Realistic Equation Of State Research Articles

Numerical models for stationary superfluid neutron stars in general relativity with realistic equations of state

We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with the respective fluid velocities. We extend the formalism by Comer and Joynt (2003) in order to calculate the equation of state (EoS) and entrainment parameters for an arbitrary relative velocity. The resulting entrainment matrix fulfills all necessary sum rules and in the limit of small relative velocity our results agree with Fermi liquid theory ones, derived to lowest order in the velocity. This formalism is applied to two new nuclear equations of state which are implemented in the numerical model. We are able to obtain precise equilibrium configurations. Resulting density profiles and moments of inertia are discussed employing both EoSs, showing the impact of entrainment and the dependence on the EoS.

Axial quasinormal modes of Einstein-Gauss-Bonnet-dilaton neutron stars

We investigate axial quasi-normal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider 8 realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling.

Magneto-rotational instability in the protolunar disk

We perform the first study of magnetohydrodynamic processes in the protolunar disk (PLD). With the use of published data on the chemical composition of the PLD, along with existing analytical models of the disk structure, we show that the high temperatures that were prevalent in the disk would have led to ionization of Na, K, SiO, Zn and, to a lesser extent, O2. For simplicity, we assume that the disk has a vapor structure. The resulting ionization fractions, together with a relatively weak magnetic field, possibly of planetary origin, would have been sufficient to trigger the magneto-rotational instability, or MRI, as demonstrated by the fact that the Elsasser criterion was met in the PLD: a magnetic field embedded in the flow would have diffused more slowly than the growth rate of the linear perturbations. We calculate the intensity of the resulting magnetohydrodynamic turbulence, as parameterized by the dimensionless ratio α of turbulent stresses to gas pressure, and obtain maximum values α∼10-2 along most of the vertical extent of the disk, and at different orbital radii. This indicates that, under these conditions, turbulent mixing within the PLD due to the MRI was likely capable of transporting isotopic and chemical species efficiently. To test these results in a conservative manner, we carry out a numerical magnetohydrodynamic simulation of a small, rectangular patch of the PLD, located at 4 Earth radii (rE) from the center of the Earth, and assuming once again that the disk is completely gaseous. We use a polytrope-like equation of state. The rectangular patch is threaded initially by a vertical magnetic field with zero net magnetic flux. This field configuration is known to produce relatively weak MRI turbulence in studies of astrophysical accretion disks. We accordingly obtain turbulence with an average intensity α∼7×10-6 over the course of 280 orbital periods (133days at 4rE). Despite this relatively low value of α, the effective turbulent diffusivity D∼1010-1011cm2s−1 of a passive tracer introduced in the flow is large enough to allow the tracer to spread across a radial distance of 10rE in ∼13–129yr, less than the estimated cooling time of the PLD of ∼250yr. Further improvements to our model will need to incorporate the energy balance in the disk, a complete two-phase structure, and a more realistic equation of state.

Highly-anisotropic Hydrodynamics for Central Collisions

The framework of leading-order anisotropic hydrodynamics is supplemented with realistic equation of state and self-consistent freeze-out prescription. The model is applied to central proton-nucleus collisions. The results are compared to those obtained within standard Israel-Stewart second-order viscous hydrodynamics. It is shown that the resulting hadron spectra are highly-sensitive to the hydrodynamic approach that has been used.

General theory of asymmetric steric interactions in electrostatic double layers.

We study the mean-field Poisson-Boltzmann equation in the context of dense ionic liquids where steric effects become important. We generalise lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other existing lattice gas approximations, not based on the Flory-Huggins Ansatz. Within the methodology presented we also invoke more realistic equations of state, such as the Carnahan-Starling approximation, that are not based on the lattice gas approximation and lead to thermodynamic functions and properties that differ strongly from the lattice gas case. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation.

Cool and luminous transients from mass-losing binary stars

We study transients produced by equatorial disk-like outflows from catastrophically mass-losing binary stars with an asymptotic velocity and energy deposition rate near the inner edge which are proportional to the binary escape velocity v_esc. As a test case, we present the first smoothed-particle radiation-hydrodynamics calculations of the mass loss from the outer Lagrange point with realistic equation of state and opacities. The resulting spiral stream becomes unbound for binary mass ratios 0.06 < q < 0.8. For synchronous binaries with non-degenerate components, the spiral-stream arms merge at a radius of ~10a, where a is the binary semi-major axis, and the accompanying shock thermalizes about 10% of the kinetic power of the outflow. The mass-losing binary outflows produce luminosities reaching up to ~10^6 L_Sun and effective temperatures spanning 500 < T_eff < 6000 K, which is compatible with many of the class of recently-discovered red transients such as V838 Mon and V1309 Sco. Dust readily forms in the outflow, potentially in a catastrophic global cooling transition. The appearance of the transient is viewing angle-dependent due to vastly different optical depths parallel and perpendicular to the binary plane. We predict a correlation between the peak luminosity and the outflow velocity, which is roughly obeyed by the known red transients. Outflows from mass-losing binaries can produce luminous (10^5 L_Sun) and cool (T_eff < 1500 K) transients lasting a year or longer, as has potentially been detected by Spitzer surveys of nearby galaxies.

A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing.For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced.Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity.Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for.

Upper critical field and (non)-superconductivity of magnetars

We construct equilibrium models of compact stars using a realistic equation of state and obtain the density range occupied by the proton superconductor in strong B-fields. We do so by combining the density profiles of our models with microscopic calculations of proton pairing gaps and the critical unpairing field H c2 above which the proton type-II superconductivity is destroyed. We find that magnetars with interior homogeneous field within the range 0.1 ≤ B 16 ≤ 2, where B 16 = B/1016 G, are partially superconducting, whereas those with B 16 > 2 are void of superconductivity. We briefly discuss the neutrino emissivity and superfluid dynamics of magnetars in the light of their (non)-superconductivity.

R-mode instability of strange stars and observations of neutron stars in LMXBs**Supported by the National Natural Science Foundation of China.

Using a realistic equation of state (EOS) of strange quark matter, namely, the modified bag model, and considering the constraints on the parameters of EOS by the observational mass limit of neutron stars, we investigate the r-mode instability window of strange stars, and find the same result as in the brief study of Haskell, Degenaar and Ho in 2012 that these instability windows are not consistent with the spin frequency and temperature observations of neutron stars in low mass X-ray binaries.

Orbital evolution of colliding star and pulsar winds in 2D and 3D: effects of dimensionality, EoS, resolution, and grid size

(abridged)The structure formed by the shocked winds of a massive star and a non-accreting pulsar in a binary suffers periodic and random variations of orbital and non-linear dynamical origin. For the 1st time, we simulate in 3 D the interaction of isotropic stellar and relativistic pulsar winds along 1 full orbit, on scales well beyond the binary size. We also investigate the impact of grid resolution and size, and of different EoOs: a gamma-constant ideal gas, and an ideal gas with gamma dependent on temperature. We carry out, with the code PLUTO, relativistic HD simulations in 2 and 3 D of the interaction of a slow wind and a relativistic wind with Gamma=2 along 1 full orbit up to ~100 x the binary size. The different 2-D simulations are carried out with equal and larger grid resolution and size, and 1 of them is done with a more realistic equation of state, than in 3 D. The simulations in 3 D confirm previous results in 2 D. The shocked flows are subject to a faster instabilities growth in 3 D, which enhances the presence of shocks, mixing, and large-scale disruption. In 2 D, higher resolution simulations confirm lower resolution results, simulations with larger grid sizes strengthen the case for the loss of global coherence of the shocked-wind structure, and simulations with 2 different EoOs yield very similar results. In addition to the KHI, we find that the Richtmyer-Meshkov and the RTI are likely acting together in the shocked flow evolution. Simulations in 3 D confirm that the interaction of stellar and pulsar winds yields structures that evolve non-linearly and get strongly entangled. The evolution is accompanied by strong kinetic energy dissipation, rapid changes in flow orientation and speed, and turbulent motion. The results strengthen the case for the loss of global coherence of the shocked structure on large scales, although higher pulsar wind speed simulations are needed.

Stiffness effects on the dynamics of the bar-mode instability of neutron stars in full general relativity

We present results on the effect of the stiffness of the equation of state on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change in the threshold for the emergence of the instability for a range of the adiabatic $\Gamma$ index from 2.0 to 3.0, including two values chosen to mimic more realistic equations of state at high densities.

Nonperturbative models of quark stars in f(R) gravity

Quark star models with realistic equation of state in nonperturbative f(R) gravity are considered. The mass-radius relation for f(R)=R+αR2 model is obtained. Considering scalar curvature R as an independent function, one can find out, for each value of central density, the unique value of central curvature for which one has solutions with the required asymptotic R→0 for r→∞. In other words, one needs a fine-tuning for R to achieve quark stars in f(R) gravity. We consider also the analogue description in corresponding scalar-tensor gravity. The fine-tuning on R is equivalent to the fine-tuning on the scalar field ϕ in this description. For distant observers, the gravitational mass of the star increases with increasing α (α>0) but the interpretation of this fact depends on frame where we work. Considering directly f(R) gravity, one can say that increasing of mass occurs by the “gravitational sphere” outside the star with some “effective mass”. On the other hand, in conformal scalar-tensor theory, we also have a dilaton sphere (or “disphere”) outside the star but its contribution to gravitational mass for distant observer is negligible. We show that it is possible to discriminate modified theories of gravity from General Relativity due to the gravitational redshift of the thermal spectrum emerging from the surface of the star.

Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs.

Design and performance prediction of radial ORC turboexpanders

In this paper, a zero-dimensional model for the design of radial turbo-expanders for ORC applications is discussed, with special reference to the estimation of losses and efficiency; a comparison between different fluids (R134a, R1234yf, R236fa, R245fa, Cyclohexane, N-Pentane) is presented and discussed, referring to a typical small-size application (50kW). In the model, different methods for the design of radial turbines are screened, with special attention to the estimation of losses, for which correlations from literature are used. Real Equations Of State (EOS) are applied to the expansion process in place of the traditionally adopted Mach relationships for ideal gas, which is a significant advancement for modeling organic fluids in ORC, often operating near to critical conditions. The results show that the total to total efficiency of the designed machines range between 0.72 and 0.80, depending on the considered fluid. Generally, higher efficiency (1.5–2.5% points) can be achieved adopting backswept-bladed rotors. The most significant losses come from the rotor secondary flows, due to the high curvature of blade profiles combined to the large pressure gradient. The best performing fluids are R236fa and R245fa, followed by R134a and R1234yf.Finally, starting from the developed design tool, an off-design analysis of turbo-expanders is presented. Once the design data are available, the characteristic curves of the expander at variable temperature, pressure and fluid mass flowrate at the expander inlet for different values of the specific speed are built. It is thus possible to evaluate the performance of the radial expanders when working far from design point. This analysis, demonstrated for R134a, shows that the total to static efficiency has a relatively modest sensitivity to the off design of the expansion ratio, especially at corrected speed below the design value.

Magnetic field configurations of a magnetar throughout its interior and exterior – core, crust and magnetosphere

We obtained the magnetic field configurations, including both poloidal and toroidal components, throughout the interior and exterior of magnetars using a realistic equation of state. We divided the magnetized star into the hydromagnetic equilibrium core, Hall equilibrium crust and twisted force-free magnetosphere. We systematically and simultaneously calculated these regions under various boundary conditions using the Green function relaxation method, and noted the following interesting characteristics of these numerical results. First, the strength and structure of core magnetic fields affect the crustal magnetic fields. Second, the current sheet on the core-crust interface affects both internal and external magnetic field configurations. Third, the twisted magnetosphere makes a cross-point of magnetic field lines, such as X-point geometry, in the magnetosphere. The X-point geometry appears and disappears according to the strength of the twisted field in the magnetosphere or the core-crust boundary conditions. Our results mean that both Hall magnetohydrodynamics secular evolution and magnetospheric dynamical evolution are deeply affected by conditions of another region and the core-crust stress of magnetars.

Galileons and strong gravity

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppresses the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.

Numerical simulation of non-equilibrium plasma flow in a cylindrical MPD thruster using a high-order flux-difference splitting method

A two-dimensional axisymmetric computational algorithm is developed to simulate the plasma flow field in a self-field MPD thruster, in order to determine the flow behavior and the electromagnetic characteristics distribution. The convective flux vector is computed by using Roe׳s scheme in combination with Powell׳s eigensystem technique, and a new modified MUSCL technique called OMUSCL2 is employed to obtain the stable high-accuracy solution. Madrane–Tadmor entropy correction is used to prevent unrealistic expansion shocks near the electrodes tips. To accurately capture the physics of plasma in the system, different physical–chemical sub-models including multi-level non-equilibrium ionization model, generalized Ohm׳s law for partially ionized plasma, micro-instabilities effects, two-temperature model, and a real equation of state are considered. Numerical results of plasma flow simulation in a cylindrical lab-scale thruster, with mass flow rate of 6g/s and total discharge current of 8kA, are presented and comparison with experimental data shows good agreement between the predicted and measured contours of enclosed current and electric potential. The estimated thrust is 16.34N which exhibits less than 5% difference compared with measured value. Furthermore, this simulation properly predicts the experimentally observed argon jet structure.

Magnetized neutron stars with realistic equations of state and neutrino cooling

We incorporate realistic, tabulated equations of state into fully relativistic simulations of magnetized neutron stars along with a neutrino leakage scheme which accounts for cooling via neutrino emission. Both these improvements utilize open-source code (GR1D) and tables from http://stellarcollapse.org. Our implementation makes use of a novel method for the calculation of the optical depth which simplifies its use with distributed adaptive mesh refinement. We present various tests with and without magnetization and preliminary results both from single stars and from the merger of a binary system.

A method for simulating two-phase pipe flow with real equations of state

Common two-fluid models for pipe flow assume local non-equilibrium regarding phase transfer. To solve the two-fluid models together with accurate equations of state for real fluids will in most cases require mechanical, thermal and chemical equilibrium between the phases. The reason is that reference equations of state for real substances typically describe full thermodynamic equilibrium. In this paper, we present a method for numerically solving an equilibrium model analysed by Morin and Flåtten in the paper A two-fluid four-equation model with instantaneous thermodynamical equilibrium, 2013.The four-equation two-fluid model with instantaneous thermodynamical equilibrium is derived from a five-equation two-fluid model with instantaneous thermal equilibrium. The four-equation model has one mass equation common for both phases, but allows for separate phasic velocities. For comparison, the five-equation two-fluid model is numerically solved, using source terms to impose thermodynamical equilibrium. These source terms are solved using a fractional-step method.We employ the highly accurate Span–Wagner equation of state for CO2, and use the simple and robust FORCE scheme with MUSCL slope limiting. We demonstrate that second-order accuracy may be achieved for smooth solutions, whereas the first-order version of the scheme even allows for a robust transition to single-phase flow, also in the presence of instantaneous phase equilibrium.

Evolution of deviations from the spherical shape of a vapor bubble in supercompression

This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3, ... with the wavelength λ = 2πR/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.