Modification of the Jeans and Toomre instability criteria for astrophysical fractal objects within nonextensive statistics

Within the formalism of Tsallis nonextensive statistics designed to describe the behavior of anomalous systems, systems with a strong gravitational interaction between their individual parts and the fractal nature of phase space, we have obtained linearized equations for the oscillations of a rigidly rotating disk by taking into account dissipative effects and give a derivation of the dispersion equation in the WKB approximation. Based on the previously derived modified Navier—Stokes hydrodynamic equations (the so-called equations of q-hydrodynamics), we have analyzed the axisymmetric oscillations of an astrophysical, differentially rotating gas—dust cosmic object and obtained modified Jeans and Toomre gravitational instability criteria for disks with a fractal phase-space structure.     

On the interaction between the URCA process and convection

The influence of the URCA process (β-decay, electron capture) on convective stability is investigated and a stability criterion is derived. The criterion contains the Schwarzschild criterion and the thermohaline convection. It is found that URCA may cause convective instability to an otherwise stable medium, but it cannot stabilize an unstable medium, only the growth rate is affected. A numerical example for the Na²³?Ne²³ URCA pair shows the regions in the ?-T plane where instability is caused (assuming given abundances of the isotopes). The evolution of C-O core of an evolved 3.5M _⊙–8M _⊙ star may be affected by formation of convective regions even prior to C¹² ignition.     

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

Solar System Research - Within the framework of Tsallis nonextensive statistics, the criteria for the Jeans gravitational instability are derived for a self-gravitating protoplanetary disk, whose...     

On the Jeans Criterion of a Stratified Heat Conducting Gaseous Medium in the Presence of Non-uniform Rotation and Magnetic Field

The problem of self-gravitational instability of an infinite, homogeneous stratified gaseous medium with finite thermal conductivity and infinite electrical conductivity, in the presence of non-uniform rotation and magnetic field in the Chandrasekhar’s frame of reference, is studied. It is found that the magnetic field, whether uniform or non-uniform, has no effect on the Jeans’ criterion for gravitational instability and remains essentially unaffected. However, the thermal conductivity has the usual stabilizing effect on the criterion that the adiabatic sound velocity occurring in the Jeans criterion is replaced by the isothermal sound velocity. Thus, the present analysis extends the results of Chandrasekhar for the case of heat conducting medium and for non-uniform rotation and magnetic field.     

Gravitational Instability of Cylindrical Viscoelastic Medium Permeated with Non Uniform Magnetic Field and Rotation

The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium.     

Grain sedimentation in a giant gaseous protoplanet

We present a calculation of the sedimentation of grains in a giant gaseous protoplanet such as that resulting from a disk instability of the type envisioned by Boss [Boss, A.P., 1998. Earth Moon Planets 81, 19-26]. Boss [Boss, A.P., 1998. Earth Moon Planets 81, 19-26] has suggested that such protoplanets would form cores through the settling of small grains. We have tested this suggestion by following the sedimentation of small silicate grains as the protoplanet contracts and evolves. We find that during the course of the initial contraction of the protoplanet, which lasts some 4×¹⁰⁵ years, even very small (>1 μm) silicate grains can sediment to create a core both for convective and non-convective envelopes, although the sedimentation time is substantially longer if the envelope is convective, and grains are allowed to be carried back up into the envelope by convection. Grains composed of organic material will mostly be evaporated before they get to the core region, while water ice grains will be completely evaporated. These results suggest that if giant planets are formed via the gravitational instability mechanism, a small heavy element core can be formed due to sedimentation of grains, but it will be composed almost entirely of refractory material. Including planetesimal capture, we find core masses between 1 and 10 M_⊕, and a total high-Z enhancement of ∼40 M_⊕. The refractories in the envelope will be mostly water vapor and organic residuals.     

The influence of gravitational acceleration on the supernova-driven Parker instability

Within a framework of 2D magnetohydrodynamic (MHD) simulations, we explore the dynamical regimes initiated by a supernova explosion in a magnetized stratified interstellar medium (ISM). We concentrate on the formation of large-scale magnetic structures and outflows connected with the Parker instability. For the sake of simplicity we only show models with a fixed explosion energy corresponding to a single supernova (SN) occurring in host galaxies with different fixed values of the gravitational acceleration g and different ratios of specific heats. We show that in general, depending on these two parameters, three different regimes are possible: a slowly growing Parker instability on time-scales much longer than the galactic rotation period for small g; the Parker instability growing at roughly the rotation period, which for ratios of specific heats larger than one is accompanied by an outflow resulting from the explosion for intermediate g; and a rapidly growing instability and a strong blow-out flow for large g . By means of numerical simulations and analytical estimates we show that the explosion energy and gravitational acceleration which separate the three regimes scale as Eg ²∼constant in the 2D case. We expect that in the 3D case this scaling law is Eg ³∼constant . Our simulations demonstrate furthermore that a single SN explosion can lead to the growth of multiple Parker loops in the disc and large-scale magnetic field loops in the halo, extending over 2–3 kpc horizontally and up to 3 kpc vertically above the mid-plane of the disc.     

Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

On the gravitational instability of a medium in non-uniform rotation and magnetic field

The effect of a non-uniform magnetic field on the gravitational instability for a non-uniformly rotating, infinitely extending axisymmetric cylinder in a homogeneous medium has been studied. The Bel and Schatzman criterion of gravitational instability for a non-uniformly rotating medium is modified under the effect of a non-uniform/uniform magnetic field acting along the tangential and axial directions. As a consequence the stabilizing and destabilizing effect of the non-uniform magnetic field is obtained, a new criterion for the magneto-gravitational instability is deduced in terms of Alfven’s wave velocity; and it is also found that the Jeans criterion determines the gravitational instability in the absence of rotation and when the non-uniform/uniform magnetic field acts along the axis of the cylinder.     

Numerical simulations of the κ-mechanism with convection

A strong coupling between convection and pulsations is known to play a major role in the disappearance of unstable modes close to the red edge of the classical Cepheid instability strip. As mean-field models of time-dependent convection rely on weakly-constrained parameters (see, e.g., Baker in Physical Processes in Comets, Stars and Active Galaxies, p. 105, 1987), we tackle this problem by the means of 2-D Direct Numerical Simulations (DNS) of the κ-mechanism with convection. Using a linear stability analysis, we first determine the physical conditions favourable for the κ-mechanism to occur inside a purely-radiative layer. Both the instability strips and the nonlinear saturation of unstable modes are then confirmed by the corresponding DNS. We next present the new simulations with convection, where a convective zone and the driving region overlap. The coupling between the convective motions and acoustic modes is then addressed by using projections onto an acoustic subspace.     

The local stability of accretion disk models with considering the role of various viscosity and cooling mechanisms

The standard thin accretion disk model can explain the soft X-ray spectra of Galactic black hole systems and AGN successfully. However, there are still a few observational documents for Radiation pressure theory in X-ray novae in black hole binary systems and AGN. The luminosity in accretion onto black holes is corresponds to L>0.01L _E . According to standard thin disk model, when the accretion rate is over a small fraction of the Eddington rate, L>0.01L _E , the inner region of the disk is radiation-pressure-dominated and thermally unstable. However, observations of the high/soft state of black hole X-ray binaries with luminosity within (0.01L _E <L<0.5L _E ) show that the disk is quite stable. Thus, this contradiction shows the objection of this model and maybe it is essential to change the standard viscosity law or one of the other basic assumptions in order to get a stable disk models. In this paper, we revisit and recalculate the thermal instability with a different models of viscosity and cooling functions and show that the choosing of an arbitrary cooling and viscosity functions can affect on the stability of a general disk model and hence maybe answer to a this problem in accretion disk theory. We choose an arbitrary functions of surface density Σ and half thickness of disk H for cooling and viscosity. Also, we discuss a general disk with thermal conduction, radial force and advection. Then, we solve the equations numerically. We obtain a fourth degree dispersions relation and discuss solutions and instability modes. This analysis shows the great sensitivity of stability of disk to the form of viscosity, so there are various effective factors to stabilize the disk. For example the exist of advection and thermal conduction can effect to stability of disks also.     

Interfacial instabilities driven by self-gravity: first numerical results

The evolution of the interstellar medium (ISM) is driven by a variety of phenomena, including turbulence, shearing flows, magnetic fields and the thermal properties of the gas. Among the most important forces at work is self-gravity, which ultimately drives protostellar collapse. As part of an ongoing study of instabilities in the ISM, Hunter, Whitaker & Lovelace have discovered another process driven by self-gravity: the instability of an interface of discontinuous density. Theory predicts that this self-gravity driven interfacial instability persists in the static limit and in the absence of a constant background acceleration. Disturbances to a density interface are found to grow on a time-scale of the order of the free-fall time, even when the perturbation wavelength is much less than the Jeans length. Here we present the first numerical simulations of this instability. The theoretical growth rate is confirmed and the non-linear morphology displayed. The self-gravity interfacial instability is shown to be fundamentally different from the Rayleigh–Taylor instability, although both exhibit similar morphologies under the condition of a high density contrast, such as is commonly found in the ISM. Such instabilities are a possible mechanism by which observed features, such as the pillars of gas seen near the boundaries of interstellar clouds, are formed.     

The red edge of the instability strip of RR Lyrae stars

The thermodynamical compling between radial pulsation and convection is studied in accordance with Unno's theory of time-dependent convection. Linear, non-adiabatic calculations are made for 11 series of RR Lyrae models to illuminate the dependence of the red edge of their instability strip on mass, luminosity, helium abundance and the convective parameter C₁.     

Coronae & Outflows from Helical Dynamos, Compatibility with the MRI, and Application to Protostellar Disks

Magnetically mediated disk outflows are a leading paradigm to explain winds and jets in a variety of astrophysical sources, but where do the fields come from? Since accretion of mean magnetic flux may be disfavored in a thin turbulent disk, and only fields generated with sufficiently large scale can escape before being shredded by turbulence, in situ field production is desirable. Nonlinear helical inverse dynamo theory can provide the desired fields for coronae and outflows. We discuss the implications for contemporary protostellar disks, where the (magneto-rotational instability (MRI)) can drive turbulence in the inner regions, and primordial protostellar disks, where gravitational instability drives the turbulence. We emphasize that helical dynamos are compatible with the magneto-rotational instability, and clarify the relationship between the two.     

Annihilation of positrons in the Galaxy

Observations of electron-positron annihilation radiation from the Galactic Center region with the SPI instrument aboard INTEGRAL are summarized. The measured width of the 511 keV line and inferred fraction of positrons annihilating through positronium formation are consistent with the annihilation taking place in the warm ISM phase, although combinations of several ISM phases are also allowed by the data. The spatial distribution of 511 keV emission suggests that positron sources are concentrated toward the Galactic bulge and avoid the Galactic disk.     

A heat engine based moist convection parametrization for Jupiter

We have developed a parametrization of Jovian moist convection based on a heat engine model of moist convection. In comparison to other moist convection schemes, this framework allows the computation of the total available convective energy TCAPE and the corresponding mass flux M as dynamic variables from the mean atmospheric state. The effects of this parametrization have been investigated both analytically and numerically. In agreement with previous numerical experiments and observations, the inclusion of moist convection leads to heat and water vapor transport from the water condensation level into higher altitudes. The time development of the modeled convective events was found to be strongly influenced by a rapid reduction of kinetic energy and a subsequent lowering of the cumulus tower's top in response to convective heating. We have tested the sensitivity of the scheme to different variations in the fractional cloud coverage and under the inclusion of external radiative forcing towards a stable/unstable temperature profile. While the time development of convective events differs in response to these variations, the general moist convective heating and moistening of the upper troposphere was a robust feature observed in all experiments.     

Turbulent viscosity and lifetime of Saturn's rings

The viscosity (the angular momentum flux) in the disk of mutually gravitating particles of Saturn's rings is investigated. The hydrodynamic theory of the gravitational Jeans-type instability of small gravity perturbations (e.g., those produced by spontaneous disturbances) of the disk is developed. It is suggested that in such a system the hydrodynamic turbulence may arise as a result of the instability. The turbulence is related to stochastic motions of “fluid” elements. The objective of this paper is to show that in the Jeans-unstable Saturnian ring disk the turbulent viscosity may exceed the ordinary microscopic viscosity substantially. The main result of local N-body simulations of planetary rings by Daisaka et al. (2001. Viscosity in a dense planetary ring with self-gravitating particles. Icarus 154, 296-312) is explained: in the presence of the gravitationally unstable density waves, the effective turbulent viscosity ν_eff is given as ν_eff=CG²Σ²/Ω³, where G, Σ, and Ω are the gravitational constant, the surface mass density of a ring, and the angular velocity, respectively, and the nondimensional correction factor C≈10. We argue that both Saturn's main rings and their irregular of the order of 100 m or even less fine-scale structure (being recurrently created and destroyed on the time scale of an order of Keplerian period ) are not likely much younger than the solar system.     

银河系厚盘及其形成机制

银河系厚盘的发现，对于研究银河系以至星系的结构和演化具有重要意义。在简单回顾银河系结构研究史和厚盘发现过程的基础上，综合介绍了人们对银河系厚盘各方面性质认识的现状，并对迄今为止所提出的几种厚盘形成机制作了比较详细的说明和讨论。就目前来看，与伴星系的并合可能是形成厚盘最为可能的机制。     

Self-gravity driven instabilities of interfaces in the interstellar medium

In order to understand star formation it is important to understand the dynamics of atomic and molecular clouds in the interstellar medium (ISM). Non-linear hydrodynamic flows are a key component to the ISM. One route by which non-linear flows arise is the onset and evolution of interfacial instabilities. Interfacial instabilities act to modify the interface between gas components at different densities and temperatures. Such an interface may be subject to a host of instabilities, including the Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov instabilities. Recently, a new density interface instability was identified. This self-gravity interfacial instability (SGI) causes any displacement of the interface to grow on roughly a free-fall time-scale, even when the perturbation wavelength is much less than the Jeans length. In previous work, we used numerical simulations to confirm the expectations of linear theory and examine the non-linear evolution of the SGI. We now continue our study by generalizing our initial conditions to allow the acceleration due to self-gravity to be non-zero across the interface. We also consider the behaviour of the SGI for perturbation wavelengths near the Jeans wavelength. We conclude that the action of self-gravity across a density interface may play a significant role in the ISM either by fuelling the growth of new instabilities or modifying the evolution of existing instabilities.