The stability of parallel-propagating circularly polarized Alfvén waves revisited

The parametric instability of parallel-propagating circularly polarized Alfven waves (pump waves) is revisited. The stability of these waves is determined by the linearized system of magnetohydrodynamic equations with periodic coefficients. The variable substitution that reduces this system of equations to a system with constant coefficients is suggested. The system with constant coefficients is used to derive the dispersion equation that was previously derived by many authors with the use of different approaches. The dependences of general stability properties on the dimensionless amplitude of the pump wave a and the ratio of the sound and Alfven speed b are studied analytically. It is shown that, for any a and b, there are such quantities k(1) and k(2) that a perturbation with the dimensionless wavenumber k is unstable if k(1)(2) 1, k(1) is a monotonically increasing function of a. For any b, k(1) tends to a limiting value approximately equal to 1.18 as a -> infinity

The central engine of gamma-ray bursters

GRBs are thought to arise in relativistic blast-wave shocks at distances of 10 to 1000 AU from the point where the explosive energy is initially released. To account for the observed duration and variability of the gamma-ray emission in most GRBs, a central engine powering the shocks must remain active for several seconds to many minutes but must strongly fluctuate in its output on much shorter timescales. We show how a neutron star differentially rotating at millisecond periods (DROMP) could be such an engine. A magnetized DROMP would repeatedly wind up toroidal magnetic fields to about 10**17 G and only release the corresponding magnetic energy, when each buoyant magnetic field torus floats up to, and breaks through, the stellar surface. The resulting rapid sub-bursts, separated by relatively quiescent phases, repeat until the kinetic energy of differential rotation is exhausted by these events. Calculated values of the energy released and of the various timescales are in agreement with observations of GRBs. The baryon loading in each sub-burst may also be consistent with theoretical requirements for a blast wave capable of giving the X-ray, optical and radio afterglows recently observed from cosmological distances. DROMPs could be created in several kinds of astrophysical events; some of these would be expected to occur at about the observed GRB rate. The requisite differential rotation could be imparted to neutron stars as they are born or at the end of their existence: some DROMPs may be created close to star forming regions while others may arise far from galaxies.Comment: 6 pages, 1 figur

Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: numerical results

Context.The stability of parallel propagating circularly polarized Alfvén waves (pump waves) has been studied for more than four decades with the use of normal mode analysis. It is well known that the normal mode analysis does not answer the question if a pump wave looks stable or unstable in a particular reference frame. To answer this question it is necessary to find out if the instability is absolute or convective in this reference frame. Aims.We extend our previous study of absolute and convective instabilities of pump waves with small amplitude to pump waves with arbitrary amplitude. Methods.To study the absolute and convective instabilities of pump waves with arbitrary amplitude we numerically implement Brigg's method. Results.We show that the wave is absolutely unstable in a reference frame moving with the velocity U with respect to the rest plasma if U satisfies the inequality Ul Ur) we study the signalling problem. We show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands, and calculate the dependences of the boundaries of these bands on U for different values of a . We also obtain the dependences of the maximum spatial amplification rate on U for different values of a . The implication of these results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft

Slow solitary waves in multi-layered magnetic structures

The propagation of slow sausage surface waves in a multi-layered magnetic configuration is considered. The magnetic configuration consists of a central magnetic slab sandwiched between two identical magnetic slabs (with equilibrium quantities different from those in the central slab) which in turn are embedded between two identical semi-infinite regions. The dispersion equation is obtained in the linear approximation. The nonlinear governing equation describing waves with a characteristic wavelength along the central slab much larger than the slab thickness is derived. Solitary wave solutions to this equation are obtained in the case where these solutions deviate only slightly from the algebraic soliton of the Benjamin-Ono equation

Transverse oscillations of two parallel coronal loops

Context. Collective oscillations of two or more coronal magnetic loops are observed very often. Aims. We study the eigenmodes of oscillations of a system consisting of two parallel magnetic loops. Methods. The linearised MHD equations for a cold plasma are solved analytically in bicylindrical coordinates using the longwavelength approximation. A dispersion equation determining the frequencies of eigenmodes is derived and solved analytically. Results. Two solutions of the dispersion relation were found. The higher frequency corresponds to the antisymmetric mode polarised in the direction parallel to the line connecting the loop centres, and the symmetric mode polarised in the perpendicular direction. Depending on the polarisation of modes corresponding to the lower frequency, the systems of two parallel loops are classified as standard and anomalous. In standard systems the lower frequency corresponds to the symmetric mode polarised in the direction parallel to the line connecting the loop centres, and the antisymmetric mode polarised in the perpendicular direction. In anomalous systems the lower frequency corresponds to the antisymmetric mode polarised in the direction parallel to the line connecting the loop centres, and the symmetric mode polarised in the perpendicular direction. The limiting case of two identical loops is studied. The results for this case are compared with recent numerical results

Cohesive property of magnetized neutron star surfaces: Computations and implications

The cohesive energy of condensed matter in strong magnetic fields is a fundamental quantity characterizing magnetized neutron star surfaces. The cohesive energy refers to the energy required to pull an atom out of the bulk condensed matter at zero pressure. Theoretical models of pulsar and magnetar magnetospheres depend on the cohesive properties of the surface matter in strong magnetic fields. For example, depending on the cohesive energy of the surface matter, an acceleration zone ("polar gap") above the polar cap of a pulsar may or may not form. Also, condensation of the neutron star surface, if it occurs, can significantly affect thermal emission from isolated neutron stars. We describe our calculations of the cohesive property of matter in strong magnetic fields, and discuss the implications of our results to the recent observations of neutron star surface emission as well as to the detection/non-detection of radio emission from magnetars.Comment: 12 pages, 4 figures. Minor changes to Author/Comments fields. To appear in Advances in Space Researc