MHD Wave Modes Resolved in Fine-Scale Chromospheric Magnetic Structures

Due to its complex and dynamic fine-scale structure, the chromosphere is a particularly challenging region of the Sun's atmosphere to understand. It is now widely accepted that to model chromospheric dynamics, even on a magnetohydrodynamic (MHD) scale, while also calculating spectral line emission, one must realistically include the effects of partial ionization and radiative transfer in a multi-fluid plasma under non-LTE conditions. Accurate quantification of MHD wave energetics must befounded on a precise identification of the actual wave mode being observed. This chapter focuses on MHD kink-mode identification, MHD sausage mode identification, and MHD torsional Alfvén wave identification. It then reviews progress in determining more accurate energy flux estimations of specific MHD wave modes observed in the chromosphere. The chapter finally examines how the discovery of these MHD wave modes has helped us advance the field of chromosphericmagnetoseismology.

Ultra-High-Resolution Observations of MHD Waves in Photospheric Magnetic Structures

This chapter reviews the recent observations of waves and oscillations manifesting in fine-scale magnetic structures in the solar photosphere, which are often interpreted as the "building blocks' of the magnetic Sun. The authors found, through phase relationships between the various waveforms, that small-scale magnetic bright points (MBPs) in the photosphere demonstrated signatures of specific magnetoacoustic waves, in particular the sausage and kink modes. Modern magnetohydrodynamic (MHD) simulations of the lower solar atmosphere clearly show how torsional motions can easily be induced in magnetic elements in the photosphere through the processes of vortical motions and/or buffeting by neighboring granules. The authors detected significant power associated with high-frequency horizontal motions, and suggested that these cases may be especially important in the creation of a turbulent environment that efficiently promotes Alfvén wave dissipation.

The periodic variations of a white-light flare observed with ULTRACAM

High time resolution observations of a white-light flare on the active star EQ PegB show evidence of intensity variations with a period of ≈10 s. The period drifts to longer values during the decay phase of the flare. If the oscillation is interpreted as an impulsively-excited, standing-acoustic wave in a flare loop, the period implies a loop length of ≈3.4 Mm and ≈6.8 Mm for the case of the fundamental mode and the second harmonic, respectively. However, the small loop lengths imply a very high modulation depth making the acoustic interpretation unlikely. A more realistic interpretation may be that of a fast-MHD wave, with the modulation of the emission being due to the magnetic field. Alternatively, the variations could be due to a series of reconnection events. The periodic signature may then arise as a result of the lateral separation of individual flare loops or current sheets with oscillatory dynamics (i.e., periodic reconnection).

Eclipse observations of high-frequency oscillations in active region coronal loops

One of the mechanisms proposed for heating the corona above solar active regions is the damping of magnetohydrodynamic (MHD) waves. Continuing on previous work, we provide observational evidence for the existence of high-frequency MHD waves in coronal loops observed during the August 1999 total solar eclipse. A wavelet analysis is used to identify twenty 4 x 4 arcsec(2) areas showing intensity oscillations. All detections lie in the frequency range 0.15 - 0.25 Hz (7 - 4 s), last for at least 3 periods at a confidence level of more than 99% and arise just outside known coronal loops. This leads us to suggest that they occur in low emission-measure or different temperature loops associated with the active region.

Transition region velocity oscillations observed by EUNIS-06

Spectroscopic measurements of NOAA AR 10871, obtained with the Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS) sounding rocket instrument on 2006 April 12, reveal velocity oscillations in the He II 303.8 angstrom emission line formed at T approximate to 5; 10(4) K. The oscillations appear to arise in a bright active region loop arcade about 25 '' wide which crosses the EUNIS slit. The period of these transition region oscillations is 26 +/- 4 s, coupled with a velocity amplitude of +/- 10 km s(-1), detected over four complete cycles. Similar oscillations are observed in lines formed at temperatures up to T approximate to 4; 10(5) K, but we find no evidence for the coupling of these velocity oscillations with corresponding phenomena in the corona. We interpret the detected oscillations as originating from an almost purely adiabatic plasma, and infer that they are generated by the resonant transmission of MHD waves through the lower active region atmospheres. Through the use of seismological techniques, we establish that the observed velocity oscillations display wave properties most characteristic of fast body global sausage modes.

Vorticity in the solar photosphere

Aims. We use magnetic and non-magnetic 3D numerical simulations of solar granulation and G-band radiative diagnostics from the resulting models to analyse the generation of small-scale vortex motions in the solar photosphere.
Methods. Radiative MHD simulations of magnetoconvection are used to produce photospheric models. Our starting point is a non-magnetic model of solar convection, where we introduce a uniform magnetic field and follow the evolution of the field in the simulated photosphere. We find two different types of photospheric vortices, and provide a link between the vorticity generation and the presence of the intergranular magnetic field. A detailed analysis of the vorticity equation, combined with the G-band radiative diagnostics, allows us to identify the sources and observational signatures of photospheric vorticity in the simulated photosphere.
Results. Two different types of photospheric vorticity, magnetic and non-magnetic, are generated in the domain. Non-magnetic vortices are generated by the baroclinic motions of the plasma in the photosphere, while magnetic vortices are produced by the magnetic tension in the intergranular magnetic flux concentrations. The two types of vortices have different shapes. We find that the vorticity is generated more efficiently in the magnetised model. Simulated G-band images show a direct connection between magnetic vortices and rotary motions of photospheric bright points, and suggest that there may be a connection between the magnetic bright point rotation and small-scale swirl motions observed higher in the atmosphere.

Low-frequency electromagnetic waves in a Hall-magnetohydrodynamic plasma with charged dust macroparticles

A linear theory for intermediate-frequency [much smaller (larger) than the electron gyrofrequency (dust plasma and dust gyrofrequencies)], long wavelength (in comparison with the ion gyroradius and the electron skin depth) electromagnetic waves in a multicomponent, homogeneous electron-ion-dust magnetoplasma is presented. For this purpose, the generalized Hall-magnetohydrodynamic (GH-MHD) equations are derived for the case with immobile charged dust macroparticles. The GH-MHD equations in a quasineutral plasma consist of the ion continuity equation, the generalized ion momentum equation, and Faraday's law with the Hall term. The GH-MHD equations are Fourier transformed and combined to obtain a general dispersion relation. The latter is analyzed to understand the influence of immobile charged dust grains on various electromagnetic wave modes in a magnetized dusty plasma. (C) 2005 American Institute of Physics.

Linear and nonlinear properties of Rao-dust-Alfven waves in magnetized plasmas

The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampere's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schrodinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed. (C) 2004 American Institute of Physics.

Photospheric magnetic vortex structures

Using direct numerical magneto-hydrodynamic (MHD) simulations, we demonstrate the evidence of two physically different types of vortex motions in the solar photosphere. Baroclinic motions of plasma in non-magnetic granules are the primary source of vorticity in granular regions of the solar photosphere, however, there is a significantly more efficient mechanism of vorticity production in strongly magnetised intergranular lanes. These swirly motions of plasma in intergranular magnetic field concentrations could be responsible for the generation of different types of MHD wave modes, for example, kink, sausage and torsional Alfven waves. These waves could transport a relevant amount of energy from the lower solar atmosphere and contribute to coronal plasma heating.

Search for Rapid Changes in the Visible-Light Corona during the 21 June 2001 Total Solar Eclipse

Some 8000 images obtained with the Solar Eclipse Coronal Imaging System (SECIS) fast-frame CCD camera instrument located at Lusaka, Zambia, during the total eclipse of 21 June 2001 have been analysed to search for short-period oscillations in intensity that could be a signature of solar coronal heating mechanisms by MHD wave dissipation. Images were taken in white-light and Fe xiv green-line (5303 ) channels over 205 seconds (frame rate 39 s(-1)), approximately the length of eclipse totality at this location, with a pixel size of four arcseconds square. The data are of considerably better quality than those that we obtained during the 11 August 1999 total eclipse (Rudawy et al.: Astron. Astrophys. 416, 1179, 2004), in that the images are much better exposed and enhancements in the drive system of the heliostat used gave a much improved image stability. Classical Fourier and wavelet techniques have been used to analyse the emission at 29 518 locations, of which 10 714 had emission at reasonably high levels, searching for periodic fluctuations with periods in the range 0.1 -aEuro parts per thousand 17 seconds (frequencies 0.06 -aEuro parts per thousand 10 Hz). While a number of possible periodicities were apparent in the wavelet analysis, none of the spatially and time-limited periodicities in the local brightness curves was found to be physically important. This implies that the pervasive Alfv,n wave-like phenomena (Tomczyk et al.: Science 317, 1192, 2007) using polarimetric observations with the Coronal Multi-Channel Polarimeter (CoMP) instrument do not give rise to significant oscillatory intensity fluctuations.

Propagating Wave Phenomena Detected in Observations and Simulations of the Lower Solar Atmosphere

We present high-cadence observations and simulations of the solar photosphere, obtained using the Rapid Oscillations in the Solar Atmosphere imaging system and the MuRAM magnetohydrodynamic (MHD) code, respectively. Each data set demonstrates a wealth of magnetoacoustic oscillatory behavior, visible as periodic intensity fluctuations with periods in the range 110–600 s. Almost no propagating waves with periods less than 140 s and 110 s are detected in the observational and simulated data sets, respectively. High concentrations of power are found in highly magnetized regions, such as magnetic bright points and intergranular lanes. Radiative diagnostics of the photospheric simulations replicate our observational results, confirming that the current breed of MHD simulations are able to accurately represent the lower solar atmosphere. All observed oscillations are generated as a result of naturally occurring magnetoconvective processes, with no specific input driver present. Using contribution functions extracted from our numerical simulations, we estimate minimum G-band and 4170 Å continuum formation heights of 100 km and 25 km, respectively. Detected magnetoacoustic oscillations exhibit a dominant phase delay of −8◦ between the G-band and 4170 Å continuum observations, suggesting the presence of upwardly propagating waves.More than 73% of MBPs (73% from observations and 96% from simulations) display upwardly propagating wave phenomena, suggesting the abundant nature of oscillatory behavior detected higher in the solar atmosphere may be traced back to magnetoconvective processes occurring in the upper layers of the Sun’s convection zone.

Observations of Sausage Modes in Magnetic Pores

We present here evidence for the observation of the magnetohydrodynamic (MHD) sausage modes in magnetic pores in the solar photosphere. Further evidence for the omnipresent nature of acoustic global modes is also found. The empirical decomposition method of wave analysis is used to identify the oscillations detected through a 4170 Å "blue continuum" filter observed with the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument. Out of phase, periodic behavior in pore size and intensity is used as an indicator of the presence of magnetoacoustic sausage oscillations. Multiple signatures of the magnetoacoustic sausage mode are found in a number of pores. The periods range from as short as 30 s up to 450 s. A number of the magnetoacoustic sausage mode oscillations found have periods of 3 and 5 minutes, similar to the acoustic global modes of the solar interior. It is proposed that these global oscillations could be the driver of the sausage-type magnetoacoustic MHD wave modes in pores.

New generalized dispersion relation for low-frequency electromagnetic waves in Hall-magnetohydrodynamic dusty plasma

A generalized linear theory for electromagnetic waves in a homogeneous dusty magnetoplasma is presented. The waves described are characterized by a frequency which is much smaller (larger) than the electron gyrofrequency (dust plasma and dust gyrofrequencies), and a long wavelength (in comparison with the ion gyroradius and the electron skin depth). The generalized Hall- magnetohydrodynamic (GH-MHD) equations are derived by assuming massive charged dust macroparticles to be immobile, and Fourier transformed to obtain a general dispersion relation. The latter is analyzed to understand the influence of immobile charged dust grains on various electromagnetic wave modes in a magnetized dusty plasma.

Refined Magnetoseismological Technique for the Solar Corona

We present a step-by-step guide of a refined magnetoseismological technique for plasma diagnostics in the Sun’s corona. Recently developed MHD wave theory which models a coronal loop as an expanding magnetic flux tube with an arbitrary longitudinal plasma density profile is applied to TRACE observations of fast kink
oscillations. The theory predicts that using the observed ratio of the first overtone and fundamental mode to predict the plasma density scale height and not taking account of loop expansion will lead to an overestimation of scale height. For the first time, the size of this correction is quantified directly from observation and for the particular case study presented here, it is found that the overestimation is approximately by a factor of 2.

A filamentation instability for streaming cosmic rays

We demonstrate that cosmic rays form filamentary structures in the precursors of supernova remnant shocks due to their self-generated magnetic fields. The cosmic ray filamentation results in the growth of a long-wavelength instability, and naturally couples the rapid non-linear amplification on small scales to larger length-scales. Hybrid magnetohydrodynamics-particle simulations are performed to confirm the effect. The resulting large-scale magnetic field may facilitate the scattering of high-energy cosmic rays as required to accelerate protons beyond the knee in the cosmic ray spectrum at supernova remnant shocks. Filamentation far upstream of the shock may also assist in the escape of cosmic rays from the accelerator.