Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

The rayleigh-taylor instability of a stratified rotating fluid through a porous medium in a two-dimensional magnetic field

The effect of finite conductivity on the Rayleigh-Taylor instability of an incompressible, viscous rotating fluid through a porous medium has been studied in the presence of a two-dimensional horizontal magnetic field. It has been shown that the solution is characterized by a variational principle. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite fluid in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that finite resistivity and porosity have a destabilizing effect on the Rayleigh-Taylor instability while rotation has a stabilizing effect.     

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper, we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be and the faster the flow rotates. The relevance to observations is briefly discussed.     

Instability of a gravitating partially-ionized plasma

The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence.     

Hot accretion flow with ordered magnetic field, outflow, and saturated conduction

The importance of thermal conduction on hot accretion flow is confirmed by observations of hot gas that surrounds Sgr A^? and a few other nearby galactic nuclei. On the other hand, the existence of outflow in accretion flows is confirmed by observations and magnetohydrodynamic (MHD) simulations. In this research, we study the influence of both thermal conduction and outflow on hot accretion flows with ordered magnetic field. Since the inner regions of hot accretion flows are, in many cases, collisionless with an electron mean free path due to Coulomb collision larger than the radius, we use a saturated form of thermal conduction, as is appropriate for weakly collisional systems. We also consider the influence of outflow on accretion flow as a sink for mass, and the radial and the angular momentum, and energy taken away from or deposited into the inflow by outflow. The magnetic field is assumed to have a toroidal component and a vertical component as well as a stochastic component. We use a radially self-similar method to solve the integrated equations that govern the behavior of such accretion flows. The solutions show that with an ordered magnetic field, both the surface density and the sound speed decrease, while the radial and angular velocities increase. We found that a hot accretion flow with thermal conduction rotates more quickly and accretes more slowly than that without thermal conduction. Moreover, thermal conduction reduces the influences of the ordered magnetic field on the angular velocities and the sound speed. The study of this model with the magnitude of outflow parameters implies that the gas temperature decreases due to mass, angular momentum, and energy loss. This property of outflow decreases for high thermal conduction.     

A magnetohydrodynamic model applied to the lower convective region in the Sun including the radial components of magnetic field and flow

In this work, some numerical solutions of magnetohydrodynamic equations are investigated in the presence of radial and azimuthal components of magnetic field with the use of previously developed algorithm. In this algorithm, the thin shell approximation and a special separation of variables is used to obtain the radial and latitudinal variations of physical parameters in spherical coordinates. The solutions are obtained via this separation of variables in the components of momentum transfer equation. The analysis yields three important parameters which are the sphericity, density and radial components shape parameters in the latitudinal distributions of physical variables. The magnetic field profile, used here, produces comparable magnetic fluxes found in previous works. There is a considerable change in density with respect to reference model. Other physical parameters also reveal important physical results. It is as well shown that the spherical symmetric distributions of physical parameters are broken for the region of study.     

The non-axisymmetrical configuration of a large-scale solar and stellar magnetic field

The non-axisymmetric and nonlinear solutions of the magnetostatic equations are given in three-dimensional space of spherical coordinates (r, θ, ?). These solutions are applied to the large-scale solar magnetic field. Their basic features are similar to a dipole field near the polar regions and the polarity reverses near the equator. These features agree with observations for the large-scale solar magnetic field. The solutions can also be applied to investigating the connection between the structure of the magnetic field and the density distribution of the corona. It is shown that the tops of the closed magnetic field associate with density enhancements. Similar results may apply to the large-scale configuration of the stellar field.     

Strange quark matter in a strong magnetic field

The stability of strange quark matter in the presence of a strong magnetic field is investigated using a dynamical, density dependent, quark mass approach to confinement. Changes in both the single particle and bulk energies of a system which are due to the strong magnetic field are also calculated. It is shown that the presence of a magnetic field makes strange quark matter energetically more stable.     

Magnetic energy buildup in a quadrupole field by photospheric shear motion

Using a two-dimensional, dissipative magnetohydrodynamic model, this paper presents a numerical simulation of the magnetic energy buildup in a quadrupolar field by photospheric shear motion. When electric current density is larger than a certain critical value, an anomalous resistivity is introduced in order to account for the dissipation caused by instabilities in high current regions. It is shown that like a bipolar field, a quadrupolar field can efficiently store magnetic free energy through photospheric shear motion. Electric current formed by shear concentrates on the separatrix and magnetic loops rooted in areas where the shear velocity gradient is large. The atmosphere is heated by anomalous resistive dissipation during the shear. Both magnetic and thermal energy increases nonlinearly with shearing displacement. When the anomalous resistivity increases or the critical current density decreases, the growth rate reduces for magnetic energy but goes up for thermal energy.     

Average velocity components in a rotating infinitely flattened self-gravitating system near an equilibrium state

The average radial and angular velocity components are obtained for a rotating two-dimensional self-gravitating system near an equilibrium state. First-order perturbation configurations of flaring straight bars emanating from the center provide examples of such systems. In these systems the average velocity field to first order is incompressible and irrotational. The second-order effects on the product of the average velocity components with the spatial density are essentially independent of the angular coordinate.     

Primeval Turbulence?

Some difficulties with the Primeval Turbulence picture for galaxy formation are considered. It is shown that the evolution of the matter turbulence one decoupled from the radiation depends very much on the assumed turbulence velocity. If the velocity is small the turbulence simply adds to the amplitude of the growing density perturbation mode, an effect almost indistinguishable from the equally ad hoc assumption of a somewhat larger initial density perturbation. If the turbulence velocity field were made large enough to provide the angular velocity of the Galaxy, or the nominal peculiar velocities of galaxies, the galaxies would have formed sooner than one would otherwise have speculated.Research supported in part by the National Science Foundation.     

Influence of accelerated particles on the large-scale magnetic field in young supernova remnants

We offer a possible explanation for the observational data on the magnetic-field structure in young supernova remnants (SN 1006, Tycho, Kepler, Cas A) that have been obtained by analyzing the polarizations of electromagnetic radiation in the radio, infrared, and other wavelength ranges. The authors of observational works interpret these data as evidence that the ordered magnetic-field component is predominantly radial, but it can be much smaller in amplitude than the stochastic field component that accounts for the bulk of the total magnetic energy. We calculate the magnetic field in supernova remnants by taking into account the shock compression of the primary field and the generation of a large-scale magnetic field by the particles accelerated at the shock front. The assumption that the field in the supernova remnant is the explosion-compressed primary field near the star is inconsistent with observational data, because the tangential (relative to the shock front) field component perpendicular to the radius must prevail in this case. However, allowing for the generation of an additional magnetic field by the electric current of the particles accelerated by a strong shock front leads us to conclude that the field components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. Such a field configuration for uniform injection does not lead to the generation of an additional magnetic field, and, in this sense, it is stable. This explains the data on the radial direction of the ordered field component. As regards the stochastic field component, we show that it is effectively generated by accelerated particles if their injection into acceleration at the shock front is nonuniform along the front. Injection nonuniformity can be caused by upstream density nonuniformities. A relative density nonuniformity of the order of several percent is enough for an observable magnetic field with scales on the order of the density nonuniformity scales to be generated.     

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

The evolution of gravitational instabilities: Amplification by coupling of perturbation modes

The frictional effect of collisions of ionized with neutral atoms on the Taylor instability of a composite plasma in porous medium is considered in presence of a variable horizontal magnetic field. The system is stable for stable density stratification. The magnetic field can stabilize a system which was unstable in its absence. The medium permeability has a decreasing or an increasing effect on the growth rates. With the increase in collisional frequency, the growth rates decrease but may have increasing influence in certain region.     

Magnetic field evolution in neutron stars

Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Breakdown of the Goldreich–Julian relation in a neutron star

The electromagnetic field in a magnetized neutron star and the underlying volume charges and currents are found. A general case of a rigidly rotating neutron star with infinite conductivity, arbitrary distribution of the internal magnetic field, arbitrarily changing angular velocity, and arbitrary surface velocity less than the velocity of light is considered. Quaternions are used to describe rotation and determine the magnetic field. It is shown that the charge density is not equal to and can exceed significantly the common Goldreich–Julian density. Moreover, corrections to the magnetic field due to stellar rotation are zero. For a rotating neutron star, twisting magnetic field lines causes charge accumulation and current flows. This fact shows a possible link between changing internal magnetic field topology and observed activity of neutron stars.     

Rayleigh-Taylor instability of rotating fluid in the presence of a vertical magnetic field

The Rayleigh-Taylor instability of two rotating superposed fluids in the presence of a vertical magnetic field has been investigated. It is shown thatn ² is purely real, wheren is the growth rate of a perturbation. In the basis of this fact it is shown that a unique dispersion relation exists if the lighter fluid lies beneath the heavier one. However, if the heavier fluid lies beneath the lighter fluid, then no unique dispersion relation exists. The effect of rotation is to slow down the rate at which potentially unstable stratification departs from the equilibrium position.     

Thin accretion disc with a corona in a central magnetic field

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona.     

Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.