Fragmentation of the Current Sheet,Anomalous Resistivity,and Acceleration of Particles

The evolution of the current sheet in the electric current direction (in the guiding magnetic field direction) is studied numerically in the 3-D particle-in-cell model with two current sheets and periodic boundary conditions. In the regime with (where v _D and are the electric current drift and electron thermal velocities, respectively) the current sheets are unstable owing to the Buneman and kink instabilities and become strongly fragmented. During their evolution, in addition to an increase of the energy of the electric field component in the guiding magnetic field direction, the energies of the electric field components in the perpendicular direction are even more enhanced. In the current sheet the anomalous resistivity (η _anom/η _C∼7×10⁵, where η _C is the classical resistivity) is generated and thus the magnetic field dissipates. Most of the dissipated magnetic energy is transformed into the electron kinetic energy in the direction of the electric current. The associated electric field accelerates the electrons from the tail of the distribution function.     

Back reaction and Hawking radiation from a Vaidya black hole

Using Damour-Ruffini’s and Hamilton-Jacobi’s methods, Hawking radiation from a Vaidya black hole is investigated. Due to non-stationary black holes, the event horizon r _H and the entropy S are all related to both the mass m(υ) and . When the back-reaction of particles’s energy to space-time is considered, we get the emission probability. It is found that the result is different from that of the stationary Schwarzschild black hole, because is the function of mass m(υ).      

On the gravitational radiation of gravitating objects

In the framework of unifying gravity and electromagnetism, we have shown that accelerating objects emit gravitational wave as those determined by Larmor formula for the accelerating charged particle. We have found new formulae for the power of Gravitational waves radiated by spinning and orbiting objects. The minimum wavelength of the gravitational wave emitted by an object of mass m and radius R is .     

A theoretical prediction of ion plasma oscillations in a neutral sheet

Starting from the Vlasov equation the steady state and stability properties of the electron sheet in the Cowley neutral sheet model of the geomagnetic tail are considered. Electrostatic ion plasma oscillations propagating from dusk to dawn are found to be unstable provided the thermal spread normal to the current is sufficiently large. Assuming the population of the neutral sheet to be supplied by the polar wind it is shown how a localisation of the cross tail electric field could lead to the instability first appearing around midnight. It is conjectured that the localisation of the cross tail electric field could continually feed the instability, so leading to enough turbulence to give enhanced reconnection of the magnetic field.List of symbols f distribution function - B magnetic field strength far from the neutral sheet - a sheet half thickness - total potential drop across the tail which is localised to the dusk end of the tail in Cowley's model - potential for the steady state electric field normal to the electron current sheet. This potential exists in that region of the tail that excludes the localised region of cross tail electric field - average velocity across the tail of electrons in the current sheet - v average velocity of the electrons normal to the current sheet - p canonical momentum of a particle - energy of a particle - KT electron energy normal to the sheet (1/2m ^e v ² ) - KT ⁱ ion energy (1/2m ⁱ V ² ) - electron gyrofrequency far from the neutral sheet - ⁱ ion gyrofrequency far from the neutral sheet - Ay steady state vector potential for the magnetic field - A –Ay/aB ₀ (normalised vector potential) When perturbing the steady state, dashes have been used to denote the time dependent first order quantities. Where no confusion could arise the dashes are dropped, e.g.Ey=Ey since there is no zero orderEy in the region considered in the stability analysis.     

On the peculiarities in the rotational frequency evolution of isolated neutron stars

The measurements of pulsar frequency second derivatives have shown that they are 10²−10⁶ times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters ν, and of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between and for both and , as well as between ν and . We interpret these dependencies as evolutionary ones due to being nearly proportional to the pulsars’ age. The derived statistical relations as well as “anomalous” values of are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of ν _ev(t), and according to the power law with n≈5, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that—several decades. This work has been supported by the Russian Foundation for Basic Research (grant No 04-02-17555), Russian Academy of Sciences (program “Evolution of Stars and Galaxies”), and by the Russian Science Support Foundation. The authors would also like to thank the anonymous referee for valuable comments.     

Monte Carlo Simulation of Solar Active-Region Energy

A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.     

On the role of plasma effects in the cosmic ray propagation and isotropization in the Galaxy

Cosmic ray (c. r.) propagation in interstellar magnetic fields is often considered in the diffusion approximation, i.e. by the diffusion equation in the coordinate space. Cosmic ray momentum distribution in this case is considered isotropic when the space gradients of c.r density are absent. This approach, with the use of an unfixed effective diffusion coefficientD independent of the energyE enables one to describe all the data available However, neither the diffusion mechanism nor the limits of applicability of the diffusion approximation is clear particularly ifD is independent ofE. Furthermore, the diffusion coefficientD must be expressed through the characteristics of the interstellar medium and possibly through the flux velocity and density of c.r. etc. One of the possible approaches for the analysis of the mechanism and characteristic features of c.r. distribution and isotropization is the account taken of the plasma effects and specifically, the study of c.r. flux instability arising when c.r. are moving in the interstellar plasma. As a result of such instability c.r. may generate waves of different types (magnetohydrodynamic, high-frequency plasma and other waves). Generation of waves and scattering on them result in isotropization of cosmic rays while their propagation under certain conditions turns out similar to that under diffusion.An attempt is made here to systematically analyse the avove mentioned plasma effects and to find out to what extent they are responsible for the behaviour of c.r. in the Galaxy. It turns out that c.r. In any case this is true if this mechanism is regarded as the only c.r. isotropization mechanizm within a wide energy range from 1 to 1000 GeV. Isotropization and spatial diffusion of c.r. up toE100–1000 GeV on the waves from external sources (for example, on the waves from the supernova shells) also proved impossible if the diffusion coefficient is assumed to be independent of c.r. energy. Some new possibilities of c.r. isotropization are also considered.A List of Notations D cosmic ray (c.r.) space diffusion coefficient - degree of c.r. anyisotropy - E,E _kin total and kinetic particle energy - p,p particle momentum and its absolute value - angle between the particle momentum direction and the magnetic field direction (z-axis) - cos - v, particle velocity and its absolute value - c light velocity - f(p),f(E) momentum and energy particle distribution function - N( > E) = N( > p) = f(p) dp/(2)³ = _E f dE c.r. particle density - c.r. spectrum index,N(>E)=KE ^–+1 - n _H neutral particle density - n=n _e=n _i ion and electron density - H niagnetic field - T temperature - thermal velocities of electrons and ions - Boltzmann constant - Alfén velocity - M, m proton and electron masses - e electron charge - wave frequency - _H =eH/Mc, = _H (Mc ²/E) gyrofrequency of a plasma proton and relativistic particle - _H =eH/mc gyrofrequency of an electron - plasma frequency - v _ii,v _ei,v _en,v _in collision frequencies between ions, electrons and ions, electrons and neutrals, ions and neutrals - growth rate of wave amplitude - k,k wave vector and its absolute value - angle between the directions of the vectorsk andH - wave energy density     

Multiple light scattering: mean number of scatterings and related problems

This is a discussion of V. A. Ambartsumyan’s studies of the mean number of scatterings for photons in scattering media and of further work and development in this area, especially at Ambartsumyan’s St. Petersburg school. The following questions are discussed briefly: (a) the traditional method for calculating the number of scatterings from the source function and critiques of this method. (b) The equation for the number N(τ; τ₀ ) of scatterings for a photon born at optical depth τ in a plane layer of optical thickness τ₀ and its use for calculating the number of scatterings, averaged over the entire ensemble of photons for a medium with arbitrary internal sources. These questions are first considered for the case of monochromatic scattering, and then for scattering in a spectral line with complete frequency redistribution (CFR). (c) The mean path length for a resonance line photon in a scattering medium with CFR and continuum absorption: the basic equations and asymptotic behavior of an optically thick layer. (d) A review of calculations of and in media that are so thick that the CFR approximation breaks down and the effects of partial frequency redistribution (PFR) become dominant. The presentation is at a semiquantitative level in many parts of this paper, with stress on physical significance rather than the mathematics, through the use of approximate and asymptotic solutions. Translated from Astrofizika, Vol. 52, No. 1, pp. 29–45 (February 2009).     

On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

K emission-line widths and the solar chromosphere

Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K_2v , K_2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K_2v , k_2R intensity ratios. One component with minor Doppler displacements acting on the normal K₂₃₂ profile, where K_2V >K_2R , produces the cases K_2v K_2R , K_2v = K_2R , K_2v <K_2R . The other component arises from dark condensations which are of size 3500 kms as seen in K_2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K₃ spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K_2R = 0.K₂-line widths are measured for all tracings where K_2v , K_2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K₂ emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K₂ intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K₂ widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K₂ widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.     

Dynamical dark energy from extra dimensions

We consider multidimensional cosmological model with a higher-dimensional product manifold M = R × × /Γ, where is d _o-dimensional Ricci-flat external (our) space and /Γ is d ₁-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits. The article is published in the original.     

Vertical Dynamics of the Energy Release Process in a Simple two-Ribbon Flare

Observations of the quiescent filament eruption and the spotless two-ribbon flare of 12 September 2000 are presented. A simple flare morphology, large spatial scales, and a suitable viewing angle provide insight into characteristics of the energy release process which is attributed to the reconnection process in the current sheet formed below the eruptive filament. The flare ribbons appeared and started to expand laterally while the filament was still recognizable, enabling simultaneous measurements of the ribbon separation w and the height of the lower edge of the filament, h. The ratio w/h estimated for the expanding portions of ribbons indicates that the width-to-length ratio of the current sheet at the onset of the fast reconnection ranges between and . The ribbon elements characterized by w/h> remained stationary. The Nançay radioheliograph data in the decimeter–meter wavelengths show one group of radio bursts ahead of the filament (moving type IV burst) and another group behind the filament. The centroids of the radio sources behind the filament were confined to the region outlined by the lower edge of the filament and the magnetic inversion line, suggestive of emission from the current sheet. Sources were preferably located close to the lower edge of the filament and some appeared close to the magnetic inversion line. Two possible explanations are discussed: one in terms of the fast-mode bow shocks in the reconnection outflow jets, and another in terms of a multiple tearing of the current sheet and subsequent coalescence of plasmoids.     

Effect of dynamical cosmological constant in presence of modified Chaplygin gas for accelerating universe

In this paper we have considered the Universe to be filled with Modified Gas and the Cosmological Constant Λ to be time-dependent with or without the Gravitational Constant G to be time-dependent. We have considered various phenomenological models for Λ, viz., and . Using these models it is possible to show the accelerated expansion of the Universe at the present epoch. Also we have shown the natures of G and Λ over the total age of the Universe. Using the statefinder parameters we have shown the diagrammatical representation of the evolution of the Universe starting from radiation era to ΛCDM model.     

GRMHD/RMHD simulations & stability of magnetized spine-sheath relativistic jets

A new general relativistic magnetohydrodynamics (GRMHD) code “RAISHIN” used to simulate jet generation by rotating and non-rotating black holes with a geometrically thin Keplarian accretion disk finds that the jet develops a spine-sheath structure in the rotating black hole case. Spine-sheath structure and strong magnetic fields significantly modify the Kelvin-Helmholtz (KH) velocity shear driven instability. The RAISHIN code has been used in its relativistic magnetohydrodynamic (RMHD) configuration to study the effects of strong magnetic fields and weakly relativistic sheath motion, c/2, on the KH instability associated with a relativistic, γ=2.5, jet spine-sheath interaction. In the simulations sound speeds up to and Alfvén wave speeds up to ∼0.56c are considered. Numerical simulation results are compared to theoretical predictions from a new normal mode analysis of the RMHD equations. Increased stability of a weakly magnetized system resulting from c/2 sheath speeds and stabilization of a strongly magnetized system resulting from c/2 sheath speeds is found.     

Small amplitude electron-acoustic solitary waves in a plasma with superthermal hot electrons

In the present investigation, Electron acoustic solitons in a plasma consisting of cold electrons, superthermal hot electrons and stationary ions are studied. The basic properties of small but finite amplitude solitary potential structures that may exist in a given plasma system have been investigated theoretically using reductive perturbation technique. It has been found that the profile of electron acoustic solitary wave structures is very sensitive to relative hot electron density, $\alpha(=\frac{n_{h0}}{n_{c0}})$ , temperature of hot to cold electrons, $\theta(=\frac{T_{h}}{T_{c}})$ and the spectral index κ. The implications of the present study may be applied to explain some features of large amplitude localized structures that may occur in the plasma sheet boundary layer.     

Velocity-height relation for antimatter meteors

A general velocity-height relation for both antimatter and ordinary matter meteor is derived. This relation can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaeyOeI0YaaSaaaeaacaWGdbaabaGaamOqaiabew8a1naaBaaa% leaacqGHEisPaeqaaaaakmaacmaabaGaaGymaiabgkHiTiaabwgaca% qG4bGaaeiCamaadmaabaGaeyOeI0YaaSaaaeaacaWGcbaabaGaamyy% aaaacaqGLbGaaeiEaiaabchacaqGOaGaaeylaiaadggacaWG6bGaai% ykaaGaay5waiaaw2faaaGaay5Eaiaaw2haaiaacYcaaaa!64FD!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right] - \frac{C}{{B\upsilon _\infty }}\left\{ {1 - {\text{exp}}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right]} \right\},\]where _z is the velocity of the meteoroid at height z, its velocity before entrance into the Earth's atmosphere, is the scale-height, and C parameter proportional to the atom-antiatom annihilation cross- section, which is experimentally unknown. The parameter B (B = DA₀/m) is the well known parameter for koinomatter (ordinary matter) meteors, D is the drag factor, ₀ is the air density at sea level, A is the cross sectional area of the meteoroid and m its mass.When the annihilation cross-section is zero — in the case of ordinary meteors — the parameter C is also zero and the above derived equation becomes % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaaiilaaaa!4CF5!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right],\]which is the well known velocity-height relation for koinomatter meteors.In the case in which the Universe contains antimatter in compact solid structure, the velocity-height relation can be found useful.Work performed mainly at the Nuclear Physics Laboratory of the National University of Athens, Greece.     

The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Both the critical content _c ( N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content _s of monopoles in a rotating relativistic object are found in this paper. The results are:

Plane and cylindrical hydromagnetic shock waves

The Chisnell-Chester-Whitham method has been used to investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial and variable azimuthal components, simultaneously for both weak and strong cases. Assuming an initial density distribution ₀=r ^–w , where is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density, and the particle velocity immediately behind the shock have also been derived for both cases.