Kelvin-Helmholtz instability in an Alfvén resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfvén driving amplitude and inversely proportional to the width of the Alfvén resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

Microflares as possible sources for coronal heating

We present a preliminary study of 27 microflares observed by Solar X-ray Spectrometer (SOXS) mission during July 2003 to August 2006. We found that all 27 microflares show the Fe-line feature peaking around 6.7 keV, which is an indicator of the presence of coronal plasma temperature ≥ 9 MK. On the other hand, the spectra of microflares show hybrid model of thermal and non-thermal emission, which further supports them as possible sources of coronal heating. Our results based on the analysis show that the energy relapsed by the microflares is good enough for heating of the active corona. We discuss our results in the light of the hybrid model of microflares production.     

Monochromatic observations of a coronal loop

An isophotal map of a small coronal loop, obtained from a coronagraph observation through a solid Fabry-Perot interferometer, is used to estimate the variation of emission per unit volume and the pressure gradient at the top and sides of the loop. The magnitude of the magnetic field necessary to maintain the estimated pressure gradients is found to be ¦H ²¦ = 30 G².     

Observations of preburst heating and magnetic field changes in a coronal loop at 20 cm wavelength

The Very Large Array (VLA) has been used at 20 cm wavelength to study the evolution of a burst loop with 4 resolution on timescales as short as 10 s. The VLA observations show that the coronal loop began to heat up and change its structure about 15 min before the eruption of two impulsive bursts. The first of these bursts occurred near the top of the loop that underwent preburst heating, while the second burst probably occurred along the legs of an adjacent loop. These observations evoke flare models in which coronal loops twist, develop magnetic instabilities and then erupt. We also combine the VLA observations with GOES X-ray data to derive a peak electron temperature of T _e = 2.5 × 10⁷ K and an average electron density of N _e 1 × 10¹⁰ cm^–3 in the coronal loop during the preburst heating phase.     

The effect of density stratification on the resonant absorption of MHD waves in coronal loops

The standing quasi-modes of the ideal magnetohydrodynamics (MHD) in a zero-β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are considered. The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone,   k = 1, 2  , modes of both the kink  ( m = 1)  and fluting  ( m = 2)  waves, where k and m are the longitudinal and azimuthal mode numbers, respectively.     

Two-dimensional pressure structure of a coronal loop

The steady-state pressure structure of a solar coronal loop is discussed using the theory of magneto-hydrodynamical turbulence in cylindrical geometry. The steady state is represented by the superposition of two Chandrasekhar-Kendall functions. This representation, in principle can delinetate the three dimensional temperature structure of the coronal loop. In this paper, we have restricted ourselves to a two dimensional modeling since only this structure submits itself to the scrutiny of the available observations. The radial as well as the axial variations of the pressure in a constant density loop are calculated. These variations are found to conform to the observed features of cool core and hot sheath of the loops as well as to the location of the temperature maximum at the apex of the loop. We find that these features are not present uniformly all along either the length of the loop or across the radius as will be shown in the text. We have also discussed the possible oscillatory nature of these pressure variations and the associated time periods have been estimated.     

Mechanisms of coronal heating

The Sun is a mysterious star. The high temperature of the chromosphere and corona present one of the most puzzling problems of solar physics. Observations show that the solar coronal heating problem is highly complex with many different facts. It is likely that different heating mechanisms are at work in solar corona. Recent observations show that Magnetic Carpet is a potential candidate for solar coronal heating.     

Energy equilibrium in a coronal magnetic loop

Temperature distribution in the cylindrically symmetric coronal magnetic loop, (i) with constant pressure and (ii) with the pressure varying along the radial distance, of the (a) hotter apex and (b) cooler apex than base is investigated analytically by considering the equilibrium between the heat conduction and radiation loss. If the temperature of the loop does not lie within one of the specified temperature ranges, then the distribution is calculated numerically.The effect of the inclusion of heating due to an external source is studied and found that it increases the length of the loop. On the basis of the observed phenomenon, that the magnetic field varies along the loop, the temperature distribution in the loop is investigated for the loop-geometries proposed by Antiochos and Sturrock (1976). It is concluded that for the larger compression in the area of cross section, the height of the loop decreases.Present investigation shows that no loop with equal apex and base temperatures can exist, but a small variation between the two temperatures supports the existence of the loop, which can be observed in nature.     

Observability of coronal heating processes

The mechanisms that could possibly heat the corona are briefly reviewed with emphasis on their observability. Observing enhanced wave flux at footpoints of active regions would confirm wave heating. Observation of nonthermal electrons in tiny coronal events (nanoflares) would confirm dissipation of current sheets. Presence of large scale flows in coronal arcades would underline the importance of turbulent resistivity for coronal heating. A comparison of HeI absorption in quiet and active regions demonstrates the difficulty of interpreting data that connect chromospheric dynamics with coronal heating. Finally, the implications of the search for observations of coronal heating processes are mentioned.     

On a possible mechanism of solar faculae heating

A new mechanism of solar faculae heating is suggested. Interaction of the convective motion with the magnetic field results in decrease of its scale down to values providing for an ohmic dissipation and leading to heating at the photospheric level. Photospheric magnetic fields, faculae and granulation are considered as a combined problem. The heating mechanism causes the observed correlation of faculae brightness with the velocity field. Some points of observation are proposed for examining the action of the suggested mechanism. The effective decreasing of the magnetic field scale may be responsible for the origin of the fine structure. The model does not contradict generally accepted ideas on the active region development.     

To the problem of solar coronal heating

We consider the adequacy of various solar coronal heating models. We show that the correlation between the intensity of the coronal Fe XIV 530.5 nm green line and the calculated magnetic field strength in the solar corona can be a useful tool for this purpose. We have established this correlation for coronal structures and magnetic fields of large spatial and temporal scales. The correlation found exhibits a strong dependence on both solar cycle phase and heliolatitude. The efficiency of a particular coronal heating mechanism is probably determined by the relative area occupied by low and high loops (including open structures). The direct current models based on slow field dissipation (DC) and the wave models based on Alfvén and magnetosonic wave dissipation (AC) are more efficient in the equatorial and polar zones, respectively.     

Two-dimensional steady-state pressure structure in a coronal loop

By expressing the magnetic field and fluid velocity in terms of two Chandrasekhar-Kendall functions (n = 0, m = 0; n = 1, m = 0) we investigated the steady-state pressure profile inside a solar coronal loop. For constant density loops, we found a two-dimensional (radial and axial) structure of pressure. This work is the modified version of the work of Krishan (1985). At the base of the loop, the pressure is found to increase steeply outwards along the radius, whereas at the apex it decreases slowly. The radial variation of pressure is found to be minimum around L/5, where L is the length of the loop measured from one foot to another one. But Krishan (1985) found that the rate of increase of pressure at the base was nearly equal to the rate of decrease of pressure at the apex, and the pressure was found nearly constant at L/4. For axial variation, we found that along the loop axis the pressure increases from the base up to z = 3L/8 and then decreases up to the apex, whereas at the surface, the pressure decreases from the base up to the apex. Krishan (1985), however, found the axial variation to be linear.     

A numerical hydrodynamic model of a heated coronal loop

The fluid equations describing a fully ionized single temperature (i.e., electron and proton temperatures assumed identical) hydrogen plasma in a coronal loop subject to a transient heating pulse (2 × 10⁹ ergs cm^–2 s^–1) centred about the loop apex have been solved numerically. An adaptive regriding scheme was used to ensure adequate spatial resolution throughout the transition region, and due regard paid to the numerical time constants. Because of the fine gridding made possible by this scheme these results represent the first reliable simulation of the impact of a downward propagating conduction front on the transition region, and the early stages of the development of the downward moving compression and upward ablation. Intensities in the O v (1371 Å) transition region line were calculated from the model results. Finally estimates have been made of the importance of the downward-streaming collisionless high-energy tail of the distribution in the transition region resulting from the very steep temperature gradients. It is shown that the mass and energy densities are not substantially altered by the non-Maxwellian tail except in so far as they are coupled to higher moments of the distribution function such as the heat flux through the fluid equations.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

The resistances of the photosphere and of a flaring coronal loop

Solar Physics - We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called “dynamo models”, which invoke an analogy between the...     

The resistances of the photosphere and of a flaring coronal loop

We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called dynamo models, which invoke an analogy between the Earth's magnetosphere-ionosphere circuit and the solar corona-photosphere circuit, are illfounded. Second, we consider the rate of coronal energy release in the impulsive phase of a modest flare, and show that, if the energy going into mass motion can be neglected, the corona must present a resistance of about 10^–3 . Classical resistivity, even in a highly filamented circuit, cannot provide so high a resistance. Anomalous resistivity due to ion sound turbulence can provide the required resistance in this case, but is insufficient to explain the very high power levels inferred in some fast spikes.     

Characteristics of transverse oscillations in a coronal loop arcade

TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.     

On the mechanism of formation of loop prominences

A mechanism is suggested for the formation of loop-type prominences in solar-active regions following flare events. The mechanism is based on the already existing idea of compression of a coronal plasma element resulting in enhanced radiation and consequent cooling of the element. A model is suggested for such a compression based on the concept of a contracting, force-free filamentary structure. If the current in a filament increases with time, then there is a radial contraction of the filament. Since the coronal plasma is frozen into the magnetic field lines of the filament, a contraction of the filament causes a compression of the filamentary plasma. This model of compression is shown to be in approximate qualitative and quantitative agreement with observations.     

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.     

Prominence condensation and magnetic levitation in a coronal loop

We describe the results of a model dynamic simulation of the formation and support of a narrow prominence at the apex of a coronal magnetic loop or arcade. The condensation process proceeds via an initial radiative cooling and pressure drop, and a secondary siphon flow from the dense chromospheric ends. The anti-buoyancy effect as the prominence forms causes a bending of the confining magnetic field, which propagates toward the semi-rigid ends of the magnetic loop. Thus, a wide magnetic hammock or well (of the normal-polarity Kippenhahn-Schlüter-type) is formed, which supports the prominence at or near the field apex. The simplicity of this 1.5-dimensional model, with its accompanying diagnostics, allows one to comprehend the various contributions to the nonlinear dynamics of prominence condensation and levitation.