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 instability in a rotating layer at highly eccentric positions of the critical level

This study follows the numerical results presented in Marsenić & Ševčík (2010) that explored the influence of the critical level position on stability of a system. The model was a horizontal fluid layer between z = ±0.5d rotating with an angular velocity Ω = Ω₀ ž about the vertical axis z . The fluid was considered to be inviscid, finitely electrically conducting and incompressible and was permeated by a horizontal magnetic field B ₀ = ℬ︁₀B₀(z) y̌ , where ℬ︁₀ was the magnitude of the field and the function B₀(z) = tanh [γ (z –z₀)]. When γ is large, the field gradient is concentrated near z = z₀, the critical level, the field being almost homogeneous elsewhere. In this way it controls the width of the magnetic shear layer associated with the current sheet. It was found that at conditions when the magnetic field gradient was large enough (γ = O (10)) and the critical level was placed close enough to the (bottom) perfectly conducting boundary (z₀ < –0.388d for γ = 80), magnetically driven convection appeared localized to a close neighbourhood of the critical level – the so called critical layer. Based on the circumstances of its rise and its properties it was identified with the resistive tearing‐mode instability. This paper presents an analytical treatment of the problem assuming γ ≥ 1. The approach consists in separation of the computational domain into an outer region where the diffusionless limit (Elsasser number Λ → ∞) applies and an inner region (the critical layer) of finite conductivity. According to the tearing‐mode theory in classical systems, the solution in the inner region is sought as long‐wavelength with respect to the width of the critical layer. The obtained solution shows features similar to the one obtained numerically and confirmed relevance of the simplifying physical assumptions made in each region. The convection in the critical layer is strictly conditioned by a sharp magnetic shear. If the shear region is removed by further positioning of the critical level towards the perfectly conducting boundary, the localized convection disappears. It is in compliance with the fact that the system is stabilised by a perfectly conducting boundary with respect to the tearing mode. Stability is then checked numerically in the layer bounded by perfectly conducting boundaries where the critical point of the magnetic field lies on one of them. The existence of a magnetically driven instability is confirmed. Depending on the value γ, it may rise as a stationary convection (for γ < 1.5) or as a wave which for γ > 16 exhibits similarity properties (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localized magnetic reconnection as a cause of extraplanar diffuse ionized gas in the Galactic halo

Many observations indicate the occurrence of ionized gas in the distant haloes of galaxies (including our own). Since photoionization by stars (mainly O stars, young stars or evolved low-mass stars depending on the kind of galaxy) does not seem to be exclusively responsible for the ionization of the hydrogen filaments that should otherwise cool fast and recombine quickly, the question arises which extra energy source can produce the quasi-stationary ionization. We show that stationary localized magnetic reconnection in current filaments may contribute to the ionization of the extraplanar halo gas. In these filaments magnetic energy is dissipated. Consequently, the ionized as well as the neutral component is heated and re-ionized on a time-scale significantly shorter than the recombination time-scale. The amount of energy required for efficient re-ionization can in principle easily be provided by the free magnetic energy. We present quasi-static models that are characterized by plasma temperatures and densities that agree well with the observed values for the diffuse ionized gas component of the interstellar medium. Plasma–neutral gas fluid simulations are made to show that the recombination-induced dynamical reconnection process indeed works in a self-regulatory way.     

Suppression of resistive hose instability in a relativistic electron–positron flow

This paper presents the effects of electron–positron pair production on the linear growth of the resistive hose instability of a filamentary beam that could lead to snake-like distortion. For both the rectangular radial density profile and the diffuse profile reflecting the Bennett-type equilibrium for a self-collimating flow, the modified eigenvalue equations are derived from a Vlasov–Maxwell equation. While for the simple rectangular profile, current perturbation is localized at the sharp radial edge, for the realistic Bennett profile with an obscure edge, it is non-locally distributed over the entire beam, removing catastrophic wave–particle resonance. The pair production effects likely decrease the betatron frequency, and expand the beam radius to increase the resistive decay time of the perturbed current; these also lead to a reduction of the growth rate. It is shown that, for the Bennett profile case, the characteristic growth distance for a preferential mode can exceed the observational length-scale of astrophysical jets. This might provide the key to the problem of the stabilized transport of the astrophysical jets including extragalactic jets up to  Mpc (∼3 × 10²⁴ cm)  scales.     

Magnetorotational instability in a rotating liquid metal annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion discs, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid metal annulus (Couette flow) is explored by local and global stability analysis. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.     

Magnetic reconnection: flares and coronal heating in active galactic nuclei

A magnetically structured accretion disc corona, generated by buoyancy instability in the disc, can account for observations of flare-like events in active galactic nuclei. We examine how Petschek magnetic reconnection, associated with MHD turbulence, can result in a violent release of energy and heat the magnetically closed regions of the corona up to canonical X-ray emitting temperatures. X-ray magnetic flares, the after effect of the energy released in slow shocks, can account for the bulk of the X-ray luminosity from Seyfert galaxies and consistently explain the observed short-time-scale variability.     

Secondary tearingmode in the nonlinear evolution of magnetorotational instability

Numerical investigation of the two‐dimensional magnetic reconnection is given in the context of the nonlinear evolution of the Magneto‐Rotational Instability (MRI). With a careful comparison to various theories using both one‐ and twodimensional analysis, it is found that a new stabilizing effect of the centrifugal force on tearing instability must be present in the specific geometry of the MRI.Magnetic reconnection might play a key role to the formation of the nonaxisymmetric structures observed in MRI experiments. The results may also be useful for the estimate of the accretion rate in various astrophysical objects. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tayler instability with Hall effect in young neutron stars

Collapse calculations indicate that the hot young neutron stars rotate differentially so that strong toroidal magnetic field components should exist in the outer shell where also the Hall effect appears to be important when the Hall parameter = ω_Bτ exceeds unity. The amplitudes of the induced toroidal magnetic fields are limited by the current‐induced Tayler instability. An important characteristics of the Hall effect is its distinct dependence on the sign of the magnetic field. We find for fast rotation that positive (negative) Hall parameters essentially reduce (increase) the stability domain. It is thus concluded that the toroidal field belts in young neutron stars induced by their differential rotation should have different amplitudes in both hemispheres which later are frozen in. Due to the effect of magnetic suppression of the heat conductivity also the brightness of the two hemispheres should be different. As a possible example for our scenario the isolated neutron star RBS 1223 is considered which has been found to exhibit different X‐ray brightness at both hemispheres (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic fields of Ap stars as a result of the Tayler instability

Ap star magnetism is often attributed to fossil magnetic fields which have not changed much since the pre‐main‐sequence epoch of the stars. Stable magnetic field configurations are known which could persist probably for the entire mainsequence life of the star, but they may not show the complexity and diversity exhibited by the Ap stars observed. We suggest that the Ap star magnetism is not a result of stable configurations, but is the result of an instability based on strong toroidal magnetic fields buried in the stars. The highly nonaxisymmetric remainders of the instability are reminiscent of the diversity of fields seen on Ap stars. The strengths of these remnant magnetic fields are actually between a few per cent up to considerable fractions of the internal toroidal field; this means field strengths of the order of kGauss being compatible with what is observed. The magnetic fields emerge at the surface rather quickly; rough estimates deliver time‐scales of the order of a few years. Since rotation stabilizes the instability, normal A stars may still host considerable, invisible toroidal magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).     

Electric charge and magnetic flux on rotating black holes in a force-free magnetosphere

The electric charge on rotating black holes is calculated to be ∼ BJ in the force-free configuration of Ghosh, with a horizon flux of ∼ BM ². This charge is gravitationally weak for B ∼10¹⁵ G , so that the Kerr metric applies. Being similar to the electric charge of a magnetar, both electric charge and magnetic flux should be, in sign and order of magnitude, continuous during stellar collapse into a black hole. Extraction of the rotational energy from newly formed black holes may proceed by interaction with the magnetic field.     

Non-ideal evolution of non-axisymmetric, force-free magnetic fields in a magnetar

Recent numerical magnetohydrodynamic calculations by Braithwaite and collaborators support the 'fossil field' hypothesis regarding the origin of magnetic fields in compact stars and suggest that the resistive evolution of the fossil field can explain the reorganization and decay of magnetar magnetic fields. Here, these findings are modelled analytically by allowing the stellar magnetic field to relax through a quasi-static sequence of non-axisymmetric, force-free states, by analogy with spheromak relaxation experiments, starting from a random field. Under the hypothesis that the force-free modes approach energy equipartition in the absence of resistivity, the output of the numerical calculations is semiquantitatively recovered: the field settles down to a linked poloidal–toroidal configuration, which inflates and becomes more toroidal as time passes. A qualitatively similar (but not identical) end state is reached if the magnetic field evolves by exchanging helicity between small and large scales according to an α-dynamo-like, mean-field mechanism, arising from the fluctuating electromotive force produced by the initial random field. The impossibility of matching a force-free internal field to a potential exterior field is discussed in the magnetar context.     

Magnetic field evolution in neutron stars

Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A transient event in AD 775 reported by al‐Tabarī: A bolide – not a nova,supernova, or kilonova

Given that the cause for the strong increase in ¹⁴C in AD 774/5 in Japanese and German trees is still a matter of debate (e.g. short gamma‐ray burst or solar super‐flare), we have searched in Arabic chronicles for reports about unusual transient celestial events. In the History of al‐Tabarī we found two (almost identical) reports about such an event. The group around caliph al‐Mansūr observed a transient event while on the way from Baghdad to Mecca on AD 775 Augusst 29– September 1 (Julian calendar). A celestial object (kawkab) was seen to fall or set (inqadda), and its trace (atharuhu) was seen for at least tens of minutes (up to 70–90 min) during morning twilight. The reports use the Arabic words kawkab and athar(uhu), which were also used in the known Arabic reports about supernovae SN 1006 and 1054, so that one might consider an interpretation as a nova‐like event. The kawkab (celestial object) was observed only during the morning twilight at a brightness of probably between about –3 and 0 mag. Such a brightness and time‐scale would be expected for optical kilonovae (at ∼3 to 9 kpc) in the context of short gamma‐ray bursts. There are no similar reports from eastern Asia for this time. However, the short reports are fully consistent with a bolide: The word kawkab can be used for meteor, the verb inqad_. d_. a normally means falling down, the word atharuhu can mean its trace. We therefore prefer the interpretation as bolide. We discuss in detail how to convert the Muslim calendar date to a date in the Julian calendar using first the calculated Islamic calendar and then considering the time when the crescent new moon could be visible at the given location. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy spectra of particles accelerated in a reconnecting current sheet with the guiding magnetic field

Electron and proton acceleration by a super-Dreicer electric field is investigated in the non-neutral reconnecting current sheet (RCS) with a non-zero longitudinal component of the magnetic field ('guiding field'). The guiding field is assumed parallel to the direction of electric field and constant within an RCS. The other two magnetic field components, transverse and tangential, are considered to vary with distances from the X null point of an RCS. The proton and electron energy spectra are calculated numerically from a motion equation using the test particle approach for model RCSs with constant and variable densities. In the presence of a strong or moderate guiding field, protons were found fully or partially separated from electrons at ejection from an RCS into the opposite, 'electron' and 'proton', semiplanes. In the case of a weak guiding field, both protons and electrons are ejected symmetrically in equal proportions as neutral beams. The particles ejected from an RCS with a very weak or very strong guiding field have power-law energy spectra with spectral indices of about 1.5 for protons and 2.0 for electrons. For a moderate guiding field, the energy spectra of electrons ejected into the opposite semiplanes are mixed, i.e. in the 'electron-dominated' semiplane power-law energy spectra for electrons and thermal-like for protons, while in the 'proton' semiplane they are symmetrically mirrored.     

Low-frequency waves in asymmetric magnetized relativistic pair plasma

The properties of waves in a pulsar magnetosphere are considered in the most general case of a non-neutral, current-carrying pair plasma with arbitrary distribution functions for electrons and positrons. General dispersion relations are derived for a strong but finite magnetic field, including gyrotropic terms caused by the deviations from quasi-neutrality and the relative streaming of electrons and positrons. It is shown how the ellipticity of the wave polarization depends on the plasma parameters and angle of propagation. Two examples of plasma distributions are analysed numerically: a waterbag distribution and a piecewise distribution that models the numerical result for pair cascades. A possible application to the interpretation of the observed circular polarization of some pulsars is discussed.     

Evidence for interchange reconnection between a coronal hole and an adjacent emerging flux region

Coronal holes are regions of dominantly monopolar magnetic field on the Sun where the field is considered to be ‘open’ towards interplanetary space. Magnetic bipoles emerging in proximity to a coronal hole boundary naturally interact with this surrounding open magnetic field. In the case of oppositely aligned polarities between the active region and the coronal hole, we expect interchange reconnection to take place, driven by the coronal expansion of the emerging bipole as well as occasional eruptive events. Using SOHO/EIT and SOHO/MDI data, we present observational evidence of such interchange reconnection by studying AR 10869 which emerged close to a coronal hole. We find closed loops forming between the active region and the coronal hole leading to the retreat of the hole. At the same time, on the far side of the active region, we see dimming of the corona which we interpret as a signature of field line ‘opening’ there, as a consequence of a topological displacement of the ‘open’ field lines of the coronal hole. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the electric field screening by electron–positron pairs in a pulsar magnetosphere

We present a steady one-dimensional model for a pulsar polar cap accelerator, where the field-aligned electric field and flow are solved self-consistently with a given current density. It is assumed that no particles return to the star. It is known that the space-charge-limited flow is accelerated to energies high enough to create electron–positron pairs if the assumed current density is high enough. We find that when pairs are created in such a space-charge-limited flow, the accelerating electric field is screened out within a short distance after pair creation, if the pair particle flux is larger than a critical value. We also find that a space charge density wave is excited in the screening region.
We find that a pair flux larger than the critical value M _c=10³–10⁵ must be reached in a layer with thickness equal to the braking distance for the decelerating component. Therefore, the required multiplicity – the number of pairs created by one primary particle – is too large to be realized in the actual pulsar magnetosphere. We suggest that in order to obtain a localized potential drop along the polar cap magnetic flux, one needs to take into account additional effects such as wave–particle interaction or quasi-periodic pair creation.