Thermal cyclotron radiation from hot coronal loops and peculiarities of the polarization structure of solar microwave emission sources: I. Brightness temperature

We discuss the possible contribution of the thermal cyclotron radiation from hot coronal magnetic loops to the observed characteristics of the microwave emission from solar active regions. Based on the simplest three-dimensional model of a loop in the shape of a hot torus, we have calculated the expected peculiarities of the frequency and polarization structures of microwave emission sources associated with sunspots and containing coronal loops. Our model calculations of the two-dimensional brightness temperature distributions at various wavelengths for the ordinary and extraordinary modes and the wavelength dependences of the brightness temperatures are presented in the first part of the work. The loop size, the electron density, and the source position on the disk have been found to affect these characteristics. Our numerical calculations of the brightness temperature distributions and spectra have confirmed the well-known assumption that under certain conditions the spectrum of a hot filament can contain cyclotron lines and the sense of the polarization can change over the range. The results obtained here refer to the brightness temperature along the line of sight that crosses the photosphere at a point with given coordinates, i.e., these are the emission characteristics at a fixed point of the source. Integrated characteristics (the flux from the entire source and its polarization) and a discussion of the hot loop model will be given in the second part of the work.     

Thermal cyclotron radiation from hot coronal loops and peculiarities of the polarization structure of solar microwave emission sources: II. Integrated characteristics

We present our calculations of the expected characteristics of the integrated spectrum of thermal cyclotron radiation from a solar active region with a coronal magnetic loop. A hot torus is considered as a three-dimensional loop model. We show that the hot-loop emission can change appreciably the emission characteristics of the active region at centimeter and decimeter wavelengths. At certain loop parameters, the emission frequency spectrum can have a nonmonotonic and complex pattern with several peaks or contain narrow-band cyclotron lines. The polarization structure of the source with a hot loop is also complex and the polarization is repeatedly reversed over the observed frequency range under certain conditions. The revealed spectral-polarization peculiarities are considered from the standpoint of whether some atypical observed properties of the emission sources associated with solar active regions can be explained.     

Cooling of a coronal flare loop through radiation and conduction

A simple method is proposed for a computation of the cooling of coronal flare loops by radiation and conduction, for various temperatures, densities, and lengths of the loops. The relative importance of conductive and radiative losses is briefly discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

High-frequency oscillations in a solar active region coronal loop

The Solar Eclipse Corona Imaging System (SECIS) was used to record high-cadence observations of the solar corona during the total solar eclipse of 1999 August 11. During the 2 min 23.5 s of totality, 6364 images were recorded simultaneously in each of the two channels: a white light channel, and the Fe  xiv (5303 Å) 'green line' channel ( T ∼2 MK) . Here we report initial results from the SECIS experiment, including the discovery of a 6-s intensity oscillation in an active region coronal loop.     

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.     

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.     

The polarization of coronal emission lines

By means of a photographic polarimeter, we attempted to measure both the amount and direction of linear polarization of all emission lines between 3400 and 9000 Å in the inner corona (1.034 r/r ₀ 1.085). Only the green and red coronal lines have been analyzed in detail. Neither of these lines shows polarization exceeding the probable error of 1.0% for 5303 and 1.8% for 6374. None of the other 17 coronal lines observed during the 7 March, 1970 solar eclipse show any obvious (>5%) polarization.Presently at the Sacramento Peak Observatory.     

Mass flow in loop type coronal transients

The white light coronagraph on Skylab observed many loop type coronal transients. These loops travel through the coronagraph's field of view (2–6R ) over a period of a few hours, after which the legs of the loops usually remain visible for a few days. In this paper we investigate the temporal changes in density and mass per unit length measured along the legs of such loops during the several days after the initial eruption. Examination of 8 transients shows that the mass and density in the legs decrease during the few hours after the top of the loop has travelled beyond the coronagraph's field of view. The mass and density then increase slowly, during the next one half to one day, then decrease again over approximately the same period. These changes are generally shown to be too rapid to be explained by solar rotation, indicating that the transient legs have a lifetime of only a few days.The results of a detailed study of the transient of 10 August 1973 are compared with the results from theoretical calculations. For the top of the loop a one-dimensional flow problem is solved, assuming a balance between gravity, inertia, and pressure gradients. The legs are modeled by a flow in a tube of constant cross section. Models for the flow in the legs were calculated under the assumption that the mass distribution is close to hydrostatic equilibrium. Using these models we can estimate that approximately 5 × 10¹⁴ g of material flow outward through the legs of this transient. We also find that the best fit to the observed average density gradient is obtained with a temperature of 1.7 × 10⁶ K.On leave from Max-Planck Institut für Physik und Astrophysik, Munich, Germany.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Dynamics of electron beams in a coronal loop and the hard X-ray burst

A numerical simulation has been made for the dynamics of non-thermal electrons (> 10keV) injected with spatial, temporal and velocity distributions into a model coronal loop. The time variations of the spatial intensity distribution and the spectrum for the expected hard X-rays are computed for many models in order to find the important physical parameters for those characteristics.The most important one is the column density of plasma, CD, along the loop. If CD is smaller than 10²⁰ cm^–2, the expected X-rays behave like the solar impulsive hard X-ray bursts, that is the spatial maximum of X-rays shifts to the top of the loop in the later phase of the burst accompanying a spectral softening. On the other hand, if CD is greater than this value, quasi-steady decay appears in the later phase. In this case the intensity distribution of X-rays above about 20 keV along the loop shows a broad maximum away from the loop top giving an extended spatial distribution of hard X-rays, and spectral hardness is kept constant. These characteristics are similar to the solar gradual hard X-ray bursts (the so-called extended burst which is not a hot thermal gradual burst).     

On the polarization of the solar coronal emission lines

The results of the spectrophotometrical measurements of the polarization in the coronal lines Fe xiv 5303 Å and Fe × 6374 Å are given. Polarization spectrograms were obtained by two spectrographs (prism and echelle types) during the solar eclipse in Mexico on 7 March, 1970 near the region of the second contact at the heights 0.06 to 0.12 R above the limb. The polarization in the green line is about 30% (for averaged height 1.08 R ). The polarization in the red line is close to the errors of the measurement and does not exceed 6%. A brief discussion of the results is also given.     

Radio signature of fragmented electron injection into a coronal loop

High-time-resolution observations of an unusual event of 1991 November 17, 07:04 UT at 2.5 and 2.85 GHz are presented. The event demonstrates sophisticated tine time structure including sudden reductions and quasi-periodic pulsations about various zero levels. It is shown that the sudden reductions (30–100 ms) can be produced with upward-injected > 100 keV electron beams filling the loss-cone. In such a case the acceleration is proceeding in a dense plasma layer with number densityn > 2.5 × 10¹⁰ cm^–3. The shortest time scale of the fragmented injection is _inj ^min 30 ms. Several different pulsating regimes arising due to the wave-particle and wave-wave interactions are considered. A theoretical mechanism with the nonlinear oscillations of Langmuir waves at the different steady-state levels provides the best agreement with the observed pulsations. The reduced steady-state level of the second train of pulsations is connected with the long (quasi-continuous) injection of electrons filling the loss-cone, which reduced the wave energy level. Physical parameters of the radio source were obtained. On the other hand, ECM nonlinear pulsations seem to be responsible for the radio pulsations observed in dMe stars.