Jeans Gravitational Instability Research Articles

Jeans analysis in fractional gravity

It has recently been demonstrated (Giusti in Phys Rev D 101:124029, 2020, https://doi.org/10.1103/PhysRevD.101.124029) that characteristic traits of Milgrom’s modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scenarios. Here, we investigate its implications on Jeans gravitational instability and related phenomena. We examine scenarios involving classical matter confined by gravity and extend our analysis to the quantum domain, through a Schrödinger–Newton approach. We also derive a generalized Lane–Emden equation associated with fractional gravity. Through comparisons between the derived stability criteria and the observed stability of Bok globules, we establish constraints on the theory’s parameters to align with observational data.

Polytropic spherical astrocosmic fluid stability in the EiBI gravity with strong collective correlative effects

We herein present a dynamical analysis of the Jeans (gravitational) instability in a viscoelastic polytropic astrocloud within the Eddington-inspired Born-Infeld (EiBI) gravity framework in spherical geometry. The zeroth-order material density curvature corrections to the effective self-gravitational potential are properly incorporated. The applied spherical normal mode analysis yields a unique form of monic cubic dispersion relation with multiparametric coefficients dependent on the diverse equilibrium astrofluidic conditions without invoking any kind of traditional quasi-classic approximation. It is seen that the positive EiBI gravity parameter (χ>0) acts as a stabilizing agent and a negative EiBI gravity parameter (χ<0) acts as a destabilizing agent against the inward non-local self-gravity action. Additionally, we find that larger astroclouds are more prone to gravitational collapse, irrespective of the χ-polarity, and vice-versa. It is further investigated that the cloud temperature plays a stabilizing role at larger wavenumbers and destabilizing at smaller wavenumbers for χ>0. However, for χ<0, the fluid temperature consistently exhibits a destabilizing effect. The viscoelastic relaxation time stabilizes the astrofluid against the self-gravity irrespective of the χ-polarity. The fluid density acts as a stabilizer for χ>0, destabilizer for χ<0, and so forth. This study could be potentially applicable in the EiBI-modified gravitational theory in exploring gravity-driven large-scale astrocosmic phenomena towards structure formation mechanism via the canonical Jeans condensation in diverse astrocosmic conditions.

Jeans Gravitational Instability of a Rotating Collisionless Magnetized Plasma with Anisotropic Pressure

Jeans Gravitational Instability of a Rotating Collisionless Magnetized Plasma with Anisotropic Pressure

Jeans Gravitational Instability of a Rotating Collisionless Magnetized Plasma with Anisotropic Pressure

The problem of self-gravitational instability of an astrophysical rotating plasma in a strong magnetic field with an anisotropic pressure tensor is studied on the basis of the Chew–Goldberger–Low (CGL) quasi-hydrodynamic equations modified by generalized polytropic laws. Using the general form of a dispersion relation obtained by the normal-mode perturbation method, a discussion is provided of the propagation of small-amplitude perturbation waves in an infinite homogeneous plasma medium for transverse, longitudinal, and oblique directions with respect to the magnetic field vector. It is shown that different polytropic indices and anisotropic pressures not only change the classical Jeans instability condition but also cause the appearance of new unstable regions. Modified Jeans instability criteria are obtained for isotropic MHD equations and anisotropic CGL equations owing to the influence of the polytropic indices on gravitational and firehose instabilities for astrophysical plasma. It is shown that in the case of a longitudinal mode of perturbation wave propagation, the Jeans instability criterion does not depend on uniform rotation. In the case of the transverse propagation regime, the presence of rotation reduces the critical wave number and exerts a stabilizing effect on the growth rate of the unstable regime.

A self-gravitating system composed of baryonic and dark matter analysed from the post-Newtonian Boltzmann equations

We study the Jeans gravitational instability for a mixture of baryonic and dark matter particles, in the post-Newtonian approximation. We adopt a kinetic model consisting of a coupled system of post-Newtonian collisionless Boltzmann equations, for each species, coupled to the post-Newtonian Poisson equations. We derive the stability criterion, accounting for both post-Newtonian corrections and the presence of dark matter. It is shown that both effects give rise to smaller Jeans masses, in comparison with the standard Jeans criterion, meaning that a smaller mass is needed to begin the gravitational collapse. Taking advantage of that, we confront the model with the observational stability of Bok globules, and show that the model correctly reproduces the data.

Jeans Instability of an Astrophysical Self-Gravitating Medium in the Presence of High Radiation Pressure and Diffuse Radiative Transfer

Within the problem of modeling the evolution of a protostellar disk, a discussion is presented on the effect of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-and-dust medium, taking into account the influence of radiation pressure perturbations and radiative diffusion transfer on the critical wavelength. Two radiative diffusion approximations are considered: the case of perfect thermal equilibrium with the same temperature of matter and radiation and the case of the time dependence of the radiation field with an energy separation between radiation and matter. An analysis of the normal regime of modes is used to derive dispersion relations, which enable the derivation of modifications of the classical Jeans instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to the system’s local thermodynamic equilibrium, where the acoustic velocity of perturbed gas propagates with the isothermal speed of sound, in the case of different temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiative media characterized by large optical depths for their dust-transformed intrinsic infrared radiation.

Quantum kinetic theory of Jeans instability in non-minimal matter-curvature coupling gravity

We present a quantum treatment of the Jeans gravitational instability in the Newtonian limit of the non-minimal matter-curvature coupling gravity model. By relying on Wigner functions, allowing for the representation of quantum states in a classical phase space, we formulate a quantum kinetic treatment of this problem, generalizing the classical kinetic approach (Gomes in Eur Phys J C 80:633, 2020). This allows us to study the interplay between non-minimal matter-curvature coupling effects, quantum effects, and kinetic (finite-temperature) effects, on the Jeans criterion. We study in detail special cases of the model (general relativity, f(R) theories, pure non-minimal coupling, etc.) and confront the model with the observed stability of Bok globules.

The Impact of Black Radiation on the Jeans Gravitational Instability Criterion in a Circumstellar Plasma Disk in View of Nonisentropic Effects

The Impact of Black Radiation on the Jeans Gravitational Instability Criterion in a Circumstellar Plasma Disk in View of Nonisentropic Effects

Jeans gravitational instability in a collisional nonextensive dusty plasma with polarization force

Jeans gravitational instability in a collisional nonextensive dusty plasma with polarization force

Джинсовская неустойчивость астрофизической самогравитирующей среды при наличии высокого радиационного давления и диффузионного переноса излучения

Within the framework of the problem of modeling the evolution of a protostellar disk, the influence of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-dust medium is discussed, taking into account the influence of radiation pressure and diffusion transfer of radiation on the critical wavelength of the perturbing wave. Two approximations of radiative diffusion are considered: 1. the case of ideal radiative equilibrium, when the temperatures of matter and radiation are the same; 2. the case of the time dependence of the radiation field, when there is an energy decoupling between radiation and matter. Using the analysis of the normal regime, dispersion relations are derived that allow one to obtain modifications of the Jeans gravitational instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to local radiation equilibrium, when the acoustic velocity of the gas coincides with the isothermal speed of sound, in the case of a difference in the temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in the gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiation media characterized by large optical depths for their own infrared radiation transformed by dust.

Jeans gravitational instability of a magnetized rotating collision-less anisotropic plasma using generalized laws of double polytropy

The problem of gravitational instability of an astrophysical magnetized rotating plasma with an anisotropic pressure tensor is investigated on the basis of the quasi-hydrodynamic Chew-Goldberger-Low (CGL) equations, modified by using generalized laws of dual polytropic theory. Using a general form of the dispersion relation obtained by the normal mode method, we discuss the propagation of oscillating magneto hydrodynamic waves of small amplitude perturbation in an infinite homogeneous plasma medium for the transverse, longitudi-nal and inclined directions with respect to the magnetic field vector. A number of modified Jeans gravitational instability criteria obtained for isotropic MHD and anisotropic CGL equations of rarefied plasma and distinguished by different orientations of the vectors of propagation of the disturbing wave, magnetic field, and rotation axis of the hydro-magnetic fluid are analyzed. It is shown that rotation and anisotropic pressure not only change the classical criterion of gravita-tional instability of astrophysical magnetized plasma, but also cause new unstable regions.

Джинсовская гравитационная неустойчивость намагниченной вращающейся бесстолкновительной анизотропной плазмы при использовании обобщенных законов двойной политропы

The problem of gravitational instability of an astrophysical magnetized rotating plasma with an anisotropic pressure tensor is investigated on the basis of the quasi-hydrodynamic Chew-Goldberger-Low (CGL) equations, modified by using generalized laws of dual polytropic theory. Using a general form of the dispersion relation obtained by the normal mode method, we discuss the propagation of oscillating magneto-hydrodynamic waves of small amplitude perturbation in an infinite homogeneous plasma medium for the transverse, longitudinal and inclined directions with respect to the magnetic field vector. A number of modified Jeans gravitational instability criteria obtained for isotropic MHD and anisotropic CGL equations of rarefied plasma and distinguished by different orientations of the vectors of propagation of the disturbing wave, magnetic field, and rotation axis of the hydromagnetic fluid are analyzed. It is shown that rotation and anisotropic pressure not only change the classical criterion of gravitational instability of astrophysical magnetized plasma, but also cause new unstable regions.

Jeans instability in Eddington-inspired Born-Infeld (EiBI) gravity: a quantum approach

This paper addresses the process of Jeans gravitational instability in the framework of Eddington-inspired Born-Infeld (EiBI) theory, by accounting for quantum effects. In the Newtonian limit, the model reduces to a generalized Schrödinger-Poisson model, which is treated in two different ways: from a quantum hydrodynamic approach and from a quantum kinetic approach, based on the Wigner (quasi-)distribution. We show that, depending on the sign of κ, EiBI gravity leads to more or less stable structures: For , EiBI gravity produces a pressure-like term that acts, together with quantum pressure, against gravity, leading to more stable structures, while for the effect goes in the opposite direction. Our approach reproduces correctly the classical hydrodynamic and kinetic results in the proper limits, which is made more transparent by introducing a nonlinear Schrödinger equation accounting for the degree of quantumness. Our results may open up a novel route for probing EiBI gravity in dense astrophysical media, where quantum effects are no longer negligible.

A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics

One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is described by an elliptic Poisson equation. We present a purely hyperbolic approach by reformulating the elliptic problem into a hyperbolic diffusion problem, which is solved in pseudotime, using the same explicit high-order discontinuous Galerkin method we use for the flow solution. The flow and the gravity solvers operate on a joint hierarchical Cartesian mesh and are two-way coupled via the source terms. A key benefit of our approach is that it allows the reuse of existing explicit hyperbolic solvers without modifications, while retaining their advanced features such as non-conforming and solution-adaptive grids. By updating the gravitational field in each Runge-Kutta stage of the hydrodynamics solver, high-order convergence is achieved even in coupled multi-physics simulations. After verifying the expected order of convergence for single-physics and multi-physics setups, we validate our approach by a simulation of the Jeans gravitational instability. Furthermore, we demonstrate the full capabilities of our numerical framework by computing a self-gravitating Sedov blast with shock capturing in the flow solver and adaptive mesh refinement for the entire coupled system.

Jeans Instability of a Protoplanetary Circular Disk Taking into Account the Magnetic Field and Radiation in Nonextensive Tsallis Kinetics

Within the framework of Tsallis nonextensive statistics, the criteria for the Jeans gravitational instability are derived for a self-gravitating protoplanetary disk, whose substance consists of a mixture of a conducting ideal q-gas and modified radiation of a photon gas. The instability criteria are derived from the corresponding dispersion relations written for both neutral disk matter and magnetized plasma with modified blackbody radiation. The thermodynamics of a photon gas are constructed based on the nonextensive Tsallis quantum entropy, which depends on the deformation parameter. It is shown that blackbody q-radiation can stabilize the state of a nonextensive medium for a purely gaseous disk, and for an electrically conducting disk, the Jeans instability criterion is modified by the magnetic field and radiation pressure only in the transverse propagation mode of the disturbance wave.

Джинсовская неустойчивость протопланетного околозвездного диска с учетом магнитного поля и излучения в неэкстенсивной кинетике Тсаллиса

Within the framework of the Tsallis non-extensive statistics, a derivation of the Jeans gravitational instability criteria is given for a self-gravitating protoplanetary disk, the substance of which consists of a mixture of a conducting ideal q-gas and modified radiation of a photon gas. The instability criteria are derived from the corresponding dispersion relations written for both neutral disk matter and magnetized plasma with modified blackbody radiation. The thermodynamics of a photon gas is constructed based on the nonextensive quantum entropy Tsallis, which depends on the deformation parameter. It is shown that blackbody radiation can stabilize the state of a nonextensive medium for a purely gaseous disk, and for an electrically conducting disk, the Jeans instability criterion is modified by a magnetic field and radiation pressure only in the transverse regime of propagation of the disturbance wave.

Jeans gravitational instability with κ-deformed Kaniadakis distribution in Eddington-inspired Born–Infield gravity**Project supported by the National Natural Science Foundation of China (Grant Nos. 11763006 and 11863004) and the Fund from the Jiangxi Provincial Key Laboratory of Fusion and Information Control (Grant No. 20171BCD40005).

Based on the framework of Kaniadakis’ statistics and its related kinetic theory, the Jeans instability for self-gravitational systems in the background of Eddington-inspired Born–Infield (EiBI) gravity is revisited. A dispersion relation generalizing the Jeans modes is derived by modifying the Maxwellian distribution to a family of power law distributions parameterized by the κ parameter. It is established that the κ-deformed Kaniadakis distribution has significant effects on the Jeans modes of the collisionless EiBI-gravitational systems. And as expected, in the limitation κ → 0, the corresponding results for Maxwellian case are recovered. The related result in the present work is valuable for the investigations involving the fields of astrophysics such as neutron stars, accretion disks, and relevant plasma physics, etc.

Non-Gaussian statistics from the generalized uncertainty principle

In many quantum gravity theories, there is the emergence of a generalized uncertainty principle (GUP), implying a minimal length of the order of the Planck length. From the statistical mechanics point of view, this prescription enters into the phase space structure by modifying the elementary cell volume, which becomes momentum-dependent. In this letter, it is pointed out that if one assumes that the total phase space volume is not affected by the minimum length prescription, the statistics that maximize the entropy are non-Gaussian but exhibit a quadratic correction over Gaussian statistics. The departure from Gaussian statistics is significant for high energies. To substantiate our point, we apply these statistics to the Unruh effect and the Jeans gravitational instability and show that—in these cases—non-Gaussian statistics produce the same effect as the GUP and capture the underlying physics behind it.

Jeans instability of rotating plasma with radiative heat-loss function and FLR corrections flowing through porous medium

The effect of rotation, porosity and finite ion Larmor radius (FLR) corrections on the gravitational instability and radiative instability of infinite homogeneous plasma has been explored, accounting for the consequences of radiative heat-loss function and thermal conductivity. The general dispersion relation is obtained by means of the normal mode analysis method with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduced for rotation axis parallel and perpendicular to the magnetic field. The stability of the medium is argued for by the Routh-Hurwitz criterion and it is found that the Jeans criterion establishes the stability of the medium. We acknowledge that the presence of the radiative heat-loss function and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. Numerical computations have been executed to show the effect of various parameters on the growth rate of the Jeans gravitational instability. We find that rotation, FLR corrections and medium porosity stabilize the growth rate as regards the structure in both the transverse mode and longitudinal mode or propagation. Our result demonstrates that the rotation, porosity and FLR corrections affect the dense molecular cloud configuration and star formation.

Jeans instability in dark matter halos

According to the theory of scale relativity, dark matter halos can be described through a generalized Schrödinger equation, involving a logarithmic non-linearity associated with an effective temperature and a source of dissipation. This wave equation can be written, via the Madelung transformation, in the form of a quantum hydrodynamic model which, once coupled to the Poisson equation, is used herein to study the Jeans gravitational instability. We consider the two cases of a static and uniform unperturbed background and the generalization including the effect of Universe expansion on the zeroth-order dynamics. In each case, the stability is ensured by the effective temperature and nonlocality effects acting against gravitational forces, whereas the dissipation source damps the density contrast evolution without modifying the threshold value of the Jeans wave number.