Realistic Equation Of State Research Articles

Compact static stars in minimal dilatonic gravity

In the version1 of this paper we presented for the first time the basic equations and relations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG). This model is locally equivalent to the f(R) theory of gravity and gives an alternative description of the effects of dark matter and dark energy using the Brans–Dicke dilaton [Formula: see text]. To outline the basic properties of the MDG model of SSSS and to compare them with general relativistic results, in this paper we use the relativistic equation of state (EOS) of neutron matter as an ideal Fermi neutron gas at zero temperature. We overcome the well-known difficulties of the physics of SSSS in the f(R) theories of gravity[Formula: see text] applying novel highly nontrivial nonlinear boundary conditions, which depend on the global properties of the solution and on the EOS. We also introduce two pairs of new notions: cosmological–energy–pressure densities and dilaton–energy–pressure densities, as well as two new EOSs for them: cosmological EOS (CEOS) and dilaton EOS (DEOS). Special attention is paid to the dilatonic sphere (in brief — disphere) of SSSS, introduced in this paper for the first time. Using several realistic EOS for neutron star (NS): SLy, BSk19, BSk20 and BSk21, and current observational two-solar-masses-limit, we derive an estimate for scalar-field-mass [Formula: see text]. Thus, the present version of the paper reflects some of the recent developments of the topic.

The Fate of Neutron Star Binary Mergers

Abstract Following merger, a neutron star (NS) binary can produce roughly one of three different outcomes: (1) a stable NS, (2) a black hole (BH), or (3) a supramassive, rotationally supported NS, which then collapses to a BH following angular momentum losses. Which of these fates occur and in what proportion has important implications for the electromagnetic transient associated with the mergers and the expected gravitational wave (GW) signatures, which in turn depend on the high density equation of state (EOS). Here we combine relativistic calculations of NS masses using realistic EOSs with Monte Carlo population synthesis based on the mass distribution of NS binaries in our Galaxy to predict the distribution of fates expected. For many EOSs, a significant fraction of the remnants are NSs or supramassive NSs. This lends support to scenarios in which a quickly spinning, highly magnetized NS may be powering an electromagnetic transient. This also indicates that it will be important for future GW observatories to focus on high frequencies to study the post-merger GW emission. Even in cases where individual GW events are too low in signal to noise to study the post merger signature in detail, the statistics of how many mergers produce NSs versus BHs can be compared with our work to constrain the EOS. To match short gamma-ray-burst (SGRB) X-ray afterglow statistics, we find that the stiffest EOSs are ruled out. Furthermore, many popular EOSs require a significant fraction of ∼60%–70% of SGRBs to be from NS–BH mergers rather than just binary NSs.

A new equation of state for core-collapse supernovae based on realistic nuclear forces and including a full nuclear ensemble

We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and three-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli- and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOSs, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOSs to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which may be an artifact, though, caused by the use of the same tabulated electron capture rates for heavy nuclei ignoring differences in the nuclear composition between the two EOSs in these computations.

The Boulware–Deser class of spacetimes radiates

We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.

The stability of relativistic stars and the role of the adiabatic index

We study the stability of three analytical solutions of the Einstein’s field equations for spheres of fluid. These solutions are suitable to describe compact objects including white dwarfs, neutron stars and supermassive stars and they have been extensively employed in the literature. We re-examine the range of stability of the Tolman VII solution, we focus on the stability of the Buchdahl solution which is under contradiction in the literature and we examine the stability of the Nariai IV solution. We found that all the mentioned solutions are stable in an extensive range of the compactness parameter. We also concentrate on the effect of the adiabatic index on the instability condition. We found that the critical adiabatic index, depends linearly on the ratio of central pressure over central energy density $$P_c/{\mathcal{E}}_c$$ , up to high values of the compactness. Finally, we examine the possibility to impose constraints, via the adiabatic index, on realistic equations of state in order to ensure stable configurations of compact objects.

Gravito-turbulence in irradiated protoplanetary discs

Using radiation hydrodynamics simulations in a local stratified shearing box with realistic equations of state and opacities, we explored the outcome of self-gravity at 50 AU in a protoplanetary disc irradiated by the central star. We found that gravito-turbulence is sustained for a finite range of the surface density, from $\sim 80$ to $\sim$ 250 gcm$^{-2}$. The disk is laminar below the range while fragments above it. In the range of gravito-turbulence, the Toomre parameter decreases monotonically from $\sim 1$ to $\sim 0.7$ as the surface density increases while an effective cooling time is almost constant at $\sim 4$ in terms of the inverse of the orbital frequency. The turbulent motions are supersonic at all heights, which dissipates through both shock waves and compressional heating. The compressional motions, occurring near the midplane, create upward flows, which not only contribute to supporting the disc but also to transporting the dissipated energy to the disc surfaces. The irradiation does not affect much the gravito-turbulence near the midplane unless the grazing angle is larger than 0.32. We also show that a simple cooling function with a constant cooling time does not approximate the realistic cooling.

On the maximum mass of magnetized white dwarfs

We develop a detailed and self-consistent numerical model for extremely-magnetised white dwarfs, which have been proposed as progenitors of overluminous Type Ia supernovae. This model can describe fully-consistent equilibria of magnetic stars in axial symmetry, with rotation, general-relativistic effects and realistic equations of state (including electron-ion interactions and taking into account Landau quantisation of electrons due to the magnetic field). We study the influence of each of these ingredients onto the white dwarf structure and, in particular, on their maximum mass. We perform an extensive stability analysis of such objects, with their highest surface magnetic fields reaching $\sim 10^{13}~G$ (at which point the star adopts a torus-like shape). We confirm previous speculations that although very massive strongly magnetised white dwarfs could potentially exist, the onset of electron captures and pycnonuclear reactions may severely limit their stability. Finally, the emission of gravitational waves by these objects is addressed, showing no possibility of detection by the currently planned space-based detector eLISA.

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.

Structure of compact stars in R-squared Palatini gravity

We analyse configurations of compact stars in the so-called R-squared gravity in the Palatini formalism. Using a realistic equation of state we show that the mass-radius configurations are lighter than their counterparts in General Relativity. We also obtain the internal profiles, which run in strong correlation with the derivatives of the equation of state, leading to regions where the mass parameter decreases with the radial coordinate in a counter-intuitive way. In order to analyse such correlation, we introduce a parametrisation of the equation of state given by multiple polytropes, which allows us to explicitly control its derivatives. We show that, even in a limiting case where hard phase transitions in matter are allowed, the internal profile of the mass parameter still presents strange features and the calculated M-R configurations also yield NSs lighter than those obtained in General Relativity.

Modeling of non-rotating neutron stars in minimal dilatonic gravity

The model of minimal dilatonic gravity (MDG), called also the massive Branse-Dicke model with $\omega =0$ , is an alternative model of gravitation, which uses one Branse-Dicke gravitation-dilaton field $\varPhi $ and offers a simultaneous explanation of the effects of dark energy (DE) and dark matter (DM). Here we present an extensive research of non-rotating neutron star models in MDG with four different realistic equations of state (EOS), which are in agreement with the latest observational data. The equations describing static spherically symmetric stars in MDG are solved numerically. The effects corresponding to DE and DM are clearly seen and discussed.

Relativistic stars in beyond Horndeski theories

This work studies relativistic stars in beyond Horndeski scalar–tensor theories that exhibit a breaking of the Vainshtein mechanism inside matter, focusing on a model based on the quartic beyond Horndeski Lagrangian. We self-consistently derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space–time and show that the Vainshtein breaking branch of the solutions is the physical branch thereby resolving several ambiguities with non-relativistic frameworks. The geometry outside the star is shown to be exactly Schwarzschild-de Sitter and therefore the parameterised post-Newtonian parameter , confirming that the external screening works at the post-Newtonian level. The Tolman–Oppenheimer–Volkoff (TOV) equations are derived and a new lower bound on the Vainshtein breaking parameter is found by requiring the existence of static spherically symmetric stars. Focusing on the unconstrained case where , we numerically solve the TOV equations for polytropic and realistic equations of state and find stars with larger radii at fixed mass. Furthermore, the maximum mass can increase dramatically and stars with masses in excess of can be found for relatively small values of the Vainshtein breaking parameter. We re-examine white dwarf stars and show that post-Newtonian corrections are important in beyond Horndeski theories and therefore the bounds coming from previous analyses should be revisited.

THE INTERNAL STRUCTURE AND PROPAGATION OF MAGNETOHYDRODYNAMICAL THERMONUCLEAR FLAMES

ABSTRACT We present general equations for non-ideal, reactive flow magnetohydrodynamics (RFMHD) in the form best suited for describing thermonuclear combustion in high-density degenerate matter of SNe Ia. The relative importance of various non-ideal effects is analyzed as a function of characteristic spatial and temporal scales of the problem. From the general RFMHD equations, we derive the one-dimensional ordinary differential equations describing the steady-state propagation of a planar thermonuclear flame front in a magnetic field. The physics of the flame is first studied qualitatively using a simple case of one-step Arrhenius kinetics, a perfect gas equation of state (EOS), and constant thermal conductivity coefficients. After that, the equations are solved, the internal flame front structure is calculated, and the flame velocity, S l , and flame thickness, δ l , are found for carbon–oxygen degenerate material of supernovae using a realistic EOS, transport properties, and detailed nuclear kinetics. The magnetic field changes the flame behavior significantly, both qualitatively and quantitatively, as compared to the non-magnetic case of classical combustion. (1) The magnetic field influences the evolutionarity of a flame front and makes it impossible for a flame to propagate steadily in a wide range of magnetic field strengths and orientations relative to the front. (2) When the flame moves steadily, it can propagate in several distinct modes, the most important being the slow C S and super-Alfvénic C sup modes. (3) The speed of the flame can be diminished or enhanced by up to several factors relative to the non-magnetic laminar flame speed.

Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity

In this paper, we study in detail the role of general relativity on the global dynamics of giant pulsar glitches as exemplified by Vela. For this purpose, we carry out numerical simulations of the spin up triggered by the sudden unpinning of superfluid vortices. In particular, we compute the exchange of angular momentum between the core neutron superfluid and the rest of the star within a two-fluid model including both (non-dissipative) entrainment effects and (dissipative) mutual friction forces. Our simulations are based on a quasi-stationary approach using realistic equations of state (EoSs). We show that the evolution of the angular velocities of both fluids can be accurately described by an exponential law. The associated characteristic rise time $\tau_{\text{r}}$, which can be precisely computed from stationary configurations only, has a form similar to that obtained in the Newtonian limit. However, general relativity changes the structure of the star and leads to additional couplings between the fluids due to frame-dragging effects. As a consequence, general relativity can have a large impact on the actual value of $\tau_{\text{r}}$: the errors incurred by using Newtonian gravity are thus found to be as large as $\sim 40 \%$ for the models considered. Values of the rise time are calculated for Vela and compared with current observational limits. Finally, we study the amount of gravitational waves emitted during a glitch. Simple expressions are obtained for the corresponding characteristic amplitudes and frequencies. The detectability of glitches through gravitational wave observatories is briefly discussed.

Parameterized neutron star and proto-neutron star equation of state at finite temperature

Read et al. proposed a parameterized equation of state (EOS) giving the pressure \(P\) as a function of the rest mass density \(\rho\) in a piecewise polytropic form for the study of neutron stars. The parameterized piecewise polytropic EOS can accurately represent many realistic EOS tables at zero temperature. We showed that the treatment can be extended to finite temperature to cover the study of neutron star at non zero temperature and proto-neutron stars. At finite temperature, two types of thermodynamic relations are needed, one for the pressure \(P\) and one for the internal energy density \(u\). We show that for many finite temperature realistic EOS tables, both the \(P\) and \(u\) can be accurately represented in piecewise polytropic forms as functions of the rest mass density \(\rho\) and temperature \(T\). The polytropic parameterization provides a framework to compare and understand the properties of the different realistic EOSs.

Dipole magnetic field of neutron stars in $$f(R)$$ f ( R ) gravity

The structure of an interior dipole magnetic field of neutron stars in $f(R)$ gravity is considered. For this purpose, the perturbative approaches are used when both the deviations from general relativity and the deformations of spherically symmetric configurations associated with the presence of the magnetic field are assumed to be small. Solutions are constructed which describe relativistic, spherically symmetric configurations consisting of a gravitating magnetized perfect fluid modeled by a realistic equation of state. Comparing configurations from general relativity and modified gravity, we reveal possible differences in the structure of the magnetic field which occur in considering neutron stars in modified gravity.

Cool and luminous transients from mass-losing binary stars

Motivated by the recently established link between luminous red novae (LRN) and catastrophic phases of binary star evolution, we perform smoothed particle hydrodynamic calculations of outflows from binary stars with realistic equation of state and opacities. We focus on the case of mass loss from the outer Lagrangian point (L2), where the resulting spiral stream experiences tidal torques from the binary and becomes unbound. As the individual spiral arms merge and collide near the binary, the outflow thermalizes about 5% of its kinetic energy. For reasonable binary parameters, the outflow can produce luminosities up to 106 L⨀ with effective temperatures between 500 and 6000 K, depending on the optical depth through the outflow. This is compatible with many examples of the LRN such as V838 Mon and V1309 Sco. The luminosity and the expansion velocity are correlated, as is roughly observed in the known LRN. The outflow readily forms dust, leading to great variations of the appearance of the transient as a function of the viewing angle. Our results are relevant for a more general class of equatorial outflows with asymptotic velocity and heating rate near the binary proportional to its orbital speed.

Gravitational-wave signal from binary neutron stars: A systematic analysis of the spectral properties

A number of works have shown that important information on the equation of state of matter at nuclear density can be extracted from the gravitational waves emitted by merging neutron-star binaries. We present a comprehensive analysis of the gravitational-wave signal emitted during the inspiral, merger and post-merger of 56 neutron-star binaries. This sample of binaries, arguably the largest studied to date with realistic equations of state, spans across six different nuclear-physics equations of state and ten masses, allowing us to sharpen a number of results recently obtained on the spectral properties of the gravitational-wave signal. Overall we find that: (i) for binaries with masses differing no more than $20\%$, the frequency at gravitational-wave amplitude's maximum is related quasi-universally with the tidal deformability of the two stars; (ii) the spectral properties vary during the post-merger phase, with a transient phase lasting a few millisecond after the merger and followed by a quasi-stationary phase; (iii) when distinguishing the spectral peaks between these two phases, a number of ambiguities in the identification of the peaks disappear, leaving a simple and robust picture; (iv) using properly identified frequencies, quasi-universal relations are found between the spectral features and the properties of the neutron stars; (v) for the most salient peaks analytic fitting functions can be obtained in terms of the stellar tidal deformability or compactness. Altogether, these results support the idea that the equation of state of nuclear matter can be constrained tightly when a signal in gravitational waves from binary neutron stars is detected.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng–Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young–Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young–Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young–Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.

Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity

This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift and the inertia of these objects and compare them with known data.

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $\chi_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $\chi_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $\chi_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $\tau$ with a power law $\sim\tau^{-a}$, two distinct solutions can be found depending on the values of $a$ and $\chi_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the non-vanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. Only for magnetic fields which are about an order of magnitude larger than expected for heavy-ion collisions, the system is substantially reheated and the lifetime of the quark phase might be extended.