Photospheric Motions Research Articles

The role of Alfvén wave heating in solar prominences

Observations have shown that magnetohydrodynamic waves over a large frequency range are ubiquitous in solar prominences. The waves are probably driven by photospheric motions and may transport energy up to prominences suspended in the corona. Dissipation of wave energy can lead to heating of the cool prominence plasma, so contributing to the local energy balance within the prominence. Here we discuss the role of Alfv\'en wave dissipation as a heating mechanism for the prominence plasma. We consider a slab-like quiescent prominence model with a transverse magnetic field embedded in the solar corona. The prominence medium is modelled as a partially ionized plasma composed of a charged ion-electron single fluid and two separate neutral fluids corresponding to neutral hydrogen and neutral helium. Friction between the three fluids acts as a dissipative mechanism for the waves. The heating caused by externally-driven Alfv\'en waves incident on the prominence slab is analytically explored. We find that the dense prominence slab acts as a resonant cavity for the waves. The fraction of incident wave energy that is channelled into the slab strongly depends upon the wave period, $P$. Using typical prominence conditions, we obtain that wave energy trapping and associated heating are negligible when $P \gtrsim 100$ s, so that it is unlikely that those waves have a relevant influence on prominence energetics. When $1$ s $\lesssim P \lesssim 100$ s the energy absorption into the slab shows several sharp and narrow peaks, that can reach up to 100%, when the incident wave frequency matches a cavity resonance of the slab. Wave heating is enhanced at those resonant frequencies. Conversely, when $P \lesssim 1$ s cavity resonances are absent, but the waves are heavily damped by the strong dissipation. We estimate that wave heating may compensate for about 10% of radiative losses of the prominence plasma.

THE DEPENDENCE OF CORONAL LOOP HEATING ON THE CHARACTERISTICS OF SLOW PHOTOSPHERIC MOTIONS

ABSTRACT The Parker hypothesis assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects the heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behavior induced by the drivers can be characterized. It is shown that heating is crucially dependent on the nature of the photospheric driver—coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events.

EQUILIBRIA, DYNAMICS, AND CURRENT SHEET FORMATION IN MAGNETICALLY CONFINED CORONAE

The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows that their magnetic fields have an asymmetric structure in the axial direction with variation length-scale $z_\ell \sim \ell B_0/b$, where $B_0$ is the intensity of the strong axial guide field, $b$ that of the orthogonal magnetic field component, and $\ell$ the scale of $\mathbf{b}$. Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length $z_\ell \gtrsim L_z$, and increasingly more asymmetric for smaller variation scales $z_\ell \lesssim L_z$. The $critical$ $length$ $z_\ell \sim L_z$ corresponds to the magnetic field intensity threshold $b \sim \ell B_0/L_z$. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore fields with intensities below such threshold evolve quasi-statically, readjusting to a nearby equilibrium, without developing nonlinear dynamics nor dissipating energy. But stronger fields cannot access their corresponding asymmetric equilibria, hence they are out-of-equilibrium and develop nonlinear dynamics. The subsequent formation of current sheets and energy dissipation is $necessary$ for the magnetic field to relax to equilibrium, since dynamically accessible equilibria have variation scales larger than the loop length $z_\ell \gtrsim L_z$, with intensities smaller than the threshold $b \lesssim \ell B_0/L_z$. The dynamical implications for magnetic fields of interest to solar and stellar coronae are investigated numerically and the impact on coronal physics discussed.

CRITICAL DECAY INDEX AT THE ONSET OF SOLAR ERUPTIONS

Magnetic flux ropes are topological structures consisting of twisted magnetic field lines that globally wrap around an axis. The torus instability model predicts that a magnetic flux rope of major radius R undergoes an eruption when its axis reaches a location where the decay index of the ambient magnetic field Bex is larger than a critical value. In the current-wire model, the critical value depends on the thickness and time evolution of the current channel. We use magnetohydrodynamic simulations to investigate whether the critical value of the decay index at the onset of the eruption is affected by the magnetic flux rope's internal current profile and/or by the particular pre-eruptive photospheric dynamics. The evolution of an asymmetric, bipolar active region is driven by applying different classes of photospheric motions. We find that the critical value of the decay index at the onset of the eruption is not significantly affected by either the pre-erupitve photospheric evolution of the active region or the resulting different magnetic flux ropes. As in the case of the current-wire model, we find that there is a "critical range" [1.3–1.5], rather than a "critical value" for the onset of the torus instability. This range is in good agreement with the predictions of the current-wire model, despite the inclusion of line-tying effects and the occurrence of tether-cutting magnetic reconnection.

Five-Minute Solar Oscillations and Ion-Cyclotron Waves in the Solar Wind

In the present paper we study impact of the photospheric 5-minute oscillations on the ion cyclotron waves in the solar wind. We proceed from the assumption that the ion cyclotron waves in solar wind are experiencing modulation with a characteristic period of 5 minutes under the influence of Alfven waves driven by photospheric motions. The theory presented in our paper predicts a deep frequency modulation of the ion cyclotron waves. The frequency modulation is expected mainly from variations in orientation of the IMF lines. In turn, the variations in orientation are caused by the Alfven waves, propagating from the Sun. To test the theoretical predictions we have analyzed records of the ultra-low-frequency (ULF) geoelectromagnetic waves in order to find the permanent quasi-monochromatic oscillations of natural origin in the Pc1-2 frequency band (0.1-5 Hz), the carrier frequency of which varies with time in a wide range. As a result we found the so-called "serpentine emission" (SE), which was observed in Antarctic at the Vostok station near the South Geomagnetic Pole. The permanency, range of frequencies, and the deep frequency modulation of SE correspond to the qualitative properties of ion cyclotron waves in the solar wind. Clearly expressed 5-minute modulation of the carrier frequency is particularly important feature of the SE in the context of this work. We believe that we have found non-trivial manifestation of the solar 5-min oscillations on the Earth.

FILAMENT CHANNEL FORMATION VIA MAGNETIC HELICITY CONDENSATION

A major unexplained feature of the solar atmosphere is the accumulation of magnetic shear, in the form of filament channels, at photospheric polarity inversion lines (PILs). In addition to free energy, this shear also represents magnetic helicity, which is conserved under reconnection. In this paper, we address the problem of filament channel formation and show how they acquire their shear and magnetic helicity. The results of 3D simulations using the Adaptively Refined Magnetohydrodynamics Solver (ARMS) are presented that support the model of filament channel formation by magnetic helicity condensation developed by \citet{Antiochos13}. We consider the supergranular twisting of a quasi-potential flux system that is bounded by a PIL and contains a coronal hole (CH). The magnetic helicity injected by the small-scale photospheric motions is shown to inverse-cascade up to the largest allowable scales that define the closed flux system: the PIL and the CH. This process produces field lines that are both sheared and smooth, and are sheared in opposite senses at the PIL and the CH. The accumulated helicity and shear flux are shown to be in excellent quantitative agreement with the helicity-condensation model. We present a detailed analysis of the simulations, including comparisons of our analytical and numerical results, and discuss their implications for observations.

CONFINED FLARES IN SOLAR ACTIVE REGION 12192 FROM 2014 OCTOBER 18 TO 29

Using the observations from the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO), we investigate six X-class and twenty-nine M-class flares occurring in solar active region (AR) 12192 from October 18 to 29. Among them, thirty (including six X- and twenty-four M-class) flares originated from the AR core and the other five M-flares appeared at the AR periphery. Four of the X-flares exhibited similar flaring structures, indicating they were homologous flares with analogous triggering mechanism. The possible scenario is: photospheric motions of emerged magnetic fluxes lead to shearing of the associated coronal magnetic field, which then yields a tether-cutting favorable configuration. Among the five periphery M-flares, four were associated with jet activities. The HMI vertical magnetic field data show that the photospheric fluxes of opposite magnetic polarities emerged, converged and canceled with each other at the footpoints of the jets before the flares. Only one M-flare from the AR periphery was followed by a coronal mass ejection (CME). From October 20 to 26, the mean decay index of the horizontal background field within the height range of 40-105 Mm is below the typical threshold for torus instability onset. This suggests that a strong confinement from the overlying magnetic field might be responsible for the poor CME production of AR 12192.

HOT PLASMA FROM SOLAR ACTIVE REGION CORES: A TEST OF AC AND DC CORONAL HEATING MODELS?

Direct current (DC) models of solar coronal heating invoke magnetic reconnection to convert magnetic free energy into heat, whereas alternating current (AC) models invoke wave dissipation. In both cases the energy is supplied by photospheric footpoint motions. For a given footpoint velocity amplitude, DC models predict lower average heating rates but greater temperature variability when compared to AC models. Therefore, evidence of hot plasma (T > 5 MK) in the cores of active regions could be one of the ways for current observations to distinguish between AC and DC models. We have analyzed data from the X-Ray Telescope (XRT) and the Atmospheric Imaging Assembly for 12 quiescent active region cores, all of which were observed in the XRT Be_thick channel. We did Differential Emission Measure (DEM) analysis and achieved good fits for each data set. We then artificially truncated the hot plasma of the DEM model at 5 MK and examined the resulting fits to the data. For some regions in our sample, the XRT intensities continued to be well-matched by the DEM predictions, even without the hot plasma. This truncation, however, resulted in unacceptable fits for the other regions. This result indicates that the hot plasma is present in these regions, even if the precise DEM distribution cannot be determined with the data available. We conclude that reconnection may be heating the hot plasma component of these active regions.

Models of coronal heating, turbulence and fast reconnection.

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.

An overview of flux braiding experiments.

In a number of papers dating back to the 1970s, Parker has hypothesized that, in a perfectly ideal environment, complex photospheric motions acting on a continuous magnetic field will result in the formation of tangential discontinuities corresponding to singular currents. I review direct numerical simulations of the problem and find that the evidence points to a tendency for thin but finite-thickness current layers to form, with thickness exponentially decreasing in time. Given a finite resistivity, these layers will eventually become important and cause the dynamical process of energy release. Accordingly, a body of work focuses on evolution under continual boundary driving. The coronal volume evolves into a highly dynamic but statistically steady state where quantities have a temporally and spatially intermittent nature and where the Poynting flux and dissipation are decoupled on short time scales. Although magnetic braiding is found to be a promising coronal heating mechanism, much work remains to determine its true viability. Some suggestions for future study are offered.

NUMERICAL SIMULATIONS OF HELICITY CONDENSATION IN THE SOLAR CORONA

ABSTRACT The helicity condensation model has been proposed by Antiochos to explain the observed smoothness of coronal loops and the observed buildup of magnetic shear at filament channels. The basic hypothesis of the model is that magnetic reconnection in the corona causes the magnetic stress injected by photospheric motions to collect only at those special locations where prominences are observed to form. In this work we present the first detailed quantitative MHD simulations of the reconnection evolution proposed by the helicity condensation model. We use the well-known ansatz of modeling the closed corona as an initially uniform field between two horizontal photospheric plates. The system is driven by applying photospheric rotational flows that inject magnetic helicity into the corona. The flows are confined to a finite region on the photosphere so as to mimic the finite flux system of a bipolar active region, for example. The calculations demonstrate that, contrary to common belief, opposite helicity twists do not lead to significant reconnection in such a coronal system, whereas twists with the same sense of helicity do produce substantial reconnection. Furthermore, we find that for a given amount of helicity injected into the corona, the evolution of the magnetic shear is insensitive to whether the pattern of driving photospheric motions is fixed or quasi-random. In all cases, the shear propagates via reconnection to the boundary of the flow region while the total magnetic helicity is conserved, as predicted by the model. We discuss the implications of our results for solar observations and for future, more realistic simulations of the helicity condensation process.

Global evaluation of coronal heating due to magnetic reconnection based on solar dynamics observatory observations

The energy flux released into the corona is estimated from magnetic reconnection events in all spatial scales, covering down to nanoflares. The reconnection model used is based on a quasi-3D configuration that approximates the braiding of magnetic field lines which is produced by photospheric motions and includes both resistive and collisionless reconnection, depending on the event size [Martinell, J.J. Rad. Effects Defec. Solids 2010, 165, 114]. This model is applied to all length scales involved in the energy release adding all them up. In order to obtain the size distribution, the observations of the Solar Dynamics Observatory (SDO) are used for two wavelengths in the far UV, together with the corresponding magnetograms and look for correlations brightness-magnetic field. Since the resolution limit of the SDO is just above the nanoflare scales, the spectral index of the energy distribution is determined and it is used to extrapolate down to nanoflare scales. An upper limit of the energy flux is obtained following two different methods, as well as an estimate for the aspect ratio of the current sheets. The energy flux estimates are in the range of which is of the order needed to maintain the hot corona.

PHOTOSPHERIC FLOW FIELD RELATED TO THE EVOLUTION OF THE SUN'S POLAR MAGNETIC PATCHES OBSERVED BYHINODESOLAR OPTICAL TELESCOPE

We investigated the role of photospheric plasma motions in the formation and evolution of polar magnetic patches using time-sequence observations with high spatial resolution. The observations were obtained with the spectropolarimeter on board the Hinode satellite. From the statistical analysis using 75 magnetic patches, we found that they are surrounded by strong converging, supergranulation associated flows during their apparent life time and that the converging flow around the patch boundary is better observed in the Doppler velocity profile in the deeper photosphere. Based on our analysis we suggest that the like-polarity magnetic fragments in the polar region are advected and clustered by photospheric converging flows thereby resulting in the formation of polar magnetic patches. Our observations show that, in addition to direct cancellation magnetic patches decay by fragmentation followed by unipolar disappearance or unipolar disappearance without fragmentation. It is possible that the magnetic patches of existing polarity fragment or diffuse away into smaller elements and eventually cancel out with opposite polarity fragments that reach the polar region around solar cycle maximum. This could be one of the possible mechanisms by which the existing polarity decay during the reversal of the polar magnetic field.

TWO-DIMENSIONAL CELLULAR AUTOMATON MODEL FOR THE EVOLUTION OF ACTIVE REGION CORONAL PLASMAS

We study a 2D cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops (EBTEL) model to compute the response of the plasma to the heating events. Using the known response of the XRT telescope on board Hinode we also obtain synthetic data. The model obeys easy to understand scaling laws relating the output (nanoflare energy, temperature, density, intensity) to the input parameters (field strength, strand length, critical misalignment angle). The nanoflares have a power-law distribution with a universal slope of -2.5, independent of the input parameters. The repetition frequency of nanoflares, expressed in terms of the plasma cooling time, increases with strand length. We discuss the implications of our results for the problem of heating and evolution of active region coronal plasmas.

GENERATION OF MAGNETOHYDRODYNAMIC WAVES IN LOW SOLAR ATMOSPHERIC FLUX TUBES BY PHOTOSPHERIC MOTIONS

Recent ground- and space-based observations reveal the presence of small-scale motions between convection cells in the solar photosphere. In these regions small-scale magnetic flux tubes are generated due to the interaction of granulation motion and background magnetic field. This paper studies the effects of these motions, on magnetohydrodynamic wave excitation from broadband photospheric drivers. Numerical experiments of linear magnetohydrodynamic wave propagation in a magnetic flux tube embedded in a realistic gravitationally stratified solar atmosphere between the photosphere and the low choromosphere (above $\beta=1$) are performed. Horizontal and vertical velocity field drivers mimic granular buffeting and solar global oscillations. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers mimic observed torsional motions in the solar photosphere. The results are analysed using a novel method for extracting the parallel, perpendicular and azimuthal components of the perturbations, which caters for both the linear and non-linear case. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated, to enable the quantification of the relative strengths of excited modes. The torsional drivers excite primarily Alfv\'en modes (~60% of the total flux) with small contributions from the slow kink mode, and, for the logarithmic spiral driver, small amounts of slow sausage mode. The horizontal and vertical drivers excite primarily slow kink or fast sausage modes respectively, with small variations dependent upon flux surface radius.

Evolution of Small-Scale Magnetic Elements in the Vicinity of Granular-Sized Swirl Convective Motions

Advances in solar instrumentation have led to a widespread usage of time series to study the dynamics of solar features, specially at small spatial scales and at very fast cadences. Physical processes at such scales are determinant as building blocks for many others occurring from the lower to the upper layers of the solar atmosphere and beyond, ultimately for understanding the bigger picture of solar activity. Ground-based (SST) and space-borne (Hinode) high-resolution solar data are analyzed in a quiet Sun region displaying negative polarity small-scale magnetic concentrations and a cluster of bright points observed in G-band and Ca II H images. The studied region is characterized by the presence of two small-scale convective vortex-type plasma motions, one of which appears to be affecting the dynamics of both, magnetic features and bright points in its vicinity and therefore the main target of our investigations. We followed the evolution of bright points, intensity variations at different atmospheric heights and magnetic evolution for a set of interesting selected regions. A description of the evolution of the photospheric plasma motions in the region nearby the convective vortex is shown, as well as some plausible cases for convective collapse detected in Stokes profiles.

APPLICATION OF A SOLAR WIND MODEL DRIVEN BY TURBULENCE DISSIPATION TO A 2D MAGNETIC FIELD CONFIGURATION

Although it is widely accepted that photospheric motions provide the energy source and that the magnetic field must play a key role in the process, the detailed mechanisms responsible for heating the Sun's corona and accelerating the solar wind are still not fully understood. Cranmer et al. (2007) developed a sophisticated, 1D, time-steady model of the solar wind with turbulence dissipation. By varying the coronal magnetic field, they obtain, for a single choice of wave properties, a realistic range of slow and fast wind conditions with a sharp latitudinal transition between the two streams. Using a 1D, time-dependent model of the solar wind of Lionello et al. (2014), which incorporates turbulent dissipation of Alfv\'en waves to provide heating and acceleration of the plasma, we have explored a similar configuration, obtaining qualitatively equivalent results. However, our calculations suggest that the rapid transition between slow and fast wind suggested by this 1D model may be disrupted in multidimensional MHD simulations by the requirement of transverse force balance.

Observations of Photospheric Vortical Motions During the Early Stage of Filament Eruption

Solar filaments/prominences exhibit rotational motion during different phases of their evolution from their formation to eruption. We have observed the rotational/vortical motion in the photosphere near the ends of ten filaments during their initial phase of eruption, at the onset of the fast rise phase. All the filaments were associated with active regions. The photospheric vortical motions we observed lasted for 4--20 minutes. In the vicinity of the conjugate ends of the filament the direction of rotation was opposite, except for two cases, where rotational motion was observed at only one end point. The sudden onset of a large photospheric vortex motion could have played a role in destabilizing the filament by transporting axial flux into the activated filament thereby increasing the outward magnetic pressure in it. The outward magnetic pressure may have pushed the filament/flux rope to the height where the torus instability criterion was satisfied, and hence it could have caused the filament instability and eruption.

SUPRATHERMAL ELECTRONS IN THE SOLAR CORONA: CAN NONLOCAL TRANSPORT EXPLAIN HELIOSPHERIC CHARGE STATES?

There have been several ideas proposed to explain how the Sun's corona is heated and how the solar wind is accelerated. Some models assume that open magnetic field lines are heated by Alfven waves driven by photospheric motions and dissipated after undergoing a turbulent cascade. Other models posit that much of the solar wind's mass and energy is injected via magnetic reconnection from closed coronal loops. The latter idea is motivated by observations of reconnecting jets and also by similarities of ion composition between closed loops and the slow wind. Wave/turbulence models have also succeeded in reproducing observed trends in ion composition signatures versus wind speed. However, the absolute values of the charge-state ratios predicted by those models tended to be too low in comparison with observations. This letter refines these predictions by taking better account of weak Coulomb collisions for coronal electrons, whose thermodynamic properties determine the ion charge states in the low corona. A perturbative description of nonlocal electron transport is applied to an existing set of wave/turbulence models. The resulting electron velocity distributions in the low corona exhibit mild suprathermal tails characterized by "kappa" exponents between 10 and 25. These suprathermal electrons are found to be sufficiently energetic to enhance the charge states of oxygen ions, while maintaining the same relative trend with wind speed that was found when the distribution was assumed to be Maxwellian. The updated wave/turbulence models are in excellent agreement with solar wind ion composition measurements.

ON THE RELATIONSHIP BETWEEN PHOTOSPHERIC FOOTPOINT MOTIONS AND CORONAL HEATING IN SOLAR ACTIVE REGIONS

Coronal heating theories can be classified as either direct current (DC) or alternating current (AC) mechanisms, depending on whether the coronal magnetic field responds quasi-statically or dynamically to the photospheric footpoint motions. In this paper we investigate whether photospheric footpoint motions with velocities of 1-2 km s{sup –1} can heat the corona in active regions, and whether the corona responds quasi-statically or dynamically to such motions (DC versus AC heating). We construct three-dimensional magnetohydrodynamic models for the Alfven waves and quasi-static perturbations generated within a coronal loop. We find that in models where the effects of the lower atmosphere are neglected, the corona responds quasi-statically to the footpoint motions (DC heating), but the energy flux into the corona is too low compared to observational requirements. In more realistic models that include the lower atmosphere, the corona responds more dynamically to the footpoint motions (AC heating) and the predicted heating rates due to Alfven wave turbulence are sufficient to explain the observed hot loops. The higher heating rates are due to the amplification of Alfven waves in the lower atmosphere. We conclude that magnetic braiding is a highly dynamic process.