state of solar modelling is still stained by tedious issues. One of these central problems is related to the disagreement between models computed with recent photospheric abundances and helioseismic constraints. The observed discrepancies raise questions on some fundamental ingredients entering the computation of solar and stellar evolution models. Aims. We used solar evolutionary models as initial conditions for reintegrating their structure using Ledoux discriminant inversions. The resulting models are defined as seismic solar models, satisfying the equations of hydrostatic equilibrium. These seismic models will allow us to better constrain the internal structure of the Sun and provide complementary information to that of calibrated standard and non-standard models. Methods. We used inversions of the Ledoux discriminant to reintegrate seismic solar models satisfying the equations of hydrostatic equilibrium. These seismic models were computed using various reference models with different equations of state, abundances, and opacity tables. We checked the robustness of our approach by confirming the good agreement of our seismic models in terms of sound speed, density, and entropy proxy inversions, as well as frequency-separation ratios of low-degree pressure modes. Results. Our method allows us to determine the Ledoux discriminant profile of the Sun with an excellent accuracy and compute full profiles of this quantity. Our seismic models show an agreement with seismic data of ≈0.1% in sound speed, density, and entropy proxy after seven iterations in addition to an excellent agreement with the observed frequency-separation ratios. They surpass all standard and non-standard evolutionary models including ad hoc modifications of their physical ingredients that aim to reproduce helioseismic constraints. Conclusions. The obtained seismic Ledoux discriminant profile, as well as the full consistent structure obtained from our reconstruction procedure paves the way for renewed attempts at constraining the solar modelling problem and the missing physical processes acting in the solar interior by breaking free from the hypotheses of evolutionary models.

The Boltzmann-radiation-hydrodynamics Simulations of Core-collapse Supernovae with Different Equations of State: The Role of Nuclear Composition and the Behavior of Neutrinos

Abstract Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the different strength of the prompt convection and the later neutrino-driven convection. The protoneutron star seen in the FS model is more compact than that in the LS model because the existence of multinuclear species softens the EOS. For the behavior of neutrinos, we examined the flux and the Eddington tensor of neutrinos. In the optically thick region, the diffusion of neutrinos and the dragging by the motion of matter determine the flux. In the optically thin region, the free-streaming determines it. The Eddington tensor is compared with that obtained from the M1-closure relation. The M1-closure scheme overestimates the contribution from the velocity-dependent terms in the semitransparent region.