Solar Wave Theory Group (SWAT)


Main overview

SWAT has grown out of the research activities of one of the SG awards (PI RvFS, PDRAs Fedun and Shelyag) after the split of the RG offer in March 2008 and the subsuming of the recent SG award (PI: MSR, PDRA Taroyan). We have further strengthened our on-going and proposed research on the coupling of the magnetized solar atmosphere, in particular on (i) the over-arching coupling mechanisms from near sub-photosphere to corona; (ii) the heating processes in the corona; (iii) small-scale dynamics and diagnostics of the atmosphere; (iv) developing MHD wave theory and magneto-seismology with applications to solar waveguides and (v) studies of solar Alfvn waves. We combine analytical theory, intensive forward MHD simulations, and data analysis (e.g. inversion) from ground- (Swedish Solar Telescope, Dunn Solar Telescope) and space-based (SoHO, TRACE, STEREO, Hinode) instrumentation. We strongly believe that a most promising advancement can be achieved when combining these three approaches. We ensure that a wide breadth of expertise, covering these methodologies, is acquired in our RA and PhD training.

Aims and objectives | Main highlights in recent years by RA: Fedun, Shelyag, Taroyan, Verth | Advancing the field | Work Packages | Expected major outcomes

Aims and objectives

Our research strategy matches well STFCs Strategy for Solar System Science 2006-16. We address one of the main three questions of solar system science of the Roadmap: "How does the Sun affect the Earth?" "Solving these general problems demands understanding of the physical processes at work in the Sun and their variation in time; the resulting solar output in the form of radiation, particles, and magnetic fields, and the details of the coupling of this output.." summarizes perfectly the Themes objectives. In particular, T1 attempts to answer the specific Roadmap questions: "What is the structure of the Sun, from its core to the outer corona and how are different regions coupled in terms of magnetic fields, dynamics and mass and energy transfer?; "What processes heat the corona, and how are they reflected in their dynamics, morphology and composition?"; and "How does energy couple..., and on what spatial and temporal scales?". To answer we try to understand the underlying physical processes through six strongly inter-linked Work Packages outlined below.

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Main highlights in recent years: a brief account of the key results by the named RAs.


(i) Large-amplitude MHD waves are routinely observed in space plasmas. Fedun et al. (PLA 2008) showed that dispersive focusing, known for the excitation of freak waves in oceans, can be responsible for the generation of short-lived large-amplitude MHD waves in space plasmas. They obtained an analytical solution of the linearized DNLS equation governing the excitation of large-amplitude MHD waves from small-amplitude wave trains due to dispersive focusing. His numerical simulations of the full DNLS equation confirm this fundamental result. (ii) Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun's interior, throughout the solar atmosphere and interplanetary space up to a wide range of applications to astrophysical plasmas. Erdélyi & Fedun (Solphys 2006) obtained the dispersion equation and solution for incompressible cylindrical waveguides embedded in twisted fields for sausage modes. Generalization to compressible plasma for sausage, kink and fluting modes is in Erdélyi & Fedun (Solphys 2007, 2009 subm). The results are relevant for magneto-seismologic studies of oscillating solar waveguides. (iii) Erdélyi & Fedun (Science 2007) shows the role of chromospheric magnetic field interaction with global solar oscillations. The numerical simulations reveal that oscillations, driven by global photospheric motions, are in fact kink modes, rather than Alfvén waves. (iv) A theory of the large-amplitude mirror type waves in non-Maxwellian space plasmas is developed. The equation governing the nonlinear dynamics of mirror waves near instability threshold is derived. The formation of solitary structures and their nonlinear dynamics has been analyzed both analytically and numerically (JGR 2008). (v) The new MHD code SAC (Sheffield Advanced Code) suitable for 3-D simulation is developed in collaboration with Shelyag (A&A 2008). Variable separation, numerical resistivity and diffusivity techniques are applied to ensure stability of the computed solution of the MHD equations in strongly stratified plasmas.

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(i) was able to demonstrate the magnetic nature of the photospheric G-band bright points (Shelyag et al., A&A, 2004), and to evaluate the effect of magnetic fields in polarimetric observations of the photosphere (Shelyag et al., A&A, 2007). (ii) Forward modelling of the quiet solar sub-photosphere was carried out to recover basic helioseismological properties, e.g. solar acoustic spectrum and time-distance diagrams (Shelyag et al., ApJ, 2006). Excellent agreement between simulations and the standard solar spectrum has been found, confirming forward modelling in helioseismology. As an application, the effect of flows embedded in the convection zone and sub-photosphere was also analysed (Shelyag et al., A&A, 2007). Measurable acoustic wave phase shifts and the corresponding wave packet propagation time differences caused by the bulk flows were predicted at solar surface. (iii) Another application was to validate the ray approximation inversion technique frequently used for observational data (Shelyag et al., A&A, 2007). It has been shown that the ray approximation inversion leads to systematic errors in the flow profiles in the sub-photosphere. (iv) Finally, a novel fully non-linear MHD code, called the Sheffield Advanced Code (SAC), designed for simulations of wave propagation in gravitationally strongly stratified media with the employment of hyper-diffusivity and hyper-resistivity stabilisation methods, has been developed and tested successfully (Shelyag, Fedun, Erdélyi, A&A, 2008). Using SAC for complex, and extremely CPU and storage intensive simulations of wave propagation and mode conversion from the photosphere to corona (Fedun, Erdélyi, Shelyag, Solar Physics, 2009), we confirmed the acoustic wave leakage in 3-D.The effect of magnetic tension in non-uniform sunspot-like localised magnetic field concentrations embedded in the gravitationally stratified solar sub-photospheric plasma was analysed (Shelyag et al., A&A, 2009). It was shown that the acoustic travel time differences depend on the magnetic field strength and geometry both directly (through mode conversion) and indirectly (through the changes in the thermal structure by the magnetic field in the simulated sunspots).

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(i) proposed a novel heating diagnostic technique for quiescent coronal loops based on the analysis of power spectra of Doppler shift time series (Taroyan et al., A&A, 2007). Studying the first two modes of oscillations allowed uniformly heated loops to be distinguished from loops heated at their footpoints! This is a very important result in light of the ongoing long debate as to how loops are heated. The method improves our understanding of the role of small-scale releases of energy in coronal heating, and may settle the observed ambiguity of power-law index for heating occurrence rate (for future work see WP200 below). (ii) An example of hot active region loop oscillations observed by SoHO/SUMER and Yohkoh/SXT was examined. The existence of standing acoustic type waves in the corona was confirmed using a combination of forward modelling and inversion (Taroyan et al., ApJ, 2007). The results of this study have attracted considerable public interest and Taroyan received wide media attention through reports and press releases (New Scientist, BBC News, NASA,, RAS, Yahoo, international TV channels, daily newspapers and science magazines worldwide). (iii) The lack of evidence for similar oscillations in cooler loops remained a puzzle. Taroyan & Bradshaw (A&A, 2008) established the distinct characteristics of standing and propagating acoustic waves and predicted their footprints observed with Hinode/EIS. These results were used by Erdélyi & Taroyan (A&A, 2008) to establish for the first time the presence of standing acoustic (longitudinal and kink) waves in EUV loops directly from Hinode/EIS measurements. The value of the magnetic field strength was derived with great accuracy. (iv) Taroyan & Erdélyi (Solphys, 2008) showed that the cut-off frequency introduced by gravitational stratification may act as a potential barrier when the temperature decreases with height. Waves trapped below the barrier could be subject to a global resonance which extends into the lower atmosphere of the Sun. (v) A new MHD instability was discovered in a compressible flow (Taroyan, PRL, 2008). An application to coronal loops with siphon flows (Taroyan, ApJ, 2009) shows that the new instability could play an important role in subtracting plasma flow energies.

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(i) developed MHD wave theory to further advance the relatively new and exciting field of coronal magneto-seismology. Properties of post-flare transversal coronal loop oscillations with the most realistic inhomogeneous magnetic field and plasma density structures thus far modelled analytically were predicted (Verth & Erdélyi, A&A 2008). Since, these waves, which have conclusively been identified as the standing fast kink mode from MHD wave theory, can have a strong dependence on both magnetic field and plasma density structure, they offer an ideal tool to probe the plasma structure of the solar corona on fine scales which may not be possible with more traditional diagnostic methods, such as spectroscopy and spectro-polarimetry. (ii) Implementing this theory, Verth et al. (ApJ 2008) proposed a refined magneto-seismological technique which could determine information about coronal plasma density fine structuring, correcting for the previously ignored but crucially important effects (e.g., geometry, inclination and tube expansion). In an observational case study, it was shown that previous attempts at determining the coronal atmospheric scale height, ignoring these important physical effects, leads to dramatic overestimation of scale height (by as much as 50%). (iii) Verth et al. (A&A 2007) proposed the novel technique of spatial magneto-seismology (the study of eigenfunction dependence on waveguide fine structuring), which potentially offers a far more accurate inversion than is possible with the traditional frequency methods alone.

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Advancing the field

(i) Our combined effort of theoretical investigations, forward modelling and ground/space-based observational campaigns are most optimal for the advancement of magnetic plasma coupling, heating and magneto-seismology research. Traditionally we are strong on theory. However, in recent years we strategically invested serious efforts and resources into direct engagement with observations (NSO, OPTICON campaigns) and instrumentation (Co-I - SDO, HiRISE or Advisor - ATST). We believe there are now just a few groups in solar MHD wave theory that have this combined in-house expertise. (ii) Our research will, as a team effort, progress along two main threads - theoretical (mathematical and numerical) understanding with observable predictions, and observed verification giving impetus to theoretical refinement. We are engaged with six Work Packages (WPs), directed at the relevant key science questions of the STFC Roadmap.

Work Packages

  1. Wave processes in the near sub-surface solar atmosphere
  2. Integrated approach to coronal heating
  3. 3-D magneto-seismology of the solar atmosphere
  4. Alfvén wave diagnostics and heating
  5. Transverse oscillations of coronal loops
  6. Flare and CME induced waves in the solar corona
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Expected major outcomes

The expected major outcomes of our research are manifold (research, innovation and training).
  • Understanding the near-subsurface physical processes and their magnetic coupling
  • Developing a novel coronal heating diagnostic and inversion method using loop oscillations
  • Understanding the role of solar MHD waves and oscillations in the governance of physical processes in the overlying solar atmosphere
  • Understanding the evolution and role of small-scale dynamics in the magnetised corona
  • Obtaining information on sub-resolution scales, magnetic field and structuring
  • Measuring MHD energy flux with a clear statement on its role in atmospheric heating
  • Comprehensive and consistent 3-D MHD model of the solar near sub-photosphere corona region
  • Understanding the origin and properties of global coronal waves with their diagnostics
  • Cohort of highly trained RAs/PhD students with possession of a series of highly transferable skills