Coronal Loop Models Research Articles

Spectroscopic studies of solar corona VI: Trend in line-width variation of coronal emission lines with height independent of the structure of coronal loops

We have obtained spectroscopic observations in coronal emission lines by choosing two lines simultaneously, one [Fe x] 6374 A and the other [Fe xi] 7892 A or [Fe xiii] 10747 A or [Fe xiv] 5303 A. We found that in 95 per cent of the coronal loops observed in 6374 A, the FWHM of the emission line increases with height above the limb irrespective of the size, shape and orientation of the loop and that in case of 5303 A line decreases with height in about 89 per cent of the coronal loops. The FWHM of 7892 A and 10747 A emission lines show intermediate behavior. The increase in the FWHM of 6374 A line with height is the steepest among these four lines. We have also studied the intensity ratio and ratio of FWHM of these lines with respect to those of 6374 A as a function height above the limb. We found that the intensity ratio of 7892 A and 10747 A lines with respect to 6374 A line increases with height and that of 5303 A to 6374 A decreases with height above the limb. This implies that temperature in coronal loops will appear to increase with height in the intensity ratio plots of 7892 A and 6374 A; and 10747 A and 6374 A whereas it will appear to decrease with height in intensity ratio of 5303 A to 6374 A lineversus height plot. These findings are up to a height of about 200 arcsec above the limb. The varying ratios with height indicate that relatively hotter and colder plasma in coronal loops interact with each other. Therefore, the observed increase in FWHM with height above the limb of coronal emission lines associated with plasma at about 1 MK may not be due to increase in non-thermal motions caused by coronal waves but due to interaction with the relatively hotter plasma. These findings also do not support the existing coronal loop models, which predict an increase in temperature of the loop with height above the limb.

Do the Line Widths of Coronal Emission Lines Increase with Height above the Limb?

In our earlier studies we obtained off-the-limb spectroscopic observations in a number of forbidden emission lines ([Fe X-XIV]) to study the physical properties and their temporal variations in steady coronal structures. Short exposure times adopted in those observations permitted us to study the variation in line widths up to about 150'' above the limb. With a view to investigating the variations in the parameters of coronal emission lines up to about 500'', we made raster scans with exposure times that are longer than the earlier exposure times by a factor of about 10. We find that the FWHM of the [Fe XIV] 5303 Å line decreases up to 300'' ± 50'' and then remains more or less the same up to 500'', while that of the [Fe X] 6374 Å line increases up to about 250'' and subsequently remains unchanged. The FWHMs of the [Fe XI] 7892 Å and [Fe XIII] 10747 Å lines show an intermediate behavior. Furthermore, the ratio of the FWHM of 6374 to 5303 Å increases from 0.93 at the limb to 1.18 at 200'' above the limb. The nonvariability in the FWHM of emission lines after about 300'' above the limb in steady coronal structures does not support the prevailing view that the nonthermal velocity increases with height due to either the coronal waves or the high-velocity solar wind. The present results indicate the inadequacy of the earlier coronal loop models. The observed variations in FWHM of the coronal emission lines with height above the limb can be explained by assuming the recent model of coronal loops proposed by Akiyama et al.

Note on the Initial Value Problem for Coronal Loop Kink Waves

Simple fluxtube models of coronal loops have previously been found to support leaky oscillations, where energy escapes from the tube laterally, thereby damping the mode. Of particular interest is the Principal Fast Leaky Kink mode (PFLK), which may be implicated in the decay of loop oscillations observed by TRACE. However, recently, M.S. Ruderman and B. Roberts, J. Plarma Phys. (in press), claimed that the PFLK mode, and many other leaky modes of oscillation, are unphysical, based on an initial value calculation. In this note, their arguments are shown to be incorrect.

Damping of magnetohydrodynamic waves by resonant absorption in the solar atmosphere

In the last decade we have been overwhelmed by an avalanche of discoveries of magnetohydrodynamic (MHD) waves by the Solar and Heliospheric Observatory and Transition Region and Coronal Explorer observatories. Both standing and propagating versions of fast magnetoacoustic and slow magnetoacoustic MHD waves have been detected. Information on the damping times and damping distances of these waves is less detailed and less accurate than that on periods and amplitudes. Nevertheless, observations show the damping times and damping lengths are often short. Also, different types of MHD waves in different types of magnetic structures likely require different damping mechanisms. The phenomenon of fast damping is well documented for the standing fast magnetosonic kink waves in coronal loops. This paper concentrates on standing fast magnetosonic waves. It reports on results on periods and damping times due to resonant absorption in one-dimensional and two-dimensional models of coronal loops. Special attention is given to multiple modes.

Coronal loops heated by turbulence-driven Alfvén waves: A two fluid model

We present the results of a thorough parameter study of coronal loop models in the aim to explore the mechanism behind coronal heating. The two-fluid coronal loops described in this paper have lengths from 10 Mm to 600 Mm and consist of protons and electrons. The loops are treated with our unique, self-consistent, steady state dynamic loop model to derive the basic parameters (as introduced by Li & Habbal 2003, ApJ, 598, L125). The only heating mechanism assumed is turbulently generated Alfven waves that carry the necessary flux from the chromosphere to energize the coronal plasma through preferential heating of the proton gas. Strong Coulomb coupling allows energy to pass efficiently from protons to electrons. We have control over the independent variables, driving scale ( l ) and Alfven amplitude ( ξ ), which influence the dissipation and flux of these resonant waves. We find “mapping” the loop parameter response to varying l with fixed ξ a useful tool to find where certain conditions for each loop length exist. From this, we are able to pin-point where the coldest solution lies. For a loop of $L=10$ Mm, the coolest loops have a maximum temperature of $T=0.75$ MK. We also focus on a $L=40$ Mm loop and vary both l and ξ so we can compare results with existing work. From this parameter mapping we can categorise the loop heating profiles. Our model indicates the existence of footpoint, non-uniformly and quasi-uniformly heated profiles. There is also strong evidence to suggest the same mechanism may apply to hot, SXT loops.

2D Feature Recognition And 3d Reconstruction In Solar Euv Images

EUV images show the solar corona in a typical temperature range of T >rsim 1 MK, which encompasses the most common coronal structures: loops, filaments, and other magnetic structures in active regions, the quiet Sun, and coronal holes. Quantitative analysis increasingly demands automated 2D feature recognition and 3D reconstruction, in order to localize, track, and monitor the evolution of such coronal structures. We discuss numerical tools that “fingerprint” curvi-linear 1D features (e.g., loops and filaments). We discuss existing finger-printing algorithms, such as the brightness-gradient method, the oriented-connectivity method, stereoscopic methods, time-differencing, and space–time feature recognition. We discuss improved 2D feature recognition and 3D reconstruction techniques that make use of additional a priori constraints, using guidance from magnetic field extrapolations, curvature radii constraints, and acceleration and velocity constraints in time-dependent image sequences. Applications of these algorithms aid the analysis of SOHO/EIT, TRACE, and STEREO/SECCHI data, such as disentangling, 3D reconstruction, and hydrodynamic modeling of coronal loops, postflare loops, filaments, prominences, and 3D reconstruction of the coronal magnetic field in general.

Coronal loop oscillations

The observed coronal loop oscillations and their damping are often theoretically described by the use of a very simple coronal loop model, viz. a straight, longitudinally invariant, axi-symmetric, and pressureless flux tube with a different density inside and outside of the loop. In this paper we generalize the model by including longitudinal density stratification and we examine how the longitudinal density stratification alters the linear eigenmodes of the system, their oscillation frequencies, and the damping rates by resonant absorption.

The effect of curvature on quasi-modes in coronal loops

This paper studies quasi-mode oscillations in models of coronal loops that include longitudinal curvature. Using a toroidal coordinate system to incorporate curvature in a basic coronal loop model, the linearized ideal MHD equations are solved for the plasma-β = 0. As a result of the curvature, quasi-modes with different poloidal wave numbers are coupled resulting in modifications of the frequencies. However, for small curvature, only the coupling of quasi-modes with a neighbouring poloidal wave number remains in first order. In addition, the quasi-mode frequencies are unchanged up to first order in the curvature. The imaginary part of the frequency, however, does change in first order, and quasi-modes are slightly more damped in realistically curved coronal loop configurations.

Progress in the Heating of Active Region Loops

Coronal heating is an important problem in solar physics. With the development of highly qualified instruments, such as TRACE, SOHO and Yohkoh, more and more observations about coronal loops have been obtained. The coronal loops' heating, being an important ingredient of coronal heating, has been paid particular attentions recently. But there are still some key issues about the structure and mechanism of the loops' heating unresolved. In this paper, after a brief review on the latest progress in both observations and modeling of coronal loops, we emphatically discuss the heating of hydrostatic loops and hydrodynamic loops based on the 1D model. The prospect of the subject is presented.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The double magnetic tube as a model of coronal loop oscillations

The new model of coronal loop in the form of the double magnetic flux tube embedded into the uniform external magnetic field is proposed to explain the coronal oscillations phenomena. We investigate the MHD-waves in the magnetic flux tube, wich consists of the dense hot cylindrical cord surrounded by the co-axial shell. The magnitudes of Alfven and sound speeds in the cord, in the shell and in the environment are correspondingly. Under the coronal conditions we have \[ C_{se}<C_{si}< V_{Ai}<V_{Ae},\\ C_{si}< V_{Am},\ C_{se}<C_{sm}<V_{Am},\\ C_{sm}<V_{Ai}.\]To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Ideal kink instability of a magnetic loop equilibrium

The force-free coronal loop model by [CITE] is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength () mode grows for average twists (at a loop aspect ratio of ≈5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increases. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field, which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.

Magnetic Loop Models: from Sun to Stars

I review recent progress in determining the nature of the loop structures that form the coronae of solar-like stars. This progress has been driven by observational advances, in particular the new results from X-ray satellites (Chandra and XMM-Newton) and the availability of surface magnetograms from Zeeman-Doppler imaging. It is now clear that stars that are similar to the Sun in mass, but which rotate more rapidly, have a very different magnetic field structure. Their surfaces are more heavily spotted, with spots appearing at all latitudes, extending all the way up to the rotation pole. Their coronae are correspondingly much brighter in X-rays, containing plasma that is hotter and denser than on the Sun. In addition, stellar coronae can support massive co-rotating prominences out to many stellar radii. Recent efforts in modelling these magnetic structures are now bringing together both the surface magnetograms and also the coronal X-ray emission. The resulting coronal loop models show complex loop structures on all scales, with much of the X-ray emission coming from high latitudes where is does not suffer rotational self-eclipse. The observed high densities and X-ray emission measures are a natural consequence of the high magnetic flux density at the surface. The stripping of the corona due to centrifugal effects at high rotation rates can also explain the saturation and supersaturation of X-ray emission with increasing rotation rates, and the recent observation of a high rotational modulation in a supersaturated star.

Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop

We study dynamical consequences of the kink instability of a twisted coronal flux rope, using the force-free coronal loop model by Titov & D\'emoulin (1999) as the initial condition in ideal-MHD simulations. When a critical value of the twist is exceeded, the long-wavelength ($m=1$) kink mode develops. Analogous to the well-known cylindrical approximation, a helical current sheet is then formed at the interface with the surrounding medium. In contrast to the cylindrical case, upward-kinking loops form a second, vertical current sheet below the loop apex at the position of the hyperbolic flux tube (generalized X line) in the model. The current density is steepened in both sheets and eventually exceeds the current density in the loop (although the kink perturbation starts to saturate in our simulations without leading to a global eruption). The projection of the field lines that pass through the vertical current sheet shows an S shape whose sense agrees with the typical sense of transient sigmoidal (forward or reverse S-shaped) structures that brighten in soft X rays prior to coronal eruptions. The upward-kinked loop has the opposite S shape, leading to the conclusion that such sigmoids do not generally show the erupting loops themselves but indicate the formation of the vertical current sheet below them that is the central element of the standard flare model.

Spatially resolved X-ray spectroscopy of cooling clusters of galaxies

We present spatially resolved X-ray spectra taken with the EPIC cameras of XMM-Newton of a sample of 17 cooling clusters and three non-cooling clusters for comparison. The deprojected spectra are analyzed with a multi-temperature model, independent of any a priori assumptions about the physics behind the cooling and heating mechanisms. All cooling clusters show a central decrement of the average temperature, most of them of a factor of . Three clusters (Sérsic 159-3, MKW 3s and Hydra A) only show a weak temperature decrement, while two others (A 399 and A 2052) have a very strong temperature decrement. All cooling clusters show a weak pressure gradient in the core. More important, at each radius within the cooling region the gas is not isothermal. The differential emission measure distribution shows a strong peak near the maximum (ambient) temperature, with a steep decline towards lower temperatures, approximately proportional to T3, or alternatively a cut-off at about a quarter to half of the maximum temperature. In general, we find a poor correlation between radio flux of the central galaxy and the temperature decrement of the cooling flow. This is interpreted as evidence that except for a few cases (like the Hydra A cluster) heating by a central AGN is not the most common cause of weak cooling flows. We investigate the role of heat conduction by electrons and find that the theoretically predicted conductivity rates are not high enough to balance radiation losses. The differential emission measure distribution has remarkable similarities with the predictions from coronal magnetic loop models. Also the physical processes involved (radiative cooling, thermal conduction along the loops, gravity) are similar for clusters loops and coronal loops. If coronal loop models apply to clusters, we find that a few hundred loops per scale height should be present. The typical loop sizes deduced from the observed emission measure distribution are consistent with the characteristic magnetic field sizes deduced from Faraday rotation measurements.

Coronal Loops Heated by Turbulence-driven Alfvn Waves

A two-fluid dynamic model of long-lived coronal loops is presented, whereby heating of the confined plasma is achieved by turbulence-driven Alfven waves. It is assumed that the nonthermal motions inferred from spectral line observations in the transition region are due to Alfven waves. It is also assumed that the turbulence is already fully developed when the waves are injected at the footpoint of the loop while the wave/turbulence energy is readily absorbed by the proton gas. The Coulomb coupling between protons and electrons subsequently heats the electron gas. The model produces a fairly uniform electron temperature in the coronal segment of the loop even though the heating is nonuniform. The model also reproduces electron densities of (1-4) × 109 cm-3, in the range inferred from observations, as well as a moderate flow speed around 10 km s-1 along the loop. The turbulence heating mechanism adopted in this Letter, however, cannot produce stable loops with temperatures T ≤ 1.3 × 106 K.

2D MHD modelling of compressible and heated coronal loops obtained via nonlinear separation of variables and compared to TRACE and SoHO observations

An analytical MHD model of coronal loops with compressible flows and including heating is compared to obser- vational data. The model is constructed via a systematic nonlinear separation of the variables method used to calculate several classes of exact MHD equilibria in Cartesian geometry and uniform gravity. By choosing a particularly versatile solution class with a large parameter space we are able to calculate models whose loop length, shape, plasma density, temperature and ve- locity profiles are fitted to loops observed with TRACE, SoHO/CDS and SoHO/SUMER. Synthetic emission profiles are also calculated and fitted to the observed emission patterns. An analytical discussion is given of the two-dimenional balance of the Lorentz force and the gas pressure gradient, gravity and inertial forces acting along and across the loop. These models are the first to include a fully consistent description of the magnetic field, 2D geometry, plasma density and temperature, flow velocity and thermodynamics of loops. The consistently calculated heating profiles which are largely dominated by radiative losses and concentrated at the footpoints are influenced by the flow and are asymmetric, being biased towards the upflow footpoint.

White-light oscillations during a flare on II Peg

We analyse the intensity oscillations observed in the gradual phase of a white-light flare on the RS CV n binary II Peg. Fast Fourier Transform power spectra and Wavelet analysis reveal a period of 220 s. The reliability of the oscillation is tested using several criteria. Oscillating coronal loop models are used to derive physical parameters such as temperature, electron density and magnetic field strength associated with the coronal loop. The derived parameters are consistent with the near-simultaneous X-ray observations of the flare. There is no evidence for oscillations in the quiescent state of the binary.

Hot Coronal Loop Oscillations Observed by SUMER: Slow Magnetosonic Wave Damping by Thermal Conduction

Recently, strongly damped Doppler shift oscillations of hot (T > 6 MK) coronal loops were observed with the Solar Ultraviolet Measurement of Emitted Radiation (SUMER) spectrometer on board the Solar and Heliospheric Observatory. The oscillations are interpreted as signatures of slow-mode magnetosonic waves excited impulsively in the loops. Using a one-dimensional MHD code, we model the oscillations and the damping of slow magnetosonic waves in a model coronal loop. We find that because of the high temperature of the loops, the large thermal conduction, which depends on temperature as T2.5, leads to rapid damping of the slow waves on a timescale comparable to observations (5.5-29 minutes). The scaling of the dissipation time with period agrees well with SUMER observations of 35 cases in 17 events. We also find that the decay time due to compressive viscosity alone is an order of magnitude longer than the observed decay times.

Systematic construction of exact 2-D MHD equilibria with steady, compressible flow in Cartesian geometry and uniform gravity

We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling solar and stellar winds and outflows (Vlahakis & Tsinganos,1998) but is derived here in Cartesian geometry in the context of the solar atmosphere for the first time. Using the method we find several new classes of solutions, some of which generalise known solutions, including the Kippenhahn & Schl\uter (1957) and Hood & Anzer (1990) solar prominence models and the Tsinganos, Surlantzis & Priest (1993) coronal loop model with flow, and some of which are completely new. Having developed the method in full and summarised the several classes of solutions, we explore in a some detail one of the classes to illustrate the general construction method. From one of the new classes of solutions we calculate two loop-like solutions, one of which is the first exact two-dimensional magnetohydrodynamic equilibrium with trans-Alfv\'enic flow.

Chromospheric Damping of Alfven Waves

We analytically study the damping of Alfven mode oscillations in the chromosphere and in coronal loops. In the partially ionized chromosphere the dominant damping process of Alfven waves is due to collisions between ions and neutrals. We calculate the damping time for Alfven waves of a given frequency, propagating through model chromospheres of various solar structures such as active region plage, quiet sun, and the penumbra and umbra of sunspots. For a given wave frequency, the maximum damping always occurs at temperature minimum heights and in the coldest structure(s), i.e., the umbra of sunspots. Energy dissipation due to ion-neutral damping of Alfven waves with an energy flux of 107 ergs cm-3 s- 1 can play a considerable role in the energy balance of umbrae, quiet sun, and plage for Alfven wave periods of the order, respectively, 50, 5, and 0.5 s. We also consider Alfven waves in coronal loops and the leakage of wave energy through the footpoints. We assume a three-layer model of coronal loops with constant Alfven speed vA (and no damping) in the corona, vA varying exponentially with height in the dissipative chromosphere, and vA again constant in the photosphere at the end of the loop. We find an exact analytical solution in the chromospheric part. Using these solutions, we estimate the leakage of wave energy from the coronal volume through the footpoint regions of the loop and find that the presence of a moderate amount of chromospheric damping can enhance the footpoint leakage. We apply this result to determine the damping time of standing waves in coronal loops. The enhanced footpoint leakage also has implications for theories of coronal heating based on resonant absorption. Finally, we find exact expressions for the damping of Alfven waves launched in the photosphere and upward propagating through the chromosphere and into the corona. The partially ionized chromosphere presents an effective barrier for upward propagating Alfven waves with periods less than a few seconds.