Zero-temperature Equation Of State Research Articles

Realistic finite-temperature effects in neutron star merger simulations

Binary neutron star mergers provide a unique probe of the dense-matter equation of state (EoS) across a wide range of parameter space, from the zero-temperature EoS during the inspiral to the high-temperature EoS following the merger. In this paper, we implement a new model for calculating parametrized finite-temperature EoS effects into numerical relativity simulations. This "M* model" is based on a two-parameter approximation of the particle effective mass and includes the leading-order effects of degeneracy in the thermal pressure and energy. We test our numerical implementation by performing evolutions of rotating single stars with zero- and non-zero temperature gradients, as well as evolutions of binary neutron star mergers. We find that our new finite-temperature EoS implementation can support stable stars over many dynamical timescales. We also perform a first parameter study to explore the role of the M* parameters in binary neutron star merger simulations. All simulations start from identical initial data with identical cold EoSs, and differ only in the thermal part of the EoS. We find that both the thermal profile of the remnant and the post-merger gravitational wave signal depend on the choice of M* parameters, but that the total merger ejecta depends only weakly on the finite-temperature part of the EoS across a wide range of parameters. Our simulations provide a first step toward understanding how the finite-temperature properties of dense matter may affect future observations of binary neutron star mergers.

Unexpected cold curve sensitivity to GGA exchange form

Finding the crystalline phase transitions along the zero-temperature equation of state (“cold curve”) of elemental solids has been a triumph of density functional theory even in the simple local-density approximation. The present work shows how quantitatively significant improvement on molecules in a generalized gradient approximation functional can result in unexpected ambiguity in the cold curve. The specific cause is obscure but some possibilities are discussed.

Dipolar bilayer with antiparallel polarization: A self-bound liquid

Dipolar bilayers with antiparallel polarization, i.e. opposite polarization in the two layers, exhibit liquid-like rather than gas-like behavior. In particular, even without external pressure a self-bound liquid puddle of constant density will form. We investigate the symmetric case of two identical layers, corresponding to a two-component Bose system with equal partial densities. The zero-temperature equation of state $E(\rho)/N$, where $\rho$ is the total density, has a minimum, with an equilibrium density that decreases with increasing distance between the layers. The attraction necessary for a self-bound liquid comes from the inter-layer dipole-dipole interaction that leads to a mediated intra-layer attraction. We investigate the regime of negative pressure towards the spinodal instability, where the bilayer is unstable against infinitesimal fluctuations of the total density, conformed by calculations of the speed of sound of total density fluctuations.

Rotating protoneutron stars: Spin evolution, maximum mass, and I-Love-Q relations

Shortly after its birth in a gravitational collapse, a proto-neutron star enters in a phase of quasi-stationary evolution characterized by large gradients of the thermodynamical variables and intense neutrino emission. In few tens of seconds the gradients smooth out while the star contracts and cools down, until it becomes a neutron star. In this paper we study this phase of the proto-neutron star life including rotation, and employing finite temperature equations of state. We model the evolution of the rotation rate, and determine the relevant quantities characterizing the star. Our results show that an isolated neutron star cannot reach, at the end of the evolution, the maximum values of mass and rotation rate allowed by the zero-temperature equation of state. Moreover, a mature neutron star evolved in isolation cannot rotate too rapidly, even if it is born from a proto-neutron star rotating at the mass-shedding limit. We also show that the I-Love-Q relations are violated in the first second of life, but they are satisfied as soon as the entropy gradients smooth out.

Dispersion Interactions and Vibrational Effects in Ice as a Function of Pressure: A First Principles Study

We present a first principles theoretical framework that accurately accounts for several properties of ice, over a wide pressure range. In particular, we show that, by using a recently developed nonlocal van der Waals functional and by taking into account hydrogen zero point motion, one can properly describe the zero temperature equation of state, the vibrational spectra, and the dielectric properties of ice at low pressure and of ice VIII, a stable phase between 2 and 60GPa. While semilocal density functionals yield a transition pressure from ice XI to VIII that is overestimated by almost an order of magnitude, we find good agreement with experiments when dispersion forces are taken into account. Zero point energy contributions do not alter the computed transition pressure, but they affect structural properties, including equilibrium volumes and bulk moduli.

Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent $s$-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

Melting curve of tantalum from first principles

We report on the first-principles calculation of the melting curve of Ta in the pressure range 0 – 300 GPa. The calculations have been performed using density functional theory DFT with generalized gradient corrections and the projector augmented wave method. The melting curve has been evaluated using the method of the coexistence of phases, with the help of an auxiliary reference potential. The melting curve obtained with the reference potential has then been corrected using free energy differences between the DFT and the reference potential, so as to obtain the DFT melting curve. The results are in good agreement with diamond anvil cell experiments at low pressure, but they rapidly diverge from these as pressure is increased, and agree well with shock-wave experiments at high pressure. A general description of the lattice dynamics and thermal properties of body-centered cubic tantalum using DFT is also presented. The equation of state at zero temperature and the phonon dispersion are investigated using both the local density approximation and the generalized gradient approximation GGA. Good agreement with the zero-temperature equation of state and zero-pressure phonon dispersions is obtained with the GGA. This agreement reinforces the reliability of the calculated melting curve.

GFMC studies of low-density neutron matter

Green's function Monte Carlo methods are used to provide benchmarks for studies of low-density neutron matter. The zero-temperature equation of state and pair correlation functions are studied for the AV8 $^\prime$ NN interaction model, and for an idealized model comprised of neutrons with a short-range interaction and an arbitrarily large (negative) scattering length. For this idealized problem the equation of state is a constant multiplied by the Fermi-gas energy, this constant is found to be nearly 1/2. Similar ratios are found for realistic NN interactions.

Equation of state for tantalum from relativistic linear combinations of Gaussian-type orbitals calculations

The zero-temperature equation of state (EOS) for tantalum (Ta) is calculated to 2.5 Mbar with the relativistic linear combinations of Gaussian type orbital--fitting-function (LCGTO-FF) method, for two density functional models: the local density approximation (LDA) and the generalized gradient approximation (GGA). The EOS is determined both with and without spin-orbit coupling included. The effect of spin-orbit coupling is found to be nearly negligible over the compression range considered, in sharp disagreement with a previous calculation using the full-potential linear muffin-tin orbital method. A serious discrepancy between 300 K diamond anvil cell data and reduced shock data for Ta is shown to result from an underestimate of the Grueneisen parameter during the reduction of the shock data. The GGA model reproduces the zero-pressure properties of Ta quite well, while the high-pressure EOS data is in better accord with the LDA calculations. Neither model provides an adequate representation for the EOS over the full range of the data.

Predicting the Liquid-Vapor Critical Point from the Crystal Anharmonicity

A ‘universal’ dependence is predicted of the reduced critical parameters (temperature, density, and pressure) on the crystal anharmonicity. The model, which employs the ‘universal’ zero-temperature equation of state in a version of fluid perturbation theory, is apparently the first to predict correctly the critical temperature and density for both the rare gases and Alkali metals.

Predicting the liquid-vapor critical point from the crystal anharmonicity

A "universal" dependence is predicted of the reduced critical parameters, k(B)T(c) / E0(gamma), V(c) / V0(gamma), and P(c)V(c)/k(B)T(c) = Z(c)(gamma), on the crystal anharmonicity gamma (closely related to the Gruneisen parameter gamma(G)). It is based on a simplified embedded-atom type approach which enables one to utilize the universal zero-temperature equation of state in a version of fluid perturbation theory. This model's critical temperature and density agree with the experimental results for both the heavy rare gases ( gamma approximately 2.85) and heavy alkali metals ( gamma approximately 1.35). Predicted critical parameters for many other liquid metals are consistent with previous estimates, but the model is not applicable when directional bonding is important.

Properties of4He in one dimension

It has been suggested recently that 4 He can be prepared and studied as a quasi one-dimensional quantum fluid. We calculate the static and dynamic properties of one-dimensional 4 He using variational methods based upon the Jastrow-Feenberg wavefunction and its extension to dynamic systems with time-dependent, correlated wavefunctions. The zero temperature equation of state shows that in one-dimension 4 He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 A -1 . We also calculate the excitation spectrum including corrections that contain multi-phonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a 3 He impurity and calculate the zero concentration chemical potential as a function of He linear density. We also compute the 3 He- 3 He effective interaction in the 4 He background and compute the energy of dimerization.

Self-interaction-corrected local-spin-density calculations for rare earth materials

The ab initio self-interaction-corrected (SIC) local-spin-density (LSD) approximation is discussed with emphasis on the ability to describe localized f -electron states in rare earth solids. Two methods for minimizing the SIC-LSD total energy functional are discussed, one using a unified Hamiltonian for all electron states, thus having the advantages of Bloch's theorem, the other one employing an iterative scheme in real space. Results for cerium and cerium compounds as well as other rare earths are presented. For the cerium compounds the onset of f -electron delocalization can be accurately described, including the intricate isostructural phase transitions in elemental cerium and CeP. In Pr and Sm the equilibrium lattice constant and zero temperature equation of state is greatly improved in comparison with the LSD results. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 799-813, 2000

InP under high pressures

The direct energy gaps, Eg, and the indirect gaps at the X point, E(X), of GaAs and AlxGa1−xAs alloys are essentially linear functions of hydrostatic pressure, P. Recent photoluminescence measurements of Tozer et al. for InP under high pressures, however, found that Eg(P) is not quite linear, but bends down slightly at high pressures. Using the first-principles pseudofunction method, we have calculated Eg and E(X) as functions of pressure, as well as the zero-temperature equation of state P(V). Our calculated gap curve for InP, Eg(P), bends down slightly, as found in photoluminescence studies. The slope dEg/dP is 8.8 meV/kbar for small pressures P, and is in good agreement with the experimental value, 8.32 meV/kbar. The observed nonlinearity in the dependence of Eg on pressure for InP is attributed to a large derivative of the bulk modulus with respect to pressure. The calculated bond length, bulk modulus, and critical pressure for a phase transition from the zinc blende to a rocksalt structure, and the unit cell volume change at this phase transition are all in good agreement with the data.

Fate of merging double white dwarfs. II - Numerical method

The authors present a new numerical method for constructing models of double white dwarf binary systems and central white dwarf-heavy disk systems. These two types of models were constructed in paper I to examine whether or not the merging white dwarfs result in a Type I supernova. In the present paper, the authors present details of their method for computing three-dimensional models of double white dwarfs with zero-temperature equation of state, and also a computational method for two-dimensional models of a system consisting of a central white dwarf and a surrounding heavy disk.

Comparison of various theoretical solid-state models applied to the equation of state of beryllium

We first compare the accuracy of band-structure and model-potential methods for calculating the total energy and pressure of beryllium at normal density ${\ensuremath{\rho}}_{0}$. The band-structure methods are the well-known augmented-plane-wave (APW) method and the recently proposed linear-muffin-tin-orbitals (LMTO) method; their results are in reasonable agreement, the first one being slightly more accurate. On the other hand, the a priori model-potential method, as proposed by Shaw, gives poorer results. The comparison of the band-structure methods is then carried on at the density $\ensuremath{\rho}=4{\ensuremath{\rho}}_{0}$. The LMTO method (the advantage of which is a very great computational efficiency) is shown to reproduce quite closely the volume variations of energy and pressure found in the APW calculation. Finally, the zero-temperature equation of state of beryllium in the range ${\ensuremath{\rho}}_{0}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}4{\ensuremath{\rho}}_{0}$ is presented. The Hugoniot curve is estimated and compared with available experimental data.

Zero-temperature equation of state of metals in the statistical model with density gradient correction

Abstract The density gradient correction to kinetic energy (nine times smaller than the original von Weizsacker correction) has been used within local density formalism to calculate the cold compression curve of metals. Numerical results are reported for Li, Be, Al and Cu. The modifications to the Thomas-Fermi-Dirac (TFD) results strongly depend, in the low compression range ( ϱ / ϱ 0 ⩽ 5), on the electron density of the material. The relative difference between the pressures in the present model and the TFD model regularly decreases with increasing compression, suggesting that TFD is reliable for ϱ / ϱ 0 ⩾ 50 in Li, ϱϱ 0 ⩾ 20 in Be and Al and ϱ / ϱ 0 ⩾ 10 in Cu.

Finite-temperature system of strongly interacting baryons

A fully relativistic finite temperature many body theory is constructed and used to examine the bulk properties of a system of strongly interacting baryons. The strong interactions are described by a two parameter phenomenological model fit to a simple description of nuclear matter at T = 0. The zero temperature equation of state for such a system which has already been discussed in the literature was developed to give a realistic description of nuclear matter. The model presented here is the exact finite temperature extension of that model. The effect of the inclusion of baryon pairs for T greater than or equal to 2mc/sup 2//k is discussed in detail. The phase transition identified with nuclear matter vanishes for system temperatures in excess of T/sub C/ = 1.034 x 10/sup 11/ /sup 0/K. All values of epsilon (P,T) correspond to systems that are causal in the sense that the locally determined speed of sound never exceeds the speed of light.