The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops

The standing quasi modes in a cylindrical incompressible flux tube with magnetic twist that undergoes a radial density structuring is considered in ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae, the dispersion relation for the MHD waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was found that a magnetic twist will increase the frequencies, damping rates and the ratio of the oscillation frequency to the damping rate of these modes. The period ratio P_1/P_2 of the fundamental and its first-overtone surface waves for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve deviations from 2 of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency bandwidth increases with increasing the magnetic twist.Comment: 18 pages, 9 figure

Resonant Cyclotron Scattering and Comptonization in Neutron Star Magnetospheres

Resonant cyclotron scattering of the surface radiation in the magnetospheres of neutron stars may considerably modify the emergent spectra and impede efforts to constraint neutron star properties. Resonant cyclotron scattering by a non-relativistic warm plasma in an inhomogeneous magnetic field has a number of unusual characteristics: (i) in the limit of high resonant optical depth, the cyclotron resonant layer is half opaque, in sharp contrast to the case of non-resonant scattering. (ii) The transmitted flux is on average Compton up-scattered by ~ $1+ 2 beta_T$, where $\beta_T$ is the typical thermal velocity in units of the velocity of light; the reflected flux has on average the initial frequency. (iii) For both the transmitted and reflected fluxes the dispersion of intensity decreases with increasing optical depth. (iv) The emergent spectrum is appreciably non-Plankian while narrow spectral features produced at the surface may be erased. We derive semi-analytically modification of the surface Plankian emission due to multiple scattering between the resonant layers and apply the model to anomalous X-ray pulsar 1E 1048.1--5937. Our simple model fits just as well as the ``canonical'' magnetar spectra model of a blackbody plus power-law.Comment: 37 pages, 10 figures, accepted by MNRAS, minor change

Transition Layer for the Heterogeneous Allen-Cahn Equation

We consider the equation \e^{2}\Delta u=(u-a(x))(u^2-1) in $\Omega$, $\frac{\partial u}{\partial \nu} =0$ on $\partial \Omega$, where $\Omega$ is a smooth and bounded domain in $\R^n$, $\nu$ the outer unit normal to \pa\Omega, and $a$ a smooth function satisfying $-1<a(x)<1$ in \ov{\Omega}. We set $K$, $\Omega_+$ and $\Omega_-$ to be respectively the zero-level set of $a$, {a>0} and {a<0}. Assuming $\nabla a \neq 0$ on $K$ and $a\ne 0$ on $\partial \Omega$, we show that there exists a sequence \e_j \to 0 such that the above equation has a solution u_{\e_j} which converges uniformly to $\pm 1$ on the compact sets of \O_{\pm} as $j \to + \infty$.Comment: 25 page

Missing bits of the solar jigsaw puzzle: small-scale, kinetic effects in coronal studies

The solar corona, anomalously hot outer atmosphere of the Sun, is traditionally described by magnetohydrodynamic, fluid-like approach. Here we review some recent developments when, instead, a full kinetic description is used. It is shown that some of the main unsolved problems of solar physics, such as coronal heating and solar flare particle acceleration can be viewed in a new light when the small-scale, kinetic plasma description methods are used.Comment: 10 pages, 6 figure