A stability property of a force-free surface bounding a vacuum gap

A force-free surface (FFS) ${\cal S}$ is a sharp boundary separating a void from a region occupied by a charge-separated force-free plasma. It is proven here under very general assumptions that there is on ${\cal S}$ a simple relation between the charge density $\mu$ on the plasma side and the derivative of \delta=\E\cdot\B along \B on the vacuum side (with \E denoting the electric field and \B the magnetic field). Combined with the condition $\delta=0$ on ${\cal S}$, this relation implies that a FFS has a general stability property, already conjectured by Michel (1979, ApJ 227, 579): ${\cal S}$ turns out to attract charges placed on the vacuum side if they are of the same sign as $\mu$. In the particular case of a FFS existing in the axisymmetric stationary magnetosphere of a "pulsar", the relation is given a most convenient form by using magnetic coordinates, and is shown to imply an interesting property of a gap. Also, a simple proof is given of the impossibility of a vacuum gap forming in a field \B which is either uniform or radial (monopolar)

Electrodynamic Structure of an Outer Gap Accelerator: Location of the Gap and the Gamma-ray Emission from the Crab Pulsar

We investigate a stationary pair production cascade in the outer magnetosphere of a spinning neutron star. The charge depletion due to global flows of charged particles, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the distribution functions of particles and gamma-rays. If no current is injected at neither of the boundaries of the accelerator, the gap is located around the conventional null surface, where the local Goldreich-Julian charge density vanishes. However, we first find that the gap position shifts outwards (or inwards) when particles are injected at the inner (or outer) boundary. Applying the theory to the Crab pulsar, we demonstrate that the pulsed TeV flux does not exceed the observational upper limit for moderate infrared photon density and that the gap should be located near to or outside of the conventional null surface so that the observed spectrum of pulsed GeV fluxes may be emitted via a curvature process. Some implications of the existence of a solution for a super Goldreich-Julian current are discussed.Comment: 17 pages, 12 figures, submitted to Ap

The diocotron instability in a pulsar cylindrical electrosphere

The physics of the pulsar inner magnetosphere remains poorly constrained by observations. Although about 2000 pulsars have been discovered to date, little is known about their emission mechanism. Large vacuum gaps probably exist and a non-neutral plasma made of electrons in some regions and of positrons in some other regions fills space to form an electrosphere. The purpose of this work is to study the stability properties of the differentially rotating equatorial disk in the pulsar's electrosphere for which the magnetic field is assumed to be dipolar. In contrast to previous studies, the magnetic field is not restricted to be uniform. A pseudo-spectral Galerkin method using Tchebyshev polynomials expansion is developed to compute the spectrum of the diocotron instability in a non-neutral plasma column confined between two cylindrically conducting walls. Moreover, the inner wall carries a given charge per unit length in order to account for the presence of a charged neutron star at the centre of the electrosphere. We show several eigenfunctions and eigenspectra obtained for different initial density profiles and electromagnetic field configurations useful for laboratory plasmas. The algorithm is very efficient in computing the fastest growing modes. Applications to a cylindrical electrosphere are also shown for several differential rotation profiles. It is found that the growth rates of the diocotron instability are of the same order of magnitude as the rotation rate.Comment: Accepted by A&

Large-Amplitude, Pair-Creating Oscillations in Pulsar and Black Hole Magnetospheres

A time-dependent model for pair creation in a pulsar magnetosphere is developed. It is argued that the parallel electric field that develops in a charge-starved region (a gap) of a pulsar magnetosphere oscillates with large amplitude. Electrons and positrons are accelerated periodically and the amplitude of the oscillations is assumed large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at $N_\pm\simeq E_{0}^2/(8\pi m_ec^2\Gamma_{\rm thr})$, where $E_0$ is the parallel electric field in the charge-starved initial state, and $\Gamma_{\rm thr}$ is the Lorentz factor for effec tive pair creation. The frequency of oscillations following the pair creation burst is given roughly by $\omega_{\rm osc}=eE_0/(8m_ec\Gamma_{\rm thr})$. A positive feedback keeps the system stable, such that the average pair creation rate balances the loss rate due to pairs escaping the magnetosphere.Comment: 21 pages, 6 figures, ApJ submitte

The magnetron instability in a pulsar's cylindrical electrosphere

(abridged) The physics of the pulsar magnetosphere remains poorly constrained by observations. Little is known about their emission mechanism. Large vacuum gaps probably exist, and a non-neutral plasma partially fills the neutron star surroundings to form an electrosphere. We showed that the differentially rotating equatorial disk in the pulsar's electrosphere is diocotron unstable and that it tends to stabilise when relativistic effects are included. However, when approaching the light cylinder, particle inertia becomes significant and the electric drift approximation is violated. In this paper, we study the most general instability, i.e. by including particle inertia effects, as well as relativistic motions. This general non-neutral plasma instability is called the magnetron instability. We linearise the coupled relativistic cold-fluid and Maxwell equations. The non-linear eigenvalue problem for the perturbed azimuthal electric field component is solved numerically. The spectrum of the magnetron instability in a non-neutral plasma column confined between two cylindrically conducting walls is computed for several cylindrical configurations. For a pulsar electrosphere, no outer wall exists. In this case, we allow for electromagnetic wave emission propagating to infinity. When the self-field induced by the plasma becomes significant, it can first increase the growth rate of the magnetron instability. However, equilibrium solutions are only possible when the self-electric field, measured by the parameter $s_{\rm e}$ and tending to disrupt the plasma configuration, is bounded to an upper limit, $s_{\rm e,max}$. For $s_{\rm e}$ close to but smaller than this value $s_{\rm e,max}$, the instability becomes weaker or can be suppressed as was the case in the diocotron regime.Comment: Accepted by A&

The Axisymmetric Pulsar Magnetosphere

We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, ${\bf E\cdot B}=0$, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. With the geometry of the field lines thus determined we compute the dynamics of the associated MHD wind. The main result is that the relativistic outflow contained in the magnetosphere is not accelerated to the extremely relativistic energies required for the flow to generate gamma rays. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely when either the force-free and/or the ideal MHD condition ${\bf E\cdot B}=0$ are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.Comment: 15 pages AAS Latex, 5 postscript figure

An annular gap acceleration model for γ\gamma-ray emission of pulsars

If the binding energy of the pulsar's surface is not so high (the case of a neutron star), both the negative and positive charges will flow out freely from the surface of the star. The annular free flow model for $\gamma$-ray emission of pulsars is suggested in this paper. It is emphasized that: (1). Two kinds of acceleration regions (annular and core) need to be taken into account. The annular acceleration region is defined by the magnetic field lines that cross the null charge surface within the light cylinder. (2). If the potential drop in the annular region of a pulsar is high enough (normally the cases of young pulsars), charges in both the annular and the core regions could be accelerated and produce primary gamma-rays. Secondary pairs are generated in both regions and stream outwards to power the broadband radiations. (3). The potential drop in the annular region grows more rapidly than that in the core region. The annular acceleration process is a key point to produce wide emission beams as observed. (4). The advantages of both the polar cap and outer gap models are retained in this model. The geometric properties of the $\gamma$-ray emission from the annular flow is analogous to that presented in a previous work by Qiao et al., which match the observations well. (5). Since charges with different signs leave the pulsar through the annular and the core regions, respectively, the current closure problem can be partially solved.Comment: 11 pages 2 figures, accepted by Chinese Journal of Astronomy and Astrophysic

The pulsar force-free magnetosphere linked to its striped wind: time-dependent pseudo-spectral simulations

(abridged) Pulsar activity and its related radiation mechanism are usually explained by invoking some plasma processes occurring inside the magnetosphere. Despite many detailed local investigations, the global electrodynamics around those neutron stars remains poorly described. Better understanding of these compact objects requires a deep and accurate knowledge of their immediate electromagnetic surrounding within the magnetosphere and its link to the relativistic pulsar wind. The aim of this work is to present accurate solutions to the nearly stationary force-free pulsar magnetosphere and its link to the striped wind, for various spin periods and arbitrary inclination. To this end, the time-dependent Maxwell equations are solved in spherical geometry in the force-free approximation using a vector spherical harmonic expansion of the electromagnetic field. An exact analytical enforcement of the divergenceless of the magnetic part is obtained by a projection method. Special care has been given to design an algorithm able to look deeply into the magnetosphere with physically realistic ratios of stellar $R_*$ to light-cylinder \rlight radius. We checked our code against several analytical solutions, like the Deutsch vacuum rotator solution and the Michel monopole field. We also retrieve energy losses comparable to the magneto-dipole radiation formula and consistent with previous similar works. Finally, for arbitrary obliquity, we give an expression for the total electric charge of the system. It does not vanish except for the perpendicular rotator. This is due to the often ignored point charge located at the centre of the neutron star. It is questionable if such solutions with huge electric charges could exist in reality except for configurations close to an orthogonal rotator. The charge spread over the stellar crust is not a tunable parameter as is often hypothesized.Comment: 16 pages, 13 figures, accepted by MNRA

The theory of pulsar winds and nebulae

We review current theoretical ideas on pulsar winds and their surrounding nebulae. Relativistic MHD models of the wind of the aligned rotator, and of the striped wind, together with models of magnetic dissipation are discussed. It is shown that the observational signature of this dissipation is likely to be point-like, rather than extended, and that pulsed emission may be produced. The possible pulse shapes and polarisation properties are described. Particle acceleration at the termination shock of the wind is discussed, and it is argued that two distinct mechanisms must be operating, with the first-order Fermi mechanism producing the high-energy electrons (above 1 TeV) and either magnetic annihilation or resonant absorption of ion cyclotron waves responsible for the 100 MeV to 1 TeV electrons. Finally, MHD models of the morphology of the nebula are discussed and compared with observation.Comment: 33 pages, to appear in Springer Lecture Notes on "Neutron stars and pulsars, 40 years after the discovery", ed W.Becke

Refractive turbulence profiling using an orbiting light source

Applied Optics, Volume 29, No. 13, pp. 1877-1885 (May 1990)The possibility of obtaining vertical profiles of refractive turbulence C2 using an orbiting monochromatic light source is examined. The method employs spatial and temporal filtering of the observed scintillation pattern arising from density fluctuations in the atmosphere to measure C2/n. The impact of atmospheric motion on the method is discussed along with ways to mitigate its effect. Single and array receiver configurations are examined and the multiple response problem inherent in array configurations is corrected by tuning the individual array elements to the array response. The method is expected to be significantly better than the existing stellar scintillometer method