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1
Buchlin, É. "Intermittent heating of the solar corona by MHD turbulence." Nonlinear Processes in Geophysics 14, no. 5 (October 24, 2007): 649–54. http://dx.doi.org/10.5194/npg-14-649-2007.
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Abstract. As the dissipation mechanisms considered for the heating of the solar corona would be sufficiently efficient only in the presence of small scales, turbulence is thought to be a key player in the coronal heating processes: it allows indeed to transfer energy from the large scales to these small scales. While Direct numerical simulations which have been performed to investigate the properties of magnetohydrodynamic turbulence in the corona have provided interesting results, they are limited to small Reynolds numbers. We present here a model of coronal loop turbulence involving shell-models and Alfvén waves propagation, allowing the much faster computation of spectra and turbulence statistics at higher Reynolds numbers. We also present first results of the forward-modelling of spectroscopic observables in the UV.
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Zou, Jitong, Aohua Mao, Xiaogang Wang, Yangyang Hua, and Tianchun Zhou. "Solar Coronal Heating Fueled by Random Bursts of Fine-scale Magnetic Reconnection in Turbulent Plasma Regions." Astrophysical Journal 943, no. 2 (February 1, 2023): 155. http://dx.doi.org/10.3847/1538-4357/acaec2.
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Abstract Coronal heating is a longstanding issue in solar physics as well as plasma physics in general. In recent years, significant resolution improvements of satellite observations have contributed to a deeper understanding of small-scale physics, e.g., magnetic reconnection processes on fine scales inside the turbulent geo-magnetosheath. Coronal plasmas feature turbulent complexity of flows and magnetic fields with similar fine scales, and thus electron magnetic reconnection is very likely to be excited in the coronal region working as one of the ways to heat the solar corona, which offers a possible new mechanism for the nanoflare model proposed by Parker. We in this paper simulate and analyze the magnetic reconnection processes on a fine scale of the electron skin depth, with a particle-in-cell treatment, and estimate its contribution to coronal heating. The result shows that the electron magnetic reconnection can provide substantial heating efficiency for heating the corona to its observed temperature, once the reconnection events are reasonably spread.
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Howson, T. A., I. De Moortel, and L. E. Fyfe. "The effects of driving time scales on heating in a coronal arcade." Astronomy & Astrophysics 643 (November 2020): A85. http://dx.doi.org/10.1051/0004-6361/202038869.
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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.
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Velli, M., F. Pucci, F. Rappazzo, and A. Tenerani. "Models of coronal heating, turbulence and fast reconnection." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2042 (May 28, 2015): 20140262. http://dx.doi.org/10.1098/rsta.2014.0262.
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Coronal heating is at the origin of the EUV and X-ray emission and mass loss from the sun and many other stars. While different scenarios have been proposed to explain the heating of magnetically confined and open regions of the corona, they must all rely on the transfer, storage and dissipation of the abundant energy present in photospheric motions, which, coupled to magnetic fields, give rise to the complex phenomenology seen at the chromosphere and transition region (i.e. spicules, jets, ‘tornadoes’). Here we discuss models and numerical simulations which rely on magnetic fields and electric currents both for energy transfer and for storage in the corona. We will revisit the sources and frequency spectrum of kinetic and electromagnetic energies, the role of boundary conditions, and the routes to small scales required for effective dissipation. Because reconnection in current sheets has been, and still is, one of the most important processes for coronal heating, we will also discuss recent aspects concerning the triggering of reconnection instabilities and the transition to fast reconnection.
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Howson, Thomas. "How Transverse Waves Drive Turbulence in the Solar Corona." Symmetry 14, no. 2 (February 15, 2022): 384. http://dx.doi.org/10.3390/sym14020384.
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Oscillatory power is pervasive throughout the solar corona, and magnetohydrodynamic (MHD) waves may carry a significant energy flux throughout the Sun’s atmosphere. As a result, over much of the past century, these waves have attracted great interest in the context of the coronal heating problem. They are a potential source of the energy required to maintain the high-temperature plasma and may accelerate the fast solar wind. Despite many observations of coronal waves, large uncertainties inhibit reliable estimates of their exact energy flux, and as such, it remains unclear whether they can contribute significantly to the coronal energy budget. A related issue concerns whether the wave energy can be dissipated over sufficiently short time scales to balance the atmospheric losses. For typical coronal parameters, energy dissipation rates are very low and, thus, any heating model must efficiently generate very small-length scales. As such, MHD turbulence is a promising plasma phenomenon for dissipating large quantities of energy quickly and over a large volume. In recent years, with advances in computational and observational power, much research has highlighted how MHD waves can drive complex turbulent behaviour in the solar corona. In this review, we present recent results that illuminate the energetics of these oscillatory processes and discuss how transverse waves may cause instability and turbulence in the Sun’s atmosphere.
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Lu, Zekun, Feng Chen, J. H. Guo, M. D. Ding, Can Wang, Haocheng Yu, Y. W. Ni, and Chun Xia. "Periodic Coronal Rain Driven by Self-consistent Heating Process in a Radiative Magnetohydrodynamic Simulation." Astrophysical Journal Letters 973, no. 1 (September 1, 2024): L1. http://dx.doi.org/10.3847/2041-8213/ad73d2.
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Abstract The periodic coronal rain and in-phase radiative intensity pulsations have been observed in multiple wavelengths in recent years. However, due to the lack of three-dimensional coronal magnetic fields and thermodynamic data in observations, it remains challenging to quantify the coronal heating rate that drives the mass cycles. In this work, based on the MURaM code, we conduct a three-dimensional radiative magnetohydrodynamic simulation spanning from the convective zone to the corona, where the solar atmosphere is heated self-consistently through dissipation resulting from magnetoconvection. For the first time, we model the periodic coronal rain in an active region. With a high spatial resolution, the simulation well resembles the observational features across different extreme-ultraviolet wavelengths. These include the realistic interweaving coronal loops, periodic coronal rain, and periodic intensity pulsations, with two periods of 3.0 hr and 3.7 hr identified within one loop system. Moreover, the simulation allows for a detailed three-dimensional depiction of coronal rain on small scales, revealing adjacent shower-like rain clumps ∼500 km in width and showcasing their multithermal internal structures. We further reveal that these periodic variations essentially reflect the cyclic energy evolution of the coronal loop under thermal nonequilibrium state. Importantly, as the driver of the mass circulation, the self-consistent coronal heating rate is considerably complex in time and space, with hour-level variations in 1 order of magnitude, minute-level bursts, and varying asymmetry reaching ten times between footpoints. This provides an instructive template for the ad hoc heating function and further enhances our understanding of the coronal heating process.
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Pontin, D. I., E. R. Priest, L. P. Chitta, and V. S. Titov. "Coronal Heating and Solar Wind Generation by Flux Cancellation Reconnection." Astrophysical Journal 960, no. 1 (December 21, 2023): 51. http://dx.doi.org/10.3847/1538-4357/ad03eb.
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Abstract In this paper, we propose that flux cancellation on small granular scales (≲1000 km) ubiquitously drives reconnection at a multitude of sites in the low solar atmosphere, contributing to chromospheric/coronal heating and the generation of the solar wind. We analyze the energy conversion in these small-scale flux cancellation events using both analytical models and three-dimensional, resistive magnetohydrodynamic (MHD) simulations. The analytical models—in combination with the latest estimates of flux cancellation rates—allow us to estimate the energy release rates due to cancellation events, which are found to be on the order 106–107 erg cm−2 s−1, sufficient to heat the chromosphere and corona of the quiet Sun and active regions, and to power the solar wind. The MHD simulations confirm the conversion of energy in reconnecting current sheets, in a geometry representing a small-scale bipole being advected toward an intergranular lane. A ribbon-like jet of heated plasma that is accelerated upward could also escape the Sun as the solar wind in an open-field configuration. We conclude that through two phases of atmospheric energy release—precancellation and cancellation—the cancellation of photospheric magnetic flux fragments and the associated magnetic reconnection may provide a substantial energy and mass flux contribution to coronal heating and solar wind generation.
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Gómez, Daniel O., and Pablo Dmitruk. "Turbulent heating of coronal active regions." Proceedings of the International Astronomical Union 3, S247 (September 2007): 269–78. http://dx.doi.org/10.1017/s1743921308014968.
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AbstractMagnetohydrodynamic turbulence has been proposed as a mechanism for the heating of coronal active regions, and has therefore been actively investigated in recent years. According to this scenario, a turbulent regime is driven by footpoint motions. The energy being pumped this way into active region loops, is efficiently transferred to small scales due to a direct energy cascade. The ensuing generation of fine scale structures, which is a natural outcome of turbulent regimes, helps to enhance the dissipation of either waves or DC currents.We present an updated overview of recent results on turbulent coronal heating. To illustrate this theoretical scenario, we simulate the internal dynamics of a coronal loop within the reduced MHD approximation. The application of a stationary velocity field at the photospheric boundary leads to a turbulent stationary regime after several photospheric turnover times. This regime is characterized by a broadband power spectrum and energy dissipation rate levels compatible with the heating requirements of active region loops. Also, the energy dissipation rate displays a complex superposition of impulsive events, which we associate to the so-called nanoflares. A statistical analysis yields a power law distribution as a function of their energies, which is consistent with those obtained from observations. We also study the distributions of peak dissipation rate and duration of these events.
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Howson, T. A., I. De Moortel, and J. Reid. "Phase mixing and wave heating in a complex coronal plasma." Astronomy & Astrophysics 636 (April 2020): A40. http://dx.doi.org/10.1051/0004-6361/201937332.
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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.
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Ionson, James A. "A Unified Theory of Coronal Heating." Symposium - International Astronomical Union 107 (1985): 139–43. http://dx.doi.org/10.1017/s0074180900075574.
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This presentation focuses upon the coronal heating problem and reports the results of Ionson's (1984) unified theory of electrodynamic heating. This generalized theory, which is based upon Ionson's (1982) LRC approach, unveils a variety of new heating mechanisms and links together previously proposed processes. Specifically, Ionson (1984) has derived a standing wave equation for the global current, I, driven by emfs that are generated by the β≳1 convection. This global electrodynamics equation has the same form as a driven LRC equation where the equivalent inductance, L=4ℓ/πc2, scales with the coronal loop length and where the equivalent capacitance, C=c2 ℓ/4πv2A, is essentially the product of the free space capacitance, ℓ/4π, and the low frequency dielectric constant, c2/v2A. The driving emf, ∊=vBa/c, is a formal integration constant associated with the convective stressing of β≳1 magnetic fields. Since the transition from the β≳1 driver to the β<1 coronal loop is typically small compared to the “wavelength” of the associated magnetic fluctuation, this integration constant is not sensitive to details of the transition zone. The total resistance, Rtot = L(1/tdiss+1/tphase+1/tleak), represents electrodynamic energy “loss” from dissipation, magnetic stress leakage out of the loop and phase-mixing. These three processes have been parameterized by appropriate timescales. Note that Rleak=L/tleak and Rphase=L/tphase do not result in resistive heating but do participate in limiting the amplitude of the global current, I. This is fairly obvious with regard to magnetic stress leakage but not for phase-mixing. The phase-mixing resistance, Rphase, represents coupling between the global current and the local current density. Since the global current is essentially an integration of the local currents, the degree of coherency between the local currents can play an important role in determining the ultimate amplitude of I. The rate at which coherency between the local currents is lost is given by the phase-mixing time, tphase. A loss of coherency implies a corresponding reduction in the amplitude of I. In this sense, Rphase measures the phase-mixing contribution to the global current limitation process.
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Howson, T. A., I. De Moortel, P. Antolin, T. Van Doorsselaere, and A. N. Wright. "Resonant absorption in expanding coronal magnetic flux tubes with uniform density." Astronomy & Astrophysics 631 (October 31, 2019): A105. http://dx.doi.org/10.1051/0004-6361/201936146.
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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.
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Kalkofen, Wolfgang. "Heating and dynamics of the quiet solar chromosphere." Proceedings of the International Astronomical Union 3, S247 (September 2007): 93–98. http://dx.doi.org/10.1017/s1743921308014725.
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AbstractThe quiet solar chromosphere in regions with negligible magnetic field is believed to be heated by acoustic waves. But their energy flux, measured in the upper photosphere with the Transition Region And Coronal Explorer (TRACE), has been found to be insufficient to account for the radiative emission from the chromosphere. Wedemeyer-Böhm et al. (2007) and Cuntz et al. (2007), employing a 3D hydrodynamical model by Wedemeyer et al. (2004), have proposed that the spatial resolution of TRACE is inadequate to resolve intensity fluctuations that occur on small spatial scales. This paper accepts the principle of spatial averaging by TRACE as a qualitative explanation for the low acoustic flux but finds that the hydrodynamical model is too much simplified in the treatment of radiative energy exchange to provide a quantitative measure of the suppression of the fluctuations. The heating mechanism of the chromosphere thus remains an open question.
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Petrova, Elena, Norbert Magyar, Tom Van Doorsselaere, and David Berghmans. "High-frequency Decayless Waves with Significant Energy in Solar Orbiter/EUI Observations." Astrophysical Journal 946, no. 1 (March 1, 2023): 36. http://dx.doi.org/10.3847/1538-4357/acb26a.
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Abstract High-frequency wave phenomena present a great deal of interest as one of the possible candidates to contribute to the energy input required to heat the corona as a part of the alternating current heating theory. However, the resolution of imaging instruments up until the Solar Orbiter has made it impossible to resolve the necessary time and spatial scales. The present paper reports on high-frequency transverse motions in a small loop located in a quiet-Sun region of the corona. The oscillations were observed with the High Resolution Imager in the Extreme Ultraviolet telescope (17.4 nm) of the Extreme Ultraviolet Imager instrument on board the Solar Orbiter. We detect two transverse oscillations in short loops with lengths of 4.5 and 11 Mm. The shorter loop displays an oscillation with a 14 s period and the longer a 30 s period. Despite the high resolution, no definitive identification as propagating or standing waves is possible. The velocity amplitudes are found to be equal to 72 and 125 km s−1, respectively, for the shorter and longer loops. Based on that, we also estimated the values of the energy flux contained in the loops—the energy flux of the 14 s oscillation is 1.9 kW m−2 and that of the 30 s oscillation is 6.5 kW m−2. While these oscillations have been observed in the quiet Sun, their energy fluxes are of the same order as the energy input required to heat the active solar corona. Numerical simulations were performed in order to reproduce the observed oscillations. The correspondence of the numerical results to the observations provides support to the estimates of energy content for the observations. Such high energy densities have not yet been observed in decayless coronal waves, and this is promising for coronal heating models based on wave damping.
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Cho, Hyerin, and Ramesh Narayan. "Analytical Model of Disk Evaporation and State Transitions in Accreting Black Holes." Astrophysical Journal 932, no. 2 (June 1, 2022): 97. http://dx.doi.org/10.3847/1538-4357/ac6d5c.
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Abstract State transitions in black hole X-ray binaries are likely caused by gas evaporation from a thin accretion disk into a hot corona. We present a height-integrated version of this process, which is suitable for analytical and numerical studies. With radius r scaled to Schwarzschild units and coronal mass accretion rate m ̇ c to Eddington units, the results of the model are independent of black hole mass. State transitions should thus be similar in X-ray binaries and an active galactic nucleus. The corona solution consists of two power-law segments separated at a break radius r b ∼ 103(α/0.3)−2, where α is the viscosity parameter. Gas evaporates from the disk to the corona for r > r b , and condenses back for r < r b . At r b , m ̇ c reaches its maximum, m ̇ c , max ≈ 0.02 ( α / 0.3 ) 3 . If at r ≫ r b the thin disk accretes with m ̇ d < m ̇ c , max , then the disk evaporates fully before reaching r b , giving the hard state. Otherwise, the disk survives at all radii, giving the thermal state. While the basic model considers only bremsstrahlung cooling and viscous heating, we also discuss a more realistic model that includes Compton cooling and direct coronal heating by energy transport from the disk. Solutions are again independent of black hole mass, and r b remains unchanged. This model predicts strong coronal winds for r > r b , and a T ∼ 5 × 108 K Compton-cooled corona for r < r b . Two-temperature effects are ignored, but may be important at small radii.
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Ulmschneider, P. "Heating of Chromospheres and Coronae." Highlights of Astronomy 11, no. 2 (1998): 831–37. http://dx.doi.org/10.1017/s153929960001889x.
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AbstractAlmost all nondegenerate stars have chromospheres and coronae. These hot outer layers are produced by mechanical heating. The heating mechanisms of chromospheres and coronae, classified as hydrodynamic and magnetic mechanisms, are reviewed here. Both types of mechanisms can be further subdivided on basis of the fluctuation frequency into acoustic and pulsational waves for hydrodynamic and into AC- and DC-mechanisms for magnetic heating. Intense heating is usually associated with the formation of very small spatial scales, which are difficult to observe. Yet, global stellar observations, because of the dependence of the mechanical energy generation on the basic stellar parameters (Teff, gravity, rotation, metallicity) can be extremely important to identify the dominant heating mechanisms.
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Azzollini, Francesco, A. Gordon Emslie, Daniel L. Clarkson, Nicolina Chrysaphi, and Eduard P. Kontar. "Plasma Motions and Compressive Wave Energetics in the Solar Corona and Solar Wind from Radio Wave Scattering Observations." Astrophysical Journal 968, no. 2 (June 1, 2024): 72. http://dx.doi.org/10.3847/1538-4357/ad4154.
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Abstract Radio signals propagating via the solar corona and solar wind are significantly affected by compressive waves, impacting the properties of solar bursts as well as sources viewed through the turbulent solar atmosphere. While static fluctuations scatter radio waves elastically, moving, turbulent, or oscillating density irregularities act to broaden the frequency of the scattered waves. Using a new anisotropic density fluctuation model from the kinetic scattering theory for solar radio bursts, we deduce the plasma velocities required to explain observations of spacecraft signal frequency broadening. The inferred velocities are consistent with motions that are dominated by the solar wind at distances ≳10 R ⊙, but the levels of frequency broadening for ≲10 R ⊙ require additional radial speeds ∼(100–300) km s−1 and/or transverse speeds ∼(20–70) km s−1. The inferred radial velocities also appear consistent with the sound or proton thermal speeds, while the speeds perpendicular to the radial direction are consistent with nonthermal motions measured via coronal Doppler-line broadening, interpreted as Alfvénic fluctuations. Landau damping of parallel propagating ion-sound (slow MHD) waves allows an estimate of the proton heating rate. The energy deposition rates due to ion-sound wave damping peak at a heliocentric distance of ∼(1–3) R ⊙ are comparable to the rates available from a turbulent cascade of Alfvénic waves at large scales, suggesting a coherent picture of energy transfer, via the cascade or/and parametric decay of Alfvén waves to the small scales where heating takes place.
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Howson, T. A., I. De Moortel, J. Reid, and A. W. Hood. "Magnetohydrodynamic waves in braided magnetic fields." Astronomy & Astrophysics 629 (September 2019): A60. http://dx.doi.org/10.1051/0004-6361/201935876.
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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.
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Santamaria, I. C., and T. Van Doorsselaere. "High frequency generation in the corona: Resonant cavities." Astronomy & Astrophysics 611 (March 2018): A10. http://dx.doi.org/10.1051/0004-6361/201731016.
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Aims. Null points are prominent magnetic field singularities in which the magnetic field strength strongly decreases in very small spatial scales. Around null points, predicted to be ubiquitous in the solar chromosphere and corona, the wave behavior changes considerably. Null points are also responsible for driving very energetic phenomena, and for contributing to chromospheric and coronal heating. In previous works we demonstrated that slow magneto-acoustic shock waves were generated in the chromosphere propagate through the null point, thereby producing a train of secondary shocks escaping along the field lines. A particular combination of the shock wave speeds generates waves at a frequency of 80 MHz. The present work aims to investigate this high frequency region around a coronal null point to give a plausible explanation to its generation at that particular frequency. Methods. We carried out a set of two-dimensional numerical simulations of wave propagation in the neighborhood of a null point located in the corona. We varied both the amplitude of the driver and the atmospheric properties to investigate the sensitivity of the high frequency waves to these parameters. Results. We demonstrate that the wave frequency is sensitive to the atmospheric parameters in the corona, but it is independent of the strength of the driver. Thus, the null point behaves as a resonant cavity generating waves at specific frequencies that depend on the background equilibrium model. Moreover, we conclude that the high frequency wave train generated at the null point is not necessarily a result of the interaction between the null point and a shock wave. This wave train can be also developed by the interaction between the null point and fast acoustic-like magneto-acoustic waves, that is, this interaction within the linear regime.
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Riazantseva, Maria O., Timofey V. Treves, Olga Khabarova, Liudmila S. Rakhmanova, Yuri I. Yermolaev, and Alexander A. Khokhlachev. "Linking Turbulent Interplanetary Magnetic Field Fluctuations and Current Sheets." Universe 10, no. 11 (November 7, 2024): 417. http://dx.doi.org/10.3390/universe10110417.
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The study aims to understand the role of solar wind current sheets (CSs) in shaping the spectrum of turbulent fluctuations and driving dissipation processes in space plasma. Local non-adiabatic heating and acceleration of charged particles in the solar wind is one of the most intriguing challenges in space physics. Leading theories attribute these effects to turbulent heating, often associated with magnetic reconnection at small-scale coherent structures in the solar wind, such as CSs and flux ropes. We identify CSs observed at 1 AU in different types of the solar wind around and within an interplanetary coronal mass ejection (ICME) and analyze the corresponding characteristics of the turbulent cascade. It is found that the spectra of fluctuations of the interplanetary magnetic field may be reshaped due to the CS impact potentially leading to local disruptions in energy transfer along the cascade of turbulent fluctuations. Case studies of the spectra behavior at the peak of the CS number show their steepening at MHD scales, flattening at kinetic scales, and merging of the spectra into a single form, with the break almost disappearing. In the broader vicinity of the CS number peak, the behavior of spectral parameters changes sharply, but not always following the same pattern. The statistical analysis shows a clear correlation between the break frequency and the CS number. These results are consistent with the picture of turbulent reconnection at CSs. The CS occurrence is found to be statistically linked with the increased temperature. In the ICME sheath, there are two CS populations observed in the hottest and coldest plasma.
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Shi, Mijie, Tom Van Doorsselaere, Patrick Antolin, and Bo Li. "Forward Modeling of Simulated Transverse Oscillations in Coronal Loops and the Influence of Background Emission." Astrophysical Journal 922, no. 1 (November 1, 2021): 60. http://dx.doi.org/10.3847/1538-4357/ac2497.
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Abstract We simulate transverse oscillations in radiatively cooling coronal loops and forward-model their spectroscopic and imaging signatures, paying attention to the influence of background emission. The transverse oscillations are driven at one footpoint by a periodic velocity driver. A standing kink wave is subsequently formed and the loop cross section is deformed due to the Kelvin–Helmholtz instability, resulting in energy dissipation and heating at small scales. Besides the transverse motions, a long-period longitudinal flow is also generated due to the ponderomotive force induced slow wave. We then transform the simulated straight loop to a semi-torus loop and forward-model their spectrometer and imaging emissions, mimicking observations of Hinode/EIS and SDO/AIA. We find that the oscillation amplitudes of the intensity are different at different slit positions, but are roughly the same in different spectral lines or channels. X-t diagrams of both the Doppler velocity and the Doppler width show periodic signals. We also find that the background emission dramatically decreases the Doppler velocity, making the estimated kinetic energy two orders of magnitude smaller than the real value. Our results show that background subtraction can help recover the real oscillation velocity. These results are helpful for further understanding transverse oscillations in coronal loops and their observational signatures. However, they cast doubt on the spectroscopically estimated energy content of transverse waves using the Doppler velocity.
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Pucci, Fulvia, K. Alkendra P. Singh, Uma Gorti, Neal J. Turner, Marco Velli, Disha Varshney, and Maria Elena Innocenti. "Applications of Fast Magnetic Reconnection Models to the Atmospheres of the Sun and Protoplanetary Disks." Astrophysical Journal 970, no. 1 (July 1, 2024): 87. http://dx.doi.org/10.3847/1538-4357/ad49a7.
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Abstract Partially ionized plasmas consist of charged and neutral particles whose mutual collisions modify magnetic reconnection compared with the fully ionized case. The collisions alter the rate and locations of the magnetic dissipation heating and the distribution of energies among the particles accelerated into the nonthermal tail. We examine the collisional regimes for the onset of fast reconnection in two environments: the partially ionized layers of the solar atmosphere, and the protoplanetary disks that are the birthplaces for planets around young stars. In both these environments, magnetic nulls readily develop into resistive current sheets in the regime where the charged and neutral particles are fully coupled by collisions, but the current sheets quickly break down under the ideal tearing instability. The current sheets collapse repeatedly, forming magnetic islands at successively smaller scales, until they enter a collisionally decoupled regime where the magnetic energy is rapidly turned into heat and charged-particle kinetic energy. Small-scale, decoupled fast reconnection in the solar atmosphere may lead to preferential heating and energization of ions and electrons that escape into the corona. In protoplanetary disks such reconnection causes localized heating in the atmospheric layers that produce much of the infrared atomic and molecular line emission observed with the Spitzer and James Webb Space Telescopes.
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Silva, Suzana S. A., Gary Verth, Erico L. Rempel, Istvan Ballai, Shahin Jafarzadeh, and Viktor Fedun. "Magnetohydrodynamic Poynting Flux Vortices in the Solar Atmosphere and Their Role in Concentrating Energy." Astrophysical Journal 963, no. 1 (February 21, 2024): 10. http://dx.doi.org/10.3847/1538-4357/ad1403.
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Abstract The nature of energy generation, transport, and effective dissipation responsible for maintaining a hot solar upper atmosphere is still elusive. The Poynting flux is a vital parameter for describing the direction and magnitude of the energy flow, which is mainly used in solar physics for estimating the upward energy generated by photospheric plasma motion. This study presents a pioneering 3D mapping of the magnetic energy transport within a numerically simulated solar atmosphere. By calculating the Finite Time Lyapunov Exponent of the energy velocity, defined as the ratio of the Poynting flux to the magnetic energy density, we precisely identify the sources and destinations of the magnetic energy flow throughout the solar atmosphere. This energy mapping reveals the presence of transport barriers in the lower atmosphere, restricting the amount of magnetic energy from the photosphere reaching the chromosphere and corona. Interacting kinematic and magnetic vortices create energy channels, breaking through these barriers and allowing three times more energy input from photospheric motions to reach the upper atmosphere than before the vortices formed. The vortex system also substantially alters the energy mapping, acting as a source and deposition of energy, leading to localized energy concentration. Furthermore, our results show that the energy is transported following a vortical motion: the Poynting flux vortex. In regions where these vortices coexist, they favor conditions for energy dissipation through ohmic and viscous heating, since they naturally create large gradients in the magnetic and velocity fields over small spatial scales. Hence, the vortex system promotes local plasma heating, leading to temperatures around a million Kelvins.
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Alberti, Tommaso, Simone Benella, Vincenzo Carbone, Giuseppe Consolini, Virgilio Quattrociocchi, and Mirko Stumpo. "Contrasting Scaling Properties of Near-Sun Sub-Alfvénic and Super-Alfvénic Regions." Universe 8, no. 7 (June 21, 2022): 338. http://dx.doi.org/10.3390/universe8070338.
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Scale-invariance has rapidly established itself as one of the most used concepts in space plasmas to uncover underlying physical mechanisms via the scaling-law behavior of the statistical properties of field fluctuations. In this work, we characterize the scaling properties of the magnetic field fluctuations in a sub-alfvénic region in contrast with those of the nearby super-alfvénic zone during the ninth Parker Solar Probe perihelion. With our observations, (i) evidence of an extended self-similarity (ESS) for both the inertial and the sub-ion/kinetic regimes during both solar wind intervals is provided, (ii) a multifractal nature of field fluctuations is observed across inertial scales for both solar wind intervals, and (iii) a mono-fractal structure of the small-scale dynamics is reported. The main novelty is that a universal character is found at the sub-ion/kinetic scale, where a unique rescaling exponent describes the high-order statistics of fluctuations during both wind intervals. Conversely, a multitude of scaling symmetries is observed at the inertial scale with a similar fractal topology and geometrical structures between the magnetic field components in the ecliptic plane and perpendicular to it, in contrast with a different level of intermittency, more pronounced during the super-alfvénic interval rather than the sub-alfvénic one, along the perpendicular direction to the ecliptic plane. The above features are interpreted in terms of the possible underlying heating and/or acceleration mechanisms in the solar corona resulting from turbulence and current sheet formation.
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Voitenko, Y., and M. Goossens. "Excitation of kinetic Alfvén turbulence by MHD waves and energization of space plasmas." Nonlinear Processes in Geophysics 11, no. 5/6 (November 16, 2004): 535–43. http://dx.doi.org/10.5194/npg-11-535-2004.
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Abstract. There is abundant observational evidence that the energization of plasma particles in space is correlated with an enhanced activity of large-scale MHD waves. Since these waves cannot interact with particles, we need to find ways for these MHD waves to transport energy in the dissipation range formed by small-scale or high-frequency waves, which are able to interact with particles. In this paper we consider the dissipation range formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field irrespectively of their frequency. We study a nonlocal nonlinear mechanism for the excitation of KAWs by MHD waves via resonant decay AW(FW)→KAW1+KAW2, where the MHD wave can be either an Alfvén wave (AW), or a fast magneto-acoustic wave (FW). The resonant decay thus provides a non-local energy transport from large scales directly in the dissipation range. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0~10-2. In turn, KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and acceleration in a variety of space plasmas. An anisotropic energy deposition in the field-aligned degree of freedom for the electrons, and in the cross-field degrees of freedom for the ions, is typical for KAWs. A few relevant examples are discussed concerning nonlinear excitation of KAWs by the MHD wave flux and consequent plasma energization in the solar corona and terrestrial magnetosphere.
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Laurent, Glenn T., Donald M. Hassler, Craig DeForest, David D. Slater, Roger J. Thomas, Thomas Ayres, Michael Davis, et al. "The Rapid Acquisition Imaging Spectrograph Experiment (RAISE) Sounding Rocket Investigation." Journal of Astronomical Instrumentation 05, no. 01 (March 2016): 1640006. http://dx.doi.org/10.1142/s2251171716400067.
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We present a summary of the solar observing Rapid Acquisition Imaging Spectrograph Experiment (RAISE) sounding rocket program including an overview of the design and calibration of the instrument, flight performance, and preliminary chromospheric results from the successful November 2014 launch of the RAISE instrument. The RAISE sounding rocket payload is the fastest scanning-slit solar ultraviolet imaging spectrograph flown to date. RAISE is designed to observe the dynamics and heating of the solar chromosphere and corona on time scales as short as 100–200[Formula: see text]ms, with arcsecond spatial resolution and a velocity sensitivity of 1–2[Formula: see text]km/s. Two full spectral passbands over the same one-dimensional spatial field are recorded simultaneously with no scanning of the detectors or grating. The two different spectral bands (first-order 1205–1251[Formula: see text]Å and 1524–1569[Formula: see text]Å) are imaged onto two intensified Active Pixel Sensor (APS) detectors whose focal planes are individually adjusted for optimized performance. RAISE reads out the full field of both detectors at 5–10[Formula: see text]Hz, recording up to 1800 complete spectra (per detector) in a single 6-min rocket flight. This opens up a new domain of high time resolution spectral imaging and spectroscopy. RAISE is designed to observe small-scale multithermal dynamics in Active Region (AR) and quiet Sun loops, identify the strength, spectrum and location of high frequency waves in the solar atmosphere, and determine the nature of energy release in the chromospheric network.
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Huang, Z., M. S. Madjarska, J. G. Doyle, and D. A. Lamb. "Coronal hole boundaries at small scales." Astronomy & Astrophysics 548 (November 22, 2012): A62. http://dx.doi.org/10.1051/0004-6361/201220079.
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Judge, P. G. "Steadiness of Coronal Heating." Astrophysical Journal 957, no. 1 (October 23, 2023): 25. http://dx.doi.org/10.3847/1538-4357/acf83a.
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Abstract The EUI instrument on the Solar Orbiter spacecraft has obtained the most stable, high-resolution images of the solar corona from its orbit with a perihelion near 0.4 au. A sequence of 360 images obtained at 17.1 nm, between 2022 October 25 19:00 and 19:30 UT, is scrutinized. One image pixel corresponds to 148 km at the solar surface. The widely held belief that the outer atmosphere of the Sun is in a continuous state of magnetic turmoil is pitted against the EUI data. The observed plasma variations appear to fall into two classes. By far the dominant behavior is a very low amplitude variation in brightness (1%) in the coronal loops, with larger variations in some footpoint regions. No hints of observable changes in magnetic topology are associated with such small variations. The larger-amplitude, more rapid, rarer, and less well organized changes are associated with flux emergence. It is suggested therefore that while magnetic reconnection drives the latter, most of the active corona is heated with no evidence of a role for large-scale (observable) reconnection. Since most coronal emission-line widths are subsonic, the bulk of coronal heating, if driven by reconnection, can only be of tangentially discontinuous magnetic fields, with angles below about 0.5c S /c A ∼ 0.3β, with β the plasma beta parameter (∼0.01) and c S and c A the sound and Alfvén speeds, respectively. If heated by multiple small flare-like events, then these must be ≲1021 erg, i.e., picoflares. But processes other than reconnection have yet to be ruled out, such as viscous dissipation, which may contribute to the steady heating of coronal loops over active regions.
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Venkatakrishnan, P. "Observable Signals of Coronal Heating Processes." Highlights of Astronomy 10 (1995): 305–6. http://dx.doi.org/10.1017/s1539299600011291.
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AbstractThe solar corona is thought to be sustained by waves, currents, turbulence or by velocity filtration. For efficient wave heating of the corona, only the Alfven waves seem to survive the effects of steepening and shock dissipation in the chromosphere (Zirker, 1993, Solar Phys. 148,43) and these can be dissipated in the corona by mode conversion or phase mixing (Priest, 1991 in XIV Consultation on Solar Physics, Karpacz). Enhanced line width of 530.3 nm coronal line seen within closed structures (Singh et al., 1982, J. Astrophys. Astron. 3,248), association of enhanced line width of HeI 1083 nm line with enhanced equivalent width (Venkatakrishnan et al., 1992, Solar Phys. 138,107), and gradients seen in the MgX 60.9 and 62.5 nm coronal line width (Hassler, et al., 1990, Astrophys. J. 348, L77), are possibly some examples of the observed signals of wave heating. Current sheets, produced in a variety of ways (Priest and Forbes, 1989, Solar Phys. 43,177; Parker, 1979, Cosmical Magnetic Fields, Ox. Univ. Press), can dissipate and provide heat. The properties of current sheets can be inferred from fill factors, emission measures (Cargill, 1994, in J.L. Burch and J.H. Waite, Jr. (eds.) Solar System Plasma Physics: Resolution of Processes in Space and Time, AGU Monograph), hard xrays (Lin et al., 1984, Astrophys. J. 283,421), and radio bursts (Benz, 1986, Solar Phys. 104,99). The association of large scale currents with enhanced transition region (deLoach et al., 1984, Solar Phys. 91,235.) and regions of enhanced magnetic shear with brighter corona (Moore et al., 1994, Proc. Kofu Symp) are of some possible interest in this context. Self consistent calculations of the turbulent cascade of energy from the scales of photospheric motions down into dissipative scales (Heyvaerts and Priest, 1992, Astrophys. J. 390,297) predict the width of coronal lines as a function of the properties of the forcing flows. Velocity filtration caused by free streaming effects off a non maxwellian boundary distribution of particles may well result in a plasma having coronal properties (Scudder, 1992a, Astrophys. J. 398,299; 1992b, Astrophys.J.11 398,319). The observable signals are the variation of line shapes with altitude.
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Froment, C., P. Antolin, V. M. J. Henriques, P. Kohutova, and L. H. M. Rouppe van der Voort. "Multi-scale observations of thermal non-equilibrium cycles in coronal loops." Astronomy & Astrophysics 633 (December 20, 2019): A11. http://dx.doi.org/10.1051/0004-6361/201936717.
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Context. Thermal non-equilibrium (TNE) is a phenomenon that can occur in solar coronal loops when the heating is quasi-constant and highly-stratified. Under such heating conditions, coronal loops undergo cycles of evaporation and condensation. The recent observations of ubiquitous long-period intensity pulsations in coronal loops and their relationship with coronal rain have demonstrated that understanding the characteristics of TNE cycles is an essential step in constraining the circulation of mass and energy in the corona. Aims. We report unique observations with the Solar Dynamics Observatory (SDO) and the Swedish 1-m Solar Telescope (SST) that link the captured thermal properties across the extreme spatiotemporal scales covered by TNE processes. Methods. Within the same coronal loop bundle, we captured 6 h period coronal intensity pulsations in SDO/AIA and coronal rain observed off-limb in the chromospheric Hα and Ca II K spectral lines with SST/CRISP and SST/CHROMIS. We combined a multi-thermal analysis of the cycles with AIA and an extensive spectral characterisation of the rain clumps with the SST. Results. We find clear evidence of evaporation-condensation cycles in the corona which are linked with periodic coronal rain showers. The high-resolution spectroscopic instruments at the SST reveal the fine-structured rain strands and allow us to probe the cooling phase of one of the cycles down to chromospheric temperatures. Conclusions. These observations reinforce the link between long-period intensity pulsations and coronal rain. They also demonstrate the capability of TNE to shape the dynamics of active regions on the large scales as well as on the smallest scales currently resolvable.
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Reale, F., G. Peres, and S. Serio. "Impulsive Heating of Coronal Loops." International Astronomical Union Colloquium 144 (1994): 215–17. http://dx.doi.org/10.1017/s0252921100025343.
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AbstractWe have made hydrodynamic calculations of steady coronal loops maintained close to steady conditions with a heating entirely made of a sequence (either randomic or periodic) of small events of energy input into the plasma. To study their observability, we synthesize the emission in bands observable by X-ray instruments, such as imaging instruments, like Yohkoh/SXT and the forthcoming SOHO/EIT. We present results for one specific calculation and discuss them in terms of the possible diagnostics of variable heating vs. steady one and of the feasibility of direct detection of loop variability.
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Subramanian, S., M. S. Madjarska, and J. G. Doyle. "Coronal hole boundaries evolution at small scales." Astronomy and Astrophysics 516 (June 2010): A50. http://dx.doi.org/10.1051/0004-6361/200913624.
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Madjarska, M. S., Z. Huang, J. G. Doyle, and S. Subramanian. "Coronal hole boundaries evolution at small scales." Astronomy & Astrophysics 545 (September 2012): A67. http://dx.doi.org/10.1051/0004-6361/201219516.
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Madjarska, M. S., and T. Wiegelmann. "Coronal hole boundaries evolution at small scales." Astronomy & Astrophysics 503, no. 3 (July 9, 2009): 991–97. http://dx.doi.org/10.1051/0004-6361/200912066.
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De Moortel, Ineke, and Philippa Browning. "Recent advances in coronal heating." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2042 (May 28, 2015): 20140269. http://dx.doi.org/10.1098/rsta.2014.0269.
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The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This ‘coronal heating problem’ requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.
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Şahin, Seray, Patrick Antolin, Clara Froment, and Thomas A. Schad. "Spatial and Temporal Analysis of Quiescent Coronal Rain over an Active Region." Astrophysical Journal 950, no. 2 (June 1, 2023): 171. http://dx.doi.org/10.3847/1538-4357/acd44b.
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Abstract The solar corona produces coronal rain, hundreds of times colder and denser material than the surroundings. Coronal rain is known to be deeply linked to coronal heating, but its origin, dynamics, and morphology are still not well understood. The leading theory for its origin is thermal instability (TI) occurring in coronal loops in a state of thermal nonequilibrium (TNE), the TNE-TI scenario. Under steady heating conditions, TNE-TI repeats in cycles, leading to long-period EUV intensity pulsations and periodic coronal rain. In this study, we investigate coronal rain on the large spatial scales of an active region (AR) and over the long temporal scales of EUV intensity pulsations to elucidate its distribution at such scales. We conduct a statistical study of coronal rain observed over an AR off limb with Interface Region Imaging Spectrograph and Solar Dynamics Observatory imaging data, spanning chromospheric to transition region (TR) temperatures. The rain is widespread across the AR, irrespective of the loop inclination, and with minimal variation over the 5.45 hr duration of the observation. Most rain has a downward (87.5%) trajectory; however, upward motions (12.5%) are also ubiquitous. The rain dynamics are similar over the observed temperature range, suggesting that the TR emission and chromospheric emission are colocated on average. The average clump widths and lengths are similar in the SJI channels and wider in the AIA 304 Å channel. We find ubiquitous long-period EUV intensity pulsations in the AR. Short-term periodicity is found (16 minutes) linked to the rain appearance, which constitutes a challenge to explain under the TNE-TI scenario.
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Nóbrega-Siverio, D., F. Moreno-Insertis, K. Galsgaard, K. Krikova, L. Rouppe van der Voort, R. Joshi, and M. S. Madjarska. "Deciphering Solar Coronal Heating: Energizing Small-scale Loops through Surface Convection." Astrophysical Journal Letters 958, no. 2 (November 30, 2023): L38. http://dx.doi.org/10.3847/2041-8213/ad0df0.
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Abstract The solar atmosphere is filled with clusters of hot small-scale loops commonly known as coronal bright points (CBPs). These ubiquitous structures stand out in the Sun by their strong X-ray and/or extreme-ultraviolet (EUV) emission for hours to days, which makes them a crucial piece when solving the solar coronal heating puzzle. In addition, they can be the source of coronal jets and small-scale filament eruptions. Here we present a novel 3D numerical model using the Bifrost code that explains the sustained CBP heating for several hours. We find that stochastic photospheric convective motions alone significantly stress the CBP magnetic field topology, leading to important Joule and viscous heating concentrated around the CBP’s inner spine at a few megameters above the solar surface. We also detect continuous upflows with faint EUV signals resembling observational dark coronal jets and small-scale eruptions when Hα fibrils interact with the reconnection site. We validate our model by comparing simultaneous CBP observations from the Solar Dynamics Observatory (SDO) and the Swedish 1‐m Solar Telescope (SST) with observable diagnostics calculated from the numerical results for EUV wavelengths as well as for the Hα line using the Multi3D synthesis code. Additionally, we provide synthetic observables to be compared with Hinode, Solar Orbiter, and the Interface Region Imaging Spectrograph (IRIS). Our results constitute a step forward in the understanding of the many different facets of the solar coronal heating problem.
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Bareford, M. R., and A. W. Hood. "Shock heating in numerical simulations of kink-unstable coronal loops." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2042 (May 28, 2015): 20140266. http://dx.doi.org/10.1098/rsta.2014.0266.
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An analysis of the importance of shock heating within coronal magnetic fields has hitherto been a neglected area of study. We present new results obtained from nonlinear magnetohydrodynamic simulations of straight coronal loops. This work shows how the energy released from the magnetic field, following an ideal instability, can be converted into thermal energy, thereby heating the solar corona. Fast dissipation of magnetic energy is necessary for coronal heating and this requirement is compatible with the time scales associated with ideal instabilities. Therefore, we choose an initial loop configuration that is susceptible to the fast-growing kink, an instability that is likely to be created by convectively driven vortices, occurring where the loop field intersects the photosphere (i.e. the loop footpoints). The large-scale deformation of the field caused by the kinking creates the conditions for the formation of strong current sheets and magnetic reconnection, which have previously been considered as sites of heating, under the assumption of an enhanced resistivity. However, our simulations indicate that slow mode shocks are the primary heating mechanism, since, as well as creating current sheets, magnetic reconnection also generates plasma flows that are faster than the slow magnetoacoustic wave speed.
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De Pontieu, Bart, Paola Testa, Juan Martínez-Sykora, Patrick Antolin, Konstantinos Karampelas, Viggo Hansteen, Matthias Rempel, et al. "Probing the Physics of the Solar Atmosphere with the Multi-slit Solar Explorer (MUSE). I. Coronal Heating." Astrophysical Journal 926, no. 1 (February 1, 2022): 52. http://dx.doi.org/10.3847/1538-4357/ac4222.
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Abstract The Multi-slit Solar Explorer (MUSE) is a proposed mission composed of a multislit extreme ultraviolet (EUV) spectrograph (in three spectral bands around 171 Å, 284 Å, and 108 Å) and an EUV context imager (in two passbands around 195 Å and 304 Å). MUSE will provide unprecedented spectral and imaging diagnostics of the solar corona at high spatial (≤0.″5) and temporal resolution (down to ∼0.5 s for sit-and-stare observations), thanks to its innovative multislit design. By obtaining spectra in four bright EUV lines (Fe ix 171 Å, Fe xv 284 Å, Fe xix–Fe xxi 108 Å) covering a wide range of transition regions and coronal temperatures along 37 slits simultaneously, MUSE will, for the first time, “freeze” (at a cadence as short as 10 s) with a spectroscopic raster the evolution of the dynamic coronal plasma over a wide range of scales: from the spatial scales on which energy is released (≤0.″5) to the large-scale (∼170″ × 170″) atmospheric response. We use numerical modeling to showcase how MUSE will constrain the properties of the solar atmosphere on spatiotemporal scales (≤0.″5, ≤20 s) and the large field of view on which state-of-the-art models of the physical processes that drive coronal heating, flares, and coronal mass ejections (CMEs) make distinguishing and testable predictions. We describe the synergy between MUSE, the single-slit, high-resolution Solar-C EUVST spectrograph, and ground-based observatories (DKIST and others), and the critical role MUSE plays because of the multiscale nature of the physical processes involved. In this first paper, we focus on coronal heating mechanisms. An accompanying paper focuses on flares and CMEs.
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Malara, F., and M. Velli. "Observations and Models of Coronal Heating." Symposium - International Astronomical Union 203 (2001): 456–66. http://dx.doi.org/10.1017/s0074180900219785.
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Energy release in the solar Corona is characterized by a sequence of space and time localized events, whose intensity follows power-law distributions. In quiet Sun regions, small energy events, possibly under the detection threshold, dominate, thus supporting the “nanoflare” scenario of coronal heating. Two complementar models of heating are discussed, in connection with the above observational features. The first model is based on Alfvénic wavepackets dissipation in 3D force-free magnetic fields; the presence of regions of chaoticity of magnetic lines allows for a fast wave dissipation, within a fraction of a solar radius. The second model describes a MHD turbulence in low-β plasma, in which magnetic energy is continuously furnished by slow photospheric motions. Energy release events corresponds dissipation of current sheets, often associated with magnetic reconnection. The resulting distribution of dissipated power follows a power law, similar to observations.
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Karampelas, K., and T. Van Doorsselaere. "Simulations of fully deformed oscillating flux tubes." Astronomy & Astrophysics 610 (February 2018): L9. http://dx.doi.org/10.1051/0004-6361/201731646.
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Context. In recent years, a number of numerical studies have been focusing on the significance of the Kelvin–Helmholtz instability in the dynamics of oscillating coronal loops. This process enhances the transfer of energy into smaller scales, and has been connected with heating of coronal loops, when dissipation mechanisms, such as resistivity, are considered. However, the turbulent layer is expected near the outer regions of the loops. Therefore, the effects of wave heating are expected to be confined to the loop’s external layers, leaving their denser inner parts without a heating mechanism. Aim. In the current work we aim to study the spatial evolution of wave heating effects from a footpoint driven standing kink wave in a coronal loop. Methods. Using the MPI-AMRVAC code, we performed ideal, three dimensional magnetohydrodynamic simulations of footpoint driven transverse oscillations of a cold, straight coronal flux tube, embedded in a hotter environment. We have also constructed forward models for our simulation using the FoMo code. Results. The developed transverse wave induced Kelvin–Helmholtz (TWIKH) rolls expand throughout the tube cross-section, and cover it entirely. This turbulence significantly alters the initial density profile, leading to a fully deformed cross section. As a consequence, the resistive and viscous heating rate both increase over the entire loop cross section. The resistive heating rate takes its maximum values near the footpoints, while the viscous heating rate at the apex. Conclusions. We conclude that even a monoperiodic driver can spread wave heating over the whole loop cross section, potentially providing a heating source in the inner loop region. Despite the loop’s fully deformed structure, forward modelling still shows the structure appearing as a loop.
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Chitta, L. P., S. K. Solanki, J. C. del Toro Iniesta, J. Woch, D. Calchetti, A. Gandorfer, J. Hirzberger, et al. "Fleeting Small-scale Surface Magnetic Fields Build the Quiet-Sun Corona." Astrophysical Journal Letters 956, no. 1 (October 1, 2023): L1. http://dx.doi.org/10.3847/2041-8213/acf136.
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Abstract Arch-like loop structures filled with million Kelvin hot plasma form the building blocks of the quiet-Sun corona. Both high-resolution observations and magnetoconvection simulations show the ubiquitous presence of magnetic fields on the solar surface on small spatial scales of ∼100 km. However, the question of how exactly these quiet-Sun coronal loops originate from the photosphere and how the magnetic energy from the surface is channeled to heat the overlying atmosphere is a long-standing puzzle. Here we report high-resolution photospheric magnetic field and coronal data acquired during the second science perihelion of Solar Orbiter that reveal a highly dynamic magnetic landscape underlying the observed quiet-Sun corona. We found that coronal loops often connect to surface regions that harbor fleeting weaker, mixed-polarity magnetic field patches structured on small spatial scales, and that coronal disturbances could emerge from these areas. We suggest that weaker magnetic fields with fluxes as low as 1015 Mx and/or those that evolve on timescales less than 5 minutes are crucial to understanding the coronal structuring and dynamics.
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Kanella, Charalambos, and Boris V. Gudiksen. "Investigating 4D coronal heating events in magnetohydrodynamic simulations." Astronomy & Astrophysics 617 (September 2018): A50. http://dx.doi.org/10.1051/0004-6361/201732494.
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Context. One candidate model for heating the solar corona is magnetic reconnection that embodies Ohmic dissipation of current sheets. When numerous small-scale magnetic reconnection events occur, then it is possible to heat the corona; if ever observed, these events would have been the speculated nanoflares. Aims. Because of the limitations of current instrumentation, nanoflares cannot be resolved. But their importance is evaluated via statistics by finding the power-law index of energy distribution. This method is however biased for technical and physical reasons. We aim to overcome limitations imposed by observations and statistical analysis. This way, we identify, and study these small-scale impulsive events. Methods. We employed a three-dimensional magnetohydrodynamic (3D MHD) simulation using the Bifrost code. We also employed a new technique to identify the evolution of 3D joule heating events in the corona. Then, we derived parameters describing the heating events in these locations, studied their geometrical properties and where they occurred with respect to the magnetic field. Results. We report on the identification of heating events. We obtain the distribution of duration, released energy, and volume. We also find weak power-law correlation between these parameters. In addition, we extract information about geometrical parameters of 2D slices of 3D events, and about the evolution of resolved joule heating compared to the total joule heating and magnetic energy in the corona. Furthermore, we identify relations between the location of heating events and the magnetic field. Conclusions. Even though the energy power index is less than 2, when classifying the energy release into three categories with respect to the energy release (pico-, nano-, and micro-events), we find that nano-events release 82% of the resolved energy. This percentage corresponds to an energy flux larger than that needed to heat the corona. Although no direct conclusions can be drawn, it seems that the most popular population among small-scale events is the one that contains nano-scale energetic events that are short lived with small spatial extend. Generally, the locations and size of heating events are affected by the magnitude of the magnetic field.
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Reid, J., P. J. Cargill, A. W. Hood, C. E. Parnell, and T. D. Arber. "Coronal energy release by MHD avalanches: Heating mechanisms." Astronomy & Astrophysics 633 (January 2020): A158. http://dx.doi.org/10.1051/0004-6361/201937051.
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The plasma heating associated with an avalanche involving three twisted magnetic threads within a coronal loop is investigated using three-dimensional magnetohydrodynamic simulations. The avalanche is triggered by the kink instability of one thread, with the others being engulfed as a consequence. The heating as a function of both time and location along the strands is evaluated. It is shown to be bursty at all times but to have no preferred spatial location. While there appears to be a level of “background” heating, this is shown to be comprised of individual, small heating events. A comparison between viscous and resistive (Ohmic) heating demonstrates that the strongest heating events are largely associated with the Ohmic heating that arises when the current exceeds a critical value. Viscous heating is largely (but not entirely) associated with smaller events. Ohmic heating dominates viscous heating only at the time of the initial kink instability. It is also demonstrated that a variety of viscous models lead to similar heating rates, suggesting that the system adjusts to dissipate the same amount of energy.
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Washinoue, Haruka, Munehito Shoda, and Takeru K. Suzuki. "The Effect of the Chromospheric Temperature on Coronal Heating." Astrophysical Journal 938, no. 2 (October 1, 2022): 126. http://dx.doi.org/10.3847/1538-4357/ac91c8.
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Abstract Recent observational and numerical studies show a variety of thermal structures in the solar chromosphere. Given that the thermal interplay across the transition region is a key to coronal heating, it is worth investigating how different thermal structures of the chromosphere yield different coronal properties. In this work, by MHD simulations of Alfvén-wave heating of coronal loops, we study how the coronal properties are affected by the chromospheric temperature. To this end, instead of solving the radiative transfer equation, we employ a simple radiative loss function so that the chromospheric temperature is easily tuned. When the chromosphere is hotter, because the chromosphere extends to a larger height, the coronal part of the magnetic loop becomes shorter, which enhances the conductive cooling. A larger loop length is therefore required to maintain the high-temperature corona against the thermal conduction. From our numerical simulations we derive a condition for the coronal formation with respect to the half loop length l loop in a simple form: l loop > aT min + l th , where T min is the minimum temperature in the atmosphere, and parameters a and l th have negative dependencies on the coronal field strength. Our conclusion is that the chromospheric temperature has a nonnegligible impact on coronal heating for loops with small lengths and weak coronal fields. In particular, the enhanced chromospheric heating could prevent the formation of the corona.
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Dammasch, I. E., W. Curdt, B. N. Dwivedi, and S. Parenti. "The redshifted footpoints of coronal loops." Annales Geophysicae 26, no. 10 (October 15, 2008): 2955–59. http://dx.doi.org/10.5194/angeo-26-2955-2008.
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Abstract. The physics of coronal loops holds the key to understanding coronal heating and the flow of mass and energy in the region. However, the energy source, structure maintenance and mass balance in coronal loops are not yet fully understood. Observations of blue- and redshifted emissions have repeatedly been used in the construction of loop models. But observations and interpretations of line shifts have been widely debated. Here we present detailed SUMER observations, which clearly show a steady downflow in both footpoints of coronal loops observed at transition region (TR) and lower corona temperatures. We also show and quantify a correlation existing between this Doppler shift and the spectral radiance. Our results indicate a strong correlation which holds from the chromosphere to the lower corona. We suggest that the downflow in the footpoints may be a common phenomenon on all scales, which could explain, why on a statistical basis bright pixels tend to be more redshifted. We conclude by presenting interpretation of such results and their implications in the light of a viable coronal loop model. The observation of steady downflow in redshifted footpoints seems to be in conflict with impulsive heating.
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Aulanier, Guillaume. "Coronal heating and flaring in QSLs." Proceedings of the International Astronomical Union 6, S273 (August 2010): 233–41. http://dx.doi.org/10.1017/s1743921311015304.
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AbstractQuasi-Separatrix Layers (QSLs) are 3D geometrical objects that define narrow volumes across which magnetic field lines have strong, but finite, gradients of connectivity from one footpoint to another. QSLs extend the concept of separatrices, that are topological objects across which the connectivity is discontinuous. Based on analytical arguments, and on magnetic field extrapolations of the Sun's coronal force-free field above observed active regions, it has long since been conjectured that QSLs are favorable locations for current sheet (CS) formation, as well as for magnetic reconnection, and therefore are good predictors for the locations of magnetic energy release in flares and coronal heating. It is only up to recently that numerical MHD simulations and solar observations, as well as a laboratory experiment, have started to address the validity of these conjectures. When put all together, they suggest that QSL reconnection is involved in the displacement of EUV and SXR brightenings along chromospheric flare ribbons, that it is related with the heating of EUV coronal loops, and that the dissipation of QSL related CS may be the cause of coronal heating in initially homogeneous, braided and turbulent flux tubes, as well as in coronal arcades rooted in the slowly moving and numerous small-scale photospheric flux concentrations, both in active region faculae and in the quiet Sun. The apparent ubiquity of QSL-related CS in the Sun's corona, which will need to be quantified with new generation solar instruments, also suggests that QSLs play an important role in stellar's atmospheres, when their surface radial magnetic fields display complex patterns.
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Reid, J., J. Threlfall, and A. W. Hood. "Self-consistent nanoflare heating in model active regions: MHD avalanches in curved coronal arcades." Proceedings of the International Astronomical Union 18, S372 (August 2022): 116–18. http://dx.doi.org/10.1017/s1743921322004690.
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AbstractMHD avalanches involve small, narrowly localized instabilities spreading across neighbouring areas in a magnetic field. Cumulatively, many small events release vast amounts of stored energy. Straight cylindrical flux tubes are easily modelled, between two parallel planes, and can support such an avalanche: one unstable flux tube causes instability to proliferate, via magnetic reconnection, and then an ongoing chain of like events. True coronal loops, however, are visibly curved, between footpoints on the same solar surface. With 3D MHD simulations, we verify the viability of MHD avalanches in the more physically realistic, curved geometry of a coronal arcade. MHD avalanches thus amplify instability across strong solar magnetic fields and disturb wide regions of plasma. Contrasting with the behaviour of straight cylindrical models, a modified ideal MHD kink mode occurs, more readily and preferentially upwards in the new, curved geometry. Instability spreads over a region far wider than the original flux tubes and than their footpoints. Consequently, sustained heating is produced in a series of ‘nanoflares’ collectively contributing substantially to coronal heating. Overwhelmingly, viscous heating dominates, generated in shocks and jets produced by individual small events. Reconnection is not the greatest contributor to heating, but is rather the facilitator of those processes that are. Localized and impulsive, heating shows no strong spatial preference, except a modest bias away from footpoints, towards the loop’s apex. Remarkable evidence emerges of ‘campfire’ like events, with simultaneous, reconnection-induced nanoflares at separate sites along coronal strands, akin to recent results from Solar Orbiter. Effects of physically realistic plasma parameters, and the implications for thermodynamic models, with energetic transport, are discussed.
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Fuentes, M. C. López, and J. A. Klimchuk. "A cellular automaton model for coronal heating." Proceedings of the International Astronomical Union 7, S286 (October 2011): 433–36. http://dx.doi.org/10.1017/s1743921312005212.
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AbstractWe present a simple coronal heating model based on a cellular automaton approach. Following Parker's suggestion (1988), we consider the corona to be made up of elemental magnetic strands that accumulate magnetic stress due to the photospheric displacements of their footpoints. Magnetic energy is eventually released in small scale reconnection events. The model consists of a 2D grid in which strand footpoints travel with random displacements simulating convective motions. Each time two strands interact, a critical condition is tested (as in self-organized critical models), and if the condition is fulfilled, the strands reconnect and energy is released. We model the plasma response to the heating events and obtain synthetic observations. We compare the output of the model with real observations from Hinode/XRT and discuss the implications of our results for coronal heating.
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Marsh, Andrew J., David M. Smith, Lindsay Glesener, James A. Klimchuk, Stephen J. Bradshaw, Juliana Vievering, Iain G. Hannah, Steven Christe, Shin-nosuke Ishikawa, and Säm Krucker. "Hard X-Ray Constraints on Small-scale Coronal Heating Events." Astrophysical Journal 864, no. 1 (August 24, 2018): 5. http://dx.doi.org/10.3847/1538-4357/aad380.
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López Ariste, A., and M. Facchin. "Superoscillations in solar MHD waves and their possible role in heating coronal loops." Astronomy & Astrophysics 614 (June 2018): A145. http://dx.doi.org/10.1051/0004-6361/201731401.
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Aims. We aim to study the presence of superoscillations in coronal magnetoacoustic (MHD) waves and their possible role in heating coronal loops through the strong and localised gradients that they generate on the wave. Methods. An analytic model is built for the transition between sausage and kink wave modes propagating along field lines in the corona. We compute in this model the local frequencies, the wave gradients, and the associated heating rates due to compressive viscosity. Results. We find superoscillations associated with the transition between wave modes accompanying the wave dislocation that shifts through the wave domain. Frequencies ten times higher than the normal frequency are found. This means that a typical three-minute coronal wave will oscillate locally in 10 to 20 s. Such high frequencies bring up strong gradients that efficiently dissipate the wave through compressive viscosity. We compute the associated heating rates; locally, they are very strong, largely compensating typical radiative losses. Conclusions. We find a new heating mechanism associated to magnetoacoustic waves in the corona. Heating due to superoscillations only happens along particular field lines with small cross sections, comparable in size to coronal loops, inside the much larger magnetic flux tubes and wave propagation domain.