The complex interaction of the magnetic field with matter is the key to some of the most puzzling observed phenomena at multiple scales across the Universe, from tokamak plasma confinement ...experiments in the laboratory to the filamentary structure of the interstellar medium. A major astrophysical puzzle is the phenomenon of coronal heating, upon which the most external layer of the solar atmosphere, the corona, is sustained at multi-million degree temperatures on average. However, the corona also conceals a cooling problem. Indeed, recent observations indicate that, even more mysteriously, like snowflakes in the oven, the corona hosts large amounts of cool material termed coronal rain, hundreds of times colder and denser, that constitute the seed of the famous prominences. Numerical simulations have shown that this cold material does not stem from the inefficiency of coronal heating mechanisms, but results from the specific spatio-temporal properties of these. As such, a large fraction of coronal loops, the basic constituents of the solar corona, are suspected to be in a state of thermal non-equilibrium (TNE), characterised by heating (evaporation) and cooling (condensation) cycles whose telltale observational signatures are long-period intensity pulsations in hot lines and thermal instability-driven coronal rain in cool lines, both now ubiquitously observed. In this paper, we review this yet largely unexplored strong connection between the observed properties of hot and cool material in TNE and instability and the underlying coronal heating mechanisms. Focus is set on the long-observed coronal rain, for which significant research already exists, contrary to the recently discovered long-period intensity pulsations. We further identify the outstanding open questions in what constitutes a new, rapidly growing field of solar physics.
Context. Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The ...nonlinear nature of the mechanism has been examined alongside the Kelvin-Helmholtz instability, which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. Aims. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Methods. Using the MPI-AMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. Results. We have observed the development of Kelvin-Helmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.
In addition to their jet-like dynamic behavior, spicules usually exhibit strong transverse speeds, multi-stranded structure, and heating from chromospheric to transition region temperatures. In this ...work we first analyze Hinode and IRIS observations of spicules and find different behaviors 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 Alfvén waves. Others exhibit a Doppler shift sign change at maximum displacement and coherent motion of their strands, suggesting a collective magnetohydrodynamic (MHD) wave. By comparing with an idealized 3D MHD simulation combined with radiative transfer modeling, we analyze 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 Mg ii k and Ca ii H source functions in the transverse cross-section, potentially allowing IRIS to capture the Kelvin-Helmholtz instability dynamics. Twists and currents propagate along the spicule at Alfvénic speeds, and the temperature variations within TWIKH rolls, produce the sudden appearance/disappearance of strands seen in Doppler velocity and in Ca ii 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.
Aims. We investigate the effects of resistivity and viscosity on the onset and growth of the Kelvin-Helmholtz instability (KHI) in an oscillating coronal loop. Methods. We modelled a standing kink ...wave in a density-enhanced loop with the three dimensional (3D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI. Results. Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of η and ν delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instability-suppressed regime (using uniform resistivity). Conclusions. From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν.
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.
ABSTRACT Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun's million-degree outer atmosphere. However, direct evidence of ...the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin-Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.
Context. Diagnostics of magnetohydrodynamic (MHD) waves in the solar atmosphere is a topic that often encounters interpretation problems, partly because of the high complexity of the solar ...atmospheric medium. Forward modelling can significantly guide interpretation, bridging the gap between numerical simulations and observations, and increasing the reliability of mode identification for applying MHD seismology. Aims. We determine the characteristics of the fast MHD sausage mode in the corona on the modulation of observable quantities, such as line intensity and spectral line broadening. Effects of the line-of-sight angle and of spatial, temporal, and spectral resolutions are considered. Methods. We take a cylindrical tube that simulates a loop in a low-β coronal environment with an optically thin background and let it oscillate with the fast sausage mode. A parametric study is performed. Results. Longitudinal structuring of the intensity modulation is obtained and set by the nodal structure of the radial velocity. The modulation is strongly dependent on the contribution function of the spectral line. Under the assumption of equilibrium ionisation, the intensity variation can be very low (≲4% for Fe ix 171) or significant (35% for Fe xii 193). Most of this variation disappears when considering the radiative relaxation times of the ions, due to the fast timescales of the sausage mode in the corona. Regardless of the ionisation state of the plasma, the variation in spectral line broadening can be significant, even for low intensity modulation. The nature of this broadening is not thermal but is mostly turbulent. This places spectrometers in clear advantage over imaging instruments for the detection of the sausage mode. The modulation of all quantities can considerably decrease with the line-of-sight angle with respect to the perpendicular to the tube axis. The spatial and temporal resolution are the main factors affecting modulation, erasing longitudinal structuring when these are on the order of the mode’s wavelength or the mode’s period, placing high constraints on instrumentation. Significant variability in all quantities can still be obtained when viewing at an angle of up to 30°, with pixel size resolutions up to one-third of the mode’s wavelength, or temporal resolution of one fifth of the mode’s period. Modulation is only weakly dependent on spectral resolution due to the mode’s inherent symmetry.
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.
Current analytical and numerical modeling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high ...resolution observations of the corona indicate that its magnetic field may tend to organize itself in fine strand-like structures of few hundred kilometers widths. The link between small structure in models and the observed widths of strand-like structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modeling of three-dimensional MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strand-like structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to Kelvin-Helmholtz instabilities that deform the cross-sectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the line-of-sight angle, last for timescales of a period, and can be observed for spatial resolutions of a tenth of loop radius.
ABSTRACT In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its ...localized nature, 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 are recent observations that indicate that in the low-amplitude regime such transverse MHD waves can also appear decay-less, a still 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 modeling 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 an 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 Alfvén 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 us to estimate the density contrast at the boundary.
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