Three dimensional evolution of differentially rotating magnetized neutron stars

We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara (2001). Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding (Shibata et al., 2011) obtained in axisymmetric simulations.Comment: 12 pages, 14 figures, accepted by PR

Stationary field-aligned MHD flows at astropauses and in astrotails. Principles of a counterflow configuration between a stellar wind and its interstellar medium wind

A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. The topological structure determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail region beyond the reverse shock. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows.Comment: 19 pages, 17 figures, accepted for publication in A&

Reconnection at the Heliopause

In this MHD-model of the heliosphere, we assume a Parker-type flow, and a Parker-type spiral magnetic field, which is extrapolated further downstream from the termination shock to the heliopause. We raise the question whether the heliopause nose region may be leaky with respect to fields and plasmas due to nonideal plasma dynamics, implying a breakdown of the magnetic barrier. We analyse some simple scenarios to find reconnection rates and circumstances, under which the heliosphere can be an "open" or a "closed" magnetosphere. We do not pretend to offer a complete solution for the heliosphere, on the basis of nonideal MHD theory, but present a prescription to find such a solution on the basis of potential fields including the knowledge of neutral points. As an example we imitate the Parker spiral as a monopole with a superposition of homogeneous asymptotical boundary conditions. We use this toy model for x < -R where R = 100 AU is the distance of the termination shock to describe the situation in the nose region of the heliopause.Comment: 12 pages, 3 figures, Advances in Space Research (in press

Impulsive phase flare energy transport by large-scale Alfven waves and the electron acceleration problem

The impulsive phase of a solar flare marks the epoch of rapid conversion of energy stored in the pre-flare coronal magnetic field. Hard X-ray observations imply that a substantial fraction of flare energy released during the impulsive phase is converted to the kinetic energy of mildly relativistic electrons (10-100 keV). The liberation of the magnetic free energy can occur as the coronal magnetic field reconfigures and relaxes following reconnection. We investigate a scenario in which products of the reconfiguration - large-scale Alfven wave pulses - transport the energy and magnetic-field changes rapidly through the corona to the lower atmosphere. This offers two possibilities for electron acceleration. Firstly, in a coronal plasma with beta < m_e/m_p, the waves propagate as inertial Alfven waves. In the presence of strong spatial gradients, these generate field-aligned electric fields that can accelerate electrons to energies on the order of 10 keV and above, including by repeated interactions between electrons and wavefronts. Secondly, when they reflect and mode-convert in the chromosphere, a cascade to high wavenumbers may develop. This will also accelerate electrons by turbulence, in a medium with a locally high electron number density. This concept, which bridges MHD-based and particle-based views of a flare, provides an interpretation of the recently-observed rapid variations of the line-of-sight component of the photospheric magnetic field across the flare impulsive phase, and offers solutions to some perplexing flare problems, such as the flare "number problem" of finding and resupplying sufficient electrons to explain the impulsive-phase hard X-ray emission.Comment: 31 pages, 6 figure

Resonant Absorption as Mode Conversion?

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.Comment: 23 pages, 8 figures, 2 tables; accepted by Solar Phys (July 9 2010

Three-dimensional stability of magnetically confined mountains on accreting neutron stars

We examine the hydromagnetic stability of magnetically confined mountains, which arise when material accumulates at the magnetic poles of an accreting neutron star. We extend a previous axisymmetric stability analysis by performing three-dimensional simulations using the ideal-magnetohydrodynamic (ideal-MHD) code \textsc{zeus-mp}, investigating the role played by boundary conditions, accreted mass, stellar curvature, and (briefly) toroidal magnetic field strength. We find that axisymmetric equilibria are susceptible to the undular sub-mode of the Parker instability but are not disrupted. The line-tying boundary condition at the stellar surface is crucial in stabilizing the mountain. The nonlinear three-dimensional saturation state of the instability is characterized by a small degree of nonaxisymmetry (\la 0.1 per cent) and a mass ellipticity of $\epsilon \sim 10^{-5}$ for an accreted mass of $M_a = 10^{-5} M_\odot$. Hence there is a good prospect of detecting gravitational waves from accreting millisecond pulsars with long-baseline interferometers such as Advanced LIGO. We also investigate the ideal-MHD spectrum of the system, finding that long-wavelength poloidal modes are suppressed in favour of toroidal modes in the nonaxisymmetric saturation state.Comment: accepted by MNRA

Global solutions to the three-dimensional full compressible magnetohydrodynamic flows

The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional full magnetohydrodynamic equations with large data is established

Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.Comment: Accepted in Journal of Scientific Computin