Neutral /zero/ Points of Magnetic Fields

Geometry of force-free magnetic field in vicinity of neutral point

Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations

Calculations of spectral darkening and visibility functions for the brightness oscillations of the Sun resulting from global solar oscillations are presented. This has been done for a broad range of the visible and infrared continuum spectrum. The procedure for the calculations of these functions includes the numerical computation of depth-dependent derivatives of the opacity caused by p modes in the photosphere. A radiative-transport code was used for this purpose to get the disturbances of the opacities from temperature and density fluctuations. The visibility and darkening functions are obtained for adiabatic oscillations under the assumption that the temperature disturbances are proportional to the undisturbed temperature of the photosphere. The latter assumption is the only way to explore any opacity effects since the eigenfunctions of p-mode oscillations have not been obtained so far. This investigation reveals that opacity effects have to be taken into account because they dominate the violet and infrared part of the spectrum. Because of this dominance, the visibility functions are negative for those parts of the spectrum. Furthermore, the darkening functions show a wavelength-dependent change of sign for some wavelengths owing to these opacity effects. However, the visibility and darkening functions under the assumptions used contradict the observations of global p-mode oscillations, but it is beyond doubt that the opacity effects influence the brightness fluctuations of the Sun resulting from global oscillations

A New Look at Mode Conversion in a Stratified Isothermal Atmosphere

Recent numerical investigations of wave propagation near coronal magnetic null points (McLaughlin and Hood: Astron. Astrophys. 459, 641,2006) have indicated how a fast MHD wave partially converts into a slow MHD wave as the disturbance passes from a low-beta plasma to a high-beta plasma. This is a complex process and a clear understanding of the conversion mechanism requires the detailed investigation of a simpler model. An investigation of mode conversion in a stratified, isothermal atmosphere, with a uniform, vertical magnetic field is carried out, both numerically and analytically. In contrast to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov: Astron. Astrophys. 112, 16, 1982a; Cally: Astrophys. J. 548, 473, 2001), this paper studies the downward propagation of waves from a low-beta to high-beta environment. A simple expression for the amplitude of the transmitted wave is compared with the numerical solution.Comment: 14 pages, 6 figure

Waves and granulation

Propagation of hydrodynamic waves is considered in frames of the one-dimensional model of granulation. An exact analytical solution of the problem is obtained. The theory is applied only to high-frequency p-modes, because the effect of gravity is neglected. It appears that acoustic waves in a structured atmosphere are not plane ones. Besides, there are hydrodynamic phonon and wave guide wave modes. The results of calculations of the wave functions for high-frequency waves with periods 100–200 s are presented. Upgoing waves are captured in integranular lanes, while downgoing ones are trapped in granules. The effect of wave capture is of greater efficiency for phonon and wave guide modes. The phase velocities of waves differ from the mean sound speed in the photosphere

Three-minute wave enhancement in the solar photosphere

It is a well-known result that the power of five-minute oscillations is progressively reduced by magnetic fields in the solar photosphere. Many authors have pointed out that this fact could be due to a complex interaction of many processes: opacity effects, MHD mode conversion and intrinsic reduced acoustic emissivity in strong magnetic fields. While five-minute oscillations are the dominant component in the photosphere, it has been shown that chromospheric heights are in turn dominated by three-minute oscillations. Two main theories have been proposed to explain their presence based upon resonance filtering in the atmospheric cavity and non linear interactions. In this work we show, through the analysis of IBIS observations of a solar pore in the photospheric Fe I 617.3 nm line, that three-minute waves are already present at the height of formation of this line and that their amplitude depends on the magnetic field strength and is strictly confined in the umbral region.Comment: A&A accepte

MHD waves in sunspots

The review addresses the spatial frequency morphology of sources of sunspot oscillations and waves, including their localization, size, oscillation periods, height localization with the mechanism of cut-off frequency that forms the observed emission variability. Dynamic of sunspot wave processes, provides the information about the structure of wave fronts and their time variations, investigates the oscillation frequency transformation depending on the wave energy is shown. The initializing solar flares caused by trigger agents like magnetoacoustic waves, accelerated particle beams, and shocks are discussed. Special attention is paid to the relation between the flare reconnection periodic initialization and the dynamics of sunspot slow magnetoacoustic waves. A short review of theoretical models of sunspot oscillations is provided.Comment: 20 pages, 6 figures, Chapter in AGU Monograph (in press), Review articl

Magneto-acoustic waves in sunspots: first results from a new 3D nonlinear magnetohydrodynamic code

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional non-linear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here we present the first results of such modeling. We have developed a 3D non-linear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-dimensional mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfv\'en wave, by calculation of the wave energy fluxes. Our main findings are the following: (1) the conversion from acoustic to the Alfv\'en mode is only observed if the the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cut-off effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level beta=1; (3) waves with frequencies above the cut-off propagate field-aligned to the chromosphere and their power becomes dominating over that of evanescent 5-minute oscillations, in agreement with observations

Dynamics of the Solar Magnetic Network. II. Heating the Magnetized Chromosphere

We consider recent observations of the chromospheric network, and argue that the bright network grains observed in the Ca II H & K lines are heated by an as yet unidentified quasi-steady process. We propose that the heating is caused by dissipation of short-period magnetoacoustic waves in magnetic flux tubes (periods less than 100 s). Magnetohydrodynamic (MHD) models of such waves are presented. We consider wave generation in the network due to two separate processes: (a) by transverse motions at the base of the flux tube; and (b) by the absorption of acoustic waves generated in the ambient medium. We find that the former mechanism leads to an efficient heating of the chromosphere by slow magnetoacoustic waves propagating along magnetic field lines. This heating is produced by shock waves with a horizontal size of a few hundred kilometers. In contrast, acoustic waves excited in the ambient medium are converted into transverse fast modes that travel rapidly through the flux tube and do not form shocks, unless the acoustic sources are located within 100 km from the tube axis. We conclude that the magnetic network may be heated by magnetoacoustic waves that are generated in or near the flux tubes.Comment: 30 pages, 8 figures, Accepted in Astrophysical Journa

Buoyancy-driven Magnetohydrodynamic Waves

Turbulent motions close to the visible solar surface may generate low-frequency internal gravity waves (IGWs) that propagate through the lower solar atmosphere. Magnetic activity is ubiquitous throughout the solar atmosphere, so it is expected that the behavior of IGWs is to be affected. In this article we investigate the role of an equilibrium magnetic field on propagating and standing buoyancy oscillations in a gravitationally stratified medium. We assume that this background magnetic field is parallel to the direction of gravitational stratification. It is known that when the equilibrium magnetic field is weak and the background is isothermal, the frequencies of standing IGWs are sensitive to the presence of magnetism. Here, we generalize this result to the case of a slowly varying temperature. To do this, we make use of the Boussinesq approximation. A comparison between the hydrodynamic and magnetohydrodynamic cases allows us to deduce the effects due to a magnetic field. It is shown that the frequency of IGWs may depart significantly from the Brunt–Väisälä frequency, even for a weak magnetic field. The mathematical techniques applied here give a clearer picture of the wave mode identification, which has previously been misinterpreted. An observational test is urged to validate the theoretical findings