Radiative decay behind strong M.H.D. shocks

The effect of radiation up on the state of gas behind strong M.H.D. shock front has been studied. The jump conditions for flow variables across the shock boundary have been obtained and temperature decay behind the shock front is determined for a optically-thin brehmsstrahlung radiation plasma. It has been found that, for a shock within strong magnetic field, the temperature decay is much quicker.     

Gravitational instability of a non-linear magnetic fluid

The problem of gravitational instability of an infinite homogenous fluid has been considered in the presence of a non-vertical magnetic field. A non-linear relation between the magnetic field and the magnetic induction proposed by P.H. Roberts (1981) in the context of neutron stars has been used. The dispersion relations have been obtained. It has been found that Jeans's criterion for instability is unaffected by this non-linear relationship even if the effect due to rotation is considered in the presence of a non-vertical magnetic field.     

Magnetic fields of chemically peculiar stars. I. The catalog of magnetic CP stars

This is the first paper of the series dedicated to the analysis of the magnetism of chemically peculiar (CP) stars of the upper Main Sequence. We use our own measurements and published data to compile a catalog of magnetic CP stars containing a total of 326 objects with confidently detected magnetic fields and 29 stars which are very likely to possess magnetic field. We obtained the data on the magnetism of the overwhelming majority of the stars solely based on the analysis of longitudinal field component B _e . The surface magnetic field, B _s , has been measured for 49 objects. Our analysis shows that the number of magnetic CP stars decreases with increasing field strength in accordance with exponential law, and stars with B _e exceeding 5kG occur rarely (about 3% objects of our list).     

Magnetic arcades in stellar coronae I. Cylindrical geometry

X-ray spectroscopy performed by different astronomical spacecrafts has shown that many active late-type stars possess coronae. For such reason, the magnetic structure of stellar coronae has raised considerable interest and, by analogy with the Sun, it is generally assumed that stellar coronae are structured by magnetic fields having the shape of arcades. Most of those coronal magnetic field configurations assume translational symmetry and are based in planar source surfaces. However, as soon as either the length or the width of such source surfaces become non negligible as compared to the stellar radius, the application of the cylindrical geometry seems to be more appropriate. Then, one way of obtaining coronal magnetic configurations is to deal with source domains extended over a cylindrical surface. In this paper we generate potential coronal arcades based on cylindrical source surfaces with non negligible length or width compared to the stellar radius. The flux function, the magnetic field components, the shape of magnetic field lines and other characteristic magnitudes have been obtained and analyzed for both cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Magnetic field in a cavity of a perfect diamagnetic material

A new method using an integral equation has been proposed in this paper for calculating the magnetic field enclosed within a perfect diamagnetic material. A magnetic field is assumed to exist inside an arbitrary cavity in a perfect diamagnetic material. Self-consistent magnetic fields inside the cavity and currents on its surface are calculated, resulting as it should in zero magnetic field outside the cavity. This method has been tested in a special case and the results have been compared to the analytical solutions. This method should be also applicable to any case concerning the interaction between magnetic fields and perfect diamagnetic materials, e.g., to cases where a perfect diamagnetic material is surrounded by a magnetic field.     

Magnetic fields of chemically peculiar and related stars. 2. Main results of 2015 and near-future prospects

We present an analytical survey of key publications concerned with the study of stellar magnetism published in 2015. We considered about 80 publications, the most significant from our point of view, presented brief reviews of them, and made generalizations. The paper considers: instruments, techniques of observations and analysis; large-scale magnetic fields of OBA stars on the Main Sequence (MS) (formation and evolution, field topology, search for new magnetic stars including the projects MiMeS, BOB, and BinaMIcS and observations with the Russian 6-m telescope, rotation and chemical abundance analysis of magnetic CP stars); magnetic fields, chemical abundance and variability of stars related to peculiar, primarily, active cool stars, solar-type stars and white dwarfs; multiple magnetic stars including interferometry data, exoplanets in a system of magnetic stars. We make a conclusion that the accuracy of magnetic field measurements has grown due to universal application of the multilinear method of observations especially with high-resolution spectropolarimeters. Usage of Zeeman-Doppler imaging technique (ZDI) when analyzing the obtained data allows us to confidently search and measure fields of complex topology of the order of 10 Gs. For the first time, a magnetic field has been detected for post-AGB stars and some other types of objects.     

The structure and oscillations of low-mass stars in the presence of a magnetic field

The equilibrium structure and oscillations of a partially degenerate standard model in the presence of a poloidal magnetic field have been studied. The magnetic field in the interior has been matched with an outside dipole field. The effect of magnetic field on the various structural parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been computed for different values of the central degeneracy of the model. We have also studied the effect of magnetic field on radial oscillations of the configuration. A variational formulation is used to compute the changes in the frequency of radial mode of oscillation. It has been shown that the changes in frequency computed for various models using a two-parameter eigenfunction are in fair agreement with the values obtained by using the exact eigenfunction.     

Parallel velocity shear instabilities in an inhomogeneous plasma

The stability of an inhomogeneous anisotropic plasma flowing along a straight magnetic field has been investigated. Both the flow velocity and the plasma density are spatially varying in a direction perpendicular to the magnetic field. The stability of an interface between an inhomogeneous anisotropic plasma flowing along the magnetic field and the non-conducting compressible gas of uniform density flowing parallel to the interface has also been discussed. The effect of gyroviscosity and inhomogeneity on the Kelvin-Helmholtz shear instability has been discussed in certain limiting situations.     

Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

Magnetic Field Extrapolations into the Corona: Success and Future Improvements

The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This technique relies on two crucial points: i) the physical assumption leading to the system of differential equations to be solved, ii) the choice and quality of the associated boundary conditions. In this review, I summarise the physical assumptions currently in use and the findings at different scales in the solar atmosphere. I concentrate the discussion on the extrapolation techniques applied to solar magnetic data and the comparison with observations in a broad range of wavelengths (from hard X-rays to radio emission).     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

The evolution of the magnetic fields of neutron stars

Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vortices; and another in which the compression and heating of the stellar crust by the accreted mass drastically reduces the ohmic decay time scale of a magnetic field configuration confined entirely to the crust. General remarks about the behaviour of the crustal field under ohmic diffusion are also made.     

Rotational circulation-preserving magnetogeostrophic flows

It has been shown that the only steady, inviscid, magnetogeostrophic rotational circulation-preverving motion whose magnetic field line pattern is that of the irrotational motion is a complex-lamellar motion whose magnetic field magnitude bears a constant value on a magnetic field line.     

On a uniformly rotating magnetic polytrope

The equilibrium general magnetic field inside a magneto-rotating star, assumed to be a polytrope, has been determined more accurately, for large general magnetic field. Furthermore the effect of such field on the structure and oscillations of a slowly rotating polytrope has been studied forn=1,0, 1.5, 2.0, and 3.0.     

Small-scale stochastic structure of the solar magnetic field

The small-scale (～10″) stochastic properties of the solar magnetic field B are analyzed in terms of the two-dimensional model of a fractal Brownian process (the mean square of the difference between the field strengths at two points separated by a distance D is proportional to D ^2H ). Digitized solar magnetograms with a 2″ resolution are used to determine the standard deviation s of the magnetic field and the exponents H at various levels of |B|. It has been established that the transition from the background magnetic field to the fields of an active region occurs near 25–50 G. A dependence of the exponent H on the magnetic field amplitude has been derived. The exponent H for the background magnetic field has been found to be much smaller than that for the fields of an active region. The relationship of the results obtained to certain fundamental properties of plasma in a magnetic field is discussed.     

An investigation of the large-scale magnetic field variations in the corona prior to and after CME eruptions

The magnetic field changes in the corona at the site of coronal mass ejections (CMEs) have been investigated using the potential field-source surface model. It is shown that a CME is accompanied by the opening of closed field lines that formed the streamer's helmet base prior to the onset of a coronal disturbance. Two to three days after the appearance of the CME, the field configuration at the location of the coronal ejection reverts approximately to the state pre-existing before the generation of the CME. The appearance of small transient open magnetic tubes has been found after eruption of the coronal mass. These magnetic tubes seem to be the analogs for transient coronal holes.Taking into account the results of calculations of the field changes in the neighbourhood of the CME occurrence site, we have suggested a possible mechanism governing the spatio-temporal correlation between some flares and CMEs. Also, a possible mechanism has been proposed for field reconfiguration in the corona, leading to loss of the equilibrium of the magnetic configuration and to the subsequent generation of a CME in the region of coronal streamer chains separating coronal holes with same-polarity magnetic field.     

Numerical computer simulation of cross-field propagation of a plasma stream in a magnetic field

A one-dimensional electrostatic particle simulation of plasma streaming perpendicular to a magnetic field with nonperiodic boundary condition has been carried out. When a bulk of plasma in injected across an ambient magnetic field, a stream of neutral plasma, consisting of equal numbers of ions and electrons, polarizes, and the resulting polarization electric field gives rise to the penetration of plasma across the magnetic field so that the integrity of plasma maintains. Computer simulation demonstrates the properties of cross-field propagation of plasma stream in a magnetic field with different plasma parameters.     

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.     

Transient MHD free convection in a rotating system

The classical Rayleigh problem has been extended to the case of the hydromagnetic free-convective flow of an electrically-conducting and incompressible viscous fluid past an infinite vertical naturally permeable wall in a rotating system. The applied transverse magnetic field is fixed with the moving wall and the magnetic Reynolds number of the flow is taken small so that the induced magnetic field can be neglected in comparison to the applied magnetic field. The permeable wall starts moving from rest in the still fluid and thus arises an initial value problem whose solution has been obtained by the Laplace transform method for two important cases impulsive as well as accelerated start of the plate. Mathematical expression for skin friction components have been also obtained in a closed form. Asymptotic behaviour of the solution is analysed for both the cases, and some interesting particular cases have also been encountered. Influence of various physical parameters occurring into the problem has been discussed with the aid of graphs and tables.