Polytropic Equation Of State Research Articles

Neutron stars in f(R,T) gravity with conserved energy-momentum tensor: Hydrostatic equilibrium and asteroseismology

We investigate the equilibrium and radial stability of spherically symmetric relativistic stars, considering a polytropic equation of state (EoS), within the framework of f(R,T) gravity with a conservative energy-momentum tensor. Both modified stellar structure equations and Chandrasekhar's pulsation equations are derived for the f(R,T)= R+ h(T) gravity model, where the function h(T) assumes a specific form in order to safeguard the conservation equation for the energy-momentum tensor. The neutron star properties, such as radius, mass, binding energy and oscillation spectrum are studied in detail. Our results show that a cusp — which signals the appearance of instability — is formed when the binding energy is plotted as a function of the compact star proper mass. We find that the squared frequency of the fundamental vibration mode passes through zero at the central-density value corresponding to such a cusp where the binding energy is a minimum.

Full analytical ultrarelativistic 1D solutions of a planar working surface

ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the hydrodynamical quantities of the problem form two shock waves separating from a contact discontinuity. The procedure is based on the extensive use of the Taub jump conditions for relativistic shock waves, the Taub adiabatic, and performing Lorentz transformations to present the solution in a system of reference adequate for an external observer at rest. The solutions are found using a set of very useful theorems related to the Lorentz factors when transforming between systems of reference. The energy dissipated inside the working surface is relevant for studies of light curves observed in relativistic astrophysical jets and so, we provide a full analytical solution for this phenomenon assuming an ultrarelativistic periodic velocity injected at the base of the jet.

Amplification of Turbulence in Contracting Prestellar Cores in Primordial Minihalos

Abstract We investigate the amplification of turbulence through gravitational contraction of the primordial gas in minihalos. We perform numerical simulations to follow the cloud collapse, assuming polytropic equations of state for different initial turbulent Mach numbers and resolutions. We find that the turbulent velocity is amplified solely by gravitational contraction, and eventually becomes comparable to the sound speed, even for small initial turbulent Mach numbers (  0 ≳ 0.05 ). We derive an analytic formula for the amplification of turbulent velocity in a collapsing cloud, and find that our numerical results are consistent with the formula. These results suggest that the turbulence can play an important role in collapsing clouds for general cases.

Generalized polytropic models in Finch-Skea spacetime

In present article, we have formulated the new physical generalized polytropic models with anisotropic matter distribution in the absence of electromagnetic field. We have assumed the Finch-Skea spacetime to develop the models, which fulfill all the criteria for the physical adequacy. Distinct physical features of the obtained models have been examined and evaluated. Furthermore, the physical quantities are presented graphically to meet the physical conditions of viable astronomical models. These results can be reduced to the different cases of uncharged anisotropic fluid such as linear, quadratic and polytropic equations of state.

A computational method for rotating, multi-layer spheroids with internal jumps

Abstract We discuss the structure of differentially rotating, multilayer spheroids containing mass-density jumps and rotational discontinuities at the interfaces. The study is based upon a scale-free, numerical method. Polytropic equations of state and cylindrical rotation profiles are assumed. The Bernoulli equation and the Poisson equation for the gravitational potential are solved for each layer separately on a common computational grid. The 2-layer (core-envelope) case is first investigated in detail. We find that the core and the envelope are not, in general, homothetical in shape (cores are more than spherical than the envelope). Besides, the occurence of a mass-density jump all along the interface is prone to a rotational discontinuity (unless the polytropic indices are the same). In particular, for given rotation laws, the mass-density jump is not uniform along the interface. Tests, trends and examples (e.g. false bipolytrope, critical rotation, degenerate configurations) are given. Next, we consider the general case of systems made of ${\cal L}>2$ layers. This includes the full equation set, the virial equation, a comprehensive step-by-step procedure and two examples of tripolytropic systems. The properties observed in the 2-layer case hold for any pairs of adjacent layers. In spite of a different internal structure, two multilayer configurations can share the same mass, same axis ratio, same size and same surface velocity (which is measured through a degeneracy parameter). Applications concern the determination of the interior of planets, exoplanets, stars and compact objects.

Spherically symmetric configuration in f(Q) gravity

General relativity can be formulated equivalently with a non-Riemannian geometry that associates with an affine connection of nonzero nonmetricity $Q$ but vanishing curvature $R$ and torsion $T$. Modification based on this description of gravity generates the $f(Q)$ gravity. In this work we explore the application of $f(Q)$ gravity to the spherically symmetric configurations. We discuss the gauge fixing and connections in this setting. We demonstrate the effects of $f(Q)$ by considering the external and internal solutions of compact stars. The external background solutions for any regular form of $f(Q)$ coincide with the corresponding solutions in general relativity, i.e., the Schwarzschild-de Sitter solution and the Reissner-Nordstr\"om-de Sitter solution with an electromagnetic field. For internal structure, with a simple model $f(Q)=Q+\alpha Q^2$ and a polytropic equation of state, we find that a negative modification ($\alpha<0$) provides support to more stellar masses while a positive one ($\alpha>0$) reduces the amount of matter of the star.

On quasineutral plasma flow in the magnetic nozzle

Exact solutions for quasineutral plasma acceleration of magnetized plasma in the paraxial magnetic nozzle are obtained. It is shown that the non-monotonic magnetic field with a local maximum of the magnetic field is a necessary condition for the formation of the quasineutral accelerating potential structure. A global nature of the accelerating potential that occurs as a result of the constraint due to the regularity condition at the sonic point is emphasized, and properties of such solutions are discussed for the case of general polytropic equation of state for electrons.

Effects of high density phase transitions on neutron star dynamics

Various theoretical arguments motivate an expectation of a phase transition in matter at extreme densities above nuclear density, accompanied by hopes that gravitational wave observations may reveal the properties of such a transition. Instead of adopting a particular theory, we consider here a generic form of first order phase transition using a piecewise polytropic equation of state, and evolve both isolated neutron stars and neutron star binaries, including unequal mass binaries and, in some cases, magnetic field, looking at dynamical effects. Of particular interest are effects that may be observable either via gravitational waves or electromagnetic observations.

An improved approach to derive the kappa distribution in polytropic plasmas

This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas 27, 122104 (2020)]. We find that the polytropic equation of state can lead to the kappa distribution without any other assumptions in one dimension. In higher dimensions, an extra assumption that the global distribution must only depend on the energy is still needed. In addition, the self-consistence of the electrostatic potential is investigated in such plasmas. This study implies that in single-component plasmas, the potential is constrained by the Lane–Emden equation. However, in two-component plasmas, any arbitrary potential could exist with a suitable background ion density. Finally, we discuss the connections between the kappa distribution and the polytrope.

Study of charged generalized polytropes with complexity factor

The objective of this manuscript is to study the generalized polytropes in the presence of charge with the help of complexity factor. For this purpose, spherical symmetry and generalized relativistic polytropic equation of state will be used in two cases: (i) for mass density $$(\mu _{o})$$ and (ii) for energy density $$(\mu )$$ , along with charge. These two cases will give two sets of differential equations, and they will be solved by mean of complexity factor. The solutions of these sets will be discussed graphically under different values of charge and parameters.

Neutron stars phenomenology with scalar–tensor inflationary attractors

In this work we shall study the implications of a subclass of E -models cosmological attractors, namely of a -attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the a -attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of a -attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman–Oppenheimer–Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman–Oppenheimer–Volkoff equations using a double shooting python-based “LSODA” numerical code. The resulting picture depends on the value of the parameter a characterizing the a -attractors. As we show, for large values of a , which do not produce a viable inflationary era, the M – R graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large a -values, the WFF1 equation of state is excluded, due to the GW170817 constraints on the radius of an M ∼ 1 . 6 M ⊙ neutron star, which must be larger than R = 10 . 6 8 − 0 . 04 + 15 km and on the radius corresponding to the maximum mass which must be larger than R = 9 . 6 − 0 . 03 + 0 . 14 km. In addition, the small a cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. A notable feature is that as the parameter a decreases, the radii of the static hydrodynamically stable neutron stars increase. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar–tensor theory.

Nonlinear Periodic Ion Acoustic Waves in a Relativistic Plasma with Isothermal Electrons and Cold Ions

Propagation of nonlinear ion acoustic waves in a relativistic electron–ion plasma is studied using the covariant formulation. Ions are assumed cold and a polytropic equation of state of the form p ...

Modelling magnetohydrodynamic equilibrium in magnetars with applications to continuous gravitational wave production

ABSTRACT Possessing the strongest magnetic fields in our Universe, magnetars mark an extremum of physical phenomena. The strength of their magnetic fields is sufficient to deform the shape of the stellar body, and when the rotational and magnetic axes are not aligned, these deformations lead to the production of gravitational waves (GWs) via a time-varying quadrupole moment. Such gravitational radiation differs from signals presently detectable by the Laser Interferometer Gravitational-Wave Observatory. These signals are continuous rather than the momentary ‘chirp’ waveforms produced by binary systems during the phases of inspiral, merger, and ringdown. Here, we construct a computational model for magnetar stellar structure with strong internal magnetic fields. We implement an n = 1 polytropic equation of state (EOS) and adopt a mixed poloidal and toroidal magnetic field model constrained by the choice of EOS. We utilize fiducial values for magnetar magnetic field strength and various stellar physical attributes. Via computational simulation, we measure the deformation of magnetar stellar structure to determine upper bounds on the strength of continuous GWs formed as a result of these deformations inducing non-axisymmetric rotation. We compute predictions of upper limit GW strain values for sources in the McGill Magnetar Catalog, an index of all detected magnetars.

Acceptability conditions and relativistic barotropic equations of state

We sketch an algorithm to generate exact anisotropic solutions starting from a barotropic EoS and setting an ansatz on the metric functions. To illustrate the method, we use a generalization of the polytropic equation of state consisting of a combination of a polytrope plus a linear term. Based on this generalization, we develop two models which are not deprived of physical meaning as well as fulfilling the stringent criteria of physical acceptability conditions. We also show that some relativistic anisotropic polytropic models may have singular tangential sound velocity for polytropic indexes greater than one. This happens in anisotropic matter configurations when the polytropic equation of state is implemented together with an ansatz on the metric functions. The generalized polytropic equation of state is free from this pathology in the tangential sound velocity.

Deep-MOND polytropes

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $\zeta(y)$ is (for $\gamma\not=1$) $[\int_0^y \zeta \bar y^2 d\bar y]^{1/2}=-yd(\zeta^{\gamma-1})/dy$. Or, $\theta^n(y)=y^{-2}[(y\theta')^2]'$, where $\theta=\zeta^{\gamma-1}$, and $n\equiv (\gamma-1)^{-1}$. I discuss properties of the solutions, contrasting them with those of their Newtonian analogues -- the Lane-Emden polytropes. Due to the stronger MOND gravity, all DML polytropes have a finite mass, and for $n<\infty$ ($\gamma>1$) all have a finite radius. (Lane-Emden spheres have a finite mass only for $n\le 5$.) I use the DML polytropes to study DML scaling relations. For example, they satisfy a universal relation (for all $\mathcal{K}$ and $\gamma$) between the total mass, $M$, and the mass-average velocity dispersion $\sigma$: $MGa_0=(9/4)\sigma^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\bar\sigma$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\bar\sigma,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $\gamma>1$), and all satisfy the above universal $M-\sigma$ relation. This more extended class of models exhibits the central-surface-densities relation: a tight relation between the baryonic and the dynamical central surface densities predicted by MOND.

Gravitational instability of non-isothermal filamentary molecular clouds in presence of external pressure

ABSTRACT Filamentary molecular clouds are omnipresent in the cold interstellar medium. Observational pieces of evidence show that the non-isothermal equations of state describe the filaments properties better than the isothermal one. In this paper, we use the logatropic and the polytropic equations of state to study the gravitational instability of the pressure-confined filaments in presence of a uniform axial magnetic field. To fully explore the parameter space, we carry out very large surveys of stability analysis that cover filaments with different radii in various magnetic fields. Our results show that for all the equations of state the instability of thinner filaments is more sensitive to the magnetic field variations than the thicker ones. Moreover, for all the equations of state, an intermediate magnetic field can entirely stabilize the thinner filaments. Albeit for the thicker ones, this effect is suppressed for the magnetic field stronger than B ≃ 70 μG.

Neutron star properties from astrophysical observations

Recently, simultaneous measurements of the masses and the radii of neutron stars from X-ray observations by the Neutron Star Interior Composition Explorer (NICER) have been reported. In addition, gravitational wave detections from the mergers of neutron star binaries allowed us to estimate the tidal deformability of neutron stars. Based on these recent observations and our works, we review their implications for the masses, radii and tidal deformabilities of neutron stars. We also discuss the basic principles of the polytropic equations of state, including sound velocities, and the implications of those equations to the properties of neutron stars.

Relativistic Bondi accretion for stiff equations of state.

We revisit Bondi accretion - steady-state, adiabatic, spherical gas flow on to a Schwarzschild black hole at rest in an asymptotically homogeneous medium - for stiff polytropic equations of state (EOSs) with adiabatic indices Γ > 5/3. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs - including the appearance of a minimum steady-state accretion rate for EOSs with Γ ≥ 5/3 - and explore limiting cases in order to examine these differences. As an example, we highlight results for Γ = 2, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultrarelativistic 'causal' EOS, P = ρ. The latter serves as a useful limit for the still undetermined neutron star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate on to a mini-black hole residing at the centre of a neutron star.

Compact objects in entangled relativity

We describe the first numerical Tolman-Oppenheimer-Volkoff solutions of compact objects in entangled relativity, which is an alternative to the framework of general relativity that does not have any additional free parameter. Assuming a simple polytropic equation of state and the conservation of the rest-mass density, we notably show that, for any given density, compact objects are always heavier (up to $\ensuremath{\sim}8%$) in entangled relativity than in general relativity---for any given central density within the usual range of neutron stars' central densities, or for a given radius of the resulting compact object.

Radial oscillations and gravitational wave echoes of strange stars for various equations of state

ABSTRACT We study the radial oscillations of non-rotating strange stars (SSs) and their characteristic echo frequencies for three equations of state (EoS), viz., MIT Bag model EoS, linear EoS, and polytropic EoS. The frequencies of radial oscillations of these compact stars are computed for these EoSs. In total, 22 lowest radial frequencies for each of these three EoSs have been computed. First, for each EoS, we have integrated Tolman–Oppenheimer–Volkoff equations numerically to calculate the radial and pressure perturbations of SSs. Next, the mass–radius relationships for these stars are obtained using these three EoSs. Then the radial frequencies of oscillations for these EoSs are calculated. Further, the characteristic gravitational wave echo frequencies and the repetition of echo frequencies of SSs are computed for these EoSs. Our numerical results show that the radial frequencies and also echo frequencies vastly depend on the model and on the value of the model parameter. Our results also show that the radial frequencies of strange stars are maximum for polytropic EoS in comparison to MIT Bag model EoS and linear EoS. Moreover, SSs with MIT Bag model EoS and linear EoS are found to emit gravitational wave echoes. Whereas, SSs with polytropic EoS are not emitting gravitational wave echoes.