Cross-Sectional Properties of Coronal Loops

Careful examination of 43 soft X-ray loops observed by Yohkoh has revealed a number of interesting properties of the loop cross section. First, the loops tend to be only slightly ( 30%) wider at their midpoints than at their footpoints, implying less-than-expected expansion of the magnetic field. Second, the variation of width along each loop tends to be modest, implying that the cross section has an approximately circular shape. And third, cross-axis intensity profiles tend to be singly-peaked and simple, implying that the cross section is approximately uniformly filled on resolvable scales. We conclude that the energy which heats the plasma is either dissipated axially symmetrically on a scale equal to a loop diameter ( 11000 km) or else is dissipated with any spatial structure, but on a scale much smaller than a loop diameter, and then transported laterally in an axisymmetric fashion (perhaps via conduction along chaotic field lines). In their present form, none of the theoretical ideas concerning the magnetic structure and heating of loops are obviously capable of explaining all of the observed properties.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Latent Heating of Coronal Loops

This paper is aimed at establishing the relationship between the large-scale magnetic fields (LSMF), coronal holes (CH), and active regions (AR) in the Sun. The LSMF structure was analyzed by calculating the vector photospheric magnetic field under a potential approximation. Synoptic maps were drawn to study the distribution of the B field component and to isolate regions where the open field lines of the unipolar magnetic field are most radial. These are the sites of occurrence of X-ray and Hei 10830 Å coronal holes detected from the SXT/Yohkoh images. It is shown that coronal holes are usually located in LSMF regions with a typical pattern of divergentB vectors and a so-called saddle configuration.B vectors from the conjugate (spaced by 90°) coronal holes converge towards the active regions between CH. Variations in AR distort coronal holes and change their boundaries. This implies that the energy regime in CH depends on the energy supply from the active region. The LSMF structure is more stable than coronal holes, remaining practically unchanged during tens of rotations of the Sun. Thus, a peculiar magnetically coupled system of LSMF/CH/AR has been revealed. A model has been suggested to describe the interaction of the emerging toroids in the convection zone and in the photosphere. The cellular convection, that develops at the center of the toroids, is responsible for the occurrence of active regions. The model qualitatively describes the observed particularities of the LSMF/CH/AR system.     

The Oscillations of Coronal Loops Including the Shell

We investigate the MHD waves in a double magnetic flux tube embedded in a uniform external magnetic field. The tube consists of a dense hot cylindrical cord surrounded by a co-axial shell. The plasma and the magnetic field are taken to be uniform inside the cord and also inside the shell. Two slow and two fast magnetosonic modes can exist in the thin double tube. The first slow mode is trapped by the cord, the other is trapped by the shell. The oscillations of the second mode have opposite phases inside the cord and shell. The speeds of the slow modes propagating along the tube are close to the tube speeds inside the cord and the shell. The behavior of the fast modes depends on the magnitude of Alfvén speed inside the shell. If it is less than the Alfvén speed inside the cord and in the environment, then the fast mode is trapped by the shell and the other may be trapped under the certain conditions. In the opposite case when the Alfvén speed in the shell is greater than those inside the cord and in the environment, then the fast mode is radiated by the tube and the other may also be radiated under certain conditions. The oscillation of the cord and the shell with opposite phases is the distinctive feature of the process. The proposed model allows to explain the basic phenomena connected to the coronal oscillations: i) the damping of oscillations stipulated in the double tube model by the radiative loss, ii) the presence of two different modes of perturbations propagating along the loop with close speeds, iii) the opposite phases of oscillations of modulated radio emission, coming from the near coronal sources having sharply different densities.     

Coronal Seismology Using Transverse Oscillations of Non-planar Coronal Loops

We continue studying the robustness of coronal seismology. We concentrate on two seismological applications: the estimate of coronal scale height using the ratio of periods of the fundamental harmonic and first overtone of kink oscillations, and the estimate of magnetic-field magnitude using the fundamental harmonic. Our analysis is based on the model of non-planar coronal loops suggested by Ruderman and Scott (Astron. Astrophys. 529, A33, 2011), which was formulated using the linearized MHD equations. We show that the loop non-planarity does not affect the ratio of periods of the fundamental harmonic and first overtone, and thus it is unimportant for the estimates of the coronal scale height. We also show that the density variation along the loop and the loop non-planarity only weakly affect the estimates of the magnetic-field magnitude. Hence, using the simplest model of coronal loops, which is a straight homogeneous magnetic cylinder, provides sufficiently accurate estimates for the magnetic-field magnitude.     

Coronal Loops Above a Sunspot Region

By analysing the data of Yohkoh soft X-ray images, vector magnetograms and 2D spectral observations, coronal loops above a large sunspot on 16–19 May 1994 have been studied. It is shown that the loops follow generally the alignment of concentrated magnetic flux. The results indicate that the soft X-ray emission is low just above the sunspot, while some loops connecting regions with opposite magnetic polarities show strong soft X-ray emission. Especially, the part of the loops near the weaker magnetic field region tends to be brighter than the one near the stronger magnetic field. The temperature around the top of the loops is typically 3 × 10⁶ K, which is higher than that at the legs of the loops by a factor of 1.5–2.0. The density near the top of the loops is about 5 x 10⁹ cm^-3, which is higher than that of the leg parts of the loops. These loops represent probably the sites where strong magnetic flux and/or current are concentrated.     

Ballooning Instability in Coronal Flare Loops

Within the framework of ideal magnetohydrodynamics the excitation of the ballooning instability in a toroidal coronal loop with a radius of cross section a and a radius of curvature R is analyzed by using the energy method. Kink oscillations are able to excite the ballooning instability when the plasma beta parameter β>2a/R. It has been suggested that this can result in the formation of cusp-shaped coronal loops. Modulation of gyrosynchrotron emission caused by kink oscillations is considered. The intensity of gyrosynchrotron emission for optically thin sources is the most sensitive to Alfvén disturbances. The obtained theoretical results are discussed in the light of Yohkoh, SOHO, TRACE, RHESSI, and Nobeyama observations.     

Segmentation of Loops from Coronal EUV Images

We present a procedure to extract bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative, which is then used to interpolate a discrete vector field of ridge points; these “ridgels” are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves that fit the observed loops. Finally, a half-automated user interface allows one to merge or split curves or eliminate or select loop fits obtained from this procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from near-simultaneous magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated by using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy.     

Nonlinear Kink Oscillations of Coronal Magnetic Loops

We studied nonlinear kink oscillations of a thin magnetic tube using the cold-plasma approximation. We assumed that the plasma density varies along the tube but does not vary in the radial direction. Using the regular perturbation method, we show that the nonlinearity does not affect the oscillation amplitude. We also calculated the nonlinear correction to the oscillation frequency, which is proportional to the oscillation amplitude squared. As an example, we considered nonlinear oscillations of a coronal magnetic loop of half-circle shape in an isothermal atmosphere with equal plasma temperatures inside and outside the loop.     

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.     

Magnetic Stereoscopy of Coronal Loops in NOAA 8891

The Solar TErrestrial RElations Observatory (STEREO) requires powerful tools for the three-dimensional (3D) reconstruction of the solar corona. Here we test such a program with data from SOHO and TRACE. By taking advantage of solar rotation, a newly developed stereoscopy tool for the reconstruction of coronal loops is applied to the solar active region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic reconstruction is composed of three steps. First, we identify loop structures in two TRACE images observed from two vantage viewpoints approximately 17 degrees apart, which corresponds to observations made about 30 hours apart. In the second step, we extrapolate the magnetic field in the corona with the linear force-free field model from the photospheric line-of-sight SOHO/MDI data. Finally, combining the extrapolated field lines and one-dimensional loop curves from two different viewpoints, we obtain the 3D loop structures with the magnetic stereoscopy tool. We demonstrate that by including the magnetic modeling this tool is more powerful than pure geometrical stereoscopy, especially in resolving the ambiguities generated by classical stereoscopy. This work will be applied to the STEREO mission in the near future.     

Determination of the True Shape of Coronal Loops

Using line of sight velocity measurements from the SUMER and CDS instruments aboard SOHO, in conjunction with a simple geometrical model, we reconstructed the true, 3D shape and the velocity of plasma flow along coronal loops. The projection of the loop on the sky and the position of the footpoints define a family of curves. Assuming that the loop is located on a plane, the line of sight velocity can be used to select the most plausible solution. For two loops, observed in the Ne viii? 770 Å and O v? 630 Å spectral lines, we find asymmetric, subsonic uni-directional flows, with velocity maxima of ≈?80 km?s^?1 near the footpoints. The loops are highly inclined with respect to the vertical, by 55^○ and 70^○, respectively; thus the true height of the loop tops from the photospheric level is ≈?20^′′, comparable to the isothermal scale height.     

Spatial Structure of Solar Coronal Magnetic Loops Revealed by Transient Microwave Brightenings

We present the measurement of magnetic field gradient in magnetic loops in the solar corona, based on the multi-wavelength Very Large Array observations of two transient microwave brightenings (TMBs) in the solar active region 7135. The events were observed at 2 cm (spatial resolution 2=) and 3.6 cm (spatial resolution 3=) with a temporal resolution of 3.3 s in a time-sharing mode. Soft X-ray data (spatial resolution 2.5=) were available from the Soft X-ray Telescope on board the Yohkoh satellite. The three-dimensional structure of simple magnetic loops, where the transient brightenings occurred, were traced out by these observations. The 2-cm and 3.6-cm sources were very compact, located near the footpoint of the magnetic loops seen in the X-ray images. For the two events reported in this paper, the projected angular separation between the centroids of 2 and 3.6-cm sources is about 2.3= and 3.1=, respectively. We interpret that the 2 and 3.6-cm sources come from thermal gyro-resonance emission. The 2-cm emission is at the 3rd harmonic originating from the gyro-resonance layer where the magnetic field is 1800 G. The 3.6-cm emission is at the 2nd harmonic, originating from the gyro-resonance layer with a magnetic field of 1500 G. The estimated magnetic field gradient near the footpoint of the magnetic loop is about 0.09 G km=¹ and 0.12 G km=¹ for the two events. These values are smaller than those observed in the photosphere and chromosphere by at least a factor of 2.     

Dynamical Features and Evolutional Characteristics of Brightening Coronal Loops

We present a detailed study of coronal loop brightenings observed in an active region on the solar limb. These brightening loops show expanding and shrinking motions in EUV coronal line images and also show downflow along the loops in Lα and Hα images. By means of time-slice analysis of the images, we found that both the expanding and shrinking motions of the loops are not real motions of plasma but apparent motions like post-flare loops, where the loops at the different height are successively heated and cooled. From a temperature analysis, the time delay between the brightenings of hot 195 Å and cool Lα loops is found to be nearly equal to the time-scale of the conduction cooling. We conclude that these loop brightenings are sources of so called Hα coronal rains.     

Transverse Oscillations of Coronal Loops with Slowly Changing Density

In this paper we study kink oscillations of coronal loops with the density varying along the loop and also slowly changing with time. Using the Wentzel?CKramers?CBrillouin (WKB) method we obtain the adiabatic invariant that determines the time dependence of the oscillation amplitude. The obtained general results are applied to kink oscillations of cooling loops. The main conclusion of this study is that cooling causes the amplification of kink oscillations.     

Scaling Law for the Heating of Solar Coronal Loops

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum Ek approximately k-3&solm0;2 and heating rate levels compatible with the energy requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfvén time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.     

Slow-Mode Oscillations and Damping of Hot Solar Coronal Loops

The effect of temperature inhomogeneity on the periods, their ratios (fundamental versus first overtone), and the damping times of the standing slow modes in gravitationally stratified solar coronal loops are studied. The effects of optically thin radiation, compressive viscosity, and thermal conduction are considered. The linearized one-dimensional magnetohydrodynamic (MHD) equations (under low-?? condition) were reduced to a fourth-order ordinary differential equation for the perturbed velocity. The numerical results indicate that the periods of nonisothermal loops (i.e., temperature increases from the loop base to apex) are smaller compared to those of isothermal loops. In the presence of radiation, viscosity, and thermal conduction, an increase in the temperature gradient is followed by a monotonic decrease in the periods (compared with the isothermal case), while the period ratio turns out to be a sensitive function of the temperature gradient and the loop lengths. We verify that radiative dissipation is not a main cooling mechanism in both isothermal and nonisothermal hot coronal loops and has a small effect on the periods. Thermal conduction and compressive viscosity are primary mechanisms in the damping of slow modes of the hot coronal loops. The periods and damping times in the presence of compressive viscosity and/or thermal conduction dissipation are consistent with the observed data in specific cases. By tuning the dissipation parameters, the periods and the damping times could be made consistent with the observations in more general cases.     

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.     

Electrostatic Wave Instability and Plasma Radiation from Coronal Loops

Polarization properties of solar and stellar radio emission require, in some cases, emission below the third or fourth coronal electron gyro level, < 3,_c; 4, _c. In the context of plasma radiation, the source parameters should be such that the intermediate magnetic field condition 1 < _p ² / _c ² < 3 is satisfied. Supposing this condition, we investigate the generation of electrostatic waves in a warm background plasma with a high-energy component of magnetically trapped electrons. We invoke the conversion of upper-hybrid waves and Bernstein waves into electromagnetic radiation as being responsible for intense radio emission from a coronal magnetic loop. Moreover, odd-half harmonic emissions in the solar radio spectrum as well as the o-mode polarization at the second harmonic of the plasma frequency are natural consequence of this proposed model.