Jeans Condition Research Articles

Jeans instability of predictive model of baryonic and fermionic dark matter with the impact of dissipative force

This study examines the Jeans instability and growth rate of a self-gravitating system made up of baryonic particles and dark matter with a source of dissipation. While treating dark matter using a quantum damped-hydrodynamic technique, we employed the classical hydrodynamic fluid approach for baryonic particles. We get the coupled system's dispersion relation by evaluating the equations. We examine the dispersion relation and the Jeans condition in various limiting circumstances and demonstrate how parameters influence growth rate with the use of graphical instances. We discovered that, irrespective of the jeans wave number, the dissipation source damps the growth rate. The study highlights how the introduction of dissipation influences the growth rate and damping effect observed in the system. Overall, the findings of this study provide valuable insights into the dynamics of self-gravitating systems and their evolution over time.

Jeans instability of a monatomic gas in the presence of thermal radiation

The Jeans instability in magneto-radiative gas dynamics [MRGD] is discussed in the framework of magneto-gas dynamics [MGD] incorporating rotation and viscosity of the medium. The system of the present problem is assumed to adopt the Landau and Lifshitz model. The dispersion relation is obtained with the help of linearized perturbation equations. We find that the Jeans condition remains valid but the expression of the critical Jeans wave number is modified. Owing to the inclusion of radiative effect the sound speed changes which means that the critical wavelength depends on the amount of rate of radiation. We hope that our discussion on the present problem will help to improve our knowledge of interstellar medium [ISM].

Effect of spin-induced magnetization and Hall current on self-gravitational instability of magnetized viscous quantum plasma

The Jeans self-gravitational instability is studied for dense quantum viscous plasma with Hall term and intrinsic magnetization generated by collective electron spin. The quantum magnetohydrodynamic model is employed to formulate the basic equations of the problem. The dispersion relation is obtained using the normal mode analysis, and further reduced for both transverse and longitudinal modes of propagation. The transverse mode of propagation is found to be unaffected by the Hall term but affected by quantum effect, viscosity, and magnetization parameters. The Jeans criterion of instability in the transverse direction is modified by Alfven velocity, magnetization parameter, and quantum effect. The non-gravitating magnetized mode is obtained in the longitudinal direction, which is modified by Hall parameter and is not affected by quantum term, whereas the gravitational mode is unaffected by the magnetization parameter but affected by viscosity and quantum parameters. It is observed that the Jeans condition of instability is affected by the quantum term. The growth rate of Jeans instability is plotted for various values of magnetization, quantum, and viscosity parameters of the quantum plasma medium.

Jeans self gravitational instability of strongly coupled quantum plasma

The Jeans self-gravitational instability is studied for quantum plasma composed of weakly coupled degenerate electron fluid and non-degenerate strongly coupled ion fluid. The formulation for such system is done on the basis of two fluid theory. The dynamics of weakly coupled degenerate electron fluid is governed by inertialess momentum equation. The quantum forces associated with the quantum diffraction effects and the quantum statistical effects act on the degenerate electron fluid. The strong correlation effects of ion are embedded in generalized viscoelastic momentum equation including the viscoelasticity and shear viscosities of ion fluid. The general dispersion relation is obtained using the normal mode analysis technique for the two regimes of propagation, i.e., hydrodynamic and kinetic regimes. The Jeans condition of self-gravitational instability is also obtained for both regimes, in the hydrodynamic regime it is observed to be affected by the ion plasma oscillations and quantum parameter while in the kinetic regime in addition to ion plasma oscillations and quantum parameter, it is also affected by the ion velocity which is modified by the viscosity generated compressional effects. The Jeans critical wave number and corresponding critical mass are also obtained for strongly coupled quantum plasma for both regimes.

Modified Jeans instability of magnetized viscous spin 1/2 quantum plasma with resistive effects and Hall current

The effect of Hall current on Jeans self-gravitational instability is examined for finitely conducting dense quantum viscous plasma in the presence of spin generated magnetization. The basic equations of the problem are constructed using quantum magneto hydrodynamic (QMHD) model. The Hall and resistivity terms are incorporated in the idealized Ohm’s law and spin induced magnetization and viscosity terms are incorporated to the momentum equations. The general dispersion relation is found to be modified due to the presence of Hall current, electrical resistivity and viscosity parameter along with the spin induced magnetization. The dispersion relation is further reduced for both transverse and longitudinal mode of propagations. In the transverse mode of propagation the Jeans condition of instability is modified due to Alfven velocity, magnetization parameter and quantum corrections, and the growth rate of instability is found to be modified due to the electrical resistivity, viscosity, magnetization parameter and quantum corrections but remains unaffected by the presence of Hall current. In longitudinal direction of propagation the gravitational mode is affected due to the viscosity and quantum parameter while the Jeans condition of instability depends only upon the quantum correction. The Alfven mode in longitudinal direction gets modified due to the electrical resistivity, Hall current, viscosity and magnetization parameter however, it is found to be independent of quantum corrections. The numerical observations are also presented to show the effect of electrical resistivity, magnetization and quantum corrections on the growth rate of instability.

The effect of spin induced magnetization on Jeans instability of viscous and resistive quantum plasma

The effect of spin induced magnetization and electrical resistivity incorporating the viscosity of the medium is examined on the Jeans instability of quantum magnetoplasma. Formulation of the system is done by using the quantum magnetohydrodynamic model. The analysis of the problem is carried out by normal mode analysis theory. The general dispersion relation is derived from set of perturbed equations to analyse the growth rate and condition of self-gravitational Jeans instability. To discuss the influence of resistivity, magnetization, and viscosity parameters on Jeans instability, the general dispersion relation is reduced for both transverse and longitudinal mode of propagations. In the case of transverse propagation, the gravitating mode is found to be affected by the viscosity, magnetization, resistivity, and magnetic field strength whereas Jeans criterion of instability is modified by the magnetization and quantum parameter. In the longitudinal mode of propagation, the gravitating mode is found to be modified due to the viscosity and quantum correction in which the Jeans condition of instability is influenced only by quantum parameter. The other non-gravitating Alfven mode in this direction is affected by finite electrical resistivity, spin induced magnetization, and viscosity. The numerical study for the growth rate of Jeans instability is carried out for both in the transverse and longitudinal direction of propagation to the magnetic field. The effect of various parameters on the growth rate of Jeans instability in quantum plasma is analysed.

A stability analysis of a self-gravitating optically thick magnetized quantum plasma including the effects of black body radiation

We have discussed the effect of black body radiation on self-gravitational instability of infinite homogeneous, optically thick quantum plasma carrying a uniform magnetic field. With the help of relevant linearized perturbation quantum magneto-hydrodynamic equations of the problem, using normal mode technique, a general dispersion relation is obtained with black body radiation, quantum correction and magnetic field. Discussed when propagation vectors are longitudinal and transverse to the magnetic field, separately. The new Jeans condition of instability due to quantum correction, magnetic field and black body radiation is discussed. We find that in transverse mode of propagation the condition of Jeans instability of gaseous plasma is modified by quantum correction, magnetic field and black body radiation. In the case of longitudinal mode, it is unaffected by a magnetic field, as this mode provides the Alfven mode separately with the gravitational mode. From the curves we found that the effects of quantum correction, black body radiation and magnetic field have a stabilizing influence.

The effect of finite Larmor radius corrections on Jeans instability of quantum plasma

The influence of finite Larmor radius (FLR) effects on the Jeans instability of infinitely conducting homogeneous quantum plasma is investigated. The quantum magnetohydrodynamic (QMHD) model is used to formulate the problem. The contribution of FLR is incorporated to the QMHD set of equations in the present analysis. The general dispersion relation is obtained analytically using the normal mode analysis technique which is modified due to the contribution of FLR corrections. From general dispersion relation, the condition of instability is obtained and it is found that Jeans condition is modified due to quantum effect. The general dispersion relation is reduced for both transverse and longitudinal mode of propagations. The condition of gravitational instability is modified due to the presence of both FLR and quantum corrections in the transverse mode of propagation. In longitudinal case, it is found to be unaffected by the FLR effects but modified due to the quantum corrections. The growth rate of Jeans instability is discussed numerically for various values of quantum and FLR corrections of the medium. It is found that the quantum parameter and FLR effects have stabilizing influence on the growth rate of instability of the system.

Magnetogravitational Instability of a Walters B’ Viscoelastic Rotating Anisotropic Heat-Conducting Fluid in Brinkman Porous Medium

Instability of a Walters B′ viscoelastic rotating anisotropic heat-conducting plasma with modified Chew–Goldberger–Low equations is discussed under a gravitational force and uniform magnetic field in a Brinkman porous medium. The general dispersion relation is obtained using normal mode analysis, and it is reduced for propagation parallel and perpendicular to the direction of the magnetic field. These conditions are discussed for the axis of rotation along and perpendicular to the magnetic field. The stability of the system in the two directions is discussed both analytically and numerically. The numerical analysis is performed to show the effects of various parameters, namely, rotation, pressure anisotropy, medium permeability, porosity of porous medium, kinematic viscosity, kinematic viscoelasticity, and heat flux on the stability of the considered system. The Jeans condition of gravitational instability is obtained for both cases of propagation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 93-112, 2014; Published online 31 July 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21064

Effect of magnetic field and radiative condensation on the Jeans instability of dusty plasma with polarization force

The Jeans instability of self-gravitating dusty plasma with polarization force is investigated considering the effects of magnetic field, dust temperature and radiative condensation. The condition of Jeans instability and expression of critical Jeans wave number are obtained which depend upon polarization force and dust temperature but these are unaffected by the presence of magnetic field. The radiative heat-loss functions also modify the Jeans condition of instability and expression of critical Jeans wave number. It is observed that the polarization force and ratio of radiative heat-loss functions have destabilizing while magnetic field and dust temperature have stabilizing influence on the growth rate of Jeans instability.

Self-gravitational instability of partially ionized plasma with radiative effects

The gravitational instability of two-component plasma is discussed to investigate the effect of the radiative heat-loss function, thermal conductivity, collision frequency of neutrals, finite electrical resistivity and viscosity of the medium on the Jeans instability. The usual Magnetohydrodynamics (MHD) equations are used for the present configuration with radiative heat-loss function and thermal conductivity. A general dispersion relation is obtained from perturbation equations using the normal mode analysis method. We find that the Jeans condition of self-gravitational instability is modified due to the presence of radiative heat-loss function and thermal conductivity. Numerical calculations have been performed to show the effect of the various parameters on the growth rate of the self-gravitational instability.

Self-gravitational instability of rotating anisotropic heat-conducting plasma

The self-gravitational instability of rotating anisotropic heat-conducting plasma with modified Chew–Goldberger–Low equations is investigated. The general dispersion relation is obtained using normal mode analysis by constructing the linearized set of equations. This dispersion relation is further reduced for propagation parallel and perpendicular to the direction of magnetic field. These conditions are discussed for axis of rotation along and perpendicular to the magnetic field. It is found that the heat flux vector does not influence the transverse mode of propagation for both cases of rotation and Jeans condition remains unchanged. In case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we get the dispersion relation, which shows the joint effect of rotation and heat flux vector. The two separate modes of propagation are obtained in terms of rotation and heat flux vector for rotation parallel to the magnetic field. It is demonstrated that the Alfvén wave and the associated firehose instability are not affected by the presence of heat flux corrections and rotation also. The numerical analysis is performed to show the effect of rotation, pressure anisotropy, and heat flux parameter on the condition of instability in the spiral arms of galaxy. The Jeans condition of gravitational instability is obtained for both the cases of propagation.

High-resolution simulations of clump-clump collisions using SPH with particle splitting

We investigate, by means of numerical simulations, the phenomenology of star formation triggered by low-velocity collisions between low-mass molecular clumps. The simulations are performed using an SPH code which satisfies the Jeans condition by invoking On-the-Fly Particle Splitting. Clumps are modelled as stable truncated (non-singular) isothermal, i.e. Bonnor-Ebert, spheres. Collisions are characterised by M_0 (clump mass), b (offset parameter, i.e. ratio of impact parameter to clump radius), and M (Mach Number, i.e. ratio of collision velocity to effective post-shock sound speed). The gas subscribes to a barotropic equation of state, which is intended to capture (i) the scaling of pre-collision internal velocity dispersion with clump mass, (ii) post-shock radiative cooling, and (iii) adiabatic heating in optically thick protostellar fragments. The efficiency of star formation is found to vary between 10% and 30% in the different collisions studied and it appears to increase with decreasing M_0, and/or decreasing b, and/or increasing M. For b ~ 5 x 10^5 cm^{-3}, are sufficient that they could be mapped in NH_3 or CS line radiation, in nearby star formation regions.

Smoothed Particle Hydrodynamics with particle splitting, applied to self-gravitating collapse

We describe and demonstrate a method for increasing the resolution locally in a Smoothed Particle Hydrodynamic (SPH) simulation, by splitting particles. We show that in simulations of self-gravitating collapse (of the sort that are presumed to occur in star formation) the method is stable, and affords great savings in computer time and memory. When applied to the standard Boss & Bodenheimer test — which has been shown to depend critically on fulfilment of the Jeans Condition — the results are comparable both with those obtained using Adaptive Mesh Refinement, and with those obtained using a standard high-resolution SPH simulation, but they are achieved with considerably less computational resource. Further development and testing is required before the method can safely be applied to more general flows.

The Jeans Condition and Collapsing Molecular Cloud Cores: Filaments or Binaries?

The 1997 and 1998 studies by Truelove and colleagues introduced the Jeans condition as a necessary condition for avoiding artificial fragmentation during protostellar collapse calculations. They found that when the Jeans condition was properly satisfied with their adaptive mesh refinement (AMR) code, an isothermal cloud with an initial Gaussian density profile collapsed to form a thin filament rather than the binary or quadruple protostar systems found in previous calculations. Using a completely different self-gravitational hydrodynamics code introduced by Boss & Myhill in 1992 (B&M), we present here calculations that reproduce the filamentary solution first obtained by Truelove et al. in 1997. The filamentary solution only emerged with very high spatial resolution with the B&M code, with effectively 12,500 radial grid points (R12500). Reproducing the filamentary collapse solution appears to be an excellent means for testing the reliability of self-gravitational hydrodynamics codes, whether grid-based or particle-based. We then show that in the more physically realistic case of an identical initial cloud with nonisothermal heating (calculated in the Eddington approximation with code B&M), thermal retardation of the collapse permits the Gaussian cloud to fragment into a binary protostar system at the same maximum density where the isothermal collapse yields a thin filament. However, the binary clumps soon thereafter evolve into a central clump surrounded by spiral arms containing two more clumps. A roughly similar evolution is obtained using the AMR code with a barotropic equation of state—formation of a transient binary, followed by decay of the binary to form a central object surrounded by spiral arms, though in this case the spiral arms do not form clumps. When the same barotropic equation of state is used with the B&M code, the agreement with the initial phases of the AMR calculation is quite good, showing that these two codes yield mutually consistent results. However, the B&M barotropic result differs significantly from the B&M Eddington result at the same maximum density, demonstrating the importance of detailed radiative transfer effects. Finally, we confirm that even in the case of isothermal collapse, an initially uniform density sphere can collapse and fragment into a binary system, in agreement with the 1998 results of Truelove et al. Fragmentation of molecular cloud cores thus appears to remain as a likely explanation of the formation of binary stars, but the sensitivity of these calculations to the numerical resolution and to the thermodynamical treatment demonstrates the need for considerable caution in computing and interpreting three-dimensional protostellar collapse calculations.

Star formation with 3-D adaptive mesh refinement: the collapse and fragmentation of molecular clouds

We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with unprecendented resolution. This code utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution. These grids are automatically and dynamically added and removed as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with methods using fixed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. The application of this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation is discussed. The simulation involves many orders of magnitude of variation in length scale as fragments form. In this paper we describe the methodology and present illustrative applications for both isothermal and nonisothermal cloud collapse. We describe the numerical Jeans condition, a new criterion for stability of self-gravitational gas dynamic problems. We find that the uniformly rotating, spherical clouds treated here first collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form filamentary singularities that do not fragment while isothermal. As the collapse enters the non-isothermal phase, we show the evolutionary sequence that leads to the formation of a binary system consisting of protostellar cores surrounded by distinct protostellar disks. The scale of the disks, of order 100 AU, is consistent with observations of gaseous disks surrounding single T-Tauri stars and debris disks surrounding systems such as Beta Pictoris.

The Jeans Mass Constraint and the Fragmentation of Molecular Cloud Cores

The collapse and fragmentation of molecular cloud cores into binary and multiple protostar systems is a demanding computational problem, in part because of the large range of length scales involved. Truelove et al. proposed that the computational cell size Δx must be smaller than 1/4 of the Jeans length, λJ, if artificial (numerical) fragmentation is to be avoided. For a uniform Cartesian grid, Truelove et al.'s Jeans condition is equivalent to ensuring that the mass of a cell never exceeds ~1/64 of a Jeans mass. It is shown here that for a nonuniform spherical grid, artificial fragmentation can be avoided provided that the cell size of a cube with approximately the same volume as the spherical coordinate cell [Δx=(ΔxrΔxθΔx)1/3] is less than λJ/4 (i.e., that the mass inside each cell is much less than a Jeans mass), even if one of the three cell lengths (Δxr, Δxθ, or Δx) exceeds λJ/4. For a nonuniform grid, resolving a small fraction of a Jeans mass is less restrictive than resolving 1/4 of a Jeans length in each coordinate direction; resolving all three Jeans lengths is desirable but not necessary in order to avoid artificial fragmentation. The well-resolved collapse of an initially Gaussian-profile cloud is then followed with both isothermal and nonisothermal (Eddington approximation radiative transfer) thermodynamics and is shown to lead to fragmentation into a binary protostar system in both cases. The Jeans mass constraint appears to be a valuable indicator of physically realistic fragmentation.

Self‐gravitational Hydrodynamics with Three‐dimensional Adaptive Mesh Refinement: Methodology and Applications to Molecular Cloud Collapse and Fragmentation

We describe a new code for numerical solution of three-dimensional self-gravitational hydrodynamics problems. This code utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution and automatically and dynamically adding and removing these grids as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with a code using fixed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. In particular, we apply this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation. The simulation involves many orders of magnitude of variation in length scale as fragments form at positions that are not a priori discernible from general initial conditions. In this paper, we describe the methodology behind this new code and present several illustrative applications. The criterion that guides the degree of adaptive mesh refinement is critical to the success of the scheme, and, for the isothermal problems considered here, we employ the Jeans condition for this purpose. By maintaining resolution finer than the local Jeans length, we set new benchmarks of accuracy by which to measure other codes on each problem we consider, including the uniform collapse of a finite pressured cloud. We find that the uniformly rotating, spherical clouds treated here first collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form filamentary singularities that do not fragment while isothermal. Our results provide numerical confirmation of recent work by Inutsuka & Miyama on this scenario of isothermal filament formation.

The Jeans Condition: A New Constraint on Spatial Resolution in Simulations of Isothermal Self-gravitational Hydrodynamics

We demonstrate with a new three-dimensional adaptive mesh refinement code that perturbations arising from discretization of the equations of self-gravitational hydrodynamics can grow into fragments in multiple-grid simulations, a process we term We present star formation calculations of isothermal collapse of dense molecular cloud cores. In simulation of a Gaussian-profile cloud free of applied perturbations, we find artificial fragmentation can be avoided across the isothermal density regime by ensuring the ratio of cell size to Jeans length, which we call the Jeans number, J ≡ Δx/λJ, is kept below 0.25. We refer to the constraint that λJ be resolved as the Jeans condition. When an m=2 perturbation is included, we again find it necessary to keep J≤0.25 to achieve a converged morphology. Collapse to a filamentary singularity occurs without fragmentation of the filament, in agreement with the predictions of Inutsuka & Miyama. Simulation beyond the time of this singularity requires an arresting agent to slow the runaway density growth. Physically, the breakdown of isothermality due to the buildup of opacity acts as this agent, but many published calculations have instead used artificial viscosity for this purpose. Because artificial viscosity is resolution dependent, such calculations produce resolution-dependent results. In the context of the perturbed Gaussian cloud, we show that use of artificial viscosity to arrest collapse results in significant violation of the Jeans condition. We also show that if the applied perturbation is removed from such a calculation, numerical fluctuations grow to produce substantial fragments not unlike those found when the perturbation is included. These findings indicate that calculations that employ artificial viscosity to halt collapse are susceptible to contamination by artificial fragmentation. The Jeans condition has important implications for numerical studies of isothermal self-gravitational hydrodynamics problems insofar as it is a necessary but not, in general, sufficient condition for convergence.

Gravitational instability of a heat-conducting plasma

The gravitational instability of an infinite, anisotropic, heat-conducting plasma is studied in this paper. It is found that, for the case of parallel propagation, the inclusion of heat-conduction terms in the fluid equations, in general, leads to overstability of the system, whereas the transverse propagation remains unaffected. We have solved numerically the dispersion relation corresponding to the parallel propagation and find that except for a range of wave numbers, the system is overstable. We also found that in the limit of vanishing zeroth-order heat flux, the condition for gravitational instability is similar to the Jeans's condition for instability for an isotropic plasma.