An Idealized Pulsar Magnetosphere: the Relativistic Force-Free Approximation

The non-dissipative relativistic force-free condition should be a good approximation to describe the electromagnetic field in much of the pulsar magnetosphere, but we may plausibly expect it to break down in singular domains. Self-consistent magnetospheric solutions are found with field lines closing both at and within the light-cylinder. In general, the detailed properties of the solutions may be affected critically by the physics determining the appropriate choice of equatorial boundary condition beyond the light-cylinder.Comment: 31 pages, 3 figure

Global MRI with Braginskii viscosity in a galactic profile

We present a global-in-radius linear analysis of the axisymmetric magnetorotational instability (MRI) in a collisional magnetized plasma with Braginskii viscosity. For a galactic angular velocity profile $\Omega$ we obtain analytic solutions for three magnetic field orientations: purely azimuthal, purely vertical and slightly pitched (almost azimuthal). In the first two cases the Braginskii viscosity damps otherwise neutrally stable modes, and reduces the growth rate of the MRI respectively. In the final case the Braginskii viscosity makes the MRI up to $2\sqrt{2}$ times faster than its inviscid counterpart, even for \emph{asymptotically small} pitch angles. We investigate the transition between the Lorentz-force-dominated and the Braginskii viscosity-dominated regimes in terms of a parameter \sim \Omega \nub/B^2 where \nub is the viscous coefficient and $B$ the Alfv\'en speed. In the limit where the parameter is small and large respectively we recover the inviscid MRI and the magnetoviscous instability (MVI). We obtain asymptotic expressions for the approach to these limits, and find the Braginskii viscosity can magnify the effects of azimuthal hoop tension (the growth rate becomes complex) by over an order of magnitude. We discuss the relevance of our results to the local approximation, galaxies and other magnetized astrophysical plasmas. Our results should prove useful for benchmarking codes in global geometries.Comment: 14 pages, 5 figure

Effects of Rotation and Relativistic Charge Flow on Pulsar Magnetospheric Structure

We propose an analytical 3-D model of the open field-line region of a neutron star (NS) magnetosphere. We construct an explicit analytic solution for arbitrary obliquity (angle between the rotation and magnetic axes) incorporating the effects of magnetospheric rotation, relativistic flow of charges (e.g. primary electron beam) along the open field lines, and E X B drift of these charges. Our solution employs the space-charge-limited longitudinal current calculated in the electrodynamic model of Muslimov & Tsygan (1992) and is valid up to very high altitudes nearly approaching the light cylinder. We assume that in the innermost magnetosphere, the NS magnetic field can be well represented by a static magnetic dipole configuration. At high altitudes the open magnetic field lines significantly deviate from those of a static dipole and tend to focus into a cylindrical bundle, swept back in the direction opposite to the rotation, and also bent towards the rotational equator. We briefly discuss some implications of our study to spin-powered pulsars.Comment: 24 pages, 3 figures, accepted for publication in Ap

Plasma Modes Along the Open Field Lines of a Neutron Star

We consider electrostatic plasma modes along the open field lines of a rotating neutron star. Goldreich-Julian charge density in general relativity is analyzed for the neutron star with zero inclination. It is found that the charge density is maximum at the polar cap and it remains almost same in certain extended region of the pole. For a steady state Goldreich-Julian charge density we found the usual plasma oscillation along the field lines; plasma frequency resembles to the gravitational redshift close to the Schwarzschild radius. We study the nonlinear plasma mode along the field lines. From the system of equations under general relativity, a second order differential equation is derived. The equation contains a term which describes the growing plasma modes near Schwarzschild radius in a black hole environment. The term vanishes with the distance far away from the gravitating object. For initially zero potential and field on the surface of a neutron star, Goldreich-Julian charge density is found to create the plasma mode, which is enhanced and propagates almost without damping along the open field lines. We briefly outline our plan to extend the work for studying soliton propagation along the open field lines of strongly gravitating objects

Dynamo action between two rotating discs

Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are sought. The kinematic eigenvalue problem is found to have growing modes for Rem>Rc≃100. The growth rate is real for the perfectly conducting and ferromagnetic cases, but may be complex for insulating boundaries. As Rem→∞ it is shown that the dynamo can be fast or slow, depending on the flow structure. In the slow case, the growth rate is governed by a magnetic boundary layer on one of the discs. The growing field saturates in a solution to the nonlinear dynamo problem. The bifurcation is found to be subcritical and nonlinear dynamos are found for Rem≳0.7Rc. Finally, the flux of magnetic energy to large r is examined, to determine which solutions might generalise to dynamos between finite discs. It is found that the fast dynamos tend to have inward energy flux, and so are unlikely to be realised in practice. Slow dynamos with outward flux are found. It is suggested that the average rotation rate should be non-zero in practice

Dynamically dominant magnetic fields in the diffuse interstellar medium

Observations show that magnetic fields in the interstellar medium (ISM) often do not respond to increases in gas density as would be naively expected for a frozen-in field. This may suggest that the magnetic field in the diffuse gas becomes detached from dense clouds as they form. We have investigated this possibility using theoretical estimates, a simple magneto-hydrodynamic model of a flow without mass conservation and numerical simulations of a thermally unstable flow. Our results show that significant magnetic flux can be shed from dense clouds as they form in the diffuse ISM, leaving behind a magnetically dominated diffuse gas.Comment: 2 pages, 1 figure. In proceedings of IAU Symposium 259: "Cosmic magnetic fields: from planets to stars and galaxies", eds. K.G. Strassmeier, A.G. Kosovichev & J.E. Beckman in pres

A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length $m$, and it is natural to ask for which outputs this is extremized. This question was posed in a previous work, where it was conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant strings $\texttt{000}\ldots$ and $\texttt{111}\ldots$ and the alternating strings $\texttt{0101}\ldots$ and $\texttt{1010}\ldots$ respectively. In the present work we confirm the minimization conjecture in the asymptotic limit using results from hidden word statistics. We show how the analytic-combinatorial methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden pattern matching problem can be applied to resolve the case of fixed output length and $n\rightarrow\infty$, by obtaining estimates for the entropy in terms of the moments of the posterior distribution and establishing its minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure

Trapped modes of the Helmholtz equation in infinite waveguides with wall indentations and circular obstacles

Trapped modes of the Helmholtz equation are investigated in infinite, two-dimensional acoustic waveg- uides with Neumann or Dirichlet walls. A robust boundary element scheme is used to study modes both inside and outside the continuous spectrum of propagating modes. An effective method for distinguishing between genuine trapped modes and spurious solutions induced by the domain truncation is presented. The method is also suitable for the detection and study of “nearly trapped modes” (NTM). These are of great practical importance as they display many features of trapped modes but do not require perfect geometry. An infinite, two-dimensional channel is considered with one or two discs on its centreline. The walls may have rectangular, triangular or smooth cavities. The combination of a circular obstacle and a rectangular cavity, in both Neumann and Dirichlet guides is studied, illustrating the possible use of a movable disc to detect wall irregularities. The numerical method is validated against known results and many new modes are identified, both inside and outside the continuous spectrum. Results obtained suggest that at least one symmetry line is an important condition for the formation of trapped mode type resonances. The addition of a symmetry- preserving geometric parameter to a problem which has a discrete embedded trapped mode solution for a specific geometry, tends to lead to a continuous set of trapped modes

Charged Condensate and Helium Dwarf Stars

White dwarf stars composed of carbon, oxygen or heavier elements are expected to crystallize as they cool down below certain temperatures. Yet, simple arguments suggest that the helium white dwarf cores may not solidify, mostly because of zero-point oscillations of the helium ions that would dissolve the crystalline structure. We argue that the interior of the helium dwarfs may instead form a macroscopic quantum state in which the charged helium-4 nuclei are in a Bose-Einstein condensate, while the relativistic electrons form a neutralizing degenerate Fermi liquid. We discuss the electric charge screening, and the spectrum of this substance, showing that the bosonic long-wavelength fluctuations exhibit a mass gap. Hence, there is a suppression at low temperatures of the boson contribution to the specific heat -- the latter being dominated by the specific heat of the electrons near the Fermi surface. This state of matter may have observational signatures.Comment: 10 pages; v2: to appear in JCAP, brief comments and section titles added, typos correcte

Fragmentation Instability of Molecular Clouds: Numerical Simulations

We simulate fragmentation and gravitational collapse of cold, magnetized molecular clouds. We explore the nonlinear development of an instability mediated by ambipolar diffusion, in which the collapse rate is intermediate to fast gravitational collapse and slow quasistatic collapse. Initially uniform stable clouds fragment into elongated clumps with masses largely determined by the cloud temperature, but substantially larger than the thermal Jeans mass. The clumps are asymmetric, with significant rotation and vorticity, and lose magnetic flux as they collapse. The clump shapes, intermediate collapse rates, and infall profiles may help explain observations not easily fit by contemporary slow or rapid collapse models.Comment: 25pp, 20 small eps figures, in press ApJ, April 1, 200