Gravitational and magnetosonic waves in gamma-ray bursts

One of the possible sources of gamma-ray bursts are merging, compact neutronstar binaries. More than 90% of the binding energy of such a binary is released in the form of gravitational waves (GWs) in the last few seconds of the spiral-in phase before the formation of a black hole. In this article we investigate whether a fraction of this GW-energy is transferred to magnetohydrodynamic waves in the magnetized plasma wind around the binary. Using the 3+1 orthonormal tedrad formalism, we study the propagation of a monochromatic, plane fronted, linearly polarized GW perpendicular to the ambient magnetic field in an ultra-relativistic wind, first in the comoving and then in the observer frame. A closed set of general relativistic magnetohydrodynamic equations is derived in the form of conservation laws for electric charge, matter energy, momentum and magnetic energy densities. We linearize these equations under the action of a monochromatic GW, which acts as a driver and find that fast magneto-acoustic waves grow, with amplitudes proportional to the GW amplitude and frequency and the strength of the background magnetic field.Comment: Accepted for publication in Astronomy & Astrophysics (A&A). 7 pages, 1 figur

On the contribution of exchange interactions to the Vlasov equation

Exchange effects play an important role in determining the equilibrium properties of dense matter systems, as well as for magnetic phenomena. There exists an extensive literature concerning, e.g., the effects of exchange interactions on the equation of state of dense matter. Here, a generalization of the Vlasov equation to include exchange effects is presented allowing for electromagnetic mean fields, thus incorporating some of the dynamic effects due to the exchange interactions. Treating the exchange term perturbatively, the correction to classical Langmuir waves in plasmas is found, and the results are compared with previous work. It is noted that the relative importance of exchange effects scales similarly with density and temperature as particle dispersive effects, but that the overall magnitude is sensitive to the details of the specific problem. The implications of our results are discussed.Comment: 9 page

A linearized kinetic theory of spin-1/2 particles in magnetized plasmas

We have considered linear kinetic theory including the electron spin properties in a magnetized plasma. The starting point is a mean field Vlasov-like equation, derived from a fully quantum mechanical treatment, where effects from the electron spin precession and the magnetic dipole force is taken into account. The general conductivity tensor is derived, including both the free current contribution, as well as the magnetization current associated with the spin contribution. We conclude the paper with an extensive discussion of the quantum-mechanical boundary where we list parameter conditions that must be satisfied for various quantum effects to be influential.Comment: 11 page

Spin induced nonlinearities in the electron MHD regime

We consider the influence of the electron spin on the nonlinear propagation of whistler waves. For this purpose a recently developed electron two-fluid model, where the spin up- and down populations are treated as different fluids, is adapted to the electron MHD regime. We then derive a nonlinear Schrodinger equation for whistler waves, and compare the coefficients of nonlinearity with and without spin effects. The relative importance of spin effects depend on the plasma density and temperature as well as the external magnetic field strength and the wave frequency. The significance of our results to various plasmas are discussed.Comment: 5 page

Nonlinear wave interaction and spin models in the MHD regime

Here we consider the influence on the electron spin in the MHD regime. Recently developed models which include spin-velocity correlations are taken as a starting point. A theoretical argument is presented, suggesting that in the MHD regime a single fluid electron model with spin correlations is equivalent to a model with spin-up and spin-down electrons constituting different fluids, but where the spin-velocity correlations are omitted. Three wave interaction of 2 shear Alfven waves and a compressional Alfven wave is then taken as a model problem to evaluate the asserted equivalence. The theoretical argument turns out to be supported, as the predictions of the two models agree completely. Furthermore, the three wave coupling coefficients obey the Manley-Rowe relations, which give further support to the soundness of the models and the validity of the assumptions made in the derivation. Finally we point out that the proposed two-fluid model can be incorporated in standard Particle-In-Cell schemes with only minor modifications.Comment: 8 page

Nonlinear coupled Alfv\'{e}n and gravitational waves

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field, and the coupling to compressional Alfv\'{e}n waves. The gravitational waves are considered in the high frequency limit and the plasma is modelled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schr\"{o}dinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected.Comment: 20 pages, revtex4, accepted in PR

Circularly polarized waves in a plasma with vacuum polarization effects

The theory for large amplitude circularly polarized waves propagating along an external magnetic field is extended in order to include also vacuum polarization effects. A general dispersion relation, which unites previous results, is derived.Comment: 5 pages (To appear in Physics of Plasmas