Review Article: MHD Wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing

Modelling observed decay-less oscillations as resonantly enhanced Kelvin-Helmholtz vortices from transverse MHD waves and their seismological application

In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfv\'en waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfv\'en waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.Comment: 8 pages, 4 figures; Accepted for publication in The Astrophysical Journal Letter

Impact of flux distribution on elementary heating events

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.PostprintPeer reviewe

JPEG2000 image compression on solar EUV images

For future solar missions as well as ground-based telescopes, efficient ways to return and process data has become increasingly important. Solar Or-biter, e.g., 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.PostprintPeer reviewe

Coronal density structure and its role in wave damping in loops

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 PDFPeer reviewe

Effect of coronal loop structure on wave heating by phase mixing

Funding: UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1), 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. R.J. Morton is grateful for support from the UKRI Future Leader Fellowship (RiPSAW - MR/T019891/1) and STFC (ST/T000384/1).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 phase-mixing of Magnetohydrodynamics (MHD) transverse waves has been proposed as a possible way to convert magnetic energy into thermal energy but increasingly, MHD models suggest this is not a sufficiently efficient mechanism. Aims. We model heating by phase-mixing of transverse MHD waves in various configurations, 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 use 3D MHD simulations of a pre-existing density enhancement in 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 (COmP). 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 ofthe 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.PostprintPostprintPeer reviewe

The effects of driving time scales on heating in a coronal arcade

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). IDM received funding from the Research Council of Norway through its Centres of Excellence scheme, project number 262622.Context. The relative importance of AC and DC heating mechanisms in maintaining the temperature of the solar corona is not well constrained. Aims. Investigate the effects of the characteristic time scales of photospheric driving on the injection and dissipation of magnetic and kinetic energy within a coronal arcade. Methods. We have conducted three dimensional MHD simulations of complex foot point driving imposed on a potential coronal arcade. We modified the typical time scales associated with the velocity driver to understand the efficiency of heating obtained using AC and DC drivers. We considered the implications for the injected Poynting flux and the spatial and temporal nature of the energy release in dissipative regimes. Results. For the same driver amplitude and complexity, long time scale velocity motions are able to inject a much greater Poynting flux of energy 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 more 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.PostprintPeer reviewe

Phase mixing and wave heating in a complex coronal plasma

Funding: UK Science and Technology Facilities Council (consolidated grants ST/N000609/1 and ST/S000402/1); European Union Horizon 2020 research and innovation programme (grant agreement No. 647214); Research Council of Norway through its Centres of Excellence scheme, project number 262622 (IDM); Carnegie Trust for the Universities of Scotland (JR).Aims. We investigate the formation of small scales and the related dissipation of magnetohydronamic (MHD) wave energy through non-linear interactions of counter-propagating, phase-mixed Alfvénic waves in a complex magnetic field. Methods. We conducted fully three-dimensional, non-ideal MHD simulations of transverse waves in complex magnetic field configurations. Continuous wave drivers were imposed on the foot points of magnetic field lines and the system was evolved for several Alfvén travel times. Phase-mixed waves were allowed to reflect off the upper boundary and the interactions between the resultant counter-streaming wave packets were analysed. Results. The complex nature of the background magnetic field encourages the development of phase mixing throughout the numerical domain, leading to a growth in alternating currents and vorticities. Counter-propagating phase-mixed MHD wave modes induce a cascade of energy to small scales and result in more efficient wave energy dissipation. This effect is enhanced in simulations with more complex background fields. High-frequency drivers excite localised field line resonances and produce efficient wave heating. However, this relies on the formation of large amplitude oscillations on resonant field lines. Drivers with smaller frequencies than the fundamental frequencies of field lines are not able to excite resonances and thus do not inject sufficient Poynting flux to power coronal heating. Even in the case of high-frequency oscillations, the rate of dissipation is likely too slow to balance coronal energy losses, even within the quiet Sun. Conclusions. For the case of the generalised phase-mixing presented here, complex background field structures enhance the rate of wave energy dissipation. However, it remains difficult for realistic wave drivers to inject sufficient Poynting flux to heat the corona. Indeed, significant heating only occurs in cases which exhibit oscillation amplitudes that are much larger than those currently observed in the solar atmosphere.PostprintPeer reviewe

Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona

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 No. 262622Context. The magnetic Kelvin-Helmholtz instability (KHI) has been proposed as a means of generating magnetohy- drodynamic turbulence and encouraging wave energy dissipation in the solar corona, particularly within transversely oscillating loops. Aims. Our goal is to determine whether the KHI encourages magnetic reconnection in oscillating flux tubes in the solar corona. This will establish whether the instability enhances the dissipation rate of energy stored in the magnetic field. Methods. We conducted a series of three-dimensional magnetohydrodynamic simulations of the KHI excited by an oscillating velocity shear. We investigated the effects of numerical resolution, field line length, and background currents on the growth rate of the KHI and on the subsequent rate of magnetic reconnection. Results. The KHI is able to trigger magnetic reconnection in all cases, with the highest rates occurring during the initial growth phase. Reconnection is found to occur preferentially along the boundaries of Kelvin-Helmholtz vortices, where the shear in the velocity and magnetic fields is greatest. The estimated rate of reconnection is found to be lowest in simulations where the KHI growth rate is reduced. For example, this is the case for shorter field lines or due to shear in the background field. Conclusions. In non-ideal regimes, the onset of the instability causes the local reconnection of magnetic field lines and enhances the rate of coronal wave heating. However, we found that if the equilibrium magnetic field is sheared across the Kelvin-Helmholtz mixing layer, the instability does not significantly enhance the rate of reconnection of the background field, despite the free energy associated with the non-potential field.PostprintPeer reviewe