Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

The generation of a large-scale Galactic magnetic field by electric currents of energetic particles

We consider the generation of a magnetic field in the Galaxy by the electric currents excited by cosmic-ray particles in the disk and halo. We assume that the sources of relativistic particles are distributed continuously and uniformly in the Galactic disk, their total power is equal to the observed value, and the particles themselves undergo anisotropic diffusion in a homogeneous medium. We take into account the differential rotation of the Galactic disk but disregard the turbulence gyrotropy (the α effect). The strength of the generated magnetic field in our model is shown to strongly depend on the symmetry of the relativistic proton and thermal electron diffusion tensors, as well as on the relations between the tensor components. In particular, if the diffusion is isotropic, then no magnetic field is generated. For the independent tensor components estimated from observed parameters of the Galactic medium and with a simultaneous allowance made for the turbulent field dissipation processes, the mechanism under consideration can provide an observable magnetic-field strength of the order of several microgauss. This mechanism does not require any seed magnetic field, which leads us to suggest that relativistic particles can give an appreciable and, possibly, determining contribution to the formation of the global Galactic magnetic field. However, a final answer can be obtained only from a nonlinear self-consistent treatment, in which the symmetry and magnitude of the particle diffusion tensor components should be determined together with the calculation of the magnetic field.     

Cosmic rays from collapsing magnetized stars

We examine the acceleration of cosmic rays in the magnetospheres of collapsing stars with initial dipole magnetic fields and various initial energy distributions of charged particles in their magnetospheres (the exponential, relativistic Maxwellian, and Boltzmann distributions were considered). When a magnetized star contracts at the gravitational collapse stage, its magnetic field grows considerably. Such a variable magnetic field generates an eddy electric field. Our calculations suggest that this electric field can accelerate charged particles to relativistic energies. In this way collapsing stars can be sources of high-energy cosmic rays in our Galaxy as well as in other galaxies.     

The motion of charged particles in a strong electromagnetic field and curvature radiation

The features of the relativistic charge particle motion and emission due to the radiative slamping in the strong electromagnetic fields are investigated. It is shown that the radiative force responsible for curvature radiation is associated with the particle drift in an inhomogeneous magnetic field. The adiabatic trajectory is obtained for the relativistic particle, moving in a strong static electron-magnetic field, particle energy being determined by the balance of the work of the electric field and the energy losses through curvature radiation.     

On the magnetohydrodynamic decollimation in compact objects

A simple analytical model of the particle-dominated outflow with zero total electric current from central rotating objects is considered. 'Exact' solutions for both relativistic and non-relativistic cases demonstrate the decollimation of the magnetic field lines in the region of the current closure. Such a decollimation can explain the presence of an energetic equatorial wind observed in many compact objects.     

Relativistic large-scale jets and minimum power requirements

The recent discovery, by the Chandra satellite, that jets of blazars are strong X-ray emitters at large scales     , lends support to the hypothesis that emitting plasma is still moving at highly relativistic speeds on these scales. In this case in fact the emission via inverse Compton scattering off cosmic background photons is enhanced and the resulting predicted X-ray spectrum accounts well for the otherwise puzzling observations. Here we point out another reason to favour relativistic large-scale jets, based on a minimum power argument: by estimating the Poynting flux and bulk kinetic powers corresponding to, at least, the relativistic particles and magnetic field responsible for the emission, one can derive the value of the bulk Lorentz factor for which the total power is minimized. It is found that both the inner and extended parts of the jet of PKS     satisfy such a condition.     

Field-aligned electric field caused by the decay of force-free magnetic field and particle acceleration

Numerical simulation for the dynamics of a coronal filamentary magnetic loop has been made under the assumption that the field is initially force-free and an electric resistivity suddenly increases at a given moment due to an appearance of ion sound waves, which can be excited due to a high current density if a characteristic radius r ₀ of the magnetic loop is about 3 km or less in a magnetic field B ₀ of 1000 G. During the resistive decay of the magnetic field a strong field-aligned electric field is created and maintained for a sufficient time to acceleratie both electrons and protons to a high energy, which is proportional to B ₀/r ₀ and can be 100 MeV if r ₀ = 10 km and B ₀ = 1000 G. If the coronal magnetic tube is composed of many such filamentary loops, the total number of accelerated electrons is consistent with the observations.     

Resolving the 180-degree ambiguity in vector magnetic field measurements: The ‘minimum’ energy solution

I present a robust algorithm that resolves the 180-deg ambiguity in measurements of the solar vector magnetic field. The technique simultaneously minimizes both the divergence of the magnetic field and the electric current density using a simulated annealing algorithm. This results in the field orientation with approximately minimum free energy. The technique is well-founded physically and is simple to implement.     

Torsional oscillations of magnetized relativistic stars

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background space–time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space–time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space–time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.     

Observations of the Blandford–Znajek process and the magnetohydrodynamic Penrose process in computer simulations of black hole magnetospheres

In this paper we report the results of axisymmetric relativistic magnetohydrodynamic (MHD) simulations for the problem of a Kerr black hole immersed in a rarefied plasma with 'uniform' magnetic field. The long-term solution shows properties that are significantly different from those of the initial transient phase studied recently by Koide. The topology of magnetic field lines within the ergosphere is similar to that of the split-monopole model with a strong current sheet in the equatorial plane. Closer inspection reveals a system of isolated magnetic islands inside the sheet and ongoing magnetic reconnection. No regions of negative hydrodynamic 'energy at infinity' are seen inside the ergosphere and the so-called MHD Penrose process does not operate. However, the rotational energy of the black hole continues to be extracted via the purely electromagnetic Blandford–Znajek mechanism. In spite of this, no strong relativistic outflows from the black hole are seen to be developing. Combined with results of other recent simulations, our results signal a potential problem for the standard MHD model of relativistic astrophysical jets should they be found at distances as small as a few tens of gravitational radii from the central black hole.     

Explosive reconnection in magnetars

The X-ray activity of anomalous X-ray pulsars and soft γ-ray repeaters may result from the heating of their magnetic corona by direct currents dissipated by magnetic reconnection. We investigate the possibility that X-ray flares and bursts observed from anomalous X-ray pulsars and soft γ-ray repeaters result from magnetospheric reconnection events initiated by development of the tearing mode in magnetically dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss the relation of the latter to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable towards the development of small-scale current sheets where resistive effects become important. Thin current sheets are found to be unstable due to the development of the resistive force-free tearing mode. The growth rate of the tearing mode is intermediate between the short Alfvén time-scale  τ_A  and a long resistive time-scale  τ_R: Γ∼ 1/(τ_Rτ_A)^1/2  , similar to the case of non-relativistic non-force-free plasma. We propose that growth of the tearing mode is related to the typical rise time of flares, ∼10 ms. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.     

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.     

Electric field measurements in solar flares

Meaurements of solar flare spectra have allowed the electric field strengths in two flares to be determined, using the Inglis-Teller formula. Further, an independently estimated value for the electron density has allowed the two components of this field, that is, the interionic component and the external component that arises, for example, through plasma instabilities, to be separately extracted. External electric field strengths 0.5 kV cm^–1 for a limb flare and 1.3 kV cm^–1 for a white-light flare are found. Estimates of electric fields strengths generated by the resistive magnetic tearing instability indicate that this process could account for a significant part of the electric field if pre-existing magnetic field strengths in the flaring regions are characterized by a few kilogauss. Other plasma processes probably contribute measurably as well.Operated by the Association of Universities for Research in Astronomy, Inc., under contract NSF AST84-18716 with the National Science Foundation.     

The Role of Solar Wind Structures in the Generation of ULF Waves in the Inner Magnetosphere

The plasma of the solar wind incident upon the Earth’s magnetosphere can produce several types of geoeffective events. Among them, an important phenomenon consists of the interrelation of the magnetospheric–ionospheric current systems and the charged-particle population of the Earth’s Van Allen radiation belts. Ultra-low-frequency (ULF) waves resonantly interacting with such particles have been claimed to play a major role in the energetic particle flux changes, particularly at the outer radiation belt, which is mainly composed of electrons at relativistic energies. In this article, we use global magnetohydrodynamic simulations along with in situ and ground-based observations to evaluate the ability of two different solar wind transient (SWT) events to generate ULF (few to tens of mHz) waves in the equatorial region of the inner magnetosphere. Magnetic field and plasma data from the Advanced Composition Explorer (ACE) satellite were used to characterize these two SWT events as being a sector boundary crossing (SBC) on 24 September 2013, and an interplanetary coronal mass ejection (ICME) in conjunction with a shock on 2 October 2013. Associated with these events, the twin Van Allen Probes measured a depletion of the outer belt relativistic electron flux concurrent with magnetic and electric field power spectra consistent with ULF waves. Two ground-based observatories apart in 90^° longitude also showed evidence of ULF-wave activity for the two SWT events. Magnetohydrodynamic (MHD) simulation results show that the ULF-like oscillations in the modeled electric and magnetic fields observed during both events are a result from the SWT coupling to the magnetosphere. The analysis of the MHD simulation results together with the observations leads to the conclusion that the two SWT structures analyzed in this article can be geoeffective on different levels, with each one leading to distinct ring current intensities, but both SWTs are related to the same disturbance in the outer radiation belt, i.e. a dropout in the relativistic electron fluxes. Therefore, minor disturbances in the solar wind parameters, such as those related to an SBC, may initiate physical processes that are able to be geoeffective for the outer radiation belt.     

Accretion of a massive magnetized torus on a rotating black hole

We present numerical simulations of the axisymmetric accretion of a massive magnetized plasma torus on a rotating black hole. We use a realistic equation of state, which takes into account neutrino cooling and energy loss due to nucleus dissociations. The calculation are performed in the ideal relativistic MHD approximation using an upwind conservative scheme that is based on a linear Riemann solver and the constrained transport method to evolve the magnetic field. The gravitational attraction of the black hole is introduced via the Kerr metric in the Kerr–Schild coordinates. We simulate various magnetic field configurations and torus models, both optically thick and thin for neutrinos.We have found an effect of alternation of the magnetic field orientation in the ultrarelativistic jet formed as a result of the collapse. The calculations show evidence for heating of the wind surrounding the collapsar by the shock waves generated at the jet–wind border. It is shown that the neutrino cooling does not significantly change either the structure of the accretion flow or the total energy release of the system. The angular momentum of the accreting matter defines the time scale of the accretion. Due to the absence of the magnetic dynamo in our calculations, the initial strength and topology of the magnetic field determines the magnetization of the black hole, jet formation properties and the total energy yield. We estimate the total energy of accretion which transformed to jets as 1.3 × 10⁵² ergs which was sufficient to explain hypernova explosions like GRB 980425 or GRB 030329.