m. ryutova and h. hagenaar- magnetic solitons: unified mechanism for moving magnetic features

8/3/2019 M. Ryutova and H. Hagenaar- Magnetic Solitons: Unified Mechanism for Moving Magnetic Features

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Solar Phys (2007) 246: 281294DOI 10.1007/s11207-007-0399-z

Magnetic Solitons: Unified Mechanism for Moving

Magnetic Features

M. Ryutova H. Hagenaar

Received: 12 January 2007 / Accepted: 30 January 2007 /Published online: 5 April 2007 Springer 2007

Abstract In a highly dynamic environment with sources and sinks of energy, flux tubesdo not in general obey local conservation laws, nor do the ensembles of flux tubes thatexhibit collective phenomena. We use the approach of energetically open dissipative sys-tems to study nonlinear waves in flux tubes and their role in the dynamics of the overlyingatmosphere. We present results of theoretical and observational studies of the propertiesof moving magnetic features (MMFs) around sunspots and the response of the overlyingatmosphere to various types of MMFs. We show that all types of MMFs, often having con-flicting properties, can be described on a unified basis by employing the model of shocksand solitons propagating along the penumbral filaments co-aligned with Evershed flows.The model is also consistent with the response of the upper atmosphere to individual MMFs,which depends on their type. For example, soliton-type bipolar MMFs mainly participate inthe formation of a moat and do not carry much energy into the upper atmosphere, whereasshock-like MMFs, with the appearance of single-polarity features, are often associated withchromospheric jets and microflares.

Keywords The Sun: nonlinear waves

Photosphere

Chromosphere and corona

1. Introduction

After the suggestion by Howard (1959) that the solar magnetic fields may be concentratedin narrow bundles of field lines, and the first direct observation of small-scale magneticfields by Sheeley (1967), flux tubes, overcoming controversies and mistrust, took their placeas a fundamental property of nature. And the physics of the Sun as well as the physics

M. Ryutova ()Lawrence Livermore National Laboratory/IGPP Livermore, Livermore, CA 94550, USAe-mail: [email protected]

H. HagenaarLockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Palo Alto, CA 94304,USA


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282 M. Ryutova, H. Hagenaar

of other stars, the interstellar medium, and other astrophysical objects, have become thephysics of structured magnetic fields. But it is solar studies, both theoretical and observa-tional, that gave a rather good understanding of the fundamental properties of flux tubes, themost important of which is the wide range of waves and oscillations excited in flux tubes

embedded in a dynamic environment. After the first fundamental results pioneered aboutthree decades ago (Wilson, 1973; Cram and Wilson, 1975; Ryutov and Ryutova, 1976; De-fouw, 1976; Roberts and Webb, 1978; Spruit, 1981; Roberts, 1981a, 1981b; Ryutova, 1981)flux-tube oscillations have evolved from a subject of study into a tool. This tool allows usto investigate, understand, and interpret the observational data, from photospheric eventsto coronal dynamics. This includes an important aspect of nonlinear dynamics of the solaratmosphere.

Roberts and Mangeney (1982) were first to point out that in the nonlinear regime mag-netic flux tubes may support solitary waves. They considered axisymmetric pulsation of theslab (the m

=0 mode of flux-tube oscillations) and obtained the Benjamen Ono equation

for the tube soliton. Later, nonlinear m = 0, as well as nonaxisymmetric surface waves inthe magnetic slab and cylinders, have been studied by Roberts (1985), Molotovshchikov andRuderman (1987), and Ruderman (1992). These studies revealed the important fact that ifthe physical parameters of the solar atmosphere (anywhere from the convective zone up tothe solar wind) correspond to the stability and evolutionary character of solitary waves, theymay provide a reliable basis for understanding strongly nonlinear dynamics throughout thewhole range of temperatures.

Ryutova and Sakai (1993) studied nonlinear kink oscillations (m = 1) of a flux tubeand showed that kink oscillations as well may evolve into shocks and solitons, and they aredescribed by a modified KdV Burgers equation. Ryutova et al. (1998) applied this equa-tion to explain the origin and properties of moving magnetic features (MMFs) in sunspotregions. Ryutova and Shine (2004), studying the response of the corona to magnetic activityin the underlying plage regions, showed that the observed properties of a coherent coronalemission may be explained by a gas of solitons generated by the ensemble of noncollinearflux tubes.

In this paper, nonlinear effects in flux-tube oscillations are employed to understand thenature of small-scale MMFs observed in sunspot penumbra and moat regions. Our goalhere is twofold: i) to consolidate all types of MMFs into one scheme and develop a unifiedmechanism describing their diverse properties and ii) to investigate the impact of MMFs on

the dynamics of the overlying atmosphere.

2. MMFs as Energetically Open Systems

2.1. Properties and Types of MMFs

The regular outward motions of bright points around sunspots observed by Sheeley (1969)and Vrabec (1971), and named moving magnetic features by Harvey and Harvey (1973),have been subsequently studied as an important agent in sunspot dynamics.

The first detailed description of the MMF properties was given by Harvey and Harvey(1973), who studied these phenomena using simultaneous magnetic and H observations of37 sunspots (during about a one-year time span). Briefly these properties can be summarizedas follows. Small (


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Magnetic Solitons 283

move outward with velocities higher than the background flows until they vanish or reachthe network. Detailed study of flows around and within the sunspots showed that, instead ofa simple radial flow, there are zones of azimuthal divergence and convergence, resulting inradial spokes of convergence, and that much of the magnetic flux emerging and moving

outward in the moat is in the vicinity of these spokes (Shine et al., 1996). Frequentlyfootpoints are not equally visible, and MMFs may appear as single-polarity features. TheMMFs produce very faint emission in the core of H, but the direction of their motion is co-aligned with the H fibrils. These properties were confirmed and extended in subsequentstudies (Muller and Mena, 1987; Brickhouse and LaBonte, 1988; Lee, 1992; Ryutova etal., 1998; Ravindra, 2006). It was found that although MMFs have these general properties,some are clearly distinct from others. As a result, MMFs were formally divided into classes,summarized by Shine and Title (2001) and extended in later studies:

1. Type I MMFs are opposite-polarity pairs seen as compact bipoles. Their initial velocities

(at the moment of emergence) may be quite high: 3 8 km s1

. Moving outward from thesunspot, they gradually slow down; at this stage the separation between the footpointsgradually increases at about 100 m s1. During their lifetime, which may be hours, theystill move with velocities higher then background plasma flows. Nearby MMFs may havequite different speeds. The inner footpoint shares the sunspots polarity.

2. Type II MMFs appear as unipolar features emitted from the edge of a sunspot. They sharethe sunspots polarity and have properties similar to those of the inner footpoint of thetype I MMFs. It is important to note that often footpoints of type I MMFs are not equallyvisible with well-pronounced inner footpoint and diffuse outer footpoint. These MMFsbelong to type II.

3. Type III MMFs also appear as a unipolar features, or opposite-polarity pairs with onefootpoint barely visible. Unlike type II, these MMFs have the polarity (of a strong foot-point) opposite to the parent sunspot. They are of smaller size, travel with higher ve-locities then the other MMFs (2 3 km s1) and are associated with bright points in thecontinuum.

4. Type I MMFs are outflowing opposite-polarity pairs with the inner footpoint havingpolarity opposite to that of the sunspot (Yurchyshyn, Wang, and Goode, 2001; Zhang,Solanki, and Wang, 2003). To distinguish them from regular type I MMFs, we use thenotation of a complex conjugate.

5. Moving dipolar features (MDFs) were found in an emerging sunspot region (Bernasconiet al., 2003). They have the remarkable property of moving inward, i.e., toward thesunspot umbra. These are slowly migrating bipoles (0.3 0.8 km s1) with the innerfootpoint having a polarity opposite to that of the sunspot.

Attempts to visualize MMFs are somehow or other connected with Harvey and Harveyssea-serpent picture. This is basically a -shaped kink formed along a thin horizontal fil-ament, which would have the appearance of a bipolar formation with the inner footpoint ofthe same polarity as the sunspot. Similarly, -shaped kinks would appear as MDF or MMFwith the inner footpoint having opposite to sunspot polarity. Figure 1 shows a possible cre-

ation and motion of MMFs sketched by different authors (Harvey and Harvey, 1973; Wilson,1986; Bernasconi et al., 2003).

It is important to note that the sketches shown in Figure 1 were not supported by ana-lytical or numerical calculations in the aforementioned papers. The fundamental problemhere is that either kind of kink is highly unstable: Under the action of magnetic tension andbuoyancy forces, a -shaped kink straightens in one to two minutes, whereas a -shaped


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Figure 1 Cartoons visualizing a possible creation and motion of MMFs: (a) Sketch given by Harvey andHarvey showing how a twisted magnetic flux tube may be separated from the main body of a sunspot andswept to the network by flows, and Wilsons (1986) sketch showing a possible formation of MMFs resultingfrom reconnections and subsequent detachment of loops; (b) visualization of MDFs migrating toward parental

sunspot given by Bernasconi et al.

kink may at best first oscillate and survive only for several minutes longer (Ryutova, Tarbell,and Shine, 2003).

But the problem goes even deeper: One needs to not only overcome the stability issue butfind the forces that keep the MMFs traveling faster than the background flows (sometimeseven upstream!) with lifetimes from tens of minutes to hours. Wilson (1973) justly con-cluded: It is hard to see how the motions could deform such a flux tube into the required

kink, far less maintain the tube in this form during the passage across the moat. Indeed, inthe frame of a conservative system such forces do not exist.

In other words, the properties of the MMFs are inconsistent with energy and momentumconservation laws and require the approach of nonconservative, energetically-open systems.Such an approach was used by Ryutova et al. (1998), who developed a theory based onnonlinear coupling of magnetic flux and plasma flows and performed numerical simulationsin the presence of a gravitational field. Continuous energy supply from the plasma flows andunbalanced dissipation make such a system energetically open and lead to development ofnonlinear shear-flow instabilities that result in the formation of a stable solitary kink. They

studied in detail and performed quantitative analysis for two major cases: type I and type IIMMFs. They found that type I MMFs have properties of a stable soliton propagating as a-shaped kink, and type II MMFs have properties of a shock-like formation. The model hasprovided very good qualitative and quantitative agreement with observations.

Here we show that an energetically-open model of nonlinear kinks describes all the ob-served types of MMFs.


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=

12||A

, (6)

vsol = ck A

3= ck

4

2. (7)

To determine whether or not the soliton is stable and evolutionary, one needs to obtain atime-dependent solution for the dissipative system (with nonzero, but small, right-hand sideassociated with dissipation). It is customary to assume that the amplitude, width, and speedof a soliton are a slowly-varying function of time. The time dependence of these parametersis determined by the energy equation, which can be obtained by multiplying Equation (1) by and integrating over a distance large compared with the size of a soliton. This procedureleads to the evolutionary equation for the amplitude (Equation (20) in Ryutova et al., 1998):

dA

dt =2.92

121/2

A3/2

16

15

12 A2

. (8)

One can see that for solitons with small enough amplitudes, when the first term in the right-hand side is a leading one, the amplitude experiences an explosive growth:

A A0(1 t /texpl)2

, (9)

where the explosion time is

12/A0/2.92. Under photospheric conditions, thistime is quite large; i.e., the phase of the explosive growth is short: After several inversegrowth rates, the amplitude gets stabilized by higher nonlinear effects (Coppi, Rosenbluth,and Sudan, 1969; Ryutova, 1988), the second term in Equation (8) becomes more important,and the amplitude of the soliton decays as

A(t) = A01+ t/tdiss

, (10)

where tdiss 12/A0.Equations (5), (6), (7), and (8) describe various types of MMFs and different scenarios

for their evolution.As previously mentioned, for positive dispersion, the solution of Equation (1) describestwo cases: i) When the solution is an evolutionary bright soliton (nonlinearity is balancedby dispersion), this represents type I MMFs with the appearance of compact bipoles alongthe line of sight, and the soliton travels with a velocity higher than the shear flow velocity.ii) When nonlinearity slightly prevails over dispersion, the soliton acquires shock-like formand propagates even faster than the solitary kink. This corresponds to type II MMFs; theshock-like kinks may be seen either as pairs of sharp and diffused fluxes or as unipolarfeatures (depending on the distortion of a kink). Three-dimensional numerical solutions forthese cases are shown in Figure 2a and 2b; Figure 2c is an analytical solution.

If the dispersion of the medium is negative, the solution is a dark soliton, forming a-shaped kink (Figure 2d). This solution corresponds to bipolar MMFs with the inner foot-point having a polarity opposite to that of the sunspot, i.e., type I. Distorted by disbalancebetween the dispersion and nonlinearity, dark solitons will appear as type III MMFs (al-most unipolar features) with the dominant polarity opposite to the parent sunspots. Figure 3combines solutions and cartoons for all types of MMFs.


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Figure 2 Numerical (Ryutova et al., 1998) and analytical solutions for nonlinear kink. (a) 3D image of astable propagating soliton corresponding to type I MMFs; lower image shows line-of-sight magnetic fieldhaving appearance of a compact bipole. (b) The same for the shock-like kink one footpoint along the lineof sight is sharp and compact while its pair is diffuse. (Right panels) Analytical solutions for solitons corre-sponding to (c) positive dispersion and (d) negative dispersion. In this case MMFs will appear with the innerfootpoint of the opposite to sunspot polarity, type I MMF.

If is negative, ck < A/3 (see Equation (7)), the solution corresponds to MDFs, slowlymigrating towardthe sunspot and againstthe outward flow. Note that at the early stage of anMMF, simple relations (5), (6), and (7), between its size (separation between the footpoints),velocity, and line-of-sight magnetic field, allow one to infer such parameters as degree ofnonlinearity and dispersive properties of the system. These parameters then may be usedfor the evaluation of their dissipative properties, which determine coupling with the upperatmosphere.

3. Response of the Upper Atmosphere to MMF Dynamics

To study the response of the overlying atmosphere to MMF dynamics, we use several setsof multi-wavelength observations of different sunspot areas from the photosphere to thecorona. Our richest data set, for 10 June 1999, consists of time series of high-resolution MDImagnetograms co-aligned with the TRACE white-light images and images in 1600 andeither Fe IX/X 171 or Fe XII 195 lines complemented by time series of H filtergramsobtained from the Swedish Vacuum Solar Telescope (SVST) on La Palma.

Figure 4 shows a sample MDI magnetogram (panel (a)) of the central sunspot co-alignedwith the image in the 700 m wings of H (panel (b)). We use the procedure of space-time slices to study temporal variability of small magnetic features. Three examples of suchslices in both wavelengths are shown in the upper- and lower-right panels (1a,b); (2a,b);

(3a,b). The population of MMFs and their association with mass flows around the sunspotare well seen in the 700 m wings of H, showing the motions at the photospheric level.More than three-quarters of the moat area is well populated by MMFs. The paths of cor-responding cuts and their directions are shown, respectively, in panels (a) and (b). The leftsides of cuts 1 and 2 and the entire cut 3 through the diameter of a moat pass through theregion well populated by MMFs. One can see different kinds of MMFs on the left sides of


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Figure 3 Analytical solutions for nonlinear kink (upper panels: vertical axes are normalized by B2, hor-izontal axes are x normalized by the flux tube radius), and cartoons depicting all types of MMFs. Balancemeans that nonlinearity is balanced by dispersion, and disbalance that nonlinearity prevails over dispersion.If at negative dispersion, < 0, the phase velocity is such that ck < A/3, a moving magnetic feature hasnegative velocity and will travel upstream toward the sunspot.

panels (1a,b) and (2a,b), and at both sides of panel (3a,b), streaming outward from sunspot;whereas the right ends of cuts 1a,b and 2a,b pass through the moat region devoid of MMFs(curved arrows in the left panels mark the region depleted of MMFs). It is interesting thatregions with a deficit of MMFs usually serve as a preferred site for coronal-loop formation(Ryutova, Hagennar and Title, 2007).

Hagenaar and Shine (2005) studied the statistical properties of MMFs using time se-quences of high-resolution magnetograms of eight sunspots. They have developed an auto-mated algorithm to find and track unipolar magnetic-field concentrations and derived flow

maps around the spots to compare plasma flow patterns with the tracks of moving magneticfeatures. We compared these results with the corresponding images of the overlying corona.The examples of the data taken on 2 November 2002 are shown in Figure 5. Panels (a) and(b) are co-aligned MDI magnetogram and the overlying corona in the TRACE 195 line.The thin white arrows show cuts made on movies revealing various kinds of MMFs flowingaway from sunspots (right panels). Panel (a) contains tracks of stable magnetic elementsobtained from the time sequence covering a period of over ten hours. In all studied cases,the number and distribution of MMFs around sunspots is uneven: One side of a sunspot mayshow a much higher population of MMFs than the other. The side of the sunspot with a smallpopulation of MMFs is indicated by thick white arrows, and, as in all studied cases, it is just

this side where large-scale coronal loops are rooted (Ryutova, Hagennar and Title, 2007).Features of individual MMFs as well as expected response of overlying atmosphere are

consistent with the model.The processes of energy transfer and release by soliton (types I and I, MDF) and shock-

like kinks (types II and III), and therefore their impact on the dynamics of the overlyingatmosphere, are quite different. Solitons, once formed, remain stable for a long time; their


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Figure 4 MDI magnetogram of a central sunspot observed on 10 June 1999 (N18.5,W5.0), and examples ofspace-time cuts. (a) MDI magnetogram scaled from 1000 to 1000 G; the region devoid of MMFs is markedby a curved arrow around the central sunspot. (Upper-right panels) Three cuts made over the central sunspotshowing space-time behavior along these cuts (panels (1a,b), (2a,b), (3a,b)). Right sides of panels (1a,b) and(2a,b) show a significant deficit of the MMFs, while the rest of the moat is well populated by the MMFs.(Lower panels) The area of the central sunspot in the 700 m wing of H. As in the magnetogram movie,the left sides of cuts 1 and 2 and the entire cut 3 pass through the region well populated by MMFs; the rightends of cuts 1 and 2 reveal very little activity of small structures.

amplitude slowly decays as 1/(1+ t /tdiss). During the passage of a soliton through the moatit gradually slows down, separation between the footpoints increases, and a kink straightensout. The slow process of energy loss by a traveling soliton may produce a faint emission inchromospheric lines, which may end up at the moat boundary by the appearance of brightpoints. Under certain and rare conditions, though, solitons may experience an explosivegrowth, as 1/(1 t /texpl)2. This corresponds to quick and violent energy release, whichmay produce jets and microflares at coronal temperatures.

A shock-like kink is a more unsteady state than a soliton. Its lifetime may be as longas that of a soliton, but to remain in a quasi-stable state, it requires an intense process of

energy supply and release. One should bear in mind that the very existence of evolutionarysoliton- and shock-like kinks is possible only in energetically-open systems, i.e., in systemswith continuous energy inflow and outflow (sources and sinks). Therefore, the intensifiedprocess of the absorption and release of energy by shock-like formation should be accompa-nied by the enhanced emission in the upper layers of atmosphere during most of its lifetime.However, the energy of a shock-like kink is concentrated in a small volume. When this vol-


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Figure 5 Correlation between the deficit of MMFs and the preferred site of the coronal-loop formation.The two left panels are MDI magnetograms of NOAA 0175, 2 November 2002. The upper image containsfour space-time cuts made over sunspots. The lower magnetogram shows paths of all outflowing unipolarmagnetic features obtained from the MDI movies covering a period of over ten hours. The upper-right panelsshow space-time behavior along four cuts. The lower-right panel is the overlying corona in the TRACE FeXII 195 line. White arrows show the side of the sunspot where the population of MMFs is low and wherelarge-scale coronal loops originated.

ume decreases, the kink quickly dissipates its energy and may cause the appearance of jets

and microflares in the overlying chromosphere and corona.Examples of different types of MMFs and their counterparts in the overlying atmosphereare shown in Figure 6. We use here our only (and short) time series of high-resolution,0.2, magnetograms taken by the SVST. Cuts 1a,b contain two MMFs, type I, marked bydouble arrows, and type II, marked by a single arrow. The size of the footpoints is about1 1.3. This type I feature was born obviously long before the SVST data were taken; itsfootpoints are already far apart, exceeding a separation of 4 . It continues a steady motionwith further gradual spreading, representing one of the numerous long-lived MMFs seenwith lower resolution in Figures 1 and 2. At transition region temperatures, as expected,this MMF is barely noticeable. Its neighbor, a type II MMF with shock-like properties, in

contrast, produces strongly-enhanced emission at the temperatures T 6 104 to 2.5 105 K during its passage throughout the moat. The third example is quite rare. This is atype I MMF born during the SVST observations. Its short path resembling the Greek is consistent with the explosive behavior leading to collapse and violent energy release.Indeed, the collapse of this MMF was accompanied by a strong and short-lived (6 minutes)microflare seen in its maximum phase on the TRACE 1600 image (panel b).


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Figure 6 Examples of different types of MMFs and their counterparts in the transition region. Upper panels:(a) SVST magnetogram of the central sunspot from Figure 1 with a resolution of 0.2 , (b) the same region inTRACE 1600 at T 6 104 to 2.5 105 K; the three straight lines show corresponding space-time slicesin the lower panels. Cut 1 contains the two most typical MMFs, type I (double arrow) and type II (singlearrows). The stable soliton (type I) leaves a very faint trace at high temperatures, while type II, which hasshock-like properties, produces strongly enhanced emission in the TR. Cut 2 shows a type I MMF (with theinner footpoint of polarity opposite the sunspots), which after about an hour of a steady state starts to shrink

and quickly disappears; this process is accompanied by the extended blinker (2b); Cut 3 shows another typeI MMF under the condition when it experiences an explosive collapse, which results in the intense, butshort-lived, microflare (snapshot in panel (b) shows its maximum phase). Panel (4) shows a long-lived typeI MMF at the MDI resolution with the inner footpoint of the same polarity as the parental sunspot (type I,bright soliton), and Panel (5) shows a type I MMF with the inner footpoint of the opposite to sunspot polarity(type I, dark soliton).

To obtain more information about the possible influence of MMFs on an overlying at-mosphere we compiled high-cadence (30 seconds) movies using co-spatial images inSVST G band centered at 4305 and Dopplergrams. Dopplergrams were computed fromH 0.350 by subtracting a blue wing from red and normalizing by their sum (courtesyof Dick Shine). For an absorption line this makes a blue shift positive.

In Figure 7 we compare space-time slices made along cuts 1 3 using Dopplergram andG-band movies. Cut 1 lies in the region of a significant deficit of the MMFs. The corre-sponding Dopplergram image (Figure 7a, upper panel) shows characteristic umbral oscil-lations and running penumbral waves. The left vertical lines in these panels mark the um-bra/penumbra boundary, and the right lines the approximate boundary of the penumbra. Therest is the moat region. One can see how regular umbra/penumbra plane waves smooth outin the moat, leaving a vague pattern of granular motions. Note here the appearance of a

short-lived chromospheric transient at UT 12:50.The bottom-left panel is a G-band image at 4305 . This line has been commonly used to

track the small-scale magnetic elements that appear as G-band bright points. The space-timeslice in the G-band passing through the region devoid of MMFs (lower panel a) shows ir-regular motions and the appearance and disappearance of a small-scale network of magneticelements.


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Figure 7 Computed Dopplergram in H 0.350 and SVST G-band images of a target area. (Left panels)Corresponding space-time images for the three cuts shown in the right panels (upper row is from a Doppler-

gram movie; lower row is from a G-band movie): (a) cut 1 is made over the region devoid of MMFs; (b) cut2 reveals unipolar type II MMF and its imprint on overlying chromosphere; (c) cut 3 shows two MMFsof type II marked by black arrows, 1 and 2, and one MMF of type I marked by white arrow, 3. See text fordetails. Tick marks in the x-axis correspond to 2.5and tick marks in the y-axis to five minutes.

The other two cuts, 2 and 3, corresponding to images in panels (b) and (c), lie in regionsdominated by type II MMFs having shock-like properties. Cut 2 reveals a typical exampleof such an MMF. Its emergence is accompanied by the strongly enhanced upflows seen inthe Dopplergram image (marked by stars). Traveling with high velocity, 6 kms1, theMMF generates along its path strong disturbances that culminate at about the time when the

MMF settles down and starts to migrate slowly toward the moat boundary (black arrows inpanels (b)). Note that a lateral motion of the H disturbance at this time is about 14 km s1,which at T 104 K is slightly supersonic.

Cut 3 reveals three features: two MMFs of type II, marked by black arrows in lowerpanel (c), and one MMF of type I, marked by a white arrow. During the passage of theMMF Number 1 through the moat, the Dopplergram movie shows how a regular pattern ofoscillations disintegrates into two distinct velocity fields associated with the ridges of upflowmaterial followed by the post-ridge downflows (marked by white arrows in the upper panel,(c)). The velocity of the ridges associated with the first MMF is over 16 km s1 and is clearlysupersonic, whereas the lateral motion of ridge 2 is about 9 kms1 and most probably is

subsonic.Summarizing the discussion of the individual MMFs, we would like to note that simple

relations among the width of a soliton and its velocity, amplitude (B2z ), and lifetime, ex-pressed in directly observable quantities, allow detailed analysis of the data and inferenceof parameters such as dissipative coefficients (which determine the lifetime of MMFs), dis-persion, and the slope of a soliton. Most importantly, these parameters may be used to study


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observational signatures of dissipation processes that are associated with the energy transferand release by MMFs.

4. Summary

The nature of small-scale moving magnetic features around sunspots with conflicting prop-erties reported in the literature has been uncertain for a long time. To make the observationsmore or less consistent, the MMFs were divided into classes. With advances in observations,the number of classes has only increased, creating more problems for the development of anadequate theory. Moreover, the properties of all types of MMFs clearly violate energy andmomentum conservation laws.

We propose a mechanism that describes the properties of all of the observed types ofMMFs on a unified basis, revealing a common nature of their origin. The mechanism is

based on the conjecture that penumbral filaments embedded in a highly dynamic environ-ment in a strongly stratified atmosphere represent an energetically-open system with contin-uous sources and sinks of energy. We show that nonlinear coupling of magnetic fields andsheared plasma flows lead to formation of a stable magnetic kink, which, depending on thelocal physical parameters, may have either soliton-like or shock-like properties. Dependingon the dispersion of the system, the kink may exhibit either the properties of a bright soliton(positive dispersion) or those of a dark soliton (negative dispersion). If nonlinearity is wellbalanced by dispersion, the kink appears as a bipolar feature, representing type I (-shapedkink), type I (-shaped kink), and MDFs (-shaped kink traveling upstream). If nonlinear-ity prevails over dispersion, the kink becomes asymmetric and acquires a shock-like form,

i.e., one side of the soliton becomes steeper than the other. Such a formation appears alongthe line of sight either as a single-polarity element or as a bipole with one sharp and onediffuse footpoint. The sign of dispersion determines whether the quasi-unipolar featurehas the same polarity as the parent sunspot (type II MMF) or is of the opposite polarity(type III MMF). As all the parameters in the theoretical descriptions of solitons are directlyobservable, the model allows us to perform quantitative analysis. Such an approach not onlyexplains the origin, the structure, and the observed properties of the MMFs but consolidatesall types of MMFs into one scheme and removes seeming contradictions in observations.

We also study the response of the overlying atmosphere to MMF dynamics. We use sev-eral sets of multi-wavelength observations of different sunspot areas from the photosphere

to the corona. We found that the impact of different types of MMFs on the overlying at-mosphere depends on their type. The MMFs seen as opposite-polarity pairs have, as reportedby Harvey and Harvey, quite faint counterparts in the chromosphere, although their pathsare well co-aligned with the H filaments and mimic the twist of a sunspot. In contrastto this, the MMFs seen as unipolar shock-like features have a clear impact on the overly-ing atmosphere, causing the dynamic changes in the hot emission lines. We also found thatsome bipolar MMFs, as predicted by theory, may exhibit an explosive behavior and lead togeneration of coronal transients. These regularities as well as the properties of individualMMFs are consistent with the shock and soliton dynamics described by the nonlinear KdVBurgers equation. Note that the observed anticorrelation between a large number of MMFsand preferable site of coronal footpoints as well is consistent with the model description ofMMFs (Ryutova, Hagennar and Title, 2007).

We believe that detailed analysis of flow maps in and around the sunspot together withthe vector magnetograms will further increase our understanding of coupling mechanismsbetween the MMFs and the overlying atmosphere. With the observations to be obtained withthe Solar-B/Hinode mission, this analysis is feasible.


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Acknowledgements We thank Dick Shine and Alan Title for collaboration and Ted Tarbell for discussions.This work was performed under the auspices of the U.S. DOE by U.C. Lawrence Livermore National Labo-ratory, under Contract No. W-7405-Eng-48 and is supported by a NASA contract at Stanford and LockheedMartin (NAG5-10483, MDI) and the TRACE project at Lockheed Martin (NAS5-3099).

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m. ryutova and h. hagenaar- magnetic solitons: unified mechanism for moving magnetic features

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