Mhd Leaky Waves in a Layered Plasma: III Numerical Solutions

We present UKIRT spectroscopy of Nova Cassiopeia 1993 (= V705 Cas) in KLNQ bands, taken in 1994 and 1995. Fitting the continuum indicates a dust temperature T ∼ 740 – 750 K in the latter part of 1994; this is similar to earlier measurements, and consistent with the “isothermal” behaviour observed in novae with optically thick dust shells. The β-index drops from 0.8 to 0.4 over the same period. This suggests grain growth; grain diameter increases from < 0.54 μm around day 256, to > 0.57 μm by day 342. The UIR features differ from those in other Galactic sources, and are similar to those in V842 Cen. This suggests fundamental differences between the UIR carriers, or environments, in novae and other Galactic sources. The silicate feature is consistent with an amorphous structure, in contrast to previous novae. We believe that grains in V705 Cas form two populations: silicates, and hydrocarbons. This revised version was published online in September 2006 with corrections to the Cover Date.     

Mhd Leaky Waves in a Layered Plasma: I Theory

In a three layer compressible plasma we study MHD leaky waves described by Fourier modes of complex frequency. We follow a matrix method that yields four transcendental dispersion relations. The roots (real or complex) make up a spectrum of pseudomodes, consisting of a complicate set of infinite branches. We derive analytical properties that allow to study the topology of the spectrum, the conditions of existence of real and complex roots, the contacts and crossings of branches of different types, etc. Our results allow to analyze any particular case of interest.     

Mhd Leaky Waves in a Layered Plasma: II Mechanisms of Leakage

The application of Fourier analysis to study leaky waves has the advantage of simplicity, but it is not clear why the complex roots of the dispersion relations represent leaky waves, nor how the leakage occurs. We investigate the different kinds of leakage that can occur in a three layer plasma, and to which Fourier pseudomodes they are associated. We find four basic mechanisms, called surface mode ..., single interface ..., trapped wave ... and lost insulation leakage. These mechanisms appear in pure form only near certain limiting cases, in which the parameters of the problem take some special values. As soon as the parameters depart significantly from the limiting values, the behavior of the leaky wave complicates and mixtures of the mechanisms occur, in varying amounts. In consequence different points of the same complex branch of the spectrum may correspond to different mechanisms. All the complex branches of the spectrum correspond to leaky waves, but in general it is not possible to classify them according to type of leakage, except close to a limiting case. Since in a three layer configuration there are many of these, the spectrum of leaky waves is very complicated.     

Numerical Simulations of Impulsively Generated Magnetosonic Waves in a Coronal Loop

We consider impulsively excited magnetosonic waves in a highly magnetized coronal loop that is approximated by a straight plasma slab of enhanced mass density. Numerical results reveal that wavelet spectra of time signatures of these waves possess characteristic shapes that depend on the position of the initial pulse: in the case of a pulse launched inside the slab, these spectra are of a tadpole shape, while for a pulse excited in the ambient medium these spectra display more complex structures with branches of long and short-period waves. These short period oscillations correspond to waves that are trapped inside the slab, and the long-period oscillations are associated with waves that propagate through the ambient medium and reach the detection point. These findings are compatible with recent theoretical studies and observations by the solar eclipse coronal imaging system (SECIS).     

Spectroscopic Observation of Coronal Waves

A time sequence over 80 min of coronal green-line spectra was obtained with a corona- graph at the Norikura Solar Observatory. Doppler velocities, line intensities, and line widths were derived through fitting a single Gaussian to the observed line profiles. Coronal waves have been clearly detected in the Doppler velocity data. The Fourier analysis shows powers in a 1–3 mHz range, and in higher frequencies (5–7 mHz) at localized regions. The propagation speed of the waves was estimated by correlation analysis. The line intensity and line width did not show clear oscillations, but their phase relationship with the Doppler velocity indicates propagating waves rather than standing waves. The existence of Alfvén waves whose speed is 500 km s^–1 or faster is possible but inconclusive, while the existence of slower waves (of the order of 100 km s^–1, possibly sound waves) is evident. The energy carried by the detected sound waves is far smaller than the required heat input rate to the quiet corona.     

Origin of Coronal Shock Waves

The basic idea of the paper is to present transparently and confront two different views on the origin of large-scale coronal shock waves, one favoring coronal mass ejections (CMEs), and the other one preferring flares. For this purpose, we first review the empirical aspects of the relationship between CMEs, flares, and shocks (as manifested by radio type II bursts and Moreton waves). Then, various physical mechanisms capable of launching MHD shocks are presented. In particular, we describe the shock wave formation caused by a three-dimensional piston, driven either by the CME expansion or by a flare-associated pressure pulse. Bearing in mind this theoretical framework, the observational characteristics of CMEs and flares are revisited to specify advantages and drawbacks of the two shock formation scenarios. Finally, we emphasize the need to document clear examples of flare-ignited large-scale waves to give insight on the relative importance of flare and CME generation mechanisms for type II bursts/Moreton waves.     

Formation of Coronal Shock Waves

Magnetosonic wave formation driven by an expanding cylindrical piston is numerically simulated to obtain better physical insight into the initiation and evolution of large-scale coronal waves caused by coronal eruptions. Several very basic initial configurations are employed to analyze intrinsic characteristics of MHD wave formation that do not depend on specific properties of the environment. It turns out that these simple initial configurations result in piston/wave morphologies and kinematics that reproduce common characteristics of coronal waves. In the initial stage, the wave and the expanding source region cannot be clearly resolved; i.e. a certain time is needed before the wave detaches from the piston. Thereafter, it continues to travel as what is called a “simple wave.” During the acceleration stage of the source region inflation, the wave is driven by the piston expansion, so its amplitude and phase-speed increase, whereas the wavefront profile steepens. At a given point, a discontinuity forms in the wavefront profile; i.e. the leading edge of the wave becomes shocked. The time/distance required for the shock formation is shorter for a more impulsive source-region expansion. After the piston stops, the wave amplitude and phase speed start to decrease. During the expansion, most of the source region becomes strongly rarefied, which reproduces the coronal dimming left behind the eruption. However, the density increases at the source-region boundary, and stays enhanced even after the expansion stops, which might explain stationary brightenings that are sometimes observed at the edges of the erupted coronal structure. Also, in the rear of the wave a weak density depletion develops, trailing the wave, which is sometimes observed as weak transient coronal dimming. Finally, we find a well-defined relationship between the impulsiveness of the source-region expansion and the wave amplitude and phase speed. The results for the cylindrical piston are also compared with the outcome for a planar wave that is formed by a one-dimensional piston, to find out how different geometries affect the evolution of the wave.     

Mhd Interpretation of LASCO Observations of a Coronal Mass Ejection as a Disconnected Magnetic Structure

We present a qualitative and quantitative comparison of a single coronal mass ejection (CME) as observed by LASCO (July 28–29, 1996) with the results of a three-dimensional axisymmetric time-dependent magnetohydrodynamic model of a flux rope interacting with a helmet streamer. The particular CME considered was selected based on the appearance of a distinct ‘tear-drop’ shape visible in animations generated from both the data and the model. The CME event begins with the brightening of a pre-existing coronal streamer which evolves into a ‘tear-drop’ shaped loop followed by a Y-shaped structure. The brightening moves slowly outward with significant acceleration reaching velocities of ∼450 km s^-1 at 30 R⊙. The observed CME characteristics are compared with the model results. On the basis of this comparison, we suggested that the observed features were caused by the evacuation of a flux rope in the closed field region of the helmet streamer (i.e., helmet dome). The flux rope manifests itself as the cavity of the quasi-static helmet streamer and the whole system becomes unstable when the flux rope reaches a threshold strength. The observed ‘tear-drop’ structure is due to the deformed flux rope. The leading edge of the flux rope interacts with the helmet dome to form the typical loop-like CME. The trailing edge of this flux rope interacts with the local bi-polar field to form the observed Y-shaped structure. The model results for the evolution of the magnetic-field configurations, velocity, and polarization brightness are directly compared with observations. Animations have been generated from both the actual data and the model to illustrate the good agreement between the observation and the model. These animations can be found on the CD-ROM which accompanies this volume. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1004923016322     

A Kinetic Model of Coronal Heating and Acceleration by Ion-Cyclotron Waves: Preliminary Results

We present a kinetic model of the heating and acceleration of coronal protons by outward-propagating ion-cyclotron waves on open, radial magnetic flux tubes. In contrast to fluid models which typically insist on bi-Maxwellian distributions and which spread the wave energy and momentum over the entire proton population, this model follows the kinetic evolution of the collisionless proton distribution function in response to the combination of the resonant wave-particle interaction and external forces. The approximation is made that pitch-angle scattering by the waves is faster than all other processes, resulting in proton distributions which are uniform over the resonant surfaces in velocity space. We further assume, in this preliminary version, that the waves are dispersionless so these resonant surfaces are portions of spheres centered on the radial sum of the Alfvén speed and the proton bulk speed. We incorporate the fact that only those protons with radial speeds less than the bulk speed will be resonant with outward-propagating waves, so this rapid interaction acts only on the sunward half of the distribution. Despite this limitation, we find that the strong perpendicular heating of the resonant particles, coupled with the mirror force, results in substantial outward acceleration of the entire distribution. The proton distribution evolves towards an incomplete shell in velocity space, and appears vastly different from the distributions assumed in fluid models. Evidence of these distinctive distributions should be observable by instruments on Solar Probe.     

A Numerical Study of the Response of the Coronal Magnetic Field to Flux Emergence

Large-scale solar eruptions, known as coronal mass ejections (CMEs), are regarded as the main drivers of space weather. The exact trigger mechanism of these violent events is still not completely clear; however, the solar magnetic field indisputably plays a crucial role in the onset of CMEs. The strength and morphology of the solar magnetic field are expected to have a decisive effect on CME properties, such as size and speed. This study aims to investigate the evolution of a magnetic configuration when driven by the emergence of new magnetic flux in order to get a better insight into the onset of CMEs and their magnetic structure. The three-dimensional, time-dependent equations for ideal magnetohydrodynamics are numerically solved on a spherical mesh. New flux emergence in a bipolar active region causes destabilisation of the initial stationary structure, finally resulting in an eruption. The initial magnetic topology is suitable for the ??breakout?? CME scenario to work. Although no magnetic flux rope structure is present in the initial condition, highly twisted magnetic field lines are formed during the evolution of the system as a result of internal reconnection due to the interaction of the active region magnetic field with the ambient field. The magnetic energy built up in the system and the final speed of the CME depend on the strength of the overlying magnetic field, the flux emergence rate, and the total amount of emerged flux. The interaction with the global coronal field makes the eruption a large-scale event, involving distant parts of the solar surface.     

Non-reflective Propagation of Kink Waves in Coronal Magnetic Loops

Propagating kink waves are ubiquitously observed in solar magnetic wave guides. We consider the possibility that these waves propagate without reflection although there is some inhomogeneity. We briefly describe the general theory of non-reflective, one-dimensional wave propagation in inhomogeneous media. This theory is then applied to kink-wave propagation in coronal loops. We consider a coronal loop of half-circle shape embedded in an isothermal atmosphere, and assume that the plasma temperature is the same inside and outside the loop. We show that non-reflective kink-wave propagation is possible for a particular dependence of the loop radius on the distance along the loop. A viable assumption that the loop radius increases from the loop footpoint to the apex imposes a lower limit on the loop expansion factor, which is the ratio of the loop radii at the apex and footpoints. This lower limit increases with the loop height; however, even for a loop that is twice as high as the atmospheric scale height, it is small enough to satisfy observational constraints. Hence, we conclude that non-reflective propagation of kink waves is possible in a fairly realistic model of coronal loops.     

Coronal Leaky Tube Waves and Oscillations Observed with Trace

Leaky tube waves are examined in the context of kink oscillations in coronal loops, observed in recent years using TRACE. It is pointed out that the standard (non-leaky) principal kink mode has a leaky bifurcated counterpart with decay time 4^–4(L/R)² P, where R and L are the loop radius and length, and P is the oscillation period. This is somewhat too long to explain the observed decays, except for very short or thick loops, but may be implicated in the initial excitation. Higher harmonics decay much more rapidly. The external solution takes the form of a wave running nearly parallel to the tube, but with a small outward component. In addition, a number of other leaky modes are described which decay on timescales of seconds, =Ra _e/a ², where a and a _e are the loop and external Alfvén speeds respectively, and which can be identified as being almost radially propagating fast magnetoacoustic waves. These are outside the currently observable range, but are likely to be important energetically.     

Observations of the 24 September 1997 Coronal Flare Waves

We report coincident observations of coronal and chromospheric flare wave transients in association with a flare, large-scale coronal dimming, metric radio activity and a coronal mass ejection. The two separate eruptions occurring on 24 September 1997 originate in the same active region and display similar morphological features. The first wave transient was observed in EUV and H data, corresponding to a wave disturbance in both the chromosphere and the solar corona, ranging from 250 to approaching 1000 km s^–1 at different times and locations along the wavefront. The sharp wavefront had a similar extent and location in both the EUV and H data. The data did not show clear evidence of a driver, however. Both events display a coronal EUV dimming which is typically used as an indicator of a coronal mass ejection in the inner corona. White-light coronagraph observations indicate that the first event was accompanied by an observable coronal mass ejection while the second event did not have clear evidence of a CME. Both eruptions were accompanied by metric type II radio bursts propagating at speeds in the range of 500–750 km s^–1, and neither had accompanying interplanetary type II activity. The timing and location of the flare waves appear to indicate an origin with the flaring region, but several signatures associated with coronal mass ejections indicate that the development of the CME may occur in concert with the development of the flare wave.     

MHD Modeling of Coronal Large-Amplitude Waves Related to CME Lift-off

We have employed a two-dimensional magnetohydrodynamic simulation code to study mass motions and large-amplitude coronal waves related to the lift-off of a coronal mass ejection (CME). The eruption of the filament is achieved by an artificial force acting on the plasma inside the flux rope. By varying the magnitude of this force, the reaction of the ambient corona to CMEs with different acceleration profiles can be studied. Our model of the ambient corona is gravitationally stratified with a quadrupolar magnetic field, resulting in an ambient Alfvén speed that increases as a function of height, as typically deduced for the low corona. The results of the simulations show that the erupting flux rope is surrounded by a shock front, which is strongest near the leading edge of the erupting mass, but also shows compression near the solar surface. For rapidly accelerating filaments, the shock front forms already in the low corona. Although the speed of the driver is less than the Alfvén speed near the top of the atmosphere, the shock survives in this region as well, but as a freely propagating wave. The leading edge of the shock becomes strong early enough to drive a metric type II burst in the corona. The speed of the weaker part of the shock front near the surface is lower, corresponding to the magnetosonic speed there. We analyze the (line-of-sight) emission measure of the corona during the simulation and recognize a wave receding from the eruption site, which strongly resembles EIT waves in the low corona. Behind the EIT wave, we clearly recognize a coronal dimming, also observed during CME lift-off. We point out that the morphology of the hot downstream region of the shock would be that of a hot erupting loop, so care has to be taken not to misinterpret soft X-ray imaging observations in this respect. Finally, the geometry of the magnetic field around the erupting mass is analyzed in terms of precipitation of particles accelerated in the eruption complex. Field lines connected to the shock are further away from the photospheric neutral line below the filament than the field lines connected to the current sheet below the flux rope. Thus, if the DC fields in the current sheet accelerate predominantly electrons and the shock accelerates ions, the geometry is consistent with recent observations of gamma rays being emitted further out from the neutral line than hard X-rays.     

Coronal Temperature Maps from Solar EUV Images: A Blind Source Separation Approach

Multi-wavelength solar images in the extreme ultraviolet (EUV) are routinely used for analysing solar features such as coronal holes, filaments, and flares. However, images taken in different bands often look remarkably similar, as each band receives contributions coming from regions with a range of different temperatures. This has motivated the search for empirical techniques that may unmix these contributions and concentrate salient morphological features of the corona in a smaller set of less redundant source images. Blind Source Separation (BSS) does precisely this. Here we show how this novel concept also provides new insight into the physics of the solar corona, using observations made by SDO/AIA. The source images are extracted using a Bayesian positive source-separation technique. We show how observations made in six spectral bands, corresponding to optically thin emissions, can be reconstructed by a linear combination of three sources. These sources have a narrower temperature response and allow for considerable data reduction, since the pertinent information from all six bands can be condensed into a single composite picture. In addition, they give access to empirical temperature maps of the corona. The limitations of the BSS technique and some applications are briefly discussed.     

On Coronal Loop Heating by Torsional Alfvén Waves

Heating of coronal loops by linear resonant Alfvén waves, excited by the footpoints motions in the photosphere, has been studied. The analysis of single-layer heating is extended to multilayer heating, in semiempirical treatment. Heating and nonthermal velocities in different layers of loops in X-ray bright points, active regions, and large-scale structures are estimated. The average value of velocity is found to be in agreement with the observations.     

Propagation of Fast Coronal Mass Ejections and Shock Waves Associated with Type II Radio-Burst Emission: An Analytic Study

Coronal mass ejections (CMEs) are large-scale eruptive events in the solar corona. Once they are expelled into the interplanetary (IP) medium, they propagate outwards and “evolve” interacting with the solar wind. Fast CMEs associated with IP shocks are a critical subject for space weather investigations. We present an analytic model to study the heliocentric evolution of fast CME/shock events and their association with type II radio-burst emissions. The propagation model assumes an early stage where the CME acts as a piston driving a shock wave; beyond this point the CME decelerates, tending to match the ambient solar wind speed and its shock decays. We use the shock speed evolution to reproduce type II radio-burst emissions. We analyse four fast CME halo events that were associated with kilometric type II radio bursts, and in-situ measurements of IP shock and CME signatures. The results show good agreement with the dynamic spectra of the type II frequency drifts and the in-situ measurements. This suggests that, in general, IP shocks associated with fast CMEs evolve as blast waves approaching 1 AU, implying that the CMEs do not drive their shocks any further at this heliocentric range.     

Propagation of the Slow Magnetoacoustic Waves in Coronal Loops Above Sunspots

The observations from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) have revealed the weak dis- turbances (WDs) propagating in the fan-like coronal loops of the active region (AR 11092) at 171 ?A, 193 ?A, and 211 ?A. These WDs seem to be a common phenomenon in this part of the active region. The disturbances originate from the bright loop foot, and propagate along the loops. The observed propagation speed decreases with the increasing temperature, and varies between 40 km/s and 121 km/s, close to and less than the sound speed in coronal loops. Consid- ering the projection effect and the different angles of the loops with respect to the line of sight, this is exactly what the slow-wave model expects. The wavelet analysis shows that the periods of the WDs observed in different wavebands have no signi?cant difference, the two distinct periods, 3 min and more than 10 min, are all detected in the three EUV wavebands. Not only the coronal loops but also the sunspot region in the chromosphere exhibit intensity oscillations with a period of the order of 3 min. This result suggests that the sunspot oscillations can propagate into the corona through the chromosphere and transition region.     

Dissipation of Standing Slow Magnetoacoustic Waves in Hot Coronal Loops

The damping of standing slow waves in hot (T>6 MK) coronal loops of semicircular shape is revisited in both the linear and nonlinear regimes. Dissipation by thermal conduction, compressive viscosity, radiative cooling, and heating are examined for nonstratified and stratified loops. We find that for typical conditions of hot SUMER loops, thermal conduction increases the period of damped oscillations over the sound-crossing time, whereas the decay times are mostly shaped by compressive viscosity. Damping from optically thin radiation is negligible. We also find that thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when compressive viscosity is added do these waves damp out at the same rate as the observed rapidly decaying modes of hot SUMER loop oscillations, in contrast to most current work, which has pointed to thermal conduction as the dominant mechanism. We compare the linear predictions with numerical hydrodynamic calculations. Under the effects of gravity, nonlinear viscous dissipation leads to a reduction of the decay time compared to the homogeneous case. In contrast, the linear results predict that the damping rates are barely affected by gravity.