The role of torsional Alfven waves in coronal heating

In the context of coronal heating, among the zoo of MHD waves that exist in the solar atmosphere, Alfven waves receive special attention. Indeed, these waves constitute an attractive heating agent due to their ability to carry over the many different layers of the solar atmosphere sufficient energy to heat and maintain a corona. However, due to their incompressible nature these waves need a mechanism such as mode conversion (leading to shock heating), phase mixing, resonant absorption or turbulent cascade in order to heat the plasma. New observations with polarimetric, spectroscopic and imaging instruments such as those on board of the japanese satellite Hinode, or the SST or CoMP, are bringing strong evidence for the existence of energetic Alfven waves in the solar corona. In order to assess the role of Alfven waves in coronal heating, in this work we model a magnetic flux tube being subject to Alfven wave heating through the mode conversion mechanism. Using a 1.5-dimensional MHD code we carry out a parameter survey varying the magnetic flux tube geometry (length and expansion), the photospheric magnetic field, the photospheric velocity amplitudes and the nature of the waves (monochromatic or white noise spectrum). It is found that independently of the photospheric wave amplitude and magnetic field a corona can be produced and maintained only for long (> 80 Mm) and thick (area ratio between photosphere and corona > 500) loops. Above a critical value of the photospheric velocity amplitude (generally a few km/s) the corona can no longer be maintained over extended periods of time and collapses due to the large momentum of the waves. These results establish several constraints on Alfven wave heating as a coronal heating mechanism, especially for active region loops.Comment: 39 pages, 8 figures; http://stacks.iop.org/0004-637X/712/49

The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model

The observed powerlaw distributions of solar flare parameters can be interpreted in terms of a nonlinear dissipative system in the state of self-organized criticality (SOC). We present a universal analytical model of a SOC process that is governed by three conditions: (i) a multiplicative or exponential growth phase, (ii) a randomly interrupted termination of the growth phase, and (iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential-growth model, which includes also a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence frequency distributions and the scatter of correlated parametyers more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar cycle modulations of the powerlaw slopes of flare frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.Comment: Part II of Paper I: The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. I. Observation

Observations of Active Region Loops with the EUV Imaging Spectrometer on Hinode

Previous solar observations have shown that coronal loops near 1 MK are difficult to reconcile with simple heating models. These loops have lifetimes that are long relative to a radiative cooling time, suggesting quasi-steady heating. The electron densities in these loops, however, are too high to be consistent with thermodynamic equilibrium. Models proposed to explain these properties generally rely on the existence of smaller scale filaments within the loop that are in various stages of heating and cooling. Such a framework implies that there should be a distribution of temperatures within a coronal loop. In this paper we analyze new observations from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. EIS is capable of observing active regions over a wide range of temperatures (\ion{Fe}{8}--\ion{Fe}{17}) at relatively high spatial resolution (1\arcsec). We find that most isolated coronal loops that are bright in \ion{Fe}{12} generally have very narrow temperature distributions ($\sigma_T \lesssim 3\times10^5$ K), but are not isothermal. We also derive volumetric filling factors in these loops of approximately 10%. Both results lend support to the filament models.Comment: Submitted to ApJ

Relationship between Hard and Soft X-ray Emission Components of a Solar Flare

X-ray observations of solar flares routinely reveal an impulsive high-energy and a gradual low-energy emission component, whose relationship is one of the key issues of solar flare study. The gradual and impulsive emission components are believed to be associated with, respectively, the thermal and nonthermal components identified in spectral fitting. In this paper, a prominent about 50 second hard X-ray (HXR) pulse of a simple GOES class C7.5 flare on 20 February 2002 is used to study the association between high energy, non-thermal and impulsive evolution, and low energy, thermal and gradual evolution. We use regularized methods to obtain time derivatives of photon fluxes to quantify the time evolution as a function of photon energy, obtaining a break energy between impulsive and gradual behavior. These break energies are consistent with a constant value of about 11 keV in agreement with those found spectroscopically between thermal and non-thermal components, but the relative errors of the former are greater than 15% and much greater than the a few percent errors found from the spectral fitting. These errors only weakly depend on assuming an underlying spectral model for the photons, pointing to the current data being inadequate to reduce the uncertainties rather than there being a problem associated with an assumed model. The time derivative method is used to test for the presence of a 'pivot energy' in this flare. Although these pivot energies are marginally consistent with a constant value of about 9 keV, its values in the HXR rise phase appear to be lower than those in the decay phase

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick--slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy loading process. The model design leads to a systematic deficit of small scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.Comment: 24 pages, 11 figures, 2 tables, accepted for publication in Solar Physic

Modeling Evolving Coronal Loops with Observations from STEREO, Hinode, and TRACE

The high densities, long lifetimes, and narrow emission measure distributions observed in coronal loops with apex temperatures near 1 MK are difficult to reconcile with physical models of the solar atmosphere. It has been proposed that the observed loops are actually composed of sub-resolution ``threads'' that have been heated impulsively and are cooling. We apply this heating scenario to nearly simultaneous observations of an evolving post-flare loop arcade observed with the EUVI/\textit{STEREO}, XRT/\textit{Hinode}, and \textit{TRACE} imagers and the EIS spectrometer on \textit{HINODE}. We find that it is possible to reproduce the extended loop lifetime, high electron density, and the narrow differential emission measure with a multi-thread hydrodynamic model provided that the time scale for the energy release is sufficiently short. The model, however, does not reproduce the evolution of the very high temperature emission observed with XRT. In XRT the emission appears diffuse and it may be that this discrepancy is simply due to the difficulty of isolating individual loops at these temperatures. This discrepancy may also reflect fundamental problems with our understanding of post-reconnection dynamics during the conductive cooling phase of loop evolution.Comment: Revised version submitted to ApJ in response to referee's comment

The Source of Three-minute Magneto-acoustic Oscillations in Coronal Fans

We use images of high spatial, spectral and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the coupling between wave phenomena observed at numerous heights in the solar atmosphere. Intensity oscillations of 3 minutes are observed to encompass photospheric umbral dot structures, with power at least three orders-of-magnitude higher than the surrounding umbra. Simultaneous chromospheric velocity and intensity time series reveal an 87 \pm 8 degree out-of-phase behavior, implying the presence of standing modes created as a result of partial wave reflection at the transition region boundary. An average blue-shifted Doppler velocity of ~1.5 km/s, in addition to a time lag between photospheric and chromospheric oscillatory phenomena, confirms the presence of upwardly-propagating slow-mode waves in the lower solar atmosphere. Propagating oscillations in EUV intensity are detected in simultaneous coronal fan structures, with a periodicity of 172 \pm 17 s and a propagation velocity of 45 \pm 7 km/s. Numerical simulations reveal that the damping of the magneto-acoustic wave trains is dominated by thermal conduction. The coronal fans are seen to anchor into the photosphere in locations where large-amplitude umbral dot oscillations manifest. Derived kinetic temperature and emission measure time-series display prominent out-of-phase characteristics, and when combined with the previously established sub-sonic wave speeds, we conclude that the observed EUV waves are the coronal counterparts of the upwardly-propagating magneto-acoustic slow-modes detected in the lower solar atmosphere. Thus, for the first time, we reveal how the propagation of 3 minute magneto-acoustic waves in solar coronal structures is a direct result of amplitude enhancements occurring in photospheric umbral dots.Comment: Accepted into ApJ (13 pages and 10 figures

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory

We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components $B_x({\bf x})$, $B_y({\bf x})$, $B_z({\bf x})$, the force-free parameter $\alpha({\bf x})$, the electric current density ${\bf j}({\bf x})$, and are accurate to second-order (of the nonlinear force-free $\alpha$-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.Comment: Solar Physics (in press), 26 pages, 11 figure