Uniform radial motion of sound in a relativistic fluid ball

We present a new class of spherically symmetric exact solutions of the general relativistic field equations. These solutions describe perfect fluid balls with infinite central pressure and central density though their ratio is finite. A member of the class has been studied in detail from which we have constructed a model of causal fluid ball with constant sound speed.     

Gravitational collapse of a dust ball — The external observer's point of view

The problem of collapse of a dust ball has been studied in detail from the point of view of an external observer (O). It is seen that although there is no material pressure from the point of view of the comoving observer, there is a non-vanishing material pressure in the ball from the point of view of O. In the early stages of collapse (w.r.t. O), this pressure is positive everywhere inside the ball, while during the later stages, if one goes outwards from the centre towards the surface of the ball, this pressure is negative up to a certain value of the radial coordinate, and then changes its sign thereafter. On the basis of this pressure, one can understand the physics of the whole scenario of collapse w.r.t. O; in particular, the important feature is that in the ultimate stages an event horizon is formed asymptotically and there is no collapse to a point (as takes place from the point of view of the comoving observer).     

Relative Equilibrium in the Three-Body Problem with a Rigid Body

In the three-body problem, where two bodies are punctual and the third is rigid, we prove the existence of some relative equilibrium configurations where the rigid body is either an homogeneous ball, an oblate or an elongated ball. In particular, we found conditions of relative equilibrium of Euler and Lagrange type and several families of relative equilibrium configurations, where the triangle of the two punctual bodies and the mass center of the rigid body is isosceles or having unequal sides. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulation of cometary magnetic tails

In order to simulate a cometary tail in a laboratory the flow of hydrogen collisionless supersonic plasma with the magnetic field frozen in was used. The wax ball served as a model of the cometary nucleus. The experimental conditions met the principle of limiting simulation. Field lines enveloped the nucleus at the day side and stretched along the flow at the night side. Tension of field lines in the magnetic tail provided the acceleration of ionized products of wax evaporation up to about 10⁶ cm s^–1. The control experiments showed that the magnetic tail is caused by currents due to the Lorentz electric field.     

Simulation of the solar wind interaction with non-magnetic celestial bodies

Laboratory experiments are described to simulate the solar wind flowing around nonmagnetic planets for three cases: non-conducting and ideally conducting planets, and a planet with a gaseous shell. A glass sphere was used as a model of a non-conducting planet (the Moon). Spatial distributions of plasma density and magnetic field strength that have been obtained agree with the data from measurements in space. However, the magnetic field does not increase before the rarefaction wave in the model experiment. A field increase was observed only for a conducting lunella: this argues in favour of the existence of a high conduction region on the Moon. A wax ball was used to model phenomena on the day-side of non-magnetic celestial bodies with a gaseoue shell (Venus, comets). Its surface easily evaporates in the plasma flow, and ionized evaporation products form an artificial ionosphere. The magnetic field frozen in the plasma flow is shown to be a determinative factor in the formation of a sharp ionospheric boundary. The supersonic plasma flow that interacts with the ionosphere gives rise to a stationary shock wave.     

The impact of fragment “L” of comet SL-9 on Jupiter

Filtergrams of high spatial and temporal resolution were obtained in the methane band centred at 892 nm during the impact of fragment L of comet Shoemaker-Levy 9 on Jupiter. The light curve shows two maxima of an emission ball observed above the limb shortly after the impact. The second maximum was the brightest and had a short life time of about 90 seconds. During it's life, the apparent height of the emission ball declined towards the surface of Jupiter; the amount of displacement is larger than the expected effect caused by Jupiter's rotation. About half an hour after the impact, a domelike feature became visible when the location of the impact rotated into the illuminated hemisphere of Jupiter.     

The signature of string ball near surface horizon of cylindrical Universe

The correspondence principle offered a unique opportunity to test cylindrically symmetric model for Universe at correspondence point “the centre of mass energies around (M _s/(g _s)²)”. First by using this symmetry, the Universe state for highly excited string “string ball” is studied and the entropy of these states is calculated. Then, to consider the string ball states, a copy of the original Hilbert space is constructed with a set of creation/annihilation operators that have the same commutation properties as the original ones. The total Hilbert space is the tensor product of the two spaces H _physical ?H _unphysical , where in this case H _physical denotes the physical quantum state space of the string ball. It is shown that string ball states can be represented by a maximally entangled two-mode squeezed state of the physical and unphysical spaces of string. Also, the entropy for these string states is calculated. It is found that Universe entropy matches the string entropy at transition point. This means that our result is consistent with correspondence principle and thus cylindrically symmetric model works. Finally the signature of bosonic string ball is studied. When string balls are produced, they evaporate to Massive particles like Higgs boson. Then Higgs bosons decay to quarks and gluons. Thus an enhancement of these partons can be a signature of bosonic string ball inside the cylindrically symmetric Universe.     

Conformally coupled Abelian gauged Q balls

A conformally coupled Abelian gauged Q ball is studied in curved space. The mass of the Q ball is calculated in terms of the conserved Q charge and the parameters in the lagrangian and a brief discussion is given on the effects produced by the conformal couplings.     

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.     

Collimation of a Central Wind by a Disk-Associated Magnetic Field

We present the results of time-dependent, numerical magnetohydrodynamic simulations of a realistic young stellar object outflow model with the addition of a disk-associated magnetic field. The outflow produced by the magnetic star-disk interaction consists of an episodic jet plus a wide-angle wind with an outflow speed comparable to that of the jet (100–200 km s^-1). An initially vertical field of ? 0.1 Gauss, embedded in the disk, has little effect on the wind launching mechanism, but we show that it collimates the entire flow (jet + wide wind) at large (several AU) distances. The collimation does not depend on the polarity of the vertical field. We also discuss the possible origin of the disk-associated field.     

Electromagnetic Field of a Cylinder with a Periodic Current: Energy Flux from a Relativistic Jet

An exact solution is obtained for the electromagnetic field surrounding an infinitely long, conducting cylinder with a periodic axial electric current. The solution simultaneously gives the field near the cylinder and in the transition to the wave zone. The flux of electromagnetic radiation emitted by the cylinder is calculated for oscillations with long wavelengths greatly exceeding the radius of the cylinder. This solution can be used to describe the electromagnetic field around narrowly collimated jets from active galactic nuclei and quasars.     

Potential field extrapolation using three components of a solar vector magnetogram with a finite field of view

The potential magnetic field from a finite planar boundary is extrapolated into the upper hemisphere using information from all three magnetic field components. The method determines, first, the transverse field associated with the observed normal magnetic intensity. Then by subtraction, the method determines the associated transverse magnetic field observed in the interior (i.e., in the field of view) of the magnetogram which is due to the normal flux exterior to the field of view of the magnetogram. Inverting this information gives an approximation to the exterior normal flux. The combination of the observed normal flux of the interior and the approximation of the exterior normal flux is employed to calculate the potential field. The formulation of the problem results in an ill-posed integral inversion problem in which a regularized solution is obtained using the singular value decomposition (SVD) technique in conjunction with an appropriate Tikhonov-Phillips filter. The technique can be applied to correcting potential field calculations which are influenced by out-of-view fluxes, e.g., for a high spatial resolution vector magnetogram with a small field of view in which there is no supporting exterior data. The problem studied is also important in providing a regularized solution of the Cauchy potential problem. The method provides a much larger range of convergence than the method of Gary and Musielak (1992), and, in fact, is stable in the total upper hemisphere.The U.S. Government right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.     

Line formation in a magnetic field

The effect of noncoherent scattering is examined for an absorption line formed in a uniform magnetic field. It is shown that the Stokes parameters of the line radiation may be computed by using the line source function in the absence of a magnetic field as a first approximation for that in the presence of a magnetic field.     

Modification of gamma-ray spectrum in a photon field

The changes in the high-energy gamma-ray spectra due to electron-photon cascading in the photon field (e.g., microwave background radiation) are investigated.The propagation of gamma-rays with an initial power-law spectrum through an isotropic monoenergetic photon field is considered. Two processes of the cascade particle-photon field interaction are taken into account, namely, the photoproduction of electron-positron pairs and the inverse Compton effect. The effect of the synchrotron energy loss by cascade electrons in a magnetic field on the cascade gamma-quantum spectrum is studied. The results may be used to estimate the absorption and the variations in the shape of the spectrum of radiation from compact gamma-ray sources in the metagalaxy.The cascade characteristics have been obtained by numerically solving the cascade equations by the moment method.     

Motion of a Rigid Body in a Tidal Field

We investigate the motion, near the equilibrium configurations, of an initially spinless rigid body subject to an external tidal field. Two cases are considered: when the center of mass of the body is at rest at the equilibrium point of the field generated by a generic mass distribution, and when it is placed on a circular orbit subject to a spherically symmetric potential. A complete analysis of the equilibrium configurations is carried out for both cases. First, we derive the conditions for the stable equilibria, and then we analyze the frequencies of oscillations around the equilibrium positions. In view of these results, we consider the problem of alignment of galaxies in clusters. After estimating the period of the oscillations induced on the galaxies by the tidal field of the cluster, we discuss the possible effect of resonances between stellar orbits inside the galaxy and the oscillations of the galaxy as a whole; this may be a mechanism responsible for producing an intracluster stellar population. This revised version was published online in July 2006 with corrections to the Cover Date.     

On magnetostatic equilibrium in a stratified atmosphere

This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction.     

Magnetic field rearrangement by accelerated particles near a shock front

We solve the self-consistent problem of the generation of a static magnetic field by the electric current of accelerated particles near a strong plane MHD shock front. We take into account the back reaction of the field on the particle diffusion tensors and the background plasma parameters near the front. Various states that differ significantly in static magnetic-field strength are shown to be possible near a strong front. If the initial field has a component normal to the front, then its components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. This field configuration for uniform particle injection at the front does not lead to the generation of an additional field, and, in this sense, it is stable. If the initial field is parallel to the front, then either its significant enhancement by two or three orders of magnitude or its suppression by several orders of magnitude is possible. The phenomenon under consideration is an example of the self-organization of plasma with a magnetic field in a strongly nonequilibrium system. It can significantly affect the efficiency of particle acceleration by the shock front and the magnetobremsstrahlung of the accelerated particles.     

Non-linear motion of a weak inhomogeneity in a magneto-active plasma

The equations of motion of a magnetic field aligned column of ionization embedded in an unbounded weakly ionized plasma immersed in an external electric field E are solved to second order terms in the strength of the initial perturbation, which is assumed to be weak. It is shown that when the Hall currents induced by the internal electrostatic field are taken into account, the centre of mass of the column will, in general, move along a curved path before acquiring the familiar $\text{E ×}\text{B}\text{B}{}^2$ drift velocity.     

Shock wave phenomena in collisions between a current loop and a plasmoid

We present the results of 3-D MHD simulations of collisions between an equilibrium current and a plasmoid. Three typical equilibrium configurations were analyzed. Our simulation results show that when a plasmoid approaches a current loop, an active region is created in front of the plasmoid bounded on the front side by a bow shock wave and on the back side by a reverse shock wave. The collision process modifies the current system and a strong electric field is also induced in the active region. An additional magnetic field generated by the induced current upsets the initial equilibrium condition. As a result, the whole loop is compressed and heated. We found that when the plasmoid approaches the loop, before reaching it the induced electric field amounts to its maximum value. The current loop is curved under the collision. The core of the plasmoid can not drive into the loop, it is sprung back by a magnetic counterpressure. This collision process between a plasmoid and a current loop may be responsible for the triggering of a solar flare observed by Yohkoh.     

Model of spiral galaxies and distribution of matter in the Milky Way system

Assuming an axisymmetric spiral galaxy to consist of 3 components, a plane-parallel distribution with an exponentially decreasing density in the z-direction, a polytropic distribution about the centre and a highly concentrated nuclear ball, we give analytic expressions for the mass density in such a system. Specific results for Milky Way are given. Our results agree with the latest observations.