The effect of a magnetic field on an adiabatic explosion

As a paradigm for various explosive processes in the interstellar medium we consider the problem of an adiabatic explosion into a uniform magnetic field which is frozen to the gas. A typical numerical run is described and reveals the following features. The outer shock becomes oblate with respect to the field lines whereas the inner hot gas prolate density and temperature contours. During the later stages the shock weakens and the explosion comes into equilibrium with the interstellar medium. The dominant feature at this stage is a concentration of accelerated material at each pole. We then try to interpret this analytically, considering the magnetic field as a small perturbation to a spherical explosion. This enables us to derive a formula for the eccentricity, which is proportional tot ^6/5. However, the linear perturbation is singular at the centre and needs to be matched to a self-similar flow there, for which we give an approximation. This similarity solution is eventually important outside the region occupied by the material initially responsible for the explosion. We give some discussion of the various asymptotic regimes involved.     

An axially symmetric explosion model in magnetogasdynamics: II

A method using Eulerian coordinate system is developed under a local radiality assumption to study a point explosion in a spheroid with axially symmetric exponential density distribution, including the effect of azimuthal magnetic field.     

Comptonization in a superstrong magnetic field. II

Institute of Cosmic Research, USSR Academy of Sciences. Translated from Astrofizika, 28, No. 2, pp. 429–442, March–April, 1988.     

Jump relations across a shock in non-ideal gas flow

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.     

Stability of the equilibrium distributions of interstellar gas,cosmic rays,and magnetic field in an external gravitational field

An interstellar medium consisting of regular and turbulent magnetic fields, thermal gas and cosmic rays is tested for stability in a stellar gravitational field. Cosmic rays are described by the diffusion-convection equation and the stability region of the system is determined. It is shown that the presence of cosmic rays is a stabilizing factor if the cosmic-ray diffusion coefficient is sufficiently small. The dependence of the maximum growth rate of instability on the cosmic-ray diffusion coefficient is qualitatively determined.     

An explosion with cylindrical symmetry in magnetogasdynamics

The propagation of magnetogasdynamic cylindrical shock waves in an exponentially increasing medium including the effects of the azimuthal magnetic field, is investigated. The shock wave moves with variable velocity and the total energy of the wave is variable. It is shown that the magnetic field has its significant effect on the pressure flow velocity and the inner expanding vacuum region.     

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.     

Energy characteristics of a relativistic Fermi gas in a magnetic field

We derive expressions for the chemical potential, pressure, and mean total energy of an extremely degenerate ideal relativistic gas of charged fermions. We take into account their static anomalous magnetic moments in the presence of a quantizing magnetic field. We examine the cases of ultra-strong magnetic fields and of weak fields in which one does not need to take into account Landau quantization when describing a Fermi gas in ultra-dense matter.Translated from Astrofizika, Vol. 37, No. 1, pp. 161–165, January–March, 1994.     

Stability of a self-gravitating homogeneous spheroid with azimuthal magnetic field. II

Leningrad State University. Translated from Astrofizika, Vol. 30, No. 3, pp. 635–642. May–June, 1989.     

Time-dependent solution for a one-dimensional piston problem in a non-ideal gas

In this article we study the effect of a non-ideal gas parameter on the piston (contact) surface when a strong shock moves into a non-uniform medium. The solution corresponding to the ideal gas can be obtained as a particular case of the analysis.     

On a Babcock-Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field, II

In a previous paper (Paper I), we studied a dynamo model of the Babcock-Leighton type (i.e., the surface eruptions of toroidal magnetic field are the source for the poloidal field) that included a thin, deep seated, generating layer (GL) for the toroidal field, B. Meridional motions (of the order of 12 m s^–1 at the surface), rising at the equator and sinking at the poles were essential for the dynamo action. The induction equation was solved by approximating the latitudinal dependence of the fields by Legendre polynomials. No solutions were found with _p = _f where _p and _f are the fluxes for the preceding and following spot, respectively. The solutions presented in Paper I, had _p = –0.5 _f , were oscillatory in time, and large radial fields, B, were present at the surface.Here, we resume the study of Paper I with a different numerical approach allowing for a much higher resolution in , the polar angle. The time dependent partial differential equations for the toroidal and poloidal field are solved with the help of a second order, time and space centered, finite difference scheme. Oscillatory solutions with _p = _f are found for various values of the meridional motions and diffusivity coefficients. The surface values of B, while considerably smaller than those of Paper I, are still unacceptably large, specially at the poles. The reason can be traced to the eruption of toroidal field at high latitudes. It appears that in order to obtain small values for the radial field in the polar regions, high latitude sources ( smaller than /4, say), must reach their maximum below the surface. Weaker meridional motions near the poles than in the equatorial region are also suggested.     

An interpretation of rapid changes in the magnetic field associated with solar flares

The energy source of a flare is the magnetic field in the corona. A topological model of the magnetic field is used here for interpreting the recently discovered drastic changes in magnetic field associated with solar flares. The following observational results are self‐consistently explained: (1) the transverse field strength decreases at outer part of active regions and increases significantly in their centers; (2) the center‐of‐mass positions of opposite magnetic polarities converge towards the magnetic neutral line just after flares onset; (3) the magnetic flux of active regions decreases steadily during the course of flares. For X‐class flares, almost 50% events show such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quasi-similar solution of the strong shock wave problem in non-ideal gas dynamics

The quasisimilar theory is used to investigate the solution of the blast wave problem with generalized geometries in a non-ideal gas satisfying the equation of state of the Van der Waals type. Here it is assumed that the distribution of normalized velocity, pressure and density are nearly similar in the narrow range of the shock strength. A comparison between approximate analytical solution and numerical solution of the problem is presented for the cylindrical geometry. The numerical solutions are presented for the generalized geometry in a non-ideal gas. It is also assessed as to how the non-idealness of the gas affects the behavior of the flow parameters.     

Partially degenerate nonrelativistic isothermal gas spheres in the presence of a magnetic field

The effect of a weak poloidal magnetic field on the equilibrium structure of a partially degenerate nonrelativistic isothermal gas sphere has been studied. Models have been computed for varying degrees of central degeneracy and the effect of the magnetic field on the various parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been looked into. It is found that as the central degeneracy parameter is increased, the central condensation in general decreases and, hence, the eccentricity of the configuration decreases.     

Effects of a helical magnetic field on the stability of a gravitating cylinder,II

The effect of an external magnetic field on an infinite gravitating cylinder is studied for axisymmetric perturbations. It is found that there is a destabilisation of the system due to the external field at very high values of the pitch of the field.     

The effect of toroidal magnetic field and differential rotation on self-gravitating polytropic models,II

In this paper we compute differentially rotating polytropic models distorted by toroidal magnetic field. In particular, we study rotating sequences, which do not terminate with a critical rotation. In the computations we use the so-called complex-plane strategy and multiple partition technique, which are numerical methods developed recently by the first author.     

Impact of magnetic field on the gas mass fraction of galaxy clusters

Magnetic fields have been observed in galaxy clusters with strengths of the order of  ~ μG. The non-thermal pressure exerted by magnetic fields also contributes to the total pressure in galaxy clusters and can in turn affect the estimates of the gas mass fraction, f_gas. In this paper, we have considered a central magnetic field strength of 5μG, motivated by observations and simulations of galaxy clusters. The profile of the magnetic field has also been taken from the results obtained from simulations and observations. The role of magnetic field has been taken into account in inferring the gas density distribution through the hydrostatic equilibrium condition (HSE) by including the magnetic pressure. We have found that the resultant gas mass fraction is smaller with magnetic field as compared to that without magnetic field. However, this decrease is dependent on the strength and the profile of the magnetic field. We have also determined the total mass using the NFW profile to check for the dependency of f_gas estimates on total mass estimators. From our analysis, we conclude that for the magnetic field strength that galaxy clusters seem to possess, the non-thermal pressure from magnetic fields has an impact of  ≈ 1 % on the gas mass fraction of galaxy clusters. However, with upcoming facilities like Square Kilometre Array (SKA), it can be further expected to improve with more precise observations of the magnetic field strength and profile in galaxy clusters, particularly in the interior region.     

Equilibrium figures with a magnetic field

A set of equations which are magnetohydrodynamic equilibrium conditions in the case of axial symmetry is solved. The possibility of splitting Maclaurin's sequence in the presence of a magnetic field is shown. The effect of a forceless magnetic field on Maclaurin'sP-ellipsoid is investigated.     

Sunspot models with twisted magnetic field

The return-flux sunspot model is generalized by including azimuthal magnetic field B _Φ . The basic equation is obtained and numerical solutions are compared with the analogous solutions for the Schlüter-Temesvary sunspot theory for two cases: B _Φ ～ B _r and B _Φ ～ rB _r . The solutions demonstrate that the twisting of the sunspot magnetic field decreases with height. Our models confirm Yun's early statement: the azimuthal field only slightly influences sunspot structure.