The Spatial and Temporal Dependence of Coronal Heating by Alfven Wave Turbulence
M. Asgari-Targhi, A. A. van Ballegooijen, S. R. Cranmer, E. E. DeLuca
备注：
Accepted for publication in the Astrophysical Journal. 12 pages (emulateapj style), 7 figures, 2 tables. Some figure resolutions were degraded to conform with arXiv file size requirements. The final journal version will also have an animated version of Figure 7 included as online supplementary material
The solar atmosphere may be heated by Alfven waves that propagate up from the convection zone and dissipate their energy in the chromosphere and corona. To further test this theory, we consider wave heating in an active region observed on 2012 March 7. A potential field model of the region is constructed, and 22 field lines representing observed coronal loops are traced through the model. Using a three-dimensional (3D) reduced magneto-hydrodynamics (MHD) code, we simulate the dynamics of Alfven waves in and near the observed loops. The results for different loops are combined into a single formula describing the average heating rate Q as function of position within the observed active region. We suggest this expression may be approximately valid also for other active regions, and therefore may be used to construct 3D, time-dependent models of the coronal plasma. Such models are needed to understand the role of thermal non-equilibrium in the structuring and dynamics of the Sun's corona.
We investigate in more detail the origin of chromospheric Alfven waves that give rise to the separation of ions and neutrals, the First Ionization Potential Effect (FIP), through the action of the ponderomotive force. In open field regions, we model the dependence of fractionation on the plasma upflow velocity through the chromosphere for both shear (or planar) and torsional Alfven waves of photospheric origin. These differ mainly through their parametric coupling to slow mode waves. Shear Alfven waves appear to reproduce observed fractionations for a wider range of model parameters, and prese…
We comment on the recent paper by Srivastava and Dwivedi (J. Astrophs. Astr. {\bf 28}, 1, 2007). In the said paper the derived dispersion relation $νη\cos^4 θk^4 + [v_A^2 - i ω(ν+ η)] \cos^2 θk^2 - ω^2 = 0$ seems to be in error. Consequently, the conclusion drawn in their paper are not reliable.
The Alfvén wave energy flux in the corona can be explored using the electron density and velocity amplitude of the waves. The velocity amplitude of Alfvén waves can be obtained from the non-thermal velocity of the spectral line profiles. Previous calculations of the Alfvén wave energy flux with height in active regions and polar coronal holes have provided evidence for the damping of Alfvén waves with height. We present off-limb Hinode EUV imaging spectrometer (EIS) observations of a long coronal loop up to 1.4~R$_\odot$. We have obtained the electron density along the loop and found the loop …
Coronal seismology is a diagnostic tool used in solar physics for measuring parameters that are otherwise hard to measure; of these parameters, magnetic field values are arguably the most important. The parameters are inferred by combining observations of waves with magnetohydrodynamic (MHD) wave theory. To date, coronal seismology has successfully been applied to various single-oscillation events. Such events are relatively rare, resulting in rare occasions to use diagnostics. Ubiquitous waves in the solar atmosphere might, however, allow for the possibility of dynamic coronal seismology, whi…
Recent observations have demonstrated that waves which are capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which time and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study [De Moortel et al., …
We used our newly developed magnetohydrodynamic (MHD) code to perform 2.5D simulations of a fast-mode MHD wave interacting with coronal holes (CH) of varying Alfvén speed which result from assuming different CH densities. We find that this interaction leads to effects like reflection, transmission, stationary fronts at the CH boundary and the formation of a density depletion that moves in the opposite direction to the incoming wave. We compare these effects with regard to the different CH densities and present a comprehensive analysis of morphology and kinematics of the associated secondary wa…
Torsional Alfvén waves are promising candidates for transport of energy across different layers of the solar atmosphere and have been theoretically predicted for decades. Previous detections of Alfvén waves so far have however mostly relied on indirect signatures. We present a first direct observational evidence of a fully resolved torsional Alfvén oscillation of a large-scale structure occurring at coronal heights. We analyse IRIS imaging and spectral observation of a surge resulting from magnetic reconnection between active region prominence threads and surrounding magnetic fieldlines. The I…
We have developed a numerical model of flare heating due to the dissipation of Alfvénic waves propagating from the corona to the chromosphere. With this model, we present an investigation of the key parameters of these waves on the energy transport, heating, and subsequent dynamics. For sufficiently high frequencies and perpendicular wave numbers, the waves dissipate significantly in the upper chromosphere, strongly heating it to flare temperatures. This heating can then drive strong chromospheric evaporation, bringing hot and dense plasma to the corona. We therefore find three important concl…
Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. We investigate the consequences for wave-based coronal heating of higher harmonics and what coronal heating observational …
Chandra [1] made an attempt to show that the work of Dwivedi and Srivastava [2] (hereinafter DS) can be investigated even analytically and their results are erroneous. Dwivedi and Srivastava [3] picked up some values of Chandra [1] and tried to show that they are not physically acceptable. Some results of Chandra [1] are not physically acceptable, as these are the outcome of the wrong approach of DS. However, the results are numerically correct whereas the results of DS are numerically wrong.
Phase mixing of Alfvén waves has been studied extensively as a possible coronal heating mechanism but without the full thermodynamic consequences considered self-consistently. It has been argued that in some cases, the thermodynamic feedback of the heating could substantially affect the transverse density gradient and even inhibit the phase mixing process. In this paper, we use MHD simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfvén waves in a coronal loop and the effect of this evaporation on the transverse de…
Context. We diagnose the properties of the plume and interplume regions in a polar coronal hole and the role of waves in the acceleration of the solar wind. Aims. We attempt to detect whether Alfven waves are present in the polar coronal holes through variations in EUV line widths. Methods. Using spectral observations performed over a polar coronal hole region with the EIS spectrometer on Hinode, we study the variation in the line width and electron density as a function of height. We use the density sensitive line pairs of Fe xii 186.88 A & 195.119 A and Fe xiii 203.82 A & 202.04 A . Results.…
It has been shown in a previous work that torsional Alfvén waves can drive turbulence in nonuniform coronal loops with a purely axial magnetic field. Here we explore the role of the magnetic twist. We model a coronal loop as a transversely nonuniform straight flux tube, anchored in the photosphere, and embedded in a uniform coronal environment. We consider that the magnetic field is twisted and control the strength of magnetic twist by a free parameter of the model. We excite the longitudinally fundamental mode of standing torsional Alfvén waves, whose temporal evolution is obtained by means o…
The dynamical response of the solar corona to surface and sub-surface perturbations depends on the chromospheric stratification, and specifically on how efficiently these layers reflect or transmit incoming Alfvén waves. While it would be desirable to include the chromospheric layers in the numerical simulations used to study such phenomena, that is most often not feasible. We defined and tested a simple approximation allowing the study of coronal phenomena while taking into account a parametrised chromospheric reflectivity. We addressed the problems of the transmission of the surface rotation…
We have performed MHD simulations of Alfven wave propagation along an open flux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photospheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy flux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave generator. This difference can be explained by the Alfven wav…
Alfvén waves are responsible for the transfer of magnetic energy in the magnetized plasma. They are involved in heating solar atmosphere and driving solar wind through various nonlinear processes. Since the magnetic field configurations directly affect the nonlinearity of Alfvén waves, it is important to investigate how they relate to the solar atmosphere and wind structure through the nonlinear propagation of Alfvén waves. In this study, we carried out the one-dimensional magnetohydrodynamic simulations to realize the above relation. The results show that when the nonlinearity of Alfvén waves…
Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small scale structures, it is still unclear whether this wave energy can maintain the million degree solar corona. The aim of this work is to assess how much energy can be converted by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal …
The normal modes of oscillation for a magnetic arcade are used to analytically solve an initial value problem and estimate the power spectra of wave frequencies generated by a reconnection event in the solar corona. Over a realistic range of parameters, I find that such a disturbance generates a peak power at $\sim10$s$\mathrm{mHz}$ frequencies, but still substantial power up to $\sim4\mathrm{Hz}$. The cadence and sensitivity of current instrumentation does not allow observations of oscillations at these frequencies, but in the near future, new instrumentation will be able to probe this regime…
Both observations and numerical simulations suggest that Alfvenic waves may carry sufficient energy to sustain the hot temperatures of the solar atmospheric plasma. However, the thermalization of wave energy is inefficient unless very short spatial scales are considered. Phase mixing is a mechanism that can take energy down to dissipation lengths, but it operates over too long a timescale. Here, we study how turbulence, driven by the nonlinear evolution of phase-mixed torsional Alfven waves in coronal loops, is able to take wave energy down to the dissipative scales much faster than the theory…
Physical processes which may lead to solar chromospheric heating are analyzed using high-resolution 1.5D non-ideal MHD modelling. We demonstrate that it is possible to heat the chromospheric plasma by direct resistive dissipation of high-frequency Alfvén waves through Pedersen resistivity. However this is unlikely to be sufficient to balance radiative and conductive losses unless unrealistic field strengths or photospheric velocities are used. The precise heating profile is determined by the input driving spectrum since in 1.5D there is no possibility of Alfvén wave turbulence. The inclusion o…
A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheri…
We study the impulsively generated non-linear Alfvén waves in the solar atmosphere, and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfvén waves at different heights of the mod…
We take stock of recent observations that identify the episodic plasma heating and injection of Alfvenic energy at the base of fast solar wind (in coronal holes). The plasma heating is associated with the occurrence of chromospheric spicules that leave the lower solar atmosphere at speeds of order 100km/s, the hotter coronal counterpart of the spicule emits radiation characteristic of root heating that rapidly reaches temperatures of the order of 1MK. Furthermore, the same spicules and their coronal counterparts ("Propagating Coronal Disturbances"; PCD) exhibit large amplitude, high speed, Alf…
Whilst there are observational indications that transverse MHD waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum…
Context. We address the heating of the solar chromosphere and the related generation of plasma inflows and outflows. Aims. We attempt to detect variations in ion temperature and vertical plasma flows, which are driven by impulsively excited two-fluid Alfvén waves. We aim to investigate the possible contribution of these waves to solar chromosphere heating and plasma outflows. Methods. We performed numerical simulations of the generation and evolution of Alfvén waves with the use of the JOANNA code, which solves the two-fluid equations for ions+electrons and neutrals, coupled by collision terms…
We use MHD simulations to detect the nonlinear effects of torsional Alfvén wave propagation in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. In Paper I we considered solutions to the linearised governing equations torsional Alfvén wave propagation and showed, using a finite difference solver we developed named WiggleWave, that in certain scenarios wave damping is stronger than what would be predicted by our analytic solutions. In this paper we consider whether damping would be further enhanced by the presence of nonlinear effects. W…
We perform magnetohydrodynamic (MHD) simulations to investigate the propagation of Alfven wave in magnetic chromosphere. We use the 1.5-dimensional expanding flux tube geometry setting and transverse perturbation at the bottom to generate the Alfven wave. Compared with previous studies, our expansion is that we include the radiative loss term introduced by Carlsson & Leenaarts (2012). We find that when an observation based transverse wave generator is applied, the spatial distribution of the time-averaged radiative loss profile in our simulation is consistent with that in the classic atmospher…
Between February 24-25, 2009, the EIS spectrometer onboard the Hinode spacecraft performed special "sit & stare" observations above the South polar coronal hole continuously over more than 22 hours. Spectra were acquired with the 1" slit placed off-limb covering altitudes up to 0.48 R$_\odot$ ($3.34\times 10^2$ Mm) above the Sun surface, in order to study with EIS the non-thermal spectral line broadenings. Spectral lines such as Fe {\sc xii} $λ$186.88, Fe {\sc xii} $λ$193.51, Fe {\sc xii} $λ$195.12 and Fe {\sc xiii} $λ$202.04 are observed with good statistics up to high altitudes and they have…
We present a measurement of the energy carried and dissipated by Alfvén waves in a polar coronal hole. Alfvén waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease with height in coronal holes, which is a signature of wave damping, but have been unable to quantify the energy lost by the waves. This is because line widths depend on both the non-thermal velocity v_nt and the ion temperature T_i. We have implemented a means to separate the T_i and v_nt contributions using the observation that at low heights…
In this paper we further develop a model for the heating of coronal loops by Alfven wave turbulence (AWT). The Alfven waves are assumed to be launched from a collection of kilogauss flux tubes in the photosphere at the two ends of the loop. Using a three-dimensional magneto-hydrodynamic (MHD) model for an active-region loop, we investigate how the waves from neighboring flux tubes interact in the chromosphere and corona. For a particular combination of model parameters we find that AWT can produce enough heat to maintain a peak temperature of about 2.5 MK, somewhat lower than the temperatures …
We present a new version of the Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently.…
We propose that coronal heating in EUV coronal plumes is weaker, not stronger, than in adjacent non-plume coronal magnetic funnels. This expectation stems from (i) the observation that an EUV plume is born as the magnetic flux at the foot of the plume's magnetic funnel becomes tightly packed together, and (ii) the observation that coronal heating in quiet regions increases in proportion to the coast-line length of the underlying magnetic network. We do not rule out the possibility that coronal heating in EUV plumes might be stronger, not weaker, but we point out how the opposite is plausible. …
Interaction of Fast Magnetoacoustic Wave with the Localized Coronal Null and Generation of the Energetic Alfvén Wave Packet
Indian Institute of Technology (BHU)（印度理工学院（贝拿勒斯印度教大学））；Institute of Physics University of Graz（格拉茨大学物理研究所）；Department of Astronomy and Astrophysics at Space Research Center, Ilia State University（伊利亚州立大学空间研究中心天文学与天体物理学系）；Evgeni Kharadze Georgian National Astrophysical Observatory（叶夫根尼·哈拉泽格鲁吉亚国家天文台）；Key Laboratory of Solar Activity and Space Weather, School of Aerospace, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学深圳航天学院太阳活动与空间天气重点实验室）；Korea Astronomy and Space Science Institute（韩国天体与空间科学研究所）
We derive a corrected analytical solution for the propagation and enhanced phase mixing of torsional Alfvén waves, in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. Further we develop a code named TAWAS which calculates the analytic solution describing torsional Alfvén waves using IDL software language. We then use TAWAS to demonstrate that both our correction to the analytic solution and the inclusion of wave reflection have a significant impact on Alfvén wave damping. We continue to utilise TAWAS by performing a parameter study in …
We present a new insight into the propagation, attenuation and dissipation of two-fluid, torsional Alfvén waves in the context of heating of the lower solar atmosphere. By means of numerical simulations of the partially-ionized plasma, we solve the set of two-fluid equations for ion plus electron and neutral fluids in three-dimensional (3D) Cartesian geometry. We implement initially a current-free magnetic field configuration, corresponding to a magnetic flux-tube that is rooted in the solar photosphere and expands into the chromosphere and corona. We put the lower boundary of our simulation r…
There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational c…
We have recently passed the 75th anniversary of one of the most important results in solar and space physics: Hannes Alfvén's discovery of Alfvén waves and the Alfvén speed. To celebrate the anniversary, this article recounts some major episodes in the history of MHD waves. Following an initially cool reception, Alfvén's ideas were propelled into the spotlight by Fermi's work on cosmic rays, the new mystery of coronal heating and, as scientific perception of interplanetary space shifted dramatically and the space race started, detection of Alfvén waves in the solar wind. From then on, interest…
The solar coronal heating problem refers to the question why the temperature of the Sun's corona is more than two orders of magnitude higher than that of its surface. Almost 70 years after the discovery, this puzzle is still one of the major challenges in astrophysics. The current basic paradigm of coronal heating is unable to explain all the observational features of the heating. Here we argue that a new paradigm is required to solve the puzzle in a self-consistent manner. The alternative approach is based on the kinetic theory of drift waves. We show, with qualitative and quantitative argume…
Coronal rain consists of cool plasma condensations formed in coronal loops as a result of thermal instability. The standard models of coronal rain formation assume that the heating is quasi-steady and localised at the coronal loop footpoints. We present an observation of magnetic reconnection in the corona and the associated impulsive heating triggering formation of coronal rain condensations. We analyse combined SDO/AIA and IRIS observations of a coronal rain event following a reconnection between threads of a low-lying prominence flux rope and surrounding coronal field lines. The reconnectio…
We use 2.5-D electromagnetic particle-in-cell simulation code to investigate the acceleration of electrons in solar coronal holes through the interaction of Alfvén waves with an interplume region. The interplume is modeled by a cavity density gradients that are perpendicular to the background magnetic field. The aim is to contribute to explain the observation of suprathermal electrons under relatively quiet sun. Simulations show that Alfvén waves in interaction with the interplume region gives rise to a strong local electric field that accelerates electrons in the direction parallel to the bac…
Alfvénic waves have been proposed as an important energy transport mechanism in coronal loops, capable of delivering energy to both the corona and chromosphere and giving rise to many observed features, of flaring and quiescent regions. In previous work, we established that resistive dissipation of waves (ambipolar diffusion) can drive strong chromospheric heating and evaporation, capable of producing flaring signatures. However, that model was based on a simplified assumption that the waves propagate instantly to the chromosphere, an assumption which the current work removes. Via a ray tracin…
We present numerical simulations of reduced magnetohydrodynamic (RMHD) turbulence in a magnetic flux tube at the center of a polar coronal hole. The model for the background atmosphere is a solution of the momentum equation, and includes the effects of wave pressure on the solar wind outflow. Alfvén waves are launched at the coronal base, and reflect at various heights due to variations in Alfvén speed and outflow velocity. The turbulence is driven by nonlinear interactions between the counter-propagating Alfvén waves. Results are presented for two models of the background atmosphere. In the f…
The subject of this study is oscillations in the lower atmosphere in coronal-hole regions, where the conditions are favorable for propagation between the atmospheric layers. Based on spectroscopic observations in photospheric and chromospheric lines, we analysed the features of the oscillations that show signs of propagation between layers of the solar atmosphere. Using the cross-spectrum wavelet algorithm, we found that both chromospheric and photospheric signals under coronal holes share a range of significant oscillations of periods around five minutes, while the signals outside of coronal …
Static distributions of temperature and wind velocity at the transition region are calculated within the framework of magnetohydrodynamics (MHD) of completely ionized hydrogen plasma. The numerical solution of the derived equations gives the width of the transition layer between the chromosphere and the corona as a self-induced opacity of high-frequency Alfven waves (AW). The domain wall is direct consequence of the self-consistent MHD treatment of AW propagation. The low-frequency MHD waves coming from the Sun are strongly reflected by the narrow transition layer, while the high-frequency wav…
We solve numerically the ideal MHD equations with an external gravitational field in 2D in order to study the effects of impulsively generated linear and non-linear Alfvén waves into isolated solar arcades and coronal funnels. We analyze the region containing the interface between the photosphere and the corona. The main interest is to study the possibility that Alfvén waves triggers the energy flux transfer toward the quiet solar corona and heat it, including the case that two consecutive waves can occur. We find that in the case of arcades, short or large, the transferred fluxes by Alfvén wa…
Using the Hinode/EIS 2$"$ spectroscopic observations, we study the intensity, velocity, and FWHM variations of the strongest Fe XII 195.12 Å line along the jet to find the signature of Alfvén waves. We simulate numerically the impulsively generated Alfvén waves within the vertical Harris current-sheet, forming the jet plasma flows, and mimicking their observational signatures. Using the FLASH code and the atmospheric model with embedded weakly expanding magnetic field configuration within a vertical Harris current-sheet, we solve the two and half-dimensional (2.5-D) ideal magnetohydrodynamic (…
The solar wind emanates from the hot and tenuous solar corona. Earlier studies using 1.5 dimensional simulations show that Alfvén waves generated in the photosphere play an important role in coronal heating through the process of non-linear mode conversion. In order to understand the physics of coronal heating and solar wind acceleration together, it is important to consider the regions from photosphere to interplanetary space as a single system. We performed 2.5 dimensional, self-consistent magnetohydrodynamic simulations, covering from the photosphere to the interplanetary space for the firs…
There is observational evidence of the presence of small-amplitude transverse magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads of solar prominences. It is believed that the waves are driven at the photosphere and propagate along the magnetic field lines up to prominences suspended in the corona. The dissipation of MHD wave energy in the partially ionized prominence plasma is a heating mechanism whose relevance needs to be explored. Here we consider a simple 1D model for a non-uniform thin thread and investigate the heating associated with dissipation of Alfven wa…
The solar atmosphere is structured and inhomogeneous both horizontally and vertically. The omnipresence of coronal magnetic loops implies gradients of the equilibrium plasma quantities like the density, magnetic field and temperature. These gradients are responsible for the excitation of drift waves that grow both within the two-component fluid description (in the presence of collisions and without it) and within the two-component kinetic descriptions (due to purely kinetic effects). In the present work the effects of the density gradient in the direction perpendicular to the magnetic field ve…
