inekede

• Kumar, A; Howson, T A; Pagano, P & Moortel, Ineke de (2025). Alfvén wave propagation, reflection, and trapping in the solar wind. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 541(4), s. 2843–2852. doi: 10.1093/mnras/staf1189. Fulltekst i vitenarkiv Vis sammendrag

  Alfvén waves are known to be important carriers of magnetic energy that could play a role in coronal heating and/or solar wind acceleration. As these waves are efficient energy carriers, how they are dissipated still remains one of the key challenges. Using a series of 1.5D magnetohydrodynamic (MHD) simulations, we explore wave energy trapping associated with field-aligned density enhancements. We examine the parameters that govern the wave reflection and trapping. The goal of our simulations is to find optimal conditions for wave trapping, which would ultimately promote the energization of the solar atmosphere. In agreement with previous studies, we find that maximum wave reflections happen only for a narrow range of density enhancement widths, namely when it is comparable to the Alfvén wave wavelength. In our paper, we explain this scale-selectivity using a semi-analytical model that demonstrates the importance of wave interference effects. As expected, we find that spatially extended regions of density inhomogeneities favour enhanced wave reflection and trapping. However, wave interference causes saturation of the reflected energy for very extended regions of varying density.

• Howson, T. A.; Moortel, Ineke de & Priest, E. R. (2025). Coronal heating driven by random foot point motions: the effects of magnetic field topology. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 539(2), s. 1820–1833. doi: 10.1093/mnras/staf548. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the effects of magnetic field geometry on energy injection and dissipation, current sheet formation, magnetic reconnection rates and plasma dynamics in the solar corona when energized by random foot point motions. Using a series of 3D magnetohydrodynamics simulations, we compared the effects of high- and low-amplitude random velocity drivers acting on two different initial magnetic fields; (a) a uniform field case and (b) a tectonics case, in which the field is anchored in localized flux patches. In all simulations, the imposed drivers stress the field, generating small scales and leading to energy dissipation through Ohmic and viscous heating. The rates of energy injection, current formation, magnetic reconnection, and the associated energy dissipation are higher when the field is concentrated in flux patches at the simulation boundary. As such, expected heating rates are larger with a tectonics field. However, when high-amplitude driving is imposed on an initially uniform field, flux patches spontaneously form as the field evolves to become a tectonics field. As a result, energy injection and dissipation rates converge to become independent of the initial field state in the high-amplitude cases. As coronal field foot points are typically embedded in concentrated flux patches, we confirm that tectonics is a viable model for coronal heating. Unsurprisingly, we find that the nature of an initial field only influences heating rates as long as this field persists. However, whether solar atmospheric heating is dominated by transverse foot-point motions, as considered here, or by flux emergence events remains an unanswered question.

• Enerhaug, Elisabeth; Carlsson, M.; Szydlarski, Mikolaj; Gudiksen, Boris Vilhelm & Moortel, Ineke de (2025). Identifying magnetohydrodynamic wave modes in the solar atmosphere: Experiments in 2D. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 701. doi: 10.1051/0004-6361/202554210. Fulltekst i vitenarkiv Vis sammendrag

  Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. They are thought to play an important role in maintaining the temperature of the solar corona and are important components of coronal seismology. However, research into reliable wave mode identification schemes is still in its early stages. Such a scheme would be a valuable tool for understanding the role of waves in the coronal heating problem. A widely renowned 2003 study in 2D on magnetoacoustic gravity (MAG) waves crossing the β  = 1 layer in the atmosphere provided valuable insights into wave propagation, from the lower to the upper atmosphere. The in-depth analyses of wave propagation through the solar atmosphere offer a valuable reference, which can be used to test other wave mode identifier schemes that could subsequently be expanded to 3D. Aims. We aim to analyse a set of wave mode identification components designed to isolate properties of fast and slow MAG waves. Methods. We recreated the 2003 experiment using the numerical code Bifrost with simplified boundary conditions. We then compared the existing wave analysis to our own scheme. Results. We show that our wave mode identification scheme is equivalent to that of the scheme used in the 2003 study. We show how physical properties such as steepening, maximum, and minimum can be deduced from the scheme. As these wave mode identifiers can be expanded to 3D, the recreation of the piston experiment along with the careful analysis of the components opens the door for further studies into how MAG waves are transmitted across the β  = 1 layer.

• Breu, C. A.; Pontin, D. I.; Priest, E. & Moortel, Ineke de (2025). On the complex nature of coronal heating. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 545(3). doi: 10.1093/mnras/staf2180. Fulltekst i vitenarkiv Vis sammendrag

  A large part of the hot corona consists of magnetically confined, bright plasma loops. These observed loops are in turn structured into bright strands. We investigate the relationship between magnetic field geometry, plasma properties, and bright strands with the help of a three-dimensional resistive magnetohydrodynamic (MHD) simulation of a coronal loop rooted in a self-consistent convection zone layer. We find that it is impossible to identify a loop as a simple coherent magnetic flux tube that coincides with plasma of nearly uniform temperature and density. The location of bright structures is determined by a complex interplay between heating, cooling, and evaporation time-scales. Current sheets form preferentially at the interfaces of magnetic flux from different sources. They may also form within bundles of magnetic field lines since motions within magnetic concentrations drive plasma flows on a range of time-scales that provide further sub-structure and can locally enhance magnetic field gradients and thus facilitate magnetic reconnection. The numerical experiment therefore possesses aspects of both the flux tube tectonics and flux braiding models. While modelling an observed coronal loop as a cylindrical flux tube is useful to understand the physics of specific heating mechanisms in isolation, it does not describe well the structure of a coronal loop rooted in a self-consistently evolving convection zone.

• Breu, C.A.; Moortel, Ineke de; Peter, H. & Solanki, S.K. (2025). Effect of numerical resolution on synthetic observables of simulated coronal loops. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 537(3), s. 2835–2849. doi: 10.1093/mnras/staf174. Fulltekst i vitenarkiv Vis sammendrag

  Increasingly realistic simulations of the corona are used to predict synthetic observables for instruments onboard both existing and upcoming heliophysics space missions. Synthetic observables play an important role in constraining coronal heating theories. Choosing the spatial resolution of numerical simulations involves a trade-off between accuracy and computational cost. Since the numerical resolution affects not only the scale of structures that can be resolved, but also thermodynamic quantities such as the average coronal density, it is important to quantify the effect on synthesized observables. Using 3D radiative magnetohydrodynamic simulations of coronal loops at three different grid spacings, from 60 km down to 12 km, we find that changes in numerical resolution lead to differences in thermodynamic quantities and stratification as well as dynamic behaviour. Higher grid resolution results in a more complex and dynamic atmosphere. The resolution affects the emission intensity as well as the velocity distribution, thereby affecting synthetic spectra derived from the simulation. The distribution of synthetic coronal loop strand sizes changes as more fine-scale structure is resolved. A number of parameters, however, seem to start to saturate from our chosen medium grid resolution on. Our study shows that while choosing a sufficiently high resolution matters when comparing forward-modelled observables with data from current and future space missions, for most purposes not much is gained by further increasing the resolution beyond a grid spacing of 24 km, which seems to be adequate for reproducing bulk loop properties and forward-modelled emission, representing a good trade-off between accuracy and computational resource.

• Breu, C.A.; Peter, H.; Solanki, S.K.; Cameron, R. & Moortel, Ineke de (2024). Non-thermal broadening of coronal lines in a 3D MHD loop model. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 530(2), s. 2361–2377. doi: 10.1093/mnras/stae899. Fulltekst i vitenarkiv Vis sammendrag

  Observed spectral profiles of emission lines from the corona are found to have widths exceeding the thermal line width. To investigate the physical mechanism, we run a 3D magnetohydrodynamics model of a single, straightened loop in which we partially resolve turbulent motions that form in response to the driving by self-consistently evolving magneto-convection in the photosphere. The convective motions shear and twist the magnetic field lines, leading to heating. From the model, we synthesize spectral profiles of emission lines forming at temperatures around and above 1 MK. The coronal heating process generates a range of velocity amplitudes and directions structured on a scale much smaller than the resolving power of current instruments, leading to a broadening of the spectral lines. Our model includes the mass exchange between corona and chromosphere, thus we also capture flows parallel to the loop axis. We find that the spectral lines show a non-thermal line broadening roughly consistent with observations for a viewing angle perpendicular to the axis. The broadening through field-parallel flows is comparable, although slightly smaller. The line broadening is independent of the instrument resolution for a perpendicular line of sight (LOS). We can connect the non-thermal line broadening to heating events and flows. While small-scale velocities along the LOS are mainly responsible for the broadening observed perpendicular to the loop, chromospheric evaporation is important for the line broadening observed along the loop. The model reproduces observed values for non-thermal line widths. In the model, these result from continuous driving by magnetoconvection, without imposing driving motions or starting from an already braided field.

• Enerhaug, Elisabeth; Howson, T.A. & Moortel, Ineke de (2024). Identifying Alfvén wave modes in the solar corona. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 681. doi: 10.1051/0004-6361/202347790. Fulltekst i vitenarkiv Vis sammendrag

  Context. Oscillations are observed to be pervasive throughout the solar corona, but it remains challenging to positively identify different wave modes. Improving this identification would provide a powerful tool for investigating coronal wave heating and improving seismological inversions. Aims. We aim to establish whether theoretical methods used to identify magnetohydrodynamical wave modes in numerical simulations can be employed on observational datasets. Methods. We applied wave identifiers based on fundamental wave characteristics such as compressibility and direction of propagation to a fully 3D numerical simulation of a transversely oscillating coronal loop. The same wave identifiers were applied to the line-of-sight integrated synthetic emission derived from the numerical simulation data to investigate whether this method could feasibly be useful for observational studies. Results. We established that for particular line(s) of sight and assumptions about the magnetic field, we can correctly identify the properties of the Alfvén mode in synthetic observations of a transversely oscillating loop. Under suitable conditions, there is a strong agreement between the simulation and synthetic emission results. Conclusions. For the first time, we have provided a proof of concept that this theoretically derived classification of magnetohydrodynamic wave modes can be applied to observational data.

• Callingham, H.; Moortel, Ineke de & Pagano, P. (2024). The evolution of the coronal loop structure due to the phase mixing of high and low-frequency Alfvén waves. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 535(2), s. 1640–1651. doi: 10.1093/mnras/stae2455. Fulltekst i vitenarkiv Vis sammendrag

  Coronal loops are known to host Alfvén waves propagating in the corona from the lower layers of the solar atmosphere and because of their internal structure, phase mixing is likely to occur. The structure of the coronal loop could be significantly affected by the thermodynamic feedback of the heating generated by phase mixing. However, this phenomenon can be sensitive to the period of the propagating Alfvén waves due to how short period waves can be easily dissipated and the way long-period waves may accumulate considerable energy in resonating coronal loops. Using the Lare2d code, a coronal loop model of a field-aligned thermodynamic equilibrium and a cross-field background heating profile is created, with an additional forcing term added to drive Alfvén waves with coronal amplitudes between ⁠. We show that high-frequency waves can generate heating corresponding to a increase of the initial coronal shell temperature, chromospheric upflows of up to   and a coronal shell mass increase of ⁠. These changes are sufficient to alter and maintain a new coronal loop density structure, broadening the region where efficient phase mixing (and therefore heating) occurs. In contrast, low-frequency waves are unable to be effectively dissipated, resulting in minimal changes to the loop structure. We see little evidence of wave energy accumulation in the corona and are unable to conclude that the dissipation of low-frequency Alfvén waves can be an effective heating mechanism in coronal loops in the setup used in this study.

• Breu, C.A.; Moortel, Ineke de & Testa, P. (2024). MUSE observations of small-scale heating events. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 531(1), s. 1671–1684. doi: 10.1093/mnras/stae1126. Fulltekst i vitenarkiv Vis sammendrag

  Constraining the processes that drive coronal heating from observations is a difficult task due to the complexity of the solar atmosphere. As upcoming missions such as the Multi-slit Solar Explorer (MUSE) will provide coronal observations with unprecedented spatial and temporal resolution, numerical simulations are becoming increasingly realistic. Despite the availability of synthetic observations from numerical models, line-of-sight effects and the complexity of the magnetic topology in a realistic set-up still complicate the prediction of signatures for specific heating processes. 3D magnetohydrodynamic (MHD) simulations have shown that a significant part of the Poynting flux injected into the solar atmosphere is carried by small-scale motions, such as vortices driven by rotational flows inside intergranular lanes. MHD waves excited by these vortices have been suggested to play an important role in the energy transfer between different atmospheric layers. Using synthetic spectroscopic data generated from a coronal loop model incorporating realistic driving by magnetoconvection, we study whether signatures of energy transport by vortices and eventual dissipation can be identified with future missions such as MUSE.

• Howson, Thomas & Moortel, Ineke de (2023). Heating and Cooling in Transversely Oscillating Coronal Loops Powered by Broadband, Multi-Directional Wave Drivers. Physics. 5(1), s. 140–160. doi: 10.3390/physics5010011. Fulltekst i vitenarkiv Vis sammendrag

  Recent studies have identified the potential for coronal wave heating to balance radiative losses in a transversely oscillating low-density loop undergoing resonant absorption, phase mixing and the Kelvin–Helmholtz instability. This result relied on a continuous, resonant oscillatory driver acting on one of the loop footpoints and similar setups with non-resonant driving produce insufficient heating. Here, we consider broadband and multi-directional drivers with power in both resonant and non-resonant frequencies. Using three-dimensional magnetohydrodynamic simulations, we impose transverse, continuous velocity drivers at the footpoints of a coronal loop, which is dense in comparison to the background plasma. We include the effects of optically thin radiation and a uniform background heating term that maintains the temperature of the external plasma but is insufficient to balance energy losses within the loop. For both broadband and multi-directional drivers, we find that the energy dissipation rates are sufficient to balance the average energy losses throughout the simulation volume. Resonant components of the wave driver efficiently inject energy into the system and these frequencies dominate the energetics. Although the mean radiative losses are balanced, the loop core cools in all cases as the wave heating rates are locally insufficient, despite the relatively low density considered here.

• Howson, T.A. & Moortel, Ineke De (2022). The effects of driving time scales on coronal heating in a stratified atmosphere. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 661. doi: 10.1051/0004-6361/202142872. Fulltekst i vitenarkiv Vis sammendrag

  Aims. We investigate the atmospheric response to coronal heating driven by random velocity fields with different characteristic time scales and amplitudes. Methods. We conducted a series of three-dimensional magnetohydrodynamic simulations of random driving imposed on a gravitationally stratified model of the solar atmosphere. In order to understand differences between alternating current (AC) and direct current (DC) heating, we considered the effects of changing the characteristic time scales of the imposed velocities. We also investigated the effects of the magnitude of the velocity driving. Results. In all cases, complex foot point motions lead to a proliferation of current sheets and energy dissipation throughout the coronal volume. For a given driving amplitude, DC driving typically leads to a greater rate of energy injection when compared to AC driving. This ultimately leads to the formation of larger currents, increased heating rates, and higher coronal temperatures in DC simulations. There is no difference in the spatial distribution of energy dissipation across simulations; however, energy release events in AC cases tend to be more frequent and last for less time than in DC cases. This results in more asymmetric temperature profiles for field lines heated by AC drivers. Higher velocity driving is associated with larger currents, higher temperatures, and the corona occupying a larger fraction of the simulation volume. In all cases, the majority of heating is associated with small energy release events, which occur much more frequently than larger events. Conclusions. When combined with observational results that highlight a greater abundance of oscillatory power in lower frequency modes, these findings suggest that energy release in the corona is more likely to be driven by longer time scale motions. In the corona, AC and DC driving occur concurrently and their effects remain difficult to isolate. The distribution of field line temperatures and the asymmetry of temperature profiles may reveal the frequency and longevity of energy release events and therefore the relative importance of AC and DC heating.

• Pascoe, D.J.; Doorsselaere, T. Van & Moortel, Ineke De (2022). Coronal Seismology Using Damping of Propagating Kink Waves. The Astrophysical Journal (ApJ). ISSN 0004-637X. 929(1). doi: 10.3847/1538-4357/ac5e30. Fulltekst i vitenarkiv Vis sammendrag

  We consider the use of propagating kink waves, such as those observed by the Coronal Multi-channel Polarimeter, as a diagnostic technique. The transverse structuring of the plasma may be inferred by the frequency-dependent wave damping, which is attributed to resonant absorption. We include the effect of reflection of waves at the loop footpoints, which leads to the asymmetry parameter, describing the ratio of driven wave power at the footpoints becoming weakly constrained. The classical model of resonant absorption based on an exponential damping profile significantly overestimates the damping rate in coronal loops with low density contrast ratios. The use of the exponential profile in an analysis of observations therefore leads to underestimates for the density contrast ratio and associated parameters such as the heating rate following phase mixing.

• Pascoe, David J.; Moortel, Ineke de; Pagano, P. & Howson, T. A. (2022). Propagating Alfvén waves in open structures with random structuring. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 516(2), s. 2181–2188. doi: 10.1093/mnras/stac2294. Fulltekst i vitenarkiv Vis sammendrag

  ABSTRACT We consider the behaviour of Alfvén waves propagating in a medium with random density perturbations. The imposed density perturbations have a broad-band 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.

• Moortel, Ineke de & Howson, Thomas A. (2022). (When) Can Wave Heating Balance Optically Thin Radiative Losses in the Corona? The Astrophysical Journal (ApJ). ISSN 0004-637X. 941(1). doi: 10.3847/1538-4357/aca072. Fulltekst i vitenarkiv Vis sammendrag

  Abstract 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 nonresonant 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 ∼5 × 10 −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 nonresonant frequency, or both, leads to cooling of the coronal loop as the energy losses are greater than the energy injection and dissipation rates.

• Pontieu, Bart Walter De; Testa, Paola; Martinez-Sykora, Juan; Antolin, Patrick; Karampelas, Konstantinos & Hansteen, Viggo Haraldson [Vis alle 26 forfattere av denne artikkelen] (2022). Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE). I. Coronal Heating. The Astrophysical Journal (ApJ). ISSN 0004-637X. 926(1). doi: 10.3847/1538-4357/ac4222. Fulltekst i vitenarkiv
• Banerjee, D.; Prasad, S. Krishna; Pant, V.; McLaughlin, J. A.; Antolin, Patrick & Magyar, Norbert [Vis alle 11 forfattere av denne artikkelen] (2021). Magnetohydrodynamic Waves in Open Coronal Structures. Space Science Reviews. ISSN 0038-6308. 217(7). doi: 10.1007/s11214-021-00849-0. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Viall, Nicholeen; Moortel, Ineke De; Downs, Cooper; Klimchuk, James A.; Parenti, Susanna & Reale, Fabio (2021). The Heating of the Solar Corona. I Raouafi, Nour E.; Vourlidas, Angelos; Zhang, Yongliang & Paxton, Larry J. (Red.), Solar Physics and Solar Wind. American Geophysical Union (AGU). ISSN 9781119507536. s. 35–82. doi: 10.1002/9781119815600.ch2. Fulltekst i vitenarkiv
• Johnston, Craig D.; Hood, Alan W.; Moortel, Ineke De; Pagano, Paolo & Howson, Thomas A. (2021). A fast multi-dimensional magnetohydrodynamic formulation of the transition region adaptive conduction (TRAC) method. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 654. doi: 10.1051/0004-6361/202140987. Fulltekst i vitenarkiv Vis sammendrag

  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, generated during the evaporation phase of impulsive heating events, can produce current layers that are significantly narrower than the transverse energy deposition.

• Fyfe, Lianne E.; Howson, Thomas A. & Moortel, Ineke De (2021). Forward modelling of heating within a coronal arcade. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 656. doi: 10.1051/0004-6361/202142028. Fulltekst i vitenarkiv Vis sammendrag

  Aims. We investigate the synthetic observational signatures generated from numerical models of coronal heating in an arcade in order to determine what features are associated with such heating and what tools can be used to identify them. Methods. We consider two simulations of coronal arcades driven by footpoint motions with different characteristic timescales. Forward modelling is then conducted, and the synthetic emission data are analysed (e.g., intensities, Doppler shifts, line widths and estimated kinetic energies). Results. The total intensity and Doppler shift perturbations clearly show the magnetic structure of the coronal arcade. Contrasts in the local Doppler velocity also highlight the locations of separatrix surfaces. The distinguishing feature of the models with short and long timescale photospheric motions (in comparison to the Alfvén travel time along a loop) is that of the frequencies. Through fast Fourier transform analysis of the Doppler velocities, it is clear that when short timescale footpoint motions are present, higher frequency perturbations are observed. For longer timescale footpoint motions, the dominant signal is that of lower frequencies; however, higher (but less powerful) frequencies were also detected, which matched the natural Alfvén frequency of the background magnetic field. Signatures of Alfvénic waves were identified in both models, with fast wave signatures observable when short timescale driving is present. Finally, we examine the estimates of the kinetic energy using the Doppler velocities and find it to be significantly underestimated within these models. Conclusions. All of the observables within this article behave as one would expect, given the evolution of the plasma parameters. Such features were, for example, Alfvén waves, fast waves, the arcade structure and separatrix surfaces. We were able to differentiate between the two models by examining the frequencies present. The Doppler velocities cannot provide accurate estimates of the total kinetic energy or even the component parallel to the line-of-sight (LOS). This is due to some of the plasma being outside the formation temperature of the ion, the multi-directional driver limiting the proportion of the velocity aligned along the LOS, and cancellation of the velocity along the LOS. The exact impact each factor has on the estimation is dependent on the setup of the model and the emission line under investigation.

• Howson, Thomas A.; Moortel, Moortel De & Pontin, David I. (2021). Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 656. doi: 10.1051/0004-6361/202141620. Fulltekst i vitenarkiv Vis sammendrag

  Context. The magnetic Kelvin-Helmholtz instability (KHI) has been proposed as a means of generating magnetohydrodynamic 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.

• Fyfe, Lyanne E.; Howson, Thomas A.; Moortel, Ineke de; Pant, Vaibhav & Doorsselaere, Tom Van (2021). Investigating coronal wave energy estimates using synthetic non-thermal line widths. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 656. doi: 10.1051/0004-6361/202141749. Fulltekst i vitenarkiv Vis sammendrag

  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 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: Alfvén 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.

• Pagano, P.; Moortel, Ineke de & Morton, R. J. (2020). Effect of coronal loop structure on wave heating through phase mixing. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 643. doi: 10.1051/0004-6361/202039209. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Fyfe, L. E.; Howson, Thomas A. & Moortel, Ineke de (2020). Forward modelling of MHD waves in braided magnetic fields. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 643. doi: 10.1051/0004-6361/202038945. Fulltekst i vitenarkiv Vis sammendrag

  Aims. We investigate synthetic observational signatures generated from numerical models of transverse waves propagating in complex (braided) magnetic fields. Methods. We consider two simulations with different levels of magnetic field braiding and impose periodic, transverse velocity perturbations at the lower boundary. As the waves reflect off the top boundary, a complex pattern of wave interference occurs. We applied the forward modelling code FoMo and analysed the synthetic emission data. We examined the line intensity, Doppler shifts, and kinetic energy along several line-of-sight (LOS) angles. Results. The Doppler shift perturbations clearly show the presence of the transverse (Alfvénic) waves. However, in the total intensity, and running difference, the waves are less easily observed for more complex magnetic fields and may be indistinguishable from background noise. Depending on the LOS angle, the observable signatures of the waves reflect some of the magnetic field braiding, particularly when multiple emission lines are available, although it is not possible to deduce the actual level of complexity. In the more braided simulation, signatures of phase mixing can be identified. We highlight possible ambiguities in the interpretation of the wave modes based on the synthetic emission signatures. Conclusions. Most of the observables discussed in this article behave in the manner expected, given knowledge of the evolution of the parameters in the 3D simulations. Nevertheless, some intriguing observational signatures are present. Identifying regions of magnetic field complexity is somewhat possible when waves are present; although, even then, simultaneous spectroscopic imaging from different lines is important in order to identify these locations. Care needs to be taken when interpreting intensity and Doppler velocity signatures as torsional motions, as is done in our setup. These types of signatures are a consequence of the complex nature of the magnetic field, rather than real torsional waves. Finally, we investigate the kinetic energy, which was estimated from the Doppler velocities and is highly dependent on the polarisation of the wave, the complexity of the background field, and the LOS angles.

• Doorsselaere, Tom Van; Srivastava, Abhishek; Antolin, Patrick; Magyar, Norbert; Farahani, Soheil Vasheghani & Tian, Hui [Vis alle 12 forfattere av denne artikkelen] (2020). Coronal Heating by MHD Waves. Space Science Reviews. ISSN 0038-6308. 216. doi: 10.1007/s11214-020-00770-y. Fulltekst i vitenarkiv Vis sammendrag

  The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The current understanding of coronal heating relies on two main mechanism: reconnection and MHD waves that may have various degrees of importance in different coronal regions. In this review we focus on recent advances in our understanding of MHD wave heating mechanisms. First, we focus on giving an overview of observational results, where we show that different wave modes have been discovered in the corona in the last decade, many of which are associated with a significant energy flux, either generated in situ or pumped from the lower solar atmosphere. Afterwards, we summarise the recent findings of numerical modelling of waves, motivated by the observational results. Despite the advances, only 3D MHD models with Alfvén wave heating in an unstructured corona can explain the observed coronal temperatures compatible with the quiet Sun, while 3D MHD wave heating models including cross-field density structuring are not yet able to account for the heating of coronal loops in active regions to their observed temperature.

• Howson, Thomas A.; Moortel, Ineke de & Fyfe, L. E. (2020). The effects of driving time scales on heating in a coronal arcade. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 643. doi: 10.1051/0004-6361/202038869. Fulltekst i vitenarkiv Vis sammendrag

  Context. The relative importance of alternating current (AC) and direct current (DC) heating mechanisms in maintaining the temperature of the solar corona is not well constrained. Aims. We aim to 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 conducted three-dimensional magnetohydrodynamic 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 that show that 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.

• Howson, Thomas A.; Moortel, Ineke de & Reid, J. (2020). Phase mixing and wave heating in a complex coronal plasma. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 636. doi: 10.1051/0004-6361/201937332. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Moortel, Ineke de; Falconer, Isobel & Stack, Robert (2020). Alfvén on heating by waves. Astronomy & Geophysics. ISSN 1366-8781. 61(2), s. 2.34–2.39. doi: 10.1093/astrogeo/ataa031. Fulltekst i vitenarkiv Vis sammendrag

  Abstract Ineke De Moortel, Isobel Falconer and Robert Stack explore the achievements and influence of Hannes Alfvén, in particular his seminal Monthly Notices paper of 1947 on the heating of the solar corona.

• Johnston, Craig D.; Cargill, P. J.; Hood, A. W.; Moortel, Ineke de; Bradshaw, S. J. & Vassekar, A. C. (2020). Modelling the solar transition region using an adaptive conduction method. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 635. doi: 10.1051/0004-6361/201936979. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Damme, H. J. Van; Moortel, Ineke de; Pagano, P. & Johnston, Craig D. (2020). Chromospheric evaporation and phase mixing of Alfvén waves in coronal loops. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 635. doi: 10.1051/0004-6361/201937266. Fulltekst i vitenarkiv Vis sammendrag

  Context. Phase mixing of Alfvén 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. Aims. In this paper, for the first time, we use magnetohydrodynamic (MHD) simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfvén waves in a coronal loop and the effect of this evaporation on the transverse density profile. Methods. The numerical simulations were performed using the Lagrangian Remap code Lare2D. 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 Alfvén wave driver was implemented. As the Alfvén 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 Alfvén waves, and the subsequent evaporation from the lower atmosphere. Results. We find that phase mixing of Alfvén 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 −1 . 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. Conclusions. 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.

• Howson, T. A.; Moortel, Ineke de; Reid, J. & Hood, A. W. (2019). Magnetohydrodynamic waves in braided magnetic fields. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 629. doi: 10.1051/0004-6361/201935876. Fulltekst i vitenarkiv Vis sammendrag

  Aims. We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field. Methods. We performed a series of three dimensional MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation. Results. Spatial gradients in the local Alfvén speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfvén speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma. Conclusions. The phase mixing of transverse MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining the observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma.

• Howson, T. A.; Moortel, Ineke de; Antolin, Patrick; Doorsselaere, Tom Van & Wright, A. N. (2019). Resonant absorption in expanding coronal magnetic flux tubes with uniform density. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 631. doi: 10.1051/0004-6361/201936146. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Pagano, P.; Damme, H. J. Van; Antolin, Patrick & Moortel, Ineke de (2019). MHD simulations of the in situ generation of kink and sausage waves in the solar corona by collision of dense plasma clumps. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 626. doi: 10.1051/0004-6361/201935539. Fulltekst i vitenarkiv Vis sammendrag

  Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar corona where the highly structured magnetic fields provide efficient wave guides for their propagation. While MHD waves have been observed originating from lower layers of the solar atmosphere, recent studies have shown that some can be generated in situ by the collision of dense counter-propagating flows. Aims. In this theoretical study, we analyse the mechanism that triggers the propagation of kink and sausage modes in the solar corona following the collision of counter-propagating flows, and how the properties of the flows affect the properties of the generated waves. Methods. To study in detail this mechanism we ran a series of ideal 2D and 3D MHD simulations where we varied the properties of the counter-propagating flows; by means of a simple technique to estimate the amplitudes of the kink and sausage modes, we investigated their role in the generation and propagation of the MHD waves. Results. We find that the amplitude of the waves is largely dependent on the kinetic energy of the flows, and that the onset of kink or sausage modes depends on the asymmetries between the colliding blobs. Moreover, the initial wavelength of the MHD waves is associated with the magnetic configuration resulting from the collision of the flows. We also find that genuine 3D systems respond with smaller wave amplitudes. Conclusions. In this study, we present a parameter space description of the mechanism that leads to the generation of MHD waves from the collision of flows in the corona. Future observations of these waves can be used to understand the properties of the plasma and magnetic field of the solar corona.

Se alle arbeider i NVA

• Moortel, Ineke de (2021). Our Dynamic Sun. Fulltekst i vitenarkiv
• Moortel, Ineke de; Howson, Tom; Pagano, Paolo & Damme, Hendrik-Jan Van (2020). Aspects of MHD wave heating in the complex solar atmosphere. Fulltekst i vitenarkiv
• Moortel, Ineke de (2020). Our 21st Century Sun. Fulltekst i vitenarkiv
• Moortel, Ineke de (2020). Our Dynamic Sun, Solar Storms and Atmospheric Effects on Earth's Communities. Fulltekst i vitenarkiv
• Moortel, Ineke de; Howson, Tom; Pagano, Paolo; Morton, Richard & Reid, Jack (2020). Aspects of MHD wave heating in the complex solar atmosphere. Fulltekst i vitenarkiv
• Enerhaug, Elisabeth; Gudiksen, Boris Vilhelm; Carlsson, Mats; Moortel, Ineke de & Howson, Tom (2025). Identifying magnetohydrodynamic wave modes in the solar atmosphere. Universitetet i Oslo. Fulltekst i vitenarkiv

Se alle arbeider i NVA