Non-stationary pair plasma in a pulsar magnetosphere and the two-stream Instability

We test a new emission mechanism in pulsar magnetospheres, eventually responsible in part for the high level of observed radio radiation. This is carried out by comparing the efficiency of the two-stream instability of Langmuir waves in a pulsar emission region, where the stationary and non-stationary characters of pair plasma outflows produced in the gap region are characterized by two different time-scales. On the shorter time-scale, the Ruderman &38; Sutherland 'sparking' phenomenon leads to the creation of pair plasma clouds, in motion along magnetic field lines, that contain particles with a large spectrum of momenta. The overlapping of particles with different energies produced in successive clouds results in an efficient 'two stream'-like instability. This effect is a consequence of the non-stationary character of the pair plasma produced in the gap region, just above the magnetic poles of the neutron star. On a long time-scale, resulting pair plasma outflows in pulsar magnetospheres can be treated as stationary. In this case, the instability which results from interaction between existing primary beam particles and the pair plasma is negligible, whereas the instability owing to interaction between electrons and positrons of the pair plasma itself, and more precisely to their relative drift motion along curved magnetic field lines, is effective. We derive characteristic features of the triggered instability, using specific distribution functions to describe either particles in the assembly of clouds or relative drifting of electrons and positrons in these same plasma clouds. Although linear and local, our treatment suggests that non-stationary effects may compete with, or even dominate over, drifting effects in parts of pulsar emission regions.     

The force-free dipole magnetosphere in nonlinear electrodynamics

Quantum electrodynamics(QED) effects may be included in physical processes of magnetar and pulsar magnetospheres with strong magnetic fields. Involving the quantum corrections, Maxwell electrodynamics is modified to nonlinear electrodynamics. In this work, we study the force-free magnetosphere in nonlinear electrodynamics in a general framework. The pulsar equation describing a steady and axisymmetric magnetosphere is derived, which now admits solutions with corrections. We derive the first-order nonlinear corrections to the near-zone dipole magnetosphere in some popular nonlinear effective theories.The field lines of the corrected dipole tend to converge on the rotational axis so that the fields in the polar region are stronger compared to the pure dipole case.     

Neutron-loaded outflows in gamma-ray bursts

The force-free limit of magnetohydrodynamics (MHD) is often a reasonable approximation to model black hole and neutron star magnetospheres. We describe a general relativistic force-free (GRFFE) formulation that allows general relativistic magnetohydrodynamic (GRMHD) codes to directly evolve the GRFFE equations of motion. Established, accurate and well-tested conservative GRMHD codes can simply add a new inversion piece of code to their existing code, while continuing to use all the already-developed facilities present in their GRMHD code. We show how to enforce the   E · B = 0  constraint and energy conservation, and we introduce a simplified general model of the dissipation of the electric field to enforce the   B ²− E ² > 0  constraint. We also introduce a simplified yet general method to resolve current sheets, without much reconnection, over many dynamical times. This formulation is incorporated into an existing GRMHD code ( harm ), which is demonstrated to give accurate and robust GRFFE results for Minkowski and black hole space–times.     

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.     

Induced Raman scattering in pulsar magnetospheres

It is shown that induced Raman scattering of electromagnetic waves in the strongly magnetized electron–positron plasma of pulsar magnetospheres may be important for wave propagation and as an effective saturation mechanism for electromagnetic instabilities. The frequencies at which strong Raman scattering occurs in the outer parts of a magnetosphere fall into the observed radio band. The typical threshold intensities for the strong Raman scattering are of the order of the observed intensities, implying that pulsar magnetospheres may be optically thick to Raman scattering of electromagnetic waves.     

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.     

Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines

Here we briefly report on results of self-consistent numerical modeling of a differentially rotating force-free magnetosphere of an aligned rotator. We show that differential rotation of the open field line zone is significant for adjusting of the global structure of the magnetosphere to the current density flowing through the polar cap cascades. We argue that for most pulsars stationary cascades in the polar cap can not support stationary force-free configurations of the magnetosphere.      

A novel look at the pulsar force-free magnetosphere

The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, \(B_{\mathrm{new}}^{0}=3.3\times10^{-4}B/P\), where \(P\) is the pulsar period. Then the 7-order scatter of the magnetic field derived from the rotational characteristics of the pulsars observed appears consistent with the \(\cot\chi\)-law, where \(\chi\) is a random quantity uniformly distributed in the interval \([0,\pi/2]\). Our result is suggestive of a unique actual magnetic field strength of the neutron stars along with a random angle between the magnetic and rotational axes and gives insight into the neutron star unification on the geometrical basis.     

Numerical simulations of aligned neutron star magnetospheres

We present detailed numerical simulations of the magnetosphere of an isolated neutron star in which the spin and magnetic dipole axes of the star are aligned. We demonstrate that stable charge distributions are always found, rather than particle outflows. A stable magnetosphere consists of a dome above the polar cap containing plasma of one charge and an equatorial belt containing plasma of the other sign: E · B =0 inside both of these. These are separated by a vacuum gap in which E · B ≠0 ( ρ =0 instead). We show that the charge distribution used in the 'standard' Goldreich–Julian pulsar model is inherently unstable: it collapses to a stable configuration that is very similar to the others illustrated here. An instructive video of this collapse is available at http://spacsun.rice.edu/~ian/. For typical pulsars, the stable solution has no particles near to the light cylinder, and if there were any there then their loss from the system would not lead to a replacement from the star (in contradiction to the explicit assumption used in the Goldreich–Julian model). We discuss the generic effects of pair creation, in particular as an additional source of ionization in the vacuum gap. The overall effect is simply to reduce the value of E · B in the vacuum gap so that the pair-production rate drops towards zero. A dome, disc and gap geometry is still the resulting solution. In conclusion, we confirm previous studies that the aligned rotator cannot make an active pulsar.     

Cyclotron absorption of radio emission within pulsar magnetospheres

Absorption of radio emission through normal cyclotron resonance within pulsar magnetospheres is considered. The optical depth for cyclotron damping is calculated using a plasma distribution with an intrinsically relativistic spread. We argue that such a broad distribution is plausible for pulsar plasmas and that it implies that a class of pulsars that should have cyclotron damping extends to include young pulsars with shorter periods and stronger magnetic fields. There is no obvious observational evidence for disruption of radio pulses, which implies that the optical depth cannot be too large. We propose that cyclotron resonance may cause marginal absorption of radio emission. It is shown that such marginal absorption produces potentially observable asymmetric features for double-peak pulse profiles with wide separation, with one peak tending to be suppressed.     

An empirical model for the beams of radio pulsars

Motivated by recent results on the location of the radio emission in pulsar magnetospheres, we have developed a model which can account for the large diversity found in the average profile shapes of pulsars. At the centre of our model lies the idea that radio emission at a particular frequency arises from a wide range of altitudes above the surface of the star, and that it is confined to a region close to the last open field lines. We assert that the radial height range over which emission occurs is responsible for the complex average pulse shapes rather than the transverse (longitudinal) range proposed in most current models. By implementing an abrupt change in the height range to discriminate between young, short-period, highly energetic pulsars and their older counterparts, we obtain the observed transition between the simple and complex average pulse profiles observed in each group respectively. Monte Carlo simulations are used to demonstrate the match of our model to real observations.     

Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ₀∝ r ^−α  , a coplanar azimuthal magnetic field   B ₀∝ r ^−γ  , a consistent self-gravity and a power-law rotation curve   v ₀∝ r ^−β  , where v ₀ is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ ⁿ   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.     

Pulsar investigation using interstellar scintillation

We discuss the resolution of pulsar magnetospheres using interstellar scintillation. The two-dimensional spatial structure of pulsar emission zones can be obtained from analysis of diffractive scintillations at low frequencies. Based on refractive and diffractive scintillation of pulsars we can also reconstruct the distribution of turbulent plasma along the line of sight, and using this analysis a new approach to pulsar distance estimation can be made. This revised version was published online in July 2006 with corrections to the Cover Date.     

The structure of black hole magnetospheres I. Schwarzschild black holes

We introduce a multipolar scheme for describing the structure of stationary, axisymmetric, force-free black hole magnetospheres in the '3+1' formalism. We focus here on Schwarzschild spacetime, giving a complete classification of the separable solutions of the stream equation. We show a transparent term-by-term analogy of our solutions with the familiar multipoles of flat-space electrodynamics. We discuss electrodynamic processes around disc-fed black holes in which our solutions find natural applications: (i) 'interior' solutions in studies of the BlandfordZnajek process of extracting the rotational energy of holes, and of the formation of relativistic jets in active galactic nuclei and 'microquasars'; (ii) 'exterior' solutions in studies of accretion disc dynamos, disc-driven winds and jets. On the strength of existing numerical studies, we argue that the poloidal field structures found here are also expected to hold with good accuracy for rotating black holes, except for the cases of the maximum possible rotation rates. We show that the closed-loop exterior solutions found here are not in contradiction with the MacdonaldThorne theorem, as these solutions, which diverge logarithmically on the horizon of the hole , only apply to those regions that exclude .     

Magnetorotational and Tayler Instabilities in the Pulsar Magnetosphere

The magnetospheres around neutron stars should be very particular because of their strong magnetic field and rapid rotation. A study of the pulsar magnetospheres is of crucial importance since it is the key issue to understand how energy outflow to the exterior is produced. In this paper, we discuss magnetohydrodynamic processes in the pulsar magnetosphere. We consider in detail the properties of magnetohydrodynamic waves that can exist in the magnetosphere and their instabilities. These instabilities lead to formation of magnetic structures and can be responsible for short-term variability of the pulsar emission.     

The effective acceleration of plasma outflow in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for a paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric magnetohydrodynamic (MHD) flow. For the large Michel magnetization parameter σ it is possible to linearize the stream equation near the force-free solution and to solve the problem self-consistently as was done by Beskin, Kuznetsova & Rafikov for a monopole magnetic field. It is shown that, on the fast magnetosonic surface (FMS), the particle Lorentz factor γ does not exceed the standard value  σ^1/3  . On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as  γ≈ ( z / R _L)^1/2  up to the distance   z ≈σ² R _L  , where   R _L= c /Ω_F  is the radius of the light cylinder. Thus, the maximal Lorentz factor is  γ_max≈σ  , which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.     

A model of solar flares triggered by interactions between force-free current loops and plasmoids

We present a model of solar flares triggered by collisions between current loops and plasmoids. We investigate a collision process between a force-free current loop and a plasmoid, by using 3-D resistive MHD code. It is shown that a current system can be induced in the front of a plasmoid, when it approaches a force-free current loop. This secondary current produced in the front of the plasmoid separates from the plasmoid and coalesces to the force-free current loop associated with the magnetic reconnection. The core of the plasmoid stays outside the reconnection region, maintaining high density. The core can be confined by the current system produced around the plasmoid. This collison process between a current loop and a plasmoid may explain the triggering of solar flares observed byYohkoh.     

Propagation of microwaves in pulsar magnetospheres

We discuss the dispersion relation of linearly-polarized waves, propagating along a strong background magnetic field embedded in an electron-positron plasma. The results are then applied to the study of the propagation conditions of coherent curvature radio radiation inside neutron stars magnetospheres, as produced by electric discharges following current pulsar models.     

The influence of magnetospheric refraction on the apparent spatial structure of a pulsar emission region

The refraction of ordinary superluminous waves in a pulsar plasma is considered. The effect is found essentially to influence the apparent spatial structure of a pulsar emission region. This is of particular importance for the interpretation of the observations of pulsar interstellar scintillations, which provide an opportunity of resolving the magnetospheres of nearby pulsars. When calculated with account for magnetospheric refraction, the dependence of transverse ray separation on pulse longitude appears to be similar to that inferred by means of interstellar interferometry. It is shown that the differences in the character of the dependences observed at various frequencies may be attributed to the frequency-dependent efficiency of refraction. Taking into account magnetospheric refraction makes it necessary to reconsider the estimate of the emission altitude derived from the apparent size of the emission region. The renewed estimate appears to be almost an order of magnitude less, so that it is consistent with the emission altitudes obtained by other methods.