Criterion For Gravitational Instability Research Articles

Tests of subgrid models for star formation using simulations of isolated disc galaxies

ABSTRACT We use smoothed particle hydrodynamics simulations of isolated Milky Way-mass disc galaxies that include cold, interstellar gas to test subgrid prescriptions for star formation (SF). Our fiducial model combines a Schmidt law with a gravitational instability criterion, but we also test density thresholds and temperature ceilings. While SF histories are insensitive to the prescription for SF, the Kennicutt–Schmidt (KS) relations between SF rate and gas surface density can discriminate between models. We show that our fiducial model, with an SF efficiency per free-fall time of 1 per cent, agrees with spatially resolved and azimuthally averaged observed KS relations for neutral, atomic, and molecular gas. Density thresholds do not perform as well. While temperature ceilings selecting cold, molecular gas can match the data for galaxies with solar metallicity, they are unsuitable for very low-metallicity gas and hence for cosmological simulations. We argue that SF criteria should be applied at the resolution limit rather than at a fixed physical scale, which means that we should aim for numerical convergence of observables rather than of the properties of gas labelled as star-forming. Our fiducial model yields good convergence when the mass resolution is varied by nearly 4 orders of magnitude, with the exception of the spatially resolved molecular KS relation at low surface densities. For the gravitational instability criterion, we quantify the impact on the KS relations of gravitational softening, the SF efficiency, and the strength of supernova feedback, as well as of observable parameters such as the inclusion of ionized gas, the averaging scale, and the metallicity.

Effects of finite Larmor radius corrections and finite electron inertia on transverse Jean’s gravitational instability of radiative plasma with Hall current for star formation in ISM

We learn the consequences of finite ion Larmor radius (FLR) corrections, finite electron inertia, Hall current and radiative heat-loss function on the Jean’s-gravitational instability of an infinite homogeneous, viscous plasma integrating the impacts of finite electrical resistivity, thermal conductivity and permeability. A general dispersion relation is derived by means of the normal mode analysis method with the assistance of linearized perturbation equations of the problem. We find that the original Jeans criterion of gravitational instability is modified into the radiative instability criterion by the inclusion of thermal conductivity and radiative heat-loss function. The finite electrical resistivity eliminates the impact of the magnetic field and the viscosity of the medium eliminates the impact of FLR from radiative instability. The Hall parameter has no impact on the transverse mode of propagation. Numerical calculations demonstrate the stabilizing impact of temperature-dependent heat-loss function, FLR corrections and the destabilizing impact of density-dependent heat-loss function, finite electron inertia on the Jean’s-gravitational instability.

Распространение магнитогидродинамических волн и гравитационная неустойчивость в астрофизической анизотропной и теплопроводной плазме

The hydrodynamic instability of a magnetised, self-gravitating rotating anisotropic plasma is analysed in the collisionless approximation and taking into account the heat flux vector on the basis of the modified Chew-Goldberger-Low equations. The dispersion relation is derived and simplified cases of propagation of small-amplitude perturbation waves are discussed, with modified analytical criteria for hydrodynamic instability obtained. In accordance with the general dispersion relation, three cases when the propagation of the perturbation wave passes across, along, and obliquely to the magnetic field vector are specifically considered. It is shown that anisotropic pressure and heat flux not only modify the classical Jeans instability criterion but also induce new unstable regions. It is found that the presence of uniform plasma rotation reduces the critical wave number and has a stabilising effect on the gravitational instability criterion for transverse propagation of the perturbation wave and has no effect in the case of its longitudinal propagation. The inclusion of thermal flows leads to the appearance of two additional wave modes. The results obtained are important for the construction of evolutionary magnetohydrodynamic models of collisionless astrophysical plasma.

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 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.

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.

Modes of propagation and instabilities in finitely conducting neutrino-modified magnetohydrodynamic viscous plasma

Low-frequency wave propagations and instabilities are studied taking into account the finite electrical resistivity and viscosity of the neutrino-coupled plasma. It is assumed that the plasma is permeated by magnetic field. The formulation and analysis of the system including the Fermi weak force due to neutrino plasma coupling is done by neutrino magneto hydrodynamics model. The general dispersion relation is derived from the set of perturbed equations to signify the role of dissipative effects on the growth rate and condition of both neutrino instability and self-gravitational instability. To discuss the influence of resistivity and viscosity on the dynamics of the system, the general dispersion relation is reduced for both perpendicular and parallel mode of propagations. The self-gravitating modes are modified by the presence of neutrinos, viscosity, and resistivity in both perpendicular and parallel modes of propagation, while the gravitational instability criterion is modified only by neutrinos. It is also observed that the number density of neutrinos works against the gravitational instability, while the neutrino beam-free energy supports the self-gravitational instability. In the case of perpendicular propagation, the neutrino beam instability criterion and growth rate are affected by dissipative effects.

Jeans instability of finitely conducting radiative rotating plasma with FLR corrections flowing through porous medium

The effect of radiative heat-loss functions, rotation, porosity, finite electrical resistivity and finite ion Larmor radius (FLR) corrections, on the gravitational instability of infinite homogeneous plasma, has been explored integrating 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. The general dispersion relation is further reduced for rotation axis parallel and perpendicular to the magnetic field. We locate that the presence of radiative heat-loss function and thermal conductivity amend the fundamental Jeans criterion of gravitational instability into 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 of the system in both the longitudinal mode and transverse mode of propagation. Our result demonstrates that the rotation, porosity and FLR corrections affect the dense molecular cloud configuration and star formation.

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 of a Protoplanetary Gas Cloud with Radiation in Nonextensive Tsallis Kinetics

In the framework of Tsallis statistics, we study the effect of medium nonextensivity on the Jeans gravitational instability criterion for a self-gravitating protoplanetary cloud, the substance of which consists of a mixture of perfect gas and blackbody radiation. Generalized Jeans instability criteria have been found from the corresponding dispersion relations obtained both for a uniform cloud with radiation and for a rotating protoplanetary cloud. An integral generalized Chandrasekhar stability criterion for a gravitating spherical cloud has also been obtained. The presented results are analyzed for various values of deformation parameters $$q,$$ dimensionality $$D$$ of the velocity space and coefficient $$\beta $$, characterizing the fraction of radiation in the total pressure of the system. It is shown that radiation stabilizes the substance of nonextensive protoplanetary clouds, and for rotating clouds, the Jeans instability criterion is modified by the Coriolis force only in the transverse modes of perturbation wave propagation.

Вывод в рамках неэкстенсивной кинетики критерия гравитационной неустойчивости Джинса для допланетного вращающегося облака с учетом радиации и магнитного поля

Вывод в рамках неэкстенсивной кинетики критерия гравитационной неустойчивости Джинса для допланетного вращающегося облака с учетом радиации и магнитного поля

A systematic development of Jeans’ criterion with rotation for gravitational instabilities

An inviscid fluid model of a self-gravitating infinite expanse of a uniformly rotating adiabatic gas cloud consisting of the continuity, Euler’s, and Poisson’s equations for that situation is considered. There exists a static homogeneous density solution to this model relating that equilibrium density to the uniform rotation. A systematic linear stability analysis of this exact solution then yields a gravitational instability criterion equivalent to that developed by Sir James Jeans in the absence of rotation instead of the slightly more complicated stability behavior deduced by Subrahmanyan Chandrasekhar for this model with rotation, both of which suffered from the same deficiency in that neither of them actually examined whether their perturbation analysis was of an exact solution. For the former case, it was not and, for the latter, the equilibrium density and uniform rotation were erroneously assumed to be independent instead of related to each other. Then this gravitational instability criterion is employed in the form of Jeans’ length to show that there is very good agreement between this theoretical prediction and the actual mean distance of separation of stars formed in the outer arms of the spiral galaxy Andromeda M31. Further, the uniform rotation determined from the exact solution relation to equilibrium density and the corresponding rotational velocity for a reference radial distance are consistent with the spectroscopic measurements of Andromeda and the observational data of the spiral Milky Way galaxy.

Jeans surface instability of an electron-ion plasma

The dispersive properties of Jeans surface instability at a charged plane interface of weakly coupled, classical self-gravitating, magnetized electron-ion plasma and vacuum, are investigated. The general dispersion relation is formulated by employing one fluid magnetohydrodynamic (MHD) model and Poisson’s equations for both electrostatic and gravitational potentials. It is shown that both the surface charge and mass density fluctuations are coupled together effectively, to enhance the growth rate of surface Jeans instability, whereas an increase in magnetic field and surface tension tends to stabilize Jeans surface instability. The modified Jeans criterion of gravitational instability is obtained by formulating a new definition of Jeans wavelength. These results may be useful to examine the gravitational collapse of self-gravitating electron-ion plasma, leading to star formation in astro-cosmic environments.

Three-dimensional small-scale instabilities of plane internal gravity waves

We study the evolution of three-dimensional (3-D), small-scale, small-amplitude perturbations on a plane internal gravity wave using the local stability approach. The plane internal wave is characterised by its non-dimensional amplitude, $A$, and the angle the group velocity vector makes with gravity, $\unicode[STIX]{x1D6F7}$. For a given $(A,\unicode[STIX]{x1D6F7})$, the local stability equations are solved on the periodic fluid particle trajectories to obtain growth rates for all two-dimensional (2-D) and 3-D perturbation wave vectors. For small $A$, the local stability approach recovers previous results of 2-D parametric subharmonic instability (PSI) while offering new insights into 3-D PSI. Higher-order triadic resonances, and associated deviations from them, are also observed at small $A$. Moreover, for small $A$, purely transverse instabilities resulting from parametric resonance are shown to occur at select values of $\unicode[STIX]{x1D6F7}$. The possibility of a non-resonant instability mechanism for transverse perturbations at finite $A$ allows us to derive a heuristic, modified gravitational instability criterion. We then study the extension of small $A$ to finite $A$ internal wave instabilities, where we recover and build upon existing knowledge of small-scale, small-amplitude internal wave instabilities. Four distinct regions of the $(A,\unicode[STIX]{x1D6F7})$-plane based on the dominant instability modes are identified: 2-D PSI, 3-D oblique, quasi-2-D shear-aligned, and 3-D transverse. Our study demonstrates the local stability approach as a physically insightful and computationally efficient tool, with potentially broad utility for studies that are based on other theoretical approaches and numerical simulations of small-scale instabilities of internal waves in various settings.

Gravitational instability in isotropic MHD plasma waves

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.

Two-component gravitational instability in spiral galaxies

We applied a criterion of gravitational instability, valid for two-component and infinitesimally thin discs, to observational data along the major axis for 7 spiral galaxies of early types. Unlike most papers, the dispersion equation corresponding to the criterion was solved directly without using any approximation. The velocity dispersion of stars in the radial direction $\sigma_R$ was limited by the range of possible values instead of a fixed value. For all galaxies, the outer regions of the disc were analyzed up to $R < 130^{"}$. The maximal and sub-maximal disc models were used to translate surface brightness into surface density. The largest destabilizing disturbance stars can exert on a gaseous disc was estimated. It was shown that the two-component criterion differs a little from the one-fluid criterion for galaxies with a large surface gas density, but it allows to explain large-scale star formation in those regions where the gaseous disc is stable. In the galaxy NGC 1167 star formation is entirely driven by the self-gravity of the stars. A comparison is made with the conventional approximations which also include the thickness effect and with models for different sound speed $c_\mathrm{g}$. It is shown that values of the effective Toomre parameter correspond to the instability criterion of a two-component disc $Q_\mathrm{eff}<1.5-2.5$. This result is consistent with previous theoretical and observational studies.

Effect of quantum correction and black body radiation on Jeans instability of porous medium

The Jeans instability of self-gravitating gaseous plasma is re-discussed in the framework of viscous, self-gravitating porous medium under the influence of quantum correction and black body radiation. The mathematical solution of the problem has been obtained through the normal mode analysis and the dispersion relation has been derived with the help of linearized perturbation equations. It is found that quantum corrections and black body radiation modify the fundamental Jeans criterion of gravitational instability and a new instability quantum corrected radiative instability is found. It is pointed here that the role of quantum correction is to stabilize the considered system by decreasing the value of critical Jeans wave-length. The stability of the system is discussed by applying Rought-Hurwitz criteria.

Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer

Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed.

Modification of the jeans instability criterion for fractal-structure astrophysical objects in the framework of nonextensive statistics

Unlike classical studies in which the gravitational instability criterion for astrophysical disks is derived in the framework of traditional kinetics or hydrodynamics, we propose to consider the totality of fluffy dust clusters of various astrophysical objects, in particular, protoplanetary subdisks, as a special type of continuous medium, i.e., fractal medium for which there are points and areas not filled with its components. Within the deformed Tsallis statistics formalism, which is intended to describe the behavior of anomalous systems with strong gravitational interaction and fractal nature of phase space, we derive, on the basis of the modified kinetic equation (with the collision integral in the Bhatnagar-Gross-Krook form), the generalized hydrodynamic Euler equations for a medium with the fractal mass dimension. Considering the linearization of the q-hydrodynamics equations, we investigate the instability of an infinitely homogeneous medium to obtain a simplified version of the modified gravitational instability criterion for an astrophysical disk with fractal structure.