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Funding: The research leading to these results has received funding from the UK Science and Technology Facilities Council (consolidated grant ST/N000609/1), the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). IDM received funding from the Research Council of Norway through its Centres of Excellence scheme, project number 262622. This work used the DiRAC Data Analytic system at the University of Cambridge, operated by the University of Cambridge High Performance Computing Service on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BEIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations 650 grant ST/K00333X/1. DiRAC is part of the National e-Infrastructure. Why the atmosphere of the Sun is orders of magnitudes hotter than its surface is a long-standing question in solar physics. Over the years, many studies have looked at the potential role of magnetohydrodynamic (MHD) waves in sustaining these high temperatures. In this study, we use 3D MHD simulations to investigate (driven) transverse waves in a coronal loop. As the boundary-driven transverse waves propagate along the flux tube, the radial density profile leads to resonant absorption (or mode coupling) and phase mixing in the boundaries of the flux tube and the large velocity shears are subject to the Kelvin Helmholtz instability (KHI). The combination of these effects leads to enhanced energy dissipation and wave heating. Considering both resonant and non-resonant boundary driving as well as different densities for the flux tube, we show that only wave heating associated with a resonant driver in a lower density loop (with a loop core density ~5x10-13 kg/m-3) is able to balance radiative losses in the loop shell. Changing the model parameters to consider a denser loop or a driver with a non-resonant frequency, or both, leads to cooling of the coronal loop as the energy losses are greater than the energy injection and dissipation rates. Publisher PDF

Funding: The research leading to these results has received funding from the UK Science and Technology Facilities Council (consolidated grant ST/N000609/1), the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). IDM received funding from the Research Council of Norway through its Centres of Excellence scheme, project number 262622. We consider the behaviour of Alfvén waves propagating in a medium with random density perturbations. The imposed density perturbations have a broadband spectrum and their characteristic spatial scale may be defined according to the peak in the spectrum. The interaction of the boundary driven Alfvén waves with the medium generates reflections most efficiently when their wavelength is comparable to the spatial scale of the density perturbations. For our monotonic driver, this leads to the generation of quasi-periodic oscillations. The periods of oscillation of the propagating Alfvén waves is no longer only associated with the driver. Additional periodicities may be associated with one or more characteristic spatial scales in the density profile, or with beating between other spectral components. Multiple wave reflections cause oscillatory power to be retained at low altitudes, increasing opportunities to contribute to heating at those locations. Publisher PDF

We have demonstrated that the Transition Region Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, successfully removing the influence of numerical resolution on the coronal density response to impulsive heating. This is achieved by adjusting the parallel thermal conductivity, radiative loss, and heating rates to broaden the transition region (TR), below a global cutoff temperature, so that the steep gradients are spatially resolved even when using coarse numerical grids. Implementing the original 1D formulation of TRAC in multi-dimensional magnetohydrodynamic (MHD) models would require tracing a large number of magnetic field lines at every time step in order to prescribe a global cutoff temperature to each field line. In this paper, we present a highly efficient formulation of the TRAC method for use in multi-dimensional MHD simulations, which does not rely on field line tracing. In the TR, adaptive local cutoff temperatures are used instead of global cutoff temperatures to broaden any unresolved parts of the atmosphere. These local cutoff temperatures are calculated using only local grid cell quantities, enabling the MHD extension of TRAC to efficiently account for the magnetic field evolution, without tracing field lines. Consistent with analytical predictions, we show that this approach successfully preserves the properties of the original TRAC method. In particular, the total radiative losses and heating remain conserved under the MHD formulation. Results from 2D MHD simulations of impulsive heating in unsheared and sheared arcades of coronal loops are also presented. These simulations benchmark the MHD TRAC method against a series of 1D models and demonstrate the versatility and robustness of the method in multi-dimensional magnetic fields. We show, for the first time, that pressure differences, ..., Comment: 18 pages, 11 figures, accepted for publication in A&A

Aims. Estimates of coronal wave energy remain uncertain as a large fraction of the energy is likely hidden in the non-thermal line widths of emission lines. In order to estimate these wave energies, many previous studies have considered the root mean squared wave amplitudes to be a factor of $\sqrt{2}$ greater than the non-thermal line widths. However, other studies have used different factors. To investigate this problem, we consider the relation between wave amplitudes and the non-thermal line widths within a variety of 3D magnetohydrodynamic (MHD) simulations. Methods. We consider the following 3D numerical models: Alfv\'en waves in a uniform magnetic field, transverse waves in a complex braided magnetic field, and two simulations of coronal heating in an arcade. We applied the forward modelling code FoMo to generate the synthetic emission data required to analyse the non-thermal line widths. Results. Determining a single value for the ratio between the non-thermal line widths and the root mean squared wave amplitudes is not possible across multiple simulations. It was found to depend on a variety of factors, including line-of-sight angles, velocity magnitudes, wave interference, and exposure time. Indeed, some of our models achieved the values claimed in recent articles while other more complex models deviated from these ratios. Conclusions. To estimate wave energies, an appropriate relation between the non-thermal line widths and root mean squared wave amplitudes is required. However, evaluating this ratio to be a singular value, or even providing a lower or upper bound on it, is not realistically possible given its sensitivity to various MHD models and factors. As the ratio between wave amplitudes and non-thermal line widths is not constant across our models, we suggest that this widely used method for estimating wave energy is not robust., Comment: 11 pages and 11 figures

Funding: VP and TVD are supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 724326). J.A.M. acknowledges UK Science and Technology Facilities Council (STFC) support from grant ST/T000384/1. L.O. acknowledges support by NASA grants NNX16AF78G, 80NSSC18K1131 and NASA Cooperative Agreement NNG11PL10A to CUA. P.A. acknowledges funding from his STFC Ernest Rutherford Fellowship (No. ST/R004285/2). IDM acknowledges support from the UK Science and Technology Facilities Council (consolidated grants ST/N000609/1 and ST/S000402/1), the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214) and the Research Council of Norway through its Centres of Excellence scheme, project number 262622. Modern observatories have revealed the ubiquitous presence of magnetohydrodynamic waves in the solar corona. The propagating waves (in contrast to the standing waves) are usually originated in the lower solar atmosphere which makes them particularly relevant to coronal heating. Furthermore, open coronal structures are believed to be the source regions of solar wind, therefore, the detection of MHD waves in these structures is also pertinent to the acceleration of solar wind. Besides, the advanced capabilities of the current generation telescopes have allowed us to extract important coronal properties through MHD seismology. The recent progress made in the detection, origin, and damping of both propagating slow magnetoacoustic waves and kink (Alfvénic) waves is presented in this review article especially in the context of open coronal structures. Where appropriate, we give an overview on associated theoretical modelling studies. A few of the important seismological applications of these waves are discussed. The possible role of Alfvénic waves in the acceleration of solar wind is also touched upon. Postprint

Context. The relative importance of AC and DC heating in maintaining the temperature of the corona is not well constrained. Aims. Investigate the effects of the characteristic time scales of photospheric driving on the injection and dissipation of energy within a coronal arcade. Methods. We have conducted three dimensional MHD simulations of foot point driving imposed on an arcade. We modified the typical driving time scales to understand the efficiency of heating obtained using AC and DC drivers. We considered the implications for the injected Poynting flux and the nature of the energy release in dissipative regimes. Results. For the same driver amplitude and complexity, long time scale motions are able to inject a much greater Poynting flux into the corona. Consequently, in non-ideal regimes, slow stressing motions result in a greater increase in plasma temperature than for wave-like driving. In dissipative simulations, Ohmic heating is found to be much more significant than viscous heating. For all drivers in our parameter space, energy dissipation is greatest close to the base of the arcade where the magnetic field strength is strongest and at separatrix surfaces, where the field connectivity changes. Across all simulations, the background field is stressed with random foot point motions (in a manner typical of DC heating studies) and even for short time scale driving, the injected Poynting flux is large given the small amplitude flows considered. For long time scale driving, the rate of energy injection was comparable to the expected requirements in active regions. The heating rates were found to scale with the perturbed magnetic field strength and not the total field strength. Conclusions. Alongside recent studies which show power within the corona is dominated by low frequency motions, our results suggest that in the closed corona, DC heating is more significant than AC heating., 14 pages, 16 figures

Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion., 20 pages, 9 figures, 1 table, accepted for publication in A&A

Context. The mechanism(s) behind coronal heating still elude(s) direct observation and modelling of viable theoretical processes and the subsequent effect on coronal structures is one of the key tools available to assess possible heating mechanisms. Wave heating via the phase mixing of magnetohydrodynamic (MHD) transverse waves has been proposed as a possible way to convert magnetic energy into thermal energy, but MHD models increasingly suggest this is not an efficient enough mechanism. Aims. We modelled heating by phase mixing transverse MHD waves in various configurations in order to investigate whether certain circumstances can enhance the heating sufficiently to sustain the million degree solar corona and to assess the impact of the propagation and phase mixing of transverse MHD waves on the structure of the boundary shell of coronal loops. Methods. We used 3D MHD simulations of a pre-existing density enhancement in a magnetised medium and a boundary driver to trigger the propagation of transverse waves with the same power spectrum as measured by the Coronal Multi-Channel Polarimeter. We consider different density structures, boundary conditions at the non-drive footpoint, characteristics of the driver, and different forms of magnetic resistivity. Results. We find that different initial density structures significantly affect the evolution of the boundary shell and that some driver configurations can enhance the heating generated from the dissipation of the MHD waves. In particular, drivers coherent on a larger spatial scale and higher dissipation coefficients can generate significant heating, although it is still insufficient to balance the radiative losses in this setup. Conclusions. We conclude that while phase mixing of transverse MHD waves is unlikely to sustain the thermal structure of the corona, there are configurations that allow for an enhanced efficiency of this mechanism. We provide possible signatures to identify the presence of such configurations, such as the location of where the heating is deposited along the coronal loop.

Phase mixing of Alfv\'en waves has been studied extensively as a possible coronal heating mechanism but without the full thermodynamic consequences considered self-consistently. It has been argued that in some cases, the thermodynamic feedback of the heating could substantially affect the transverse density gradient and even inhibit the phase mixing process. In this paper, we use MHD simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfv\'en waves in a coronal loop and the effect of this evaporation on the transverse density profile. The numerical simulations were performed using the Lare2D code. We set up a 2D loop model consisting of a field-aligned thermodynamic equilibrium and a cross-field (background) heating profile. A continuous, sinusoidal, high-frequency Alfv\'en wave driver was implemented. As the Alfv\'en waves propagate along the field, they undergo phase mixing due to the cross-field density gradient in the coronal part of the loop. We investigated the presence of field-aligned flows, heating from the dissipation of the phase-mixed Alfv\'en waves, and the subsequent evaporation from the lower atmosphere. We find that phase mixing of Alfv\'en waves leads to modest heating in the shell regions of the loop and evaporation of chromospheric material into the corona with upflows of the order of only 5-20 m/s. Although the evaporation leads to a mass increase in the shell regions of the loop, the effect on the density gradient and, hence, on the phase mixing process, is insignificant. This paper self-consistently investigates the effect of chromospheric evaporation on the cross-field density gradient and the phase mixing process in a coronal loop. We found that the effects in our particular setup (small amplitude, high frequency waves) are too small to significantly change the density gradient., Comment: 11 pages, 12 figures, accepted for publication in A&A

Aim. We investigate synthetic observational signatures generated from numerical models of transverse waves propagating in braided magnetic fields. Methods. We examine two simulations with different levels of magnetic field braiding and impose a periodic, transverse wave driver at the lower boundary. After waves reflect off the top boundary, a complex pattern of wave interference forms. We analyse the synthetic emission produced by the forward modelling code, FoMo. We examine line intensity, Doppler shifts and kinetic energy along several line-of-sight (LOS) angles. Results. The Doppler shifts showed the presence of transverse waves. However, when analysing the intensity, waves are less easily observed for more complex magnetic fields and may be mistaken for background noise. Depending on the LOS angle, the observable signatures of waves reflect some of the magnetic field braiding, particularly when multiple emission lines are available. In the more braided simulation, signatures of phase mixing can be identified. We identify possible ambiguities in the interpretation of wave modes based on the synthetic emission signatures. Conclusions. Most of the observables within this article behave as expected, given knowledge of the evolution of the parameters in 3D space. However, some intriguing observational signatures are present. Detecting regions of magnetic field complexity is somewhat possible when waves are present. However, simultaneous spectroscopic imaging from different lines is important to identify these locations. Care needs to be taken when interpreting intensity and Doppler velocity signatures as torsional motions as, in our setup, such signatures were a consequence of the magnetic field complexity and not torsional waves. Finally, the kinetic energy, estimated with Doppler velocities, is dependent on the polarisation of the wave, complexity of the background field and the LOS., Comment: 15 pages and 22 figures

Thermal non-equilibrium (TNE) is believed to be a potentially important process in understanding some properties of the magnetically closed solar corona. Through one-dimensional hydrodynamic models, this paper addresses the importance of the numerical spatial resolution, footpoint heating timescales and background heating on TNE. Inadequate transition region (TR) resolution can lead to significant discrepancies in TNE cycle behaviour, with TNE being suppressed in under-resolved loops. A convergence on the periodicity and plasma properties associated with TNE required spatial resolutions of less than 2 km for a loop of length 180 Mm. These numerical problems can be resolved using an approximate method that models the TR as a discontinuity using a jump condition, as proposed by Johnston et al. (2017a,b). The resolution requirements (and so computational cost) are greatly reduced while retaining good agreement with fully resolved results. Using this approximate method we (i) identify different regimes for the response of coronal loops to time-dependent footpoint heating including one where TNE does not arise and (ii) demonstrate that TNE in a loop with footpoint heating is suppressed unless the background heating is sufficiently small. The implications for the generality of TNE are discussed., 15 pages, 10 figures, 1 table, accepted for publication in A&A

This research has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214). Aims . This paper presents 2.5D numerical experiments of Alfvén wave phase mixing and aims to assess the effects of nonlinearities on the wave behaviour and dissipation. In addition, this paper aims to quantify how effective the model presented here is at providing energy to the coronal volume. Methods . The model is presented and explored through the use of several numerical experiments which were carried outusing the Lare2D code (Arber et al. 2001). The experiments study footpoint driven Alfvén waves in the neighbourhood of a two-dimensional x-type null point, with initially uniform density and plasma pressure. A continuous sinusoidal driver with a constant frequency is used. Each experiment uses different driver amplitudes to compare weakly nonlinear experiments with linear experiments. Results . It was found that the wave trains phase-mix due to variations in the length of each field line as well asvariations in the field strength. The nonlinearities reduce the amount of energy entering the domain, as they reduce the effectiveness of the driver, but they have relatively little effect on the damping rate (for the range of amplitudes studied). The nonlinearities produce density structures which change the natural frequencies of the field lines and hence cause the resonant locations to move. The shifting of the resonant location causes the Poynting flux associated with the driver to decrease. Reducing the magnetic diffusivity increased the energy build-up on the resonant field lines, however, it has little effect on the total amount of energy entering the system. From an order of magnitude estimate, it was shown that the Poynting flux in our experiments was comparable to the energy requirements of the Quiet Sun corona, although a (possibly unphysically) large amount of magnetic diffusion was used, and it remains unclear if the model is able to provide enough energy under actual coronal conditions. Postprint

Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. Aims. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. Methods. We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum. Results. We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin–Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. Conclusions. This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.

Funding: UK Science and Technology Facilities Council (consolidated grant ST/N000609/1), the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214); STFC Ernest RutherfordFellowship (grant agreement No. ST/R004285/1) (PA); European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 724326) (TVD); partial supported by the Leverhulme Trust (through research grant RPG-2016-071) (ANW). Aims. We investigate the transfer of energy between a fundamental standing kink mode and azimuthal Alfvén waves within an expanding coronal magnetic flux tube. We consider the process of resonant absorption in a loop with a non-uniform Alfvén frequency profile but in the absence of a radial density gradient. Methods. Using the three dimensional magnetohydrodynamic (MHD) code, Lare3d, we modelled a transversely oscillating magnetic flux tube that expands radially with height. An initially straight loop structure with a magnetic field enhancement was allowed to relax numerically towards a force-free state before a standing kink mode was introduced. The subsequent dynamics, rate of wave damping and formation of small length scales are considered. Results. We demonstrate that the transverse gradient in Alfvén frequency required for the existence of resonant field lines can be associated with the expansion of a high field-strength flux tube from concentrated flux patches in the lower solar atmosphere. This allows for the conversion of energy between wave modes even in the absence of the transverse density profile typically assumed in wave heating models. As with standing modes in straight flux tubes, small scales are dominated by the vorticity at the loop apex and by currents close to the loop foot points. The azimuthal Alfvén wave exhibits the structure of the expanded flux tube and is therefore associated with smaller length scales close to the foot points of the flux tube than at the loop apex. Conclusions. Resonant absorption can proceed throughout the coronal volume, even in the absence of visible, dense, loop structures. The flux tube and MHD waves considered are difficult to observe and our model highlights how estimating hidden wave power within the Sun’s atmosphere can be problematic. We highlight that, for standing modes, the global properties of field lines are important for resonant absorption and coronal conditions at a single altitude will not fully determine the nature of MHD resonances. In addition, we provide a new model in partial response to the criticism that wave heating models cannot self-consistently generate or sustain the density profile upon which they typically rely. Postprint

In addition to their jet-like dynamic behaviour, spicules usually exhibit strong transverse speeds, multi-stranded structure and heating from chromospheric to transition region temperatures. In this work we first analyse \textit{Hinode} \& \textit{IRIS} observations of spicules and find different behaviours in terms of their Doppler velocity evolution and collective motion of their sub-structure. Some have a Doppler shift sign change that is rather fixed along the spicule axis, and lack coherence in the oscillatory motion of strand-like structure, matching rotation models or long wavelength torsional Alfv��n waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective MHD wave. By comparing with an idealised 3-D MHD simulation combined with radiative transfer modelling, we analyse the role of transverse MHD waves and associated instabilities in spicule-like features. We find that Transverse Wave Induced Kelvin-Helmholtz (TWIKH) rolls lead to coherence of strand-like structure in imaging and spectral maps, as seen in some observations. The rapid transverse dynamics and the density and temperature gradients at the spicule boundary lead to ring-shaped \ion{Mg}{2} k and \ion{Ca}{2} H source functions in the transverse cross-section, potentially allowing IRIS to capture the KHI dynamics. Twists and currents propagate along the spicule at Alfv��nic speeds, and the temperature variations within TWIKH rolls produce sudden appearance / disappearance of strands seen in Doppler velocity and in \ion{Ca}{2} H intensity. However, only a mild intensity increase in higher temperature lines is obtained, suggesting there is an additional heating mechanism at work in spicules., Accepted for publication in The Astrophysical Journal

We proposed that the use of an approximate “jump condition” at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region.

This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214) and from the UK Science and Technology Facilities Council. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. Context. Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small-scale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the million-degree hot solar corona. Aims. The aim of this work is to assess how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona. Methods. To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phase-mix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver. Results. When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that i) phase-mixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell, ii) this energy is able to balance the radiative losses only in the localised region involved in the heating, and iii) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system. Conclusions. Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phase-mixing can contribute on a global scale to the heating of the solar corona. Postprint

© 2017. The American Astronomical Society. All rights reserved. Magnetohydrodynamic (MHD) waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints but also by wave processes that localize the wave power in undetectable spatial scales. In this study, we conduct 3D MHD simulations and forward modeling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin-Helmholtz instability (KHI), resonant absorption, and phase mixing. In the presence of a cross-loop temperature gradient, we find that emission lines sensitive to the loop core catch different signatures compared to those that are more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity and Doppler velocity modulation produced by KHI mixing. In all of the considered models, common signatures include an intensity and loop width modulation at half the kink period, a fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, and overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.″33 and a spectral resolution of 25 km s-1, although we do obtain severe over-estimation of the line width. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and KHI motions. We estimate this hidden wave energy to be a factor of 5-10 of the observed value. journal_title: The Astrophysical Journal article_type: paper article_title: Observational Signatures of Transverse Magnetohydrodynamic Waves and Associated Dynamic Instabilities in Coronal Flux Tubes copyright_information: © 2017. The American Astronomical Society. All rights reserved. date_received: 2016-11-23 date_accepted: 2017-02-02 date_epub: 2017-02-22 ispartof: Astrophysical Journal vol:836 issue:2 status: published

The research leading to these results has received funding from the UK Science and Technology Facilities Council (consolidated grant ST/N000609/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, density-enhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube’s magnetic field. Results. The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop’s density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a non-zero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode. Conclusions. The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures. Postprint

For future solar missions as well as ground-based telescopes, efficient ways to return and process data have become increasingly important. Solar Orbiter, e.g., which is the next ESA/NASA mission to explore the Sun and the heliosphere, is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals. Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand, face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000 (from the Joint Photographic Experts Group 2000) image compression at different bit rates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to-noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disk and off-limb coronal-loop oscillation time-series observed by AIA/SDO., Comment: 25 pages, published in Solar Physics

This work used the COSMA Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. I.D.M was funded by the Science and Technology Facilities Council (UK). The research leading to these results has also received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). J.O was funded by the Science and Technology Facilities Council (UK) by Doctoral Grant [ST/K502327/1]. Context. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, which can subsequently be released by magnetic reconnection. Aims. We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions. Methods. 3D magnetohydrodynamic (MHD) simulations using Lare3D are carried out, where flux tubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The flux tubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect. Results. Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the flux tubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four-source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of the background field between the flux tubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two- and four-source cases. The cases with two flux tubes are always more energetic than the corresponding four flux tube cases, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two-source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver. Postprint

This project has received funding from the Science and Technology Facilities Council (UK) and the European Research Council (ERC) under the European Unionʼs Horizon 2020 research and innovation program (grant agreement No 647214). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/2007-2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/about). It has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption and phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the self-consistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave-damping processes are inhibited. For the case of phase mixing we argue that (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient, and the rapid damping of oscillations may have to be accompanied by a separate (non-wave-based) heating mechanism to sustain the required density structuring. Publisher PDF

Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias toward enhancement of emission in the blue wing of the emission line due to in-phase behavior of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line of sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations. © 2010. The American Astronomical Society. All rights reserved. ispartof: ASTROPHYSICAL JOURNAL LETTERS vol:724 issue:2 pages:L194-L198 status: published

This research has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program ( grant agreement No. 647214). This work is supported by the European Research Council under the SeismoSun Research Project No. 321141 (DJP). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 724326). This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. Context. Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves . In particular, recent observations show that standing oscill ations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. Aims. We investigate the consequences for wave-based coronal hea ting of higher harmonics and what coronal heating observational signatures we may use to infer the presence of higher harmonic kink oscillations. Methods. We perform a set of non-ideal MHD simulations where the damping of the kink oscillation of a flux tube via mode coupling is modelled. Our MHD simulation parameters are based on the seismological inversion of an observation for which the first three harmonics are detected. We study the phase-mixing of Alfvén waves that leads to the deposition of heat in the system, and we apply the seismological inversion techniques to the MHD simulation output. Results. We find that the heating due to phase-mixing of the Alfvén wave s triggered by the damping of the kink oscillation is relatively small, however we can illustrate i) how the heating location drifts due to the subsequent damping of lower order harmonics. We also address the role of the higher order harmonics and the width of the boundary shell in the energy deposition. Conclusions. We conclude that the coronal heating due to phase-mixing see ms not to provide enough energy to maintain the thermal structure of the solar corona even when multi-harmonics oscillations are included, and these oscillations play an inhibiting role in the development of smaller scale structures. Postprint

Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfven waves. To investigate the nature of transverse waves propagating in the solar corona and their potential for use as a coronal diagnostic in MHD seismology, we perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of both a uniform medium and one with loop-like density structure and perform a parametric study for our structuring parameters. When density structuring is present, resonant absorption in inhomogeneous layers leads to the coupling of the kink mode to the Alfven mode. The decay of the propagating kink wave as energy is transferred to the local Alfven mode is in good agreement with a modified interpretation of the analysis of Ruderman & Roberts for standing kink modes. Numerical simulations support the most general interpretation of the observed loop oscillations as a coupling of the kink and Alfven modes. This coupling may account for the observed predominance of outward wave power in longer coronal loops since the observed damping length is comparable to our estimate based on an assumption of resonant absorption as the damping mechanism.

The magnetic field strength inside a model coronal loop is estimated using coronal seismology, to examine the reliability of magnetic field strengths derived from observed, transverse coronal loop oscillations. Three-dimensional numerical simulations of the interaction of an external pressure pulse with a coronal loop (modeled as a three-dimensional density enhancement inside a two-dimensional magnetic arcade) are analyzed and the observed properties of the excited transverse loop oscillations are used to derive the value of the local magnetic field strength, following the method of Nakariakov & Ofman. Due to the (unexpected) change in periodicity, the magnetic field derived from our observed oscillation is substantially different from the actual (input) magnetic field value (approximately 50%). Coronal seismology can derive useful information about the local magnetic field, but the combined effect of the loop curvature, the density ratio, and aspect ratio of the loop appears to be more important than previously expected.

Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers.

Context. The propagation and damping of slow MHD waves in the solar atmosphere are investigated by numerical simulations and forward modelling, with particular emphasis placed on waves with periodicities of the order of five minutes.Aims. We extend a coronal model by adding an equilibrium temperature gradient allowing study of wave propagation from the transition region to the corona.Methods. A 1D model is used that includes gravitational stratification and damping by thermal conduction, optically thin radiation, and compressive viscosity. Forward modelling of the simulation results, for both uniform and non-uniform equilibrium temperature profiles, is undertaken to establish the observational consequences of the physical processes involved for TRACE, SoHO/CDS, and Hinode/EIS.Results. The presence of thermal conduction causes a phase shift between the wave velocity, energy, and density. This shift may be observable by comparing Doppler velocity and intensity observations. Phase shifts are also seen between intensity observations by different instruments and between different spectral lines. This is an observational effect that arises due to the forward modelling process in which observations are synthesised, but it is not seen in the simulation results. Oscillations from the transition region are found to dominate the coronal emission for TRACE 171 A by nearly two orders of magnitude.

In this paper, forward modelling is used to investigate the relation between given temperature and density perturbations and the resulting (synthesised) intensity perturbations, as would be observed by, e.g., TRACE and EIS (onboard Hinode). Complex and highly non-linear interactions between the components which make up the intensity (density, ionisation balance and emissivity) mean that it is non-trivial to reverse this process, i.e., obtain the density and temperature perturbations associated with observed intensity oscillations. In particular, it is found that the damping rate does not often ‘survive’ the forward modelling process, highlighting the need for a very careful interpretation of observed (intensity) damping rates. With a few examples, it is demonstrated that in some cases even the period of the oscillations can be altered and that it is possible for two different sets of input temperature and density to lead to very similar intensities (the well-known ‘ill-posed’ inversion process).

The Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—"propagating coronal disturbances" (PCDs) with apparent speeds of the order of 100–120 km s−1. That signal has a clear signature in the slit-jaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg iih (2803 A) line. In analyzing the Mg iih line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg iih, the evolution of the Si iv line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jet-like features in the IRIS Si iv slit-jaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs.

A sequence of TRACE 171 A observations taken on 2001 May 13 shows evidence of flare-induced, transverse coronal loop oscillations. We revisit this particular data set and present evidence of the presence of spatially resolved higher harmonics in the transverse loop displacements. The oscillations are identified as the second-harmonic, fast MHD kink waves (periods of 577-672 s), with higher harmonics (250-346 s) also present. The apparent absence of the fundamental mode and the fact that it is the second harmonic (P2) that dominates the oscillatory behavior of this particular loop may shed more light on either the excitation and/or the damping mechanism(s) of flare-induced, transverse loop oscillations.

High-cadence TRACE observations show that outward-propagating intensity dis- turbances are a common feature in large, quiescent coronal loops. Analysis of the fre- quency distribution of these modes shows peaks at both three- and five-minute periods, indicating that they may be driven by the solar surface oscillations (p modes). The energy flux contained within the coronal intensity disturbances is of the order of (1.1 ± 0.4) × 10 3 ergs cm −2 s −1 . A simple order-of-magnitude estimate of the damping rate of the rele- vant p modes allows us to put an observational constraint on the damping of p modes and shows that leakage into the overlying coronal atmosphere might be able to account for a significant fraction of p-mode damping.

Aims. Photospheric motions acting on the coronal magnetic field have the potential to build up huge amounts of magnetic energy. The energy may be released through magnetic reconnection, and so a detailed understanding of the 3D process is crucial if its implications for coronal heating are to be fully addressed. Methods. A 3D MHD experiment is described in which misaligned magnetic flux tubes are subjected to simple spinning boundary motions. Results. The resulting shear between adjacent flux systems generates a twisted central separator current sheet that extends vertically throughout the domain. Current density is amplified to a sufficient extent that reconnection begins, and occurs everywhere along the separator current sheet, while the separatrix current sheets that exist in the early stages of the experiment are found to be unimportant in the systems dynamical evolution. In 2D cross-sections, the reconnection process exhibits many similarities to the regime of flux pile-up reconnection.

The coronal magnetic field is constantly subjected to a variety of photospheric, footpoint motions, leading to the build up, and subsequent release, of magnetic energy. Two different types of footpoint motions are considered here, namely (large scale) rotating and (small scale) spinning, using 3D numerical MHD simulations. The initial model consists of two aligned, thin flux tubes, which are forced to interact due to the boundary driving of the footpoints. Two variations of this setup are studied, namely with and without an additional, constant, background magnetic field. The nature of the boundary motions determines the shape of the central current sheet, the driving force of the reconnection process, as well as the efficiency of the build up of quasi-separatrix layers (when $B_{\rm bg} \ne 0$). The reconnection process is more efficient for the rotating of the flux sources and when a background magnetic field is added. In general, heating due to large and small scale motions is of comparable magnitude when no background field is present. However, with an additional background magnetic field, heating due to small scale footpoint motions seems substantially more efficient.

The aim of this paper is two-fold: to increase the number of examples of observed longitudinal oscillations in coronal loops and to find evidence of the small temporal and spatial scales of these loop oscillations. Increasing the number of observed longitudinal oscillations allows for improvement in the statistics of the measured parameters, providing more accurate values for numerical and theoretical models. Furthermore, the small temporal and spatial scales of these loop oscillations could give indication of a driving force, symptomatic of coupling with the global p-modes. We found evidence that individual loop strands of wide coronal loop footpoints oscillate independently for short time periods. These strands have a diameter of the order of a few Mm, and the timescales on which the oscillations exist are typically less than an hour. We suggest that this is indicative of the oscillating strands being driven by the leakage of the global 5 min p-modes up into the corona, as simulated by De Pontieu et al. (2005, ApJ, 624, L61). Additionally, we find 25 further examples, added to those of De Moortel et al. (2002a, Sol. Phys., 209, 89), of outwardly propagating slow MHD waves in coronal loop footpoints. The datasets are taken from JOP83, observed between April 21st 2003 and May 3rd 2003, in the TRACE 171 A bandpass. The intensity oscillations travel outwards with a propagation speed of order v = 99.7 ± 3.9 kms−1 and they are of small amplitude, with variations of approximately 3.7 ± 0.2% of the background intensity. These disturbances are only detected for short distances, around 8.3 ± 0.6 Mm along the loops, and the main period of oscillation is around 300 s. A second peak of period was found at around 200 s, however no correlation with the presence of a sunspot was observed within this study. Using these measured parameters we have estimated the energy flux to be of order 313 ± 26 erg cm−2 s−1.

There are now many observations of waves in the solar corona with periods around 5 minutes. The source of these waves is uncertain, although global p-modes in the photosphere are an obvious candidate, given the similarity of the dominant periods. However, p-modes are traditionally considered evanescent in the upper photosphere, and it has been unclear how they could propagate through the chromosphere into the corona. Using a numerical model, we show that photospheric oscillations with periods around 5 minutes can actually propagate into the corona so long as they are guided along an inclined magnetic flux tube. The nonverticality of the flux tube increases the acoustic cutoff period to values closer to the dominant periods of the photospheric oscillations, thus allowing tunneling or even direct propagation into the outer atmosphere. The photospheric oscillations develop into shocks, which drive chromospheric spicules and reach the corona. We suggest that Transition Region and Coronal Explorer (TRACE) observations of propagating magnetoacoustic waves in the corona represent these shocked and tunneled photospheric oscillations. We also explore how seismology of these waves could be exploited to determine the connectivity between photosphere and corona.

The properties of slow MHD waves in a two dimensional model are investigated, in a low-beta plasma. Including a horizontal density variation causes "phase mixing" and coupling between slow and fast MHD waves. The effects of different density profiles, different driving frequencies, different values for the viscosity coefficient and plasma beta (

This paper investigates the possibility of automating the detection of propagating intensity perturbations in coronal loops using wavelet analysis. Two different sets of TRACE 171 A images are studied using the automated wavelet routine presented by McAteer et al. (2004). Both localised, short-lived periodicities and sustained, periodic, oscillations are picked up by the routine, with the results dependent to a large extent on the signal-to-noise ratio of the dataset. At present, the automation is only partial; the relevance of the detected periodicity and the identification of the coronal structure supporting it still have to be determined by the user, as does the judging of the accuracy of the results. Care has to be taken when interpreting the results of the wavelet analysis, and a good knowledge of all possible factors that might influence or distort the results is a necessity. Despite these limitations, wavelet analysis can play an important role in automatically identifying a variety of phenomena and in the analysis of the ever-growing (observational or simulated) datasets.

The most commonly used methods to analyse (observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration.

This paper continues the study of De Moortel & Hood ([CITE]) into the propagation of slow MHD waves in the solar corona. Firstly, the damping due to optically thin radiation is investigated and compared to the effect of thermal conduction. In a second stage, gravitational stratification is included in the model and it is found that this increases the damping length significantly. Finally, the effect of different magnetic field geometries on the damping of the slow waves is investigated. As a first approximation, a purely radial magnetic field is considered and although the amplitudes of the perturbations decrease due to the divergence of the field, the effect is small compared to the effect of thermal conduction. A more realistic local geometry, estimated from the observations, is investigated and it is demonstrated that a general area divergence can cause a significant, additional, decrease of the amplitudes of the perturbations. The results of numerical simulations, incorporating the effects of gravitational stratification, the magnetic field geometry and thermal conduction are compared with TRACE observations of propagating waves in coronal loops. It is found that a combination of thermal conduction and (general) area divergence yields detection lengths that are in good agreement with observed values.

A theoretical description of slow MHD wave propagation in the solar corona is presented. Two dierent damping mechanisms, namely thermal conduction and compressive viscosity, are included and discussed in detail. We revise the proper- ties of the "thermal" mode, which is excited when thermal conduction is included. The thermal mode is purely decaying in the case of standing waves, but is oscillatory and decaying in the case of driven waves. When thermal conduction is dominant, the waves propagate largely undamped, at the slower, isothermal sound speed. This implies that there is a minimum damping time (or length) that can be obtained by thermal conduction alone. The results of numerical simulations are compared with TRACE observations of propagating waves, driven by boundary motions, and standing waves observed by SUMER/SOHO, excited by an initial impulse. For typical coronal conditions, thermal conduction appears to be the dominant damping mechanism.

Joint Observing Program (JOP) 83 Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer (SOHO/CDS) and Transition Region and Coronal Explorer (TRACE) data is analysed for evidence of propagating intensity oscillations along loop structures in the solar corona. A propagating intensity oscillation with a minimum estimated speed of 50-195 km s 1 is observed within a TRACE 171 A coronal loop using a running dierence method. Co-spatial and co- temporal CDS and TRACE observations of this loop are analysed using a wavelet analysis method. The TRACE data shows a propagating oscillation with a period of300 s. This period is also observed with CDS suggesting propagating oscillations at chromospheric, transition region and coronal temperatures in the He i ,O v and Mgix lines.

In this paper, we determine the temperature profile along the footpoints of large coronal loops observed by TRACE in both the 171 A and 195 A passbands. The temperature along the lower part of these coronal loops only shows small variations and can probably be considered to be isothermal. Using the obtained temperature profile T(s) and an estimate of the column depth along the loop, we then determine the pressure along the lower part of the observed coronal loops and hence the value of the pressure scale length. The obtained scale lengths correspond in order-of-magnitude with the theoretically predicted gravitational scale height. We show that the differences between the observed and predicted scale heights are unlikely to be caused by (significant) flows along the loops but could possibly be a consequence of the inclination of the loops. This implies that the quasi-periodic intensity oscillations observed in the loops are most probably caused by compressive waves propagating upward at the coronal sound speed.

There as yet remain few examples of well observed, transversal oscillations in coronal loops. Such oscillations have the potential to yield much information on the nature of the solar corona, as demonstrated by the analysis of Nakariakov et al. (1999) of a transversely oscillating loop observed in the TRACE 171 A passband on 14th July, 1998. Their analysis extracts a decaying loop oscillation signal from the data which is then considered in the light of the substantial body of theoretically and computationally derived knowledge of the dynamics of coronal loops. The analysis presented in this paper approaches the reduction of the same dataset using wavelet techniques described by De Moortel & Hood (2000) and De Moortel et al. (2002). The authors show that the value of the decay exponent N in a decaying oscillating time series of the form exp( kt N ) is measurable from a wavelet transform of the time series (for some decay constant k and time t). The application of these techniques shows that the value of the decay exponent in the 14th July, 1998 event is not well determined by the data, i.e., the associated error is very large. Since the value of the decay exponent implies the presence of particular decay mechanisms and not others, the large error associated with the exponent value implies that a wide range of mechanisms should be considered when discussing the physics behind this event. Comments are also made on the time dependence of the oscillation wavelet scale. Two additional examples of transversal coronal loop oscillations are also analysed.

High cadence, 171 A, TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. These oscillations are interpreted as propagating slow magneto- acoustic waves. Using a wavelet analysis, we found periods of the order of 282 93 s. However, a careful study of the location of the footpoints revealed a distinct separation between those loops that support oscillations with periods smaller than 200 s and periods larger than 200 s. It was found that loops that are situated above sunspot regions display intensity oscillations with a period of the order of 172 32 s, whereas oscillations in \non-sunspot" loops show periods of the order of 321 74 s. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. This result suggests that the underlying oscillations can propagate through the transition region and into the corona.

This paper expands on the suggestion of De Moortel & Hood ([CITE]) that it will be possible to infer coronal plasma properties by making a detailed study of the wavelet transform of observed oscillations. TRACE observations, taken on 14 July 1998, of a flare-excited, decaying coronal loop oscillation are used to illustrate the possible applications of wavelet analysis. It is found that a decay exponent gives the best fit to the double logarithm of the wavelet power, thus suggesting an e damping profile for the observed oscillation. Additional examples of transversal loop oscillations, observed by TRACE on 25 October 1999 and 21 March 2001, are analysed and a damping profile of the form e, with and respectively, is suggested. It is demonstrated that an e damping profile of a decaying oscillation survives the wavelet transform, and that the value of both the decay coefficient e and the exponent n can be extracted by taking a double logarithm of the normalised wavelet power at a given scale. By calculating the wavelet power analytically, it is shown that a sufficient number of oscillations have to be present in the analysed time series to be able to extract the period of the time series and to determine correct values for both the damping coefficient and the decay exponent from the wavelet transform.

In this paper, we give a detailed discussion of the parameters of longitudinal oscillations in coronal loops, described in Paper I. We found a surprising absence of correlations between the measured variables, with the exception of a relation between the estimated damping length and the period of the intensity variations. Only for 2 out of the 38 cases presented in Paper I did we find a significant perturbation in the 195 A TRACE data. The loops supporting the propagating disturbances were typically stable, quiescent loops and the total luminosity of the analyzed structures generally varied by no more than 10%. The observed density oscillations are unlikely to be flare-driven and are probably caused by an underlying driver exciting the loop footpoints. It was demonstrated that the rapid damping of the perturbations could not simply be explained as a consequence of the decreasing intensity along the loops. However, we found that (slightly enhanced) thermal conduction alone could account for the observed damping lengths and wavelengths, and, additionally, explain the correlation between propagation period and damping length.

Context: Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions. Aims: The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Our previous work suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions. Methods: We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated. Results: The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed. Publisher PDF

International audience; In Fall 2008 NASA selected a large international consortium to produce a comprehensive automated feature-recognition system for the Solar Dynamics Observatory (SDO). The SDO data that we consider are all of the Atmospheric Imaging Assembly (AIA) images plus surface magnetic-field images from the Helioseismic and Magnetic Imager (HMI). We produce robust, very efficient, professionally coded software modules that can keep up with the SDO data stream and detect, trace, and analyze numerous phenomena, including flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, coronal mass ejections (CMEs), coronal oscillations, and jets. We also track the emergence and evolution of magnetic elements down to the smallest detectable features and will provide at least four full-disk, nonlinear, force-free magnetic field extrapolations per day. The detection of CMEs and filaments is accomplished with Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO) and ground-based Hα data, respectively. A completely new software element is a trainable feature-detection module based on a generalized image-classification algorithm. Such a trainable module can be used to find features that have not yet been discovered (as, for example, sigmoids were in the pre-Yohkoh era). Our codes will produce entries in the Heliophysics Events Knowledgebase (HEK) as well as produce complete catalogs for results that are too numerous for inclusion in the HEK, such as the X-ray bright-point metadata. This will permit users to locate data on individual events as well as carry out statistical studies on large numbers of events, using the interface provided by the Virtual Solar Observatory. The operations concept for our computer vision system is that the data will be analyzed in near real time as soon as they arrive at the SDO Joint Science Operations Center and have undergone basic processing. This will allow the system to produce timely space-weather alerts and to guide the selection and production of quicklook images and movies, in addition to its prime mission of enabling solar science. We briefly describe the complex and unique data-processing pipeline, consisting of the hardware and control software required to handle the SDO data stream and accommodate the computer-vision modules, which has been set up at the Lockheed-Martin Space Astrophysics Laboratory (LMSAL), with an identical copy at the Smithsonian Astrophysical Observatory (SAO).

Quasi-periodic disturbances have been observed in the outer solar atmosphere for many years now. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to observed velocities and periods. However, recent observations have questioned this interpretation, as periodic disturbances in Doppler velocity, line width and profile asymmetry were found to be in phase with the intensity oscillations (De Pontieu et al. (2010),Tian1 et al. (2011))}, suggesting the disturbances could be quasi-periodic upflows. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and non sunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at non sunspot locations do not show a clear temperature dependence. We also considered on what scale the underlying driver is affecting the properties of the PDs. Finally, we found that removing the contribution due to the cooler ions in the 193 A wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be contributed to the cool component of 193\AA., Comment: 26 Papges, 15 Figures