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1.
It has been demonstrated in the past that single, two-dimensional coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of two-dimensional, time-dependent MHD simulations, we present evidence that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints towards the photospheric neutral line is included. Unlike the model recently proposed by van Ballegooijen and Martens (1989), the photospheric footpoint velocity in our model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, we find that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in our calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size. 相似文献
2.
In this paper, we reconstruct the finite energy force-free magnetic field of the active region NOAA 8100 on 4 November 1997
above the photosphere. In particular, the 3-D magnetic field structures before and after a 2B/X2 flare at 05:58 UT in this
region are analyzed. The magnetic field lines were extrapolated in close coincidence with the Yohkoh soft X-ray (SXR) loops accordingly. It is found that the active region is composed of an emerging flux loop, a complex loop
system with differential magnetic field shear, and large-scale, or open field lines. Similar magnetic connectivity has been
obtained for both instants but apparent changes of the twisting situations of the calculated magnetic field lines can be observed
that properly align with the corresponding SXR coronal loops. We conclude that this flare was triggered by the interaction
of an emerging flux loop and a large loop system with differential magnetic field shear, as well as large-scale, or open field
lines. The onset of the flare was at the common footpoints of several interacting magnetic loops and confined near the footpoints
of the emerging flux loop. The sheared configuration remained even after the energetic flare, as demonstrated by calculated
values of the twist for the loop system, which means that the active region was relaxed to a lower energy state but not completely
to the minimum energy state (two days later another X-class flare occurred in this region). 相似文献
3.
Simple analytic models for the passive evolution of arcade-like magnetic fields through a series of force-free equilibria are presented. At the photospheric boundary, the normal magnetic field component is prescribed together with either the longitudinal field component or the photospheric shear. Analytic progress is made by considering either cylindrically symmetric solutions or using the separation of variables technique.
Two distinct cylindrically symmetric force-free fields are obtained that possess the same normal field component and photospheric shear. The scond field contains a magnetic bubble. As the shear increases beyond a critical value, so the magnetic energy of the first configuration exceeds that of the second. The possibility is therefore suggested of an eruption of the first field outwards towards the second. Such an eruptive instability is proposed as the origin of a two-ribbon solar flare.A new analytic solution to the force-free field equations, of separable form, is discovered and it is pointed out that the existence of shear in a magnetic field does not preclude it from being potential.Now at AWRE, Aldermaston, Reading, Berkshire. 相似文献
4.
Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis.Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. This value depends on the aspect ratio of the loop, the ratio of the plasma to magnetic pressure and the detailed transverse magnetic structure. For a force-free field of uniform twist the critical twist is 3.3, and for other fields it is typically between 2 and 6. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability. 相似文献
5.
S. Vargas Domínguez D. MacTaggart L. Green L. van Driel-Gesztelyi A. W. Hood 《Solar physics》2012,278(1):33-45
Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett.
673, 215, 2008; Astrophys. J.
697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic
field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity
inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To
investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett.
716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures
observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures
that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either
side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube
emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube
along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation
driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work
demonstrates the important relationship between theory and observations for the successful discovery and interpretation of
signatures of flux emergence. 相似文献
6.
The heating of the solar corona by resistive turbulence of coronal magnetic fields is considered. The theory of this process, based on the Taylor-Heyvaerts-Priest hypothesis and a magnetic relaxation equation, is developed. Such an approach allows one to obtain the successive magnetic reconnection configurations and energy balance of the coronal magnetic field in response to prescribed motions of the photospheric footpoints. Two specific models of the coronal magnetic configuration are investigated, namely an array of closely packed flux tubes and a two-dimensional magnetic arcade. 相似文献
7.
We have selected 104 active regions with a δ magnetic configuration from 1996 to 2002 to study how important a role the kink
instability plays in such active regions. In this study, we employ the systematic tilt angle of each active region as a proxy
for the writhe of a flux tube and the force-free parameter, αbest, as a proxy for the magnetic field twist in the flux tube. It is found that 65–67% of the active regions have the same sign
of twist and writhe. About 34% (32%) of the active regions violate (follow) the Hale-Nicholson and Joy's Laws (HNJL) but follow
(violate) the hemispheric helicity rule (HHR). Sixty-one (61) of the 104 active regions studied each produced more than five
large flares. Active regions violating HNJL, but following HHR, have a much stronger tendency to produce X-class flares and/or
strong proton events. Comparing with previous studies for active regions with well-defined (simpler) bipolar magnetic configuration,
it is found that the numbers following both HNJL and HHR are significantly lower in the δ-configuration case, while numbers
violating one of the laws and the rule significantly increase with the increase of the magnetic complexity of the active regions.
These results support the prediction for the presence of a kink instability, that the twist and writhe of the magnetic fields
exhibit the same sign for δ active regions (Linton et al., Astrophys. J. 507, 40, 1998, Astrophys. J. 522, 1205, 1999; Fan et al., Astrophys. J. 521, 460, 1999). Finally, we analyze possible origins of the twist and writhe of the magnetic fields for the active regions studied. 相似文献
8.
Takashi Sakurai 《Solar physics》1985,95(2):311-321
The magnetic field structure of five flares observed by HINOTORI spacecraft is studied. The double source structure of impulsive flares seems to indicate hard X-ray emission from the two footpoints of a flaring loop, but the potential field computation does not reproduce a loop connecting the two sources. Therefore the magnetic field could be in a sheared configuration and the force-free field modeling would be the next step to examine. On the other hand gradual flares are characterized by hard X-ray sources located in the corona, 2–4 x 104 km above the photosphere. The potential field modeling is found to give a reasonable fitting in this type of flares, and the hard X-ray sources are located at the top of the magnetic loop or arcade. This configuration is consistent with the thick-target trap model of the hard X-ray bursts. 相似文献
9.
Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 1030 ergs to several 1031 ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
10.
S. Régnier 《Solar physics》2012,277(1):131-151
In the last decades, force-free-field modelling has been used extensively to describe the coronal magnetic field and to better
understand the physics of solar eruptions at different scales. Especially the evolution of active regions has been studied
by successive equilibria in which each computed magnetic configuration is subject to an evolving photospheric distribution
of magnetic field and/or electric-current density. This technique of successive equilibria has been successful in describing
the rate of change of the energetics for observed active regions. Nevertheless the change in magnetic configuration due to
the increase/decrease of electric current for different force-free models (potential, linear and nonlinear force-free fields)
has never been studied in detail before. Here we focus especially on the evolution of the free magnetic energy, the location
of the excess of energy, and the distribution of electric currents in the corona. For this purpose, we use an idealised active
region characterised by four main polarities and a satellite polarity, allowing us to specify a complex topology and sheared
arcades to the coronal magnetic field but no twisted flux bundles. We investigate the changes in the geometry and connectivity
of field lines, the magnetic energy and current-density content as well as the evolution of null points. Increasing the photospheric
current density in the magnetic configuration does not dramatically change the energy-storage processes within the active
region even if the magnetic topology is slightly modified. We conclude that for reasonable values of the photospheric current
density (the force-free parameter α<0.25 Mm−1), the magnetic configurations studied do change but not dramatically: i) the original null point stays nearly at the same location, ii) the field-line geometry and connectivity are slightly modified, iii) even if the free magnetic energy is significantly increased, the energy storage happens at the same location. This extensive
study of different force-free models for a simple magnetic configuration shows that some topological elements of an observed
active region, such as null points, can be reproduced with confidence only by considering the potential-field approximation.
This study is a preliminary work aiming at understanding the effects of electric currents generated by characteristic photospheric
motions on the structure and evolution of the coronal magnetic field. 相似文献
11.
In this paper we extend previous work of Browning and Priest (1984, 1986) by studying the equilibrium path of twisted and untwisted thin flux tubes in a stratified, isothermal atmosphere using as the ambient field a linear force-free field. When an untwisted flux tube is considered, we find that shearing the magnetic arcade provides a different form to change the parameter which characterizes the external atmosphere, but at the same time this introduces a limitation in the width allowed for the external arcade. Also, the critical width found for the different analytical cases considered is always greater than one arch of the ambient arcade which prevents an eruption inside the arcade. In the case of twisted flux tubes, an analytical solution can be found for the critical
c
, which separates regimes of strong and weak gravity, and the shape of the flux tube is now dependent on , a parameter which represents the magnetic field enhancement of the loop at the photosphere. 相似文献
12.
S. S. Hasan 《Solar physics》1980,67(2):267-283
The equilibrium and stability of a loop in which energy storage occurs prior to a solar flare is discussed. Working on the hypothesis, that the onset of the flare begins only after sufficient magnetic energy has been stored in the loop typical values of parameters which describe the equilibrium are found for a magnetic field with a constant twist. The stability of this configuration is examined next and it is shown that for the force-free case, the structure is always unstable to kinking for any degree of twist. However, a slight deviation from the force-free configuration, through the presence of a small positive transverse pressure gradient, can stabilize the loops for moderate degrees of twist. The range of wave-numbers for which instability occurs and the maximum growth rates are also presented. Lastly, it is shown that the pressure gradients required to stabilize a pre-flare loop do not lead to conflict with observations. 相似文献
13.
G. Valori L. M. Green P. Démoulin S. Vargas Domínguez L. van Driel-Gesztelyi A. Wallace D. Baker M. Fuhrmann 《Solar physics》2012,278(1):73-97
We study the flux emergence process in NOAA active region 11024, between 29 June and 7 July 2009, by means of multi-wavelength
observations and nonlinear force-free extrapolation. The main aim is to extend previous investigations by combining, as much
as possible, high spatial resolution observations to test our present understanding of small-scale (undulatory) flux emergence,
whilst putting these small-scale events in the context of the global evolution of the active region. The combination of these
techniques allows us to follow the whole process, from the first appearance of the bipolar axial field on the east limb, until
the buoyancy instability could set in and raise the main body of the twisted flux tube through the photosphere, forming magnetic
tongues and signatures of serpentine field, until the simplification of the magnetic structure into a main bipole by the time
the active region reaches the west limb. At the crucial time of the main emergence phase high spatial resolution spectropolarimetric
measurements of the photospheric field are employed to reconstruct the three-dimensional structure of the nonlinear force-free
coronal field, which is then used to test the current understanding of flux emergence processes. In particular, knowledge
of the coronal connectivity confirms the identity of the magnetic tongues as seen in their photospheric signatures, and it
exemplifies how the twisted flux, which is emerging on small scales in the form of a sea-serpent, is subsequently rearranged
by reconnection into the large-scale field of the active region. In this way, the multi-wavelength observations combined with
a nonlinear force-free extrapolation provide a coherent picture of the emergence process of small-scale magnetic bipoles,
which subsequently reconnect to form a large-scale structure in the corona. 相似文献
14.
In their “mixing time” theory of magnetic heating of the corona by slow photospheric motion, Heyvaerts and Priest (1984) neglected certain second-order terms in the calculation of the energy and retained the linear part of the perturbed magnetic field which led to infinite displacements. In this paper, we revised these points. Our main results are: (1) the heating efficiency we obtained is greater than what they found. (2) Dissipation-free, linear evolution of the force-free field of coronal arcade is impossible. (3) The possibility of reconnection of field lines of non-linear force-free field is clarified in terms of the field configuration and it is pointed out that reconnection is most likely at a height equal to about one width of the arcade. 相似文献
15.
Oscillations of magnetic flux tubes are of great importance as they contain information about the geometry and fine structure
of the flux tubes. Here we derive and analytically solve in terms of Kummer’s functions the linear governing equations of
wave propagation for sausage surface and body modes (m=0) of a magnetically twisted compressible flux tube embedded in a compressible uniformly magnetized plasma environment in cylindrical geometry. A general dispersion relation is obtained for such flux
tubes. Numerical solutions for the phase velocity are obtained for a wide range of wavenumbers and for varying magnetic twist.
The effect of magnetic twist on the period of oscillations of sausage surface modes for different values of the wavenumber
and vertical magnetic field strength is calculated for representative photospheric and coronal conditions. These results generalize
and extend previous studies of MHD waves obtained for incompressible or for compressible but nontwisted flux tubes. It is
found that magnetic twist may change the period of sausage surface waves of the order of a few percent when compared to counterparts
in straight nontwisted flux tubes. This information will be most relevant when high-resolution observations are used for diagnostic
exploration of MHD wave guides in analogy to solar-interior studies by means of global eigenoscillations in helioseismology. 相似文献
16.
The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main-phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (\(2\pi \) radians of twist), and then main-phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist. 相似文献
17.
The temperature and density are obtained for coronal plasma in thermal and hydrostatic equilibrium and located in a force-free magnetic arcade. The isotherms are found to be inclined to the magnetic field lines and so care should be taken in inferring the magnetic structure from observed emission.When the coronal pressure becomes too great, the equilibrium ceases to exist and the material cools to form a quiescent prominence. The same process can be initiated at low heating rates when the width or shear of the arcade exceeds a critical value.We suggest that the prominence should be modelled as a dynamic structure with plasma always draining downwards. Material is continually sucked up along field lines of the ambient arcade and into the region lacking a hot equilibrium, where it cools to form new prominence material. 相似文献
18.
We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration. 相似文献
19.
Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time. 相似文献
20.
Using a 28-hour time series of line-of-sight magnetograms taken by the Michelson Doppler Imager (MDI), we determined the magnetic flux variations and the rate of magnetic helicity transport at the footpoints of a filament in active region NOAA 8375. The filament was characterized by a positive helicity change due to shearing motions in both footpoints and showed several partial eruptions during the observing time. In particular, we considered 4 events registered in the Hα daily reports of Solar Geophysical Data. We found a strong temporal correlation between filament eruptions and helicity transport from the photospheric magnetic structures at the filament footpoints into the corona: in at least one footpoint, all of the events were preceded by an evident increase and followed by a small decrease of the emerging magnetic flux and of the magnetic helicity change due to shearing motions. We compared these two mechanisms of helicity transport and found that the predominant role to drive filament instability is played by emergence of new magnetic flux from the convection zone. 相似文献