Multiwavelength studies of MHD waves in the solar chromosphere: An Overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.

Observations of ubiquitous compressive waves in the Sun's chromosphere

The details of the mechanism(s) responsible for the observed heating and dynamics of the solar atmosphere still remain a mystery. Magnetohydrodynamic waves are thought to have a vital role in this process. Although it has been shown that incompressible waves are ubiquitous in off-limb solar atmospheric observations, their energy cannot be readily dissipated. Here we provide, for the first time, on-disk observation and identification of concurrent magnetohydrodynamic wave modes, both compressible and incompressible, in the solar chromosphere. The observed ubiquity and estimated energy flux associated with the detected magnetohydrodynamic waves suggest the chromosphere is a vast reservoir of wave energy with the potential to meet chromospheric and coronal heating requirements. We are also able to propose an upper bound on the flux of the observed wave energy that is able to reach the corona based on observational constraints, which has important implications for the suggested mechanism(s) for quiescent coronal heating. © 2012 Macmillan Publishers Limited. All rights reserved.

Alfvén Waves in the Solar Atmosphere: From Theory to Observations

Alfvén waves are considered to be viable transporters of the non-thermal energy required to heat the Sun's quiescent atmosphere. An abundance of recent observations, from state-of-the-art facilities, have reported the existence of Alfvén waves in a range of chromospheric and coronal structures. Here, we review the progress made in disentangling the characteristics of transverse kink and torsional linear magnetohydrodynamic (MHD) waves. We outline the simple, yet powerful theory describing their basic properties in (non-)uniform magnetic structures, which closely resemble the building blocks of the real solar atmosphere.

The Dynamics of Rapid Redshifted and Blueshifted Excursions in the Solar Hα Line

We analyze high temporal and spatial resolution time-series of spectralscans of the Hα line obtained with the CRisp Imaging SpectroPolarimeter instrument mounted on the Swedish Solar Telescope.The data reveal highly dynamic, dark, short-lived structures known asRapid Redshifted and Blueshifted Excursions (RREs, RBEs) that areon-disk absorption features observed in the red and blue wings ofspectral lines formed in the chromosphere. We study the dynamics of RREsand RBEs by tracking their evolution in space and time, measuring thespeed of the apparent motion, line of sight (LOS) Doppler velocity, andtransverse velocity of individual structures. A statistical study oftheir measured properties shows that RREs and RBEs have similaroccurrence rates, lifetimes, lengths, and widths. They also displaynon-periodic, nonlinear transverse motions perpendicular to their axesat speeds of 4-31 km s-1. Furthermore, both typesof structures either appear as high speed jets and blobs that aredirected outwardly from a magnetic bright point with speeds of50-150 km s-1, or emerge within a few seconds. Astudy of the different velocity components suggests that the transversemotions along the LOS of the chromospheric flux tubes are responsiblefor the formation and appearance of these redshifted/blueshiftedstructures. The short lifetime and fast disappearance of the RREs/RBEssuggests that, similar to type II spicules, they are rapidly heated totransition region or even coronal temperatures. We speculate that theKelvin-Helmholtz instability triggered by observed transversemotions of these structures may be a viable mechanism for their heating.

Propagating waves and magnetohydrodynamic mode coupling in the quiet-sun network

High-cadence multiwavelength optical observations were taken with the Dunn Solar Telescope at the National Solar Observatory, Sacramento Peak, accompanied by Advanced Stokes Polarimeter vector magnetograms. A total of 11 network bright points (NBPs) have been studied at different atmospheric heights using images taken in wave bands centered on Mg I b(1) - 0.4 Angstrom, Halpha, and Ca II K-3. Wavelet analysis was used to study wave packets and identify traveling magnetohydrodynamic waves. Wave speeds were estimated through the temporal cross-correlation of signals, in selected frequency bands of wavelet power, in each wavelength. Four mode-coupling cases were identified, one in each of four of the NBPs, and the variation of the associated Fourier power with height was studied. Three of the detected mode-coupling, transverse-mode frequencies were observed in the 1.2-1.6 mHz range (mean NBP apparent flux density magnitudes over 99-111 Mx cm(-2)), with the final case showing 2.0-2.2 mHz (with 142 Mx cm(-2)). Following this, longitudinal-mode frequencies were detected in the range 2.6-3.2 mHz for three of our cases, with 3.9-4.1 mHz for the remaining case. After mode coupling, two cases displayed a decrease in longitudinal-mode Fourier power in the higher chromosphere.

Similarities between ion waves in plasmas and gravity waves in incompressible fluids

Some similarities between ion waves in plasmas and gravity waves in incompressible fluids are investigated. It is shown that for zero ion temperature the ion-wave dispersion relation is similar to that of gravity waves in a stratified liquid between rigid, horizontal walls; for large wavelength the ion waves behave as the surface gravity waves of shallow-water theory. The general character of the pattern of ion waves arising in steady plasma flows is analyzed for arbitrary ion temperature, wavelength, and acoustic mach number (which is based on the ion-acoustic speed), and is compared to the pattern of surface gravity waves in steady water flows when surface tension is taken into account.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Predicting Australian adults' sun-safe behaviour : examining the role of personal and social norms

Objectives To address the scarcity of comprehensive, theory-based research in the Australian context, this study, using a theory of planned behaviour (TPB) framework, investigated the role of personal and social norms to identify the key predictors of adult Australians' sun-safe intentions and behaviour. Design The study used a prospective design with two waves of data collection, 1 week apart. Methods Participants were 816 adults (48.2% men) aged between 18 and 88 years recruited from urban, regional, and rural areas of Australia. At baseline, participants completed a questionnaire assessing the standard TPB predictors (attitude, subjective norm, and perceived behavioural control [PBC]), past behaviour, behavioural intention, and additional measures of group norm for the referent groups of friends and family, image norm, personal norm, personal choice/responsibility, and Australian identity. Seventy-one per cent of the participants (n = 577) reported on their sun-safe behaviour in the subsequent week. Results Via path modelling, past behaviour, attitude, group norm (friends), personal norm, and personal choice/responsibility emerged as independent predictors of intentions which, in turn, predicted sun-safe behaviour prospectively. Past behaviour, but not PBC, had direct effects on sun-safe behaviour. The model explained 61.6% and 43.9% of the variance in intention and behaviour, respectively. Conclusions This study provides support for the use of a comprehensive theoretical decision-making model to explain Australian adults' sun-safe intentions and behaviours and identifies viable targets for health-promoting messages in this high-risk context.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Accelerating Waves in Polar Coronal Holes as Seen by EIS and SUMER

We present EIS/Hinode and SUMER/SOHO observations of propagating disturbances detected in coronal lines in inter-plume and plume regions of a polar coronal hole. The observation was carried out on 2007 November 13 as part of the JOP196/HOP045 program. The SUMER spectroscopic observation gives information about fluctuations in radiance and on both resolved (Doppler shift) and unresolved (Doppler width) line-of-sight velocities, whereas EIS 40 `'wide slot images detect fluctuations only in radiance but maximize the probability of overlapping field of view between the two instruments. From distance-time radiance maps, we detect the presence of propagating waves in a polar inter-plume region with a period of 15-20 minutes and a propagation speed increasing from 130 +/- 14 km s(-1) just above the limb to 330 +/- 140 km s(-1) around 160 `' above the limb. These waves can be traced to originate from a bright region of the on-disk part of the coronal hole where the propagation speed is in the range of 25 +/- 1.3 to 38 +/- 4.5 km s(-1), with the same periodicity. These on-disk bright regions can be visualized as the base of the coronal funnels. The adjacent plume region also shows the presence of propagating disturbances with the same range of periodicity but with propagation speeds in the range of 135 +/- 18 to 165 +/- 43 km s(-1) only. A comparison between the distance-time radiance map of the two regions indicates that the waves within the plumes are not observable (may be getting dissipated) far off-limb, whereas this is not the case in the inter-plume region. A correlation analysis was also performed to find out the time delay between the oscillations at several heights in the off-limb region, finding results consistent with those from the analysis of the distance-timemaps. To our knowledge, this result provides first spectroscopic evidence of the acceleration of propagating disturbances in the polar region close to the Sun (within 1.2 R/R-circle dot), which provides clues to the understanding of the origin of these waves. We suggest that the waves are likely either Alfvenic or fast magnetoacoustic in the inter-plume region and slow magnetoacoustic in the plume region. This may lead to the conclusion that inter-plumes are a preferred channel for the acceleration of the fast solar wind.

On the possibility of an alpha-sq omega-type dynamo in a thin layer inside the sun

If the solar dynamo operates in a thin layer of 10,000-km thickness at the interface between the convection zone and the radiative core, using the facts that the dynamo should have a period of 22 years and a half-wavelength of 40 deg in the theta-direction, it is possible to impose restrictions on the values which various dynamo parameters are allowed to have. It is pointed out that the dynamo should be of alpha-sq omega nature, and kinematical calculations are presented for free dynamo waves and for dynamos in thin rectangular slabs with appropriate boundary conditions. An alpha-sq omega dynamo is expected to produce a significant poloidal field which does not leak to the solar surface. It is found that the turbulent diffusity eta and alpha-coefficient are restricted to values within about a factor of 10, the median values being eta of about 10 to the 10th sq cm/sec and alpha of about 10 cm/sec. On the basis of mixing length theory, it is pointed out that such values imply a reasonable turbulent velocity of the order 30 m/s, but rather small turbulent length scales like 300 km.

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Propagating MHD Waves in Coronal Holes

Coronal holes are the coolest and darkest regions of the upper solar atmosphere, as observed both on the solar disk and above the solar limb. Coronal holes are associated with rapidly expanding open magnetic fields and the acceleration of the high-speed solar wind. During the years of the solar minima, coronal holes are generally confined to the Sun's polar regions, while at solar maxima they can also be found at lower latitudes. Waves, observed via remote sensing and detected in-situ in the wind streams, are most likely responsible for the wind and several theoretical models describe the role of MHD waves in the acceleration of the fast solar wind. This paper reviews the observational evidences of detection of propagating waves in these regions. The characteristics of the waves, like periodicities, amplitude, speed provide input parameters and also act as constraints on theoretical models of coronal heating and solar wind acceleration.