Relativistic Equation Of State Research Articles

The Morphology and Dynamics of Relativistic Jets with Relativistic Equation of State

We study the effect of plasma composition on the dynamics and morphology of relativistic astrophysical jets. Our work is based on a relativistic total variation diminishing simulation code. We use a relativistic equation of state in the simulation code that accounts for the thermodynamics of a multispecies plasma, which is a mixture of electrons, positrons, and protons. To study the effect of plasma composition, we consider various jet models. These models are characterized by the same injection parameters, same jet kinetic luminosity, and the same Mach numbers. The evolution of these models shows that the plasma composition affects the propagation speed of the jet head, the structure of the jet head, and the morphology, despite fixing the initial parameters. We conclude that electron-positron jets are the slowest and show more pronounced turbulent structures in comparison to other plasma compositions. The area and locations of the hot-spots also depend on the composition of the jet plasma. Our results also show that boosting mechanisms are an important aspect of multi-dimensional simulations, which are also influenced by the change in composition.

Study of general relativistic magnetohydrodynamic accretion flow around black holes

ABSTRACT We present a novel approach to study the global structure of steady, axisymmetric, advective, magnetohydrodynamic (MHD) accretion flow around black holes in full general relativity (GR). Considering ideal MHD conditions and relativistic equation of state (REoS), we solve the governing equations to obtain all possible smooth global accretion solutions. We examine the dynamical and thermodynamical properties of accreting matter in terms of the flow parameters, namely energy (${\cal E}$), angular momentum (${\cal L}$), and local magnetic fields. For a vertically integrated GRMHD flow, we observe that toroidal component (bϕ) of the magnetic fields generally dominates over radial component (br) at the disc equatorial plane. This evidently suggests that toroidal magnetic field indeed plays important role in regulating the disc dynamics. We further notice that the disc remains mostly gas pressure (pgas) dominated (β = pgas/pmag > 1, pmag refers magnetic pressure) except at the near horizon region, where magnetic fields become indispensable (β ∼ 1). We observe that Maxwell stress is developed that eventually yields angular momentum transport inside the disc. Towards this, we calculate the viscosity parameter (α) that appears to be radially varying. In addition, we examine the underlying scaling relation between α and β, which clearly distinguishes two domains coexisted along the radial extent of the disc. Finally, we discuss the utility of the present formalism in the realm of GRMHD simulation studies.

Shocks in Radiatively Driven Time-dependent, Relativistic Jets around Black Holes

We study time-dependent relativistic jets under the influence of the radiation field of the accretion disk. The accretion disk consists of an inner compact corona and an outer sub-Keplerian disk. The thermodynamics of the fluid is governed by a relativistic equation of state (EOS) for multispecies fluid that enables us to study the effect of composition on jet dynamics. Jets originate from the vicinity of the central black hole, where the effect of gravity is significant and traverses large distances where only special relativistic treatment is sufficient. So we have modified the flat metric to include the effect of gravity. In this modified relativistic framework we have developed a new total variation diminishing routine along with a multispecies EOS for the purpose. We show that the acceleration of jets crucially depends on flow composition. All the results presented are transonic in nature; starting from very low injection velocities, the jets can achieve high Lorentz factors. For sub-Eddington luminosities, lepton-dominated jets can be accelerated to Lorentz factors >50. The change in radiation field due to variation in the accretion disk dynamics will be propagated to the jet in a finite amount of time. Hence, any change in radiation field due to a change in disk configuration will affect the lower part of the jet before it affects the outer part. This can drive shock transition in the jet flow. Depending on the disk oscillation frequency, amplitude, and jet parameters, these shocks can collide with each other and may trigger shock cascades.

Effect of Fluid Composition on a Jet Breaking out of a Cocoon in Gamma-Ray Bursts: A Relativistic de Laval Nozzle Treatment

In this paper we carry out a semi-analytic general relativistic study of a Gamma-Ray Bursts (GRB) jet that is breaking out of a cocoon or stellar envelope. We solve hydrodynamic equations with the relativistic equation of state that takes care of fluid composition. In short GRBs, a general relativistic approach is required to account for curved spacetime in strong gravity. The piercing of the jet through the cocoon resembles a de Laval nozzle and the jet may go through recollimation shock transitions. We show that the possibility of shock transition and the shock properties are sensitive to the matter composition and the cocoon strength. Obtained Lorentz factors in thermally driven jets comfortably reach few ×10.

The Highly Accurate Relation Between the Radius and Mass of the White Dwarf Star From Zero to Finite Temperature

In this research, first considering the electron–electron interaction in the high-density Fermi electron gas at T = 0 K, this interaction causes the pressure 2/137 time less than the original value. However, the pressure of the Fermi electron gas should have something to do with temperature. Then, we estimate the temperature effect using statistical mechanics and find that the complicated form of the pressure p depends on temperature at the given particle number N and volume V. According to this, the central density–mass (ρc-M), central density–radius (ρc-R), and mass–radius (M-R) relations of the white dwarf star are obtained by considering the equation of state (EOS). Traditional formula gives the problematic mass–radius relation R∝M−1/3 for the low-density white dwarf stars because it leads to R→∞ and p→0 when M→0. We correct this relation and obtain two reasonable relations in the relativistic and nonrelativistic regions. In our EOS calculations, the central density is divided into the high-, middle-, and low-density regions. All three relations are almost unchanged until 108 K in the high-density region. The temperature effect mainly affects the middle- and low-density regions, and it becomes explicitly above 107 K. Our calculations can explain Sloan Digital Sky Survey observations where some white dwarf stars with a radius of more than 8 × 103 km have larger mass than the predictions by the relativistic EOS at T = 0 K. This result tells us that the temperature effect is important for the low and middle central-density white dwarf star and also useful to estimate the inner temperature of a white dwarf star.

Exact solution of one-dimensional relativistic jet with relativistic equation of state

ABSTRACT We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar particles in flat space-time and the thermodynamics of fluid is governed by a relativistic equation of state. We obtain the exact solution of jets impinging on denser ambient media. The time variation of the cross-section of the jet-head is modelled and incorporated. We present the initial condition that gives rise to a reverse shock. If the jet-head cross-section increases in time, the jet propagation speed slows down significantly and the reverse-shock may recede opposite to the propagation direction of the jet. We show that the composition of jet and ambient medium can affect the jet solution significantly. For instance, the propagation speed depends on the composition and is maximum for a pair-dominated jet, rather than a pure electron-positron or electron-proton jet. The propagation direction of the reverse-shock may also strongly depend on the composition of the jet.

Study of relativistic magnetized outflows with relativistic equation of state

ABSTRACT We study relativistic magnetized outflows using relativistic equation of state having variable adiabatic index (Γ) and composition parameter (ξ). We study the outflow in special relativistic magnetohydrodynamic regime, from sub-Alfvénic to super-fast domain. We showed that, after the solution crosses the fast point, magnetic field collimates the flow and may form a collimation-shock due to magnetic field pinching/squeezing. Such fast, collimated outflows may be considered as astrophysical jets. Depending on parameters, the terminal Lorentz factors of an electron–proton outflow can comfortably exceed few tens. We showed that due to the transfer of angular momentum from the field to the matter, the azimuthal velocity of the outflow may flip sign. We also study the effect of composition (ξ) on such magnetized outflows. We showed that relativistic outflows are affected by the location of the Alfvén point, the polar angle at the Alfvén point and also the angle subtended by the field lines with the equatorial plane, but also on the composition of the flow. The pair dominated flow experiences impressive acceleration and is hotter than electron–proton flow.

Minimal plateau inflationary cosmologies and constraints from reheating

With the growing consensus on simple power law inflation models not being favored by the PLANCK observations, dynamics for the non-standard inflation gain significant interest in the recent past. In this paper, we analyze in detail a class of supergravity inspired phenomenological inflationary models with non-polynomial potential based on Maity (2017 Nucl. Phys. B 919 560), and compare the model predictions with the currently most favored Starobinsky and its generalized -attractor models in the plane constrained by PLANCK. Importantly for a wide range of parameter space, our model provides successful inflation in the sub-Planckian regime. We also have performed model independent analysis of reheating in terms of the effective equation of state parameter. In particular, we consider two stages of reheating dynamics with generalized inflaton equation of state in the initial and relativistic equation of state in the later phase. Finally, we show how our generalized reheating analysis constrains the inflation models under consideration.

Low angular momentum relativistic hot accretion flow around Kerr black holes with variable adiabatic index

We study the relativistic, time-independent, low angular momentum, inviscid, advective accretion flow around Kerr black hole. Considering the relativistic equation of state (REoS), we examine the transonic properties of the flow and find that there exists an upper bound of the location of the physically accepted critical point ($r^{\rm max}_{\rm out}$). However, no such limit exists when an ideal gas equation of state (IEoS) is assumed to describe the flow. Further, we calculate the global accretion solutions that contain shock waves and separate the domain of parameter space in angular momentum ($\lambda$) and energy (${\cal E}$) plane. We find ample disagreement between the shock parameter spaces obtained for REoS and IEoS, respectively. In general, post-shock flow (equivalently post-shock corona, hereafter PSC) is characterized by shock location ($r_s$) and compression ratio ($R$, measure of density compression across the shock front) which are uniquely determined for flow with given input parameters, namely $({\cal E}, \lambda)$. Using $r_s$ and $R$, we empirically compute the oscillation frequency ($\nu_{QPO}$) of the shock front which is in general quasi-periodic (QP) in nature and retrace the domain of shock parameter space in the $r_s-R$ plane in terms of $\nu_{QPO}$ for REoS around the weakly as well as rapidly rotating black holes. Finally, we indicate the relevance of the present work to explain the plausible origin of high frequency QPO (HFQPO) and its connection with the spin ($a_k$) of the Galactic black hole sources.

Limitations of the pseudo-Newtonian approach in studying the accretion flow around a Kerr black hole

We study the relativistic accretion flow around a generic stationary axisymmetric space-time and obtain an effective potential ($\Phi^{\rm eff}$) that accurately mimics the general relativistic features of Kerr black hole having spin $0\le a_k <1$. Considering the accretion disc confined around the equatorial plane of a rotating black hole and using the relativistic equation of state, we examine the properties of the relativistic accretion flow and compare it with the same obtained form semi-relativistic as well as non-relativistic accretion flows. Towards this, we first investigate the transonic properties of the accretion flow around the rotating black hole where good agreement is observed for relativistic and semi-relativistic flows. Further, we study the non-linearities such as shock waves in accretion flow. Here also we find that the shock properties are in agreement for both relativistic and semi-relativistic flows irrespective of the black hole spin ($a_k$), although it deviates significantly for non-relativistic flow. In fact, when the particular shocked solutions are compared for flows with identical outer boundary conditions, the positions of shock transition in relativistic and semi-relativistic flows agree well with deviation of $6-12\%$ for $0 \le a_k \le 0.99$, but vast disagreement is observed for non-relativistic flow. In addition, we compare the parameter space for shock to establish the fact that relativistic as well as semi-relativistic accretion flow dynamics do show close agreement irrespective of $a_k$ values, whereas non-relativistic flow fails to do so. With these findings, we point out that semi-relativistic flow including $\Phi^{\rm eff}$ satisfactorily mimics the relativistic accretion flows around Kerr black hole. Finally, we discuss the possible implications of this work in the context of dissipative advective accretion flow around Kerr black holes.

Maximum Mass of Hybrid Stars in the Quark Bag Model

The effect of model parameters in the equation of state for quark matter on the magnitude of the maximum mass of hybrid stars is examined. Quark matter is described in terms of the extended MIT bag model including corrections for one-gluon exchange. For nucleon matter in the range of densities corresponding to the phase transition, a relativistic equation of state is used that is calculated with two particle correlations taken into account based on using the Bonn meson-exchange potential. The Maxwell construction is used to calculate the characteristics of the first order phase transition and it is shown that for a fixed value of the strong interaction constant $\alpha_s$, the baryon concentrations of the coexisting phases grow monotonically as the bag constant B increases. It is shown that for a fixed value of the strong interaction constant $\alpha_s$, the maximum mass of a hybrid star increases as the bag constant $B$ decreases. For a given value of the bag parameter $B$, the maximum mass rises as the strong interaction constant $\alpha_s$ increases. It is shown that the configurations of hybrid stars with maximum masses equal to or exceeding the mass of the currently known most massive pulsar are possible for values of the strong interaction constant $\alpha_s>0.6$ and sufficiently low values of the bag constant.

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.

General relativistic study of astrophysical jets with internal shocks

We explore the possibility of formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry ($\theta=0$) in a Schwarzschild metric. We use two models for the jet geometry, (i) a conical geometry and (ii) a geometry with non-conical cross-section. Jet with conical geometry is smooth flow. While the jet with non-conical cross section undergoes multiple sonic point and even standing shock. The jet shock becomes stronger, as the shock location is situated further from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium is that, these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically, a jet with energy $1.8~c^2$, will achieve a terminal speed of $v_\infty=0.813c$ for jet with any geometry. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is $40\rg$, then in addition, a steady shock will form at $\rsh \sim 7.5\rg$ and compression ratio of $R\sim 2.7$. Moreover, electron-proton jet seems to harbour the strongest shock. We discuss possible consequences of such a scenario.

Asymmetric nuclear matter and neutron star properties within the extended Brueckner theory

Microscopically, the equation of state (EOS) and other properties of asymmetric nuclear matter at zero temperature have been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF) and the extended BHF approaches by using the self-consistent Green’s function approach or by including a phenomenological three-body force. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. We can calculate the total mass and radius for neutron stars using various equations of state at high densities in $ \beta$ -equilibrium without hyperons. A comparison with other microscopic predictions based on non-relativistic and density-dependent relativistic mean-field calculations has been done. It is found that relativistic EOS yields however larger mass and radius for neutron star than predictions based on non-relativistic approaches. Also the three-body force plays a crucial role to deduce the theoretical value of the maximum mass of neutron stars in agreement with recent measurements of the neutron star mass.

Dynamics of neutrino lumps in growing neutrino quintessence

We investigate the formation and dissipation of large scale neutrino structures in cosmologies where the time evolution of dynamical dark energy is stopped by a growing neutrino mass. In models where the coupling between neutrinos and dark energy grows with the value of the scalar cosmon field, the evolution of neutrino lumps depends on the neutrino mass. For small masses the lumps form and dissolve periodically, leaving only a small backreaction of the neutrino structures on the cosmic evolution. This process heats the neutrinos to temperatures much above the photon temperature such that neutrinos acquire again an almost relativistic equation of state. The present equation of state of the combined cosmon-neutrino fluid is very close to -1. In contrast, for larger neutrino masses the lumps become stable. The highly concentrated neutrino structures entail a large backreaction similar to the case of a constant neutrino-cosmon coupling. A present average neutrino mass of around 0.5 eV seems so far compatible with observation. For masses lower than this value, neutrino induced gravitational potentials remain small, making the lumps difficult to detect.

Hadron yield ratios in an effective relativistic equation of state

We investigate an effective relativistic equation of state at finite values of tem- perature and baryon chemical potential with the inclusion of the full octet of baryons, the Delta-isobars and the lightest pseudoscalar and vector meson degrees of freedom. These last particles have been introduced within a phenomenological approach by taking into account of an effective chemical potential and mass depending on the self-consistent interaction between baryons. In this framework, we study of the hadron yield ratios mea- sured in central heavy ion collisions over a broad energy range. It is well known that mesons play a crucial role in the hadronic Equation of State (EOS) especially in the regime of low baryon density and high temperature. Such particles are strongly interacting in the environment with the other particles. In this contribution, we are going to study an effective relativistic mean field model with the inclusion of the full octet of baryons, the Δ-isobars and the lightest pseudoscalar and vector mesons, by requiring the global conservation of baryon number, electric charge fraction and zero net strangeness. The meson degrees of freedom are incorporated in the EOS as a quasi-particle Bose gas with an effective meson chemical potential μ ∗ and an effective mass m ∗ expressed in terms of the σ, ω, ρ meson fields, responsible for the self-consistent mean field interaction (1). In this framework the hadron yield ratios have been studied and compared with the experimental ratios measured in central heavy ion collisions from AGS to RHIC energy range.

Relativistic EOS for supernova simulations

We study the relativistic equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and baryon density for the use of supernova simulations. This work is based on the relativistic mean-field theory (RMF) and the Thomas-Fermi approximation. The Thomas-Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We compare the EOS tables in detail.

The relativistic equation of state in accretion and wind flows

In the present study we derive a 4-velocity distribution function for the relativistic ideal gas following the original approach of Maxwell–Boltzmann (MB). Using this distribution function, the relativistic equation of state (EOS): ρ-ρ0=(γ-1)-1p, is expressed in the parametric form: ρ=ρ0f(λ),and p=ρ0g(λ), where λ is a parameter related to the kinetic energy, and hence, to the temperature of the gas. In the nonrelativistic limit, this distribution function perfectly reduces to original MB distribution and the EOS reduces to ρ-ρ0=32p, whereas in the extreme ultra-relativistic limit, the EOS becomes ρ=3p correctly. Using these parametric equations the adiabatic index γ=cpcv and the sound speed as are calculated as a function of λ. They also satisfy the inequalities: 43⩽γ⩽53 and as⩽13 perfectly. The computed distribution function, adiabatic index γ, and the sound speed as are compared with the results obtained from the canonical ensemble theory which nicely match with the standard results (Synge, 1957 and Chandrasekhar, 1939). The main advantage in using the EOS is that the probability distribution function can be factorized and therefore, may be helpful to solve complex dynamics of the astrophysical system. Interestingly, in one of the astrophysical application revels that shocks in accretion flows become unlikely and except for the region very nearby the compact object, the EOS remains non-relativistic (Mondal and Basu, 2011). We therefore, conclude that the new form of EOS will be helpful to verify many conventional ideas in many astrophysical problems.

On Poynting-flux-driven bubbles and shocks around merging neutron star binaries

Merging binaries of compact relativistic objects (neutron stars and black holes) are thought to be progenitors of short gamma-ray bursts and sources of gravitational waves, hence their study is of great importance for astrophysics. Because of the strong magnetic field of one or both binary members and high orbital frequencies, these binaries are strong sources of energy in the form of Poynting flux (e.g., magnetic-field-dominated outflows, relativistic leptonic winds, electromagnetic and plasma waves). The steady injection of energy by the binary forms a bubble (or a cavity) filled with matter with the relativistic equation of state, which pushes on the surrounding plasma and can drive a shock wave in it. Unlike the Sedov-von Neumann-Taylor blast wave solution for a point-like explosion, the shock wave here is continuously driven by the ever-increasing pressure inside the bubble. We calculate from the first principles the dynamics and evolution of the bubble and the shock surrounding it and predict that such systems can be observed as radio sources a few hours before and after the merger. At much later times, the shock is expected to settle onto the Sedov-von Neumann-Taylor solution, thus resembling an explosion.

Bose-Einstein condensate general relativistic stars

We analyze the possibility that due to their superfluid properties some compact astrophysical objects may contain a significant part of their matter in the form of a Bose-Einstein condensate. To study the condensate we use the Gross-Pitaevskii equation, with arbitrary non-linearity. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. The non-relativistic and Newtonian Bose-Einstein gravitational condensate can be described as a gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index one. In the framework of the Thomas-Fermi approximation the structure of the Newtonian gravitational condensate is described by the Lane-Emden equation, which can be exactly solved. The case of the rotating condensate is also discussed. General relativistic configurations with quartic non-linearity are studied numerically with both non-relativistic and relativistic equations of state, and the maximum mass of the stable configuration is determined. Condensates with particle masses of the order of two neutron masses (Cooper pair) and scattering length of the order of 10-20 fm have maximum masses of the order of 2 M_sun, maximum central density of the order of 0.1-0.3 10^16 g/cm^3 and minimum radii in the range of 10-20 km. In this way we obtain a large class of stable astrophysical objects, whose basic astrophysical parameters (mass and radius) sensitively depend on the mass of the condensed particle, and on the scattering length. We also propose that the recently observed neutron stars with masses in the range of 2-2.4 M_sun are Bose-Einstein Condensate stars.