Self-consistent electromagnetic field in a nearly co-rotating magnetosphere

An example of the self-consistent solution which belongs to the non-trivial solution, obtained in a previous paper (Kaburaki, 1985), is found in a nearly co-rotating inner magnetosphere. Though the stellar wind is neglected there compared with the co-rotatinal velocity, drift motion around the magnetic axis, which is a manifestation of inertial effects, is determined self-consistently with the electromagnetic field. In this process, explicit expressions for the energy integral in the rotating frame and for the density distribution are also obtained. These expressions contain a fundamental length, which is to be evaluated according to physical conditions of a magnetosphere and determines the asymptotic-kinetic energy of a plasma particle at infinity. The electric current associated with the drift motion is too small to alter the original magnetic field, but the electric field is modified by the inertial effects even in the inner magnetosphere. The integrated Ohm's law is used to describe a force balance in the rotating frame, in the limits of weak and strong magnetic field.     

Magnetar corona

Persistent high-energy emission of magnetars is produced by a plasma corona around the neutron star, with total energy output of ～10³⁶ erg/s. The corona forms as a result of sporadic starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by curl B and regulates the self-induction e.m.f. by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light-crossing time ～10^?4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. The voltage along the magnetic field lines is maintained near threshold for ignition of pair production, in the regime of self-organized criticality. The voltage is found to be about ～1 GeV which is in agreement with the observed dissipation rate ～10³⁶ erg/s. The coronal particles impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and the corona is the likely source of the observed 100 keV emission. The corona also emits curvature radiation up to 10¹⁴ Hz and can supply the observed IR-optical luminosity.     

On the possible observational manifestation of the impact of a supernova shock on the neutron star magnetosphere

The impact of a supernova explosion on the magnetosphere of a neutron star in a massive binary system is considered. The supernova shock impact on a plasma-filled neutron star magnetosphere can give rise to a long magnetospheric tail with a considerable store of magnetic energy. Magnetic reconnection in the formed current sheet can transform the magnetic energy stored in the tail into the kinetic energy of charged particles. The plasma instabilities excited by beams of accelerated relativistic particles can lead to the formation of a short pulse of coherent radio emission with parameters similar to those measured for the bright extragalactic millisecond radio burst detected in 2007.     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

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.     

On one mechanism for the generation of a reverse solar wind shock in the magnetosheath in front of the Earth’s magnetosphere

A possible mechanism for the generation of a reverse fast shock in the magnetosheath in the solar wind flow around the Earth’s magnetosphere is considered. It is shown that such a shock can emerge through the breaking of a nonlinear fast magnetosonic compression wave reflected from the magnetopause toward the bow shock rear. In this case, the magnetopause is represented as a tangential discontinuity with a zero normal magnetic field component at it and the mechanism under consideration is assumed to be secondary with respect to the sudden disturbance of the bow shock-Earth’s magnetosphere system by a nonstationary solar wind shock. A possible confirmation of the process under study by in-situ SC3 experimental observations of the bow shock front motion on the Cluster spacecraft is pointed out.     

Magnetic activity in accretion disc boundary layers

We use three-dimensional magnetohydrodynamic simulations to study the structure of the boundary layer between an accretion disc and a non-rotating, unmagnetized star. Under the assumption that cooling is efficient, we obtain a narrow but highly variable transition region in which the radial velocity is only a small fraction of the sound speed. A large fraction of the energy dissipation occurs in high-density gas adjacent to the hydrostatic stellar envelope, and may therefore be reprocessed and largely hidden from view of the observer. As suggested by Pringle , the magnetic field energy in the boundary layer is strongly amplified by shear, and exceeds that in the disc by an order of magnitude. These fields may play a role in generating the magnetic activity, X-ray emission and outflows in disc systems where the accretion rate is high enough to overwhelm the stellar magnetosphere.     

Thermal emission areas of heated neutron star polar caps

Observed hot spots on neutron stars are often associated with polar caps heated by the backflow of energetic electrons or positrons from accelerators on bundles of open magnetic field lines. Three effects are discussed that may be relevant to formation of hot spots and their areas. (1) The area of a polar cap is proportional to the ratio of the star’s surface dipole field to the local field at the polar cap. Because the field is coupled to the evolving spin of the superfluid core of the star, this ratio can depend on the stellar spin and its history. (2) The hot emission area may appear smaller to a distant observer when emitted X-rays propagate through electron-positron plasma created in the magnetosphere. The X-rays then change their energy spectrum because of cyclotron resonant scattering by pairs. (3) Hot spots may form on the star’s surface as a result of crust motions that are driven by the pull of core flux tubes pinned to the crust. Such motions twist the footprints of closed magnetic loops of the magnetosphere and induce an electric current in the loop, which will heat those footprints.     

MHD simulations of the long-term evolution of a dipolar magnetosphere surrounded by an accretion disk

The evolution of a stellar, initially dipole type magnetosphere interacting with an accretion disk is investigated using numerical ideal MHD simulations. The simulations follow several 1000 Keplerian periods of the inner disk (for animated movies see http://www.aip.de～cfendt).Our model prescribes a Keplerian disk around a rotating star as a fixed boundary condition. The initial magnetic field distribution remains frozen into the star and the disk. The mass flow rate into the corona is fixed for both components. The initial dipole type magnetic field develops into a spherically radial outflow pattern with two main components – a disk wind and a stellar wind – both evolving into a quasi-stationary final state. A neutral field line divides both components, along which small plasmoids are ejected in irregular time intervals. The half opening angle of the stellar wind cone varies from 30° to55° depending on the ratio of the mass flow rates of disk wind and stellar wind. The maximum speed of the outflow is about the Keplerian speed at the inner disk radius. An axial jet forms during the first decades of rotations. However, this feature does not survive on the very long time scale and a pressure driven low velocity flow along the axis evolves. Within a cone of 15° along the axis the formation of knots may be observed if the stellar wind is weak. With the chosen mass flow rates and field strength we see almost no indication for a flow self-collimation. This is due to the weak net poloidal electric current in the magnetosphere which is in difference to typical jet models.     

On accretion flow penetration of magnetospheres

We address the problem of plasma penetration of astrophysical magnetospheres, an important issue in a wide variety of contexts, ranging from accretion in cataclysmic variables to flows in protostellar systems. We point out that under well-defined conditions, penetration can occur without any turbulent mixing (driven, for example, by Rayleigh–Taylor or Kelvin–Helmholtz instabilities) caused by charge polarization effects, if the inflowing plasma is bounded in the direction transverse to both the flow velocity and the magnetic field. Depolarization effects limit the penetration depth, which nevertheless can, under specific circumstances, be comparable to the size of the magnetosphere. We discuss the effect of ambient medium on plasma propagation across the stellar magnetic field and determine the criteria for deep magnetosphere penetration. We show that, under conditions appropriate to magnetized white dwarfs in AM Her type cataclysmic variables, charge polarization effects can lead to deep penetration of the magnetosphere.     

Determination of the electromagnetic field produced by a magnetic oblique-rotator

The structure of the corotating region, which forms an inner portion of a stellar magnetosphere, is reconsidered in a quasi-neutral case by taking into account the inertial effects of electrons as well as that of ions up to the first order in their mass ratio (δ=m_?/m₊). It is emphasized first that the magnetosphere is not globally equipotential even in the frame rotating with a central star (i.e. ?#0, where ? is the ‘non-Backus’ potential) due at least to the inertial effects of plasma particles. However, it is shown that the condition ?=0 is asymptotically recovered in the corotating region owing to the presence of the drift current which can be taken into account only when δ is not entirely neglected. This fact suggests that the deviation of the plasma motion in the outer magnetosphere from the corotation can be attributed to the non-zero ?. A globally self-consistent solution is obtained under this condition (?=0). In contrast with the solutions in the ‘force-free’ and the ‘mass-less-electron’ approximations, this solution has a disk structure in the corotation zone in which the plasma and the current density are concentrated to a thin disk near the magnetic equator. Owing to this sheet current in the disk the lines of force of the stellar magnetic field are modified to form a very elongated shape (the magnetodisk) if the plasma β-value is fairly large. Such a disk structure seems to be a common feature in the high β inner magnetospheres of various types of stars.     

Coherent amplification and pulsar phenomena

A modification of the rotating-star model has been developed to interpret the periodic energy bursts from pulsars. This new configuration involves -directed oscilltion modes in the stellar atmosphere or magnetosphere, and most aspects of the typical pulse characteristics are well accounted for. Gain is provided by resonant interactions with particles trapped in the stellar magnetic field. The most significant feature is the fact that highly directional beaming of the output energy results as a natural consequence of coherence between the radiation fields emerging from various locations about the pulsar; and a localized radiation origin is not required.     

Energetics of the aligned pulsar magnetosphere

An energy analysis is performed on two explicit models, due to Jackson, of a pulsar with aligned magnetic and rotational axes. The unknown parameters of these models are determined by calculating the minimum total energy states of the models. It is found that the minimum energy analysis favors states with extended, dynamically active magnetospheres with a high degrees of corotation. By calculating total power input to the magnetosphere via collisions in the stellar crust, and the total power radiated due to azimuthal drift motion, it is determined that the minimum energy states are the only states where a power balance can be achieved. Consideration of a local power balance condition and dissipative flows in the magnetosphere shows that neither model is completely self-consistent, but one is considerably better than the other. Properties of both models and implications for other models are discussed.     

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc–magnetosphere boundary. The instability is Rayleigh–Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, Θ≲ 30°, between the star's rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.     

Accretion disc–stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned, and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc–magnetosphere interaction is large , and consider different outer boundary conditions. In general the field line twisting produces field line inflation (e.g. Bardou & Heyvaerts), and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc, and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be caused by the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in the light of the significant effect that field line twisting has on the magnetic torque resulting from star–disc interactions.     

Laboratory Simulations of Bow Shocks and Magnetospheres

Laboratory experiments using a plasma wind generated by laser-target interaction are proposed and analyzed to investigate the creation of a shock in front of the magnetosphere and the dynamo mechanism. The proposed experiments and simulations are thought to be relevant to understanding the electron acceleration mechanisms at work in shock-driven magnetic dipole confined plasma in compact magnetized stars.     

TeV gamma-rays from accreting magnetars in massive binaries

This paper focuses on neutron stars (NS) of the magnetar type inside massive binary systems. We determine the conditions under which the matter from the stellar wind can penetrate the inner magnetosphere of the magnetar. At a certain distance from the NS surface, the magnetic pressure can balance the gravitational pressure of the accreting matter, creating a very turbulent, magnetized transition region. It is suggested that this region provides good conditions for the acceleration of electrons to relativistic energies. These electrons lose energy due to the synchrotron process and inverse Compton (IC) scattering of the radiation from the nearby massive stellar companion, producing high-energy radiation from X-rays up to ∼TeV γ-rays. The primary γ-rays can be further absorbed in the stellar radiation field, developing an IC  e^±  pair cascade. We calculate the synchrotron X-ray emission from primary electrons and secondary  e^±  pairs and the IC γ-ray emission from the cascade process. It is shown that quasi-simultaneous observations of the TeV γ-ray binary system LSI +61 303 in the X-ray and TeV γ-ray energy ranges can be explained with such an accreting magnetar model.     

Reconnection X-winds: spin-down of low-mass protostars

We investigate the interaction of a protostellar magnetosphere with a large-scale magnetic field threading the surrounding accretion disc. It is assumed that a stellar dynamo generates a dipolar-type field with its magnetic moment aligned with the disc magnetic field. This leads to a magnetic neutral line at the disc mid-plane and gives rise to magnetic reconnection, converting closed protostellar magnetic flux into open field lines. These are simultaneously loaded with disc material, which is then ejected in a powerful wind. This process efficiently brakes down the protostar to 10–20 per cent of the break-up velocity during the embedded phase.     

A hybrid simulation of Mercury’s magnetosphere for the MESSENGER encounters in year 2008

The latest measurements from the two encounters of the MESSENGER spacecraft in year 2008 have discovered several interesting features of the magnetosphere of Mercury. We have performed high-resolution 3D hybrid model calculations to simulate the solar wind interaction with the Hermean magnetosphere during the first two Mercury encounters of the MESSENGER spacecraft in 2008. It is found that the global structure of the Hermean magnetosphere is significantly controlled by the direction of the interplanetary magnetic field. The bow shock size and shape and the magnetotail configuration have very large differences in these two encounters with northward-pointing and southward-pointing interplanetary magnetic field, respectively. Comparisons are also given with the observed magnetic field profiles and the computational results. In general, good agreement can be found including the interesting feature of the relatively thick magnetopause current layer at outbound measurements. Our work shows that 3D hybrid simulation is a promising method to study in detail the Hermean magnetosphere in parallel with the post-MOI observations of the MESSENGER spacecraft and the Bepi-Colombo mission in future.