MOVING MAGNETIC FEATURES AROUND AR 10930 FROM HIGH-RESOLUTION DATA OBSERVED BY HINODE/SOT

We made animations of the time series of Stokes V/I magnetograms, Fe i, G-band, and Ca ii H filtergrams to investigate the motion of MMFs around the sunspots' penumbrae. MMFs' configurations and associated bright points are studied by comparing the magnetograms and their corresponding filtergrams. Bad images in the time series were removed and the final data set consists of 533 NFI frames and 470 BFI frames. The active region was first tracked in each data set by adjusting the heliographic coordinates, and then co-aligned using a two-dimensional Fourier transform cross-correlation program. The alignment of NFI images with the BFI images was achieved as follows: the NFI magnetograms and filtergrams were first interpolated into the same spatial resolution as that of BFI, and then were co-aligned and registered with the BFI G-band images.

We intend to observe the filigrees, the granulations, and MMFs' precursors. But these features are hard to identify and follow with naked eye: the precursors are buried among strong magnetic background of the penumbra fibrils; the filigrees and the granulations are nebulous and change rapidly.

In order to highlight these features of interest, a spatial domain edge detection algorithm is applied to the time sequences to sharpen the fine details of the images and reduce noise. The results of Prewitt, Roberts, and Canny (Canny 1986) edge detection operators are added to the original image to enhance the contrast of the edges. Let I be the source image, then the filtered image can be denoted as

$$\begin{eqnarray} I^{\prime } & = & I-\mathrm{mean}(I)+ a_1\sqrt{{G^P_x}^2+{G^P_y}^2} \nonumber\\ && + a_2\sqrt{ {G^R_x}^2 +{G^R_y}^2}+ a_3\cdot \mathrm{Canny}(I), \end{eqnarray} \tag{ 1 }$$

where $G^P_x$ and $G^P_y$ ($G^R_x$ and $G^R_y$) are the horizontal and vertical results of Prewitt (Roberts) kernels, respectively, convoluted with the original data array, and $\mathtt {mean}(I)$ is the arithmetic mean of the source image I. The row and column masks of the Prewitt (Roberts) operator are 3 × 3 (2 × 2) matrices. The Canny operator first performs noise reduction by Gaussian convolution, computes the gradient vectors, and then, through a process known as non-maximal suppression, traces intensity discontinuities with thin lines in the output image $\mathtt {Canny}(I)$. Parameters a₁, a₂, and a₃ are set manually.

The effects of this image processing technique are shown in Figure 3. In the original Fe i and G-band filtergrams (Figures 3(a) and (b)), the penumbra fibrils and the moat granulations are blurry. But after edge enhancement, their boundaries become clearer and easier to identify. Similarly, the filigrees and dark features also have a much higher contrast with the background. In the original magnetograms (Figure 3(c)), due to the strong magnetic strength of the penumbra, it is difficult to isolate any feature inside the sunspot. In the enhanced image, the penumbra fibrils are clearly visible.

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On magnetogram animations, magnetic elements of various sizes, shapes, strengths, velocities, and polarities are mixed and interacting in the inner moat region. This complexity makes the manual measurement of MMF's geometric and magnetic properties time-consuming and biased by observers. To avoid this problem, we developed a set of routines for the determination of the size, shape, magnetic flux, and center flux density of MMFs by measuring their best-fitting Gaussian surface.

The best-fitting Gaussian bulb of a magnetic object's flux density can be denoted as

$$\begin{eqnarray} B(x^{\prime },y^{\prime }) & = & B^n+A \exp \left(-{\frac{x^{\prime 2}}{2{\sigma _{x^{\prime }}}^2}}-{\frac{y^{\prime 2}}{2{\sigma _{y^{\prime }}}^2}} \right), \end{eqnarray} \tag{ 2 }$$

where x' and y' are the coordinates in the intrinsic frame whose abscissa and ordinate coincide with the bulb's longer and shorter axes, Bⁿ is the background magnetic strength, coefficient A is the amplitude of B, and $\sigma _{x^{\prime }}$ ($\sigma _{y^{\prime }}$) is the x' (y') spread of the bulb. The measured profiles of MMFs' flux density (Section 4.1) suggest that the above two-dimensional Gaussian approximation is proper for MMFs.

The flux ϕ of the magnetic object measured by integrating the net flux density over an bulb-centered rectangle $(w_{x^{\prime }}\times w_{y^{\prime }}=2\gamma _{x^{\prime }}\sigma _{x^{\prime }}\times 2\gamma _{y^{\prime }}\sigma _{y^{\prime }})$ is

$$\begin{equation} \phi (w_{x^{\prime }},w_{y^{\prime }}) = \int _{-\gamma _{y^{\prime }}\sigma _{y^{\prime }}}^{\gamma _{y^{\prime }}\sigma _{y^{\prime }}}\! \int _{-\gamma _{x^{\prime }}\sigma _{x^{\prime }}}^{\gamma _{x^{\prime }}\sigma _{x^{\prime }}} (B(x^{\prime },y^{\prime })-B^n) \cdot {{ d}}x^{\prime }{{ d}}y^{\prime } \end{equation} \tag{ 3 }$$

$$\begin{equation} = 2\pi A\sigma _{x^{\prime }}\sigma _{y^{\prime }}\left (\mathrm{erf}\left(\frac{\gamma _{x^{\prime }}}{\sqrt{2}} \right) \cdot \mathrm{erf} \left(\frac{\gamma _{y^{\prime }}}{\sqrt{2}} \right)\right), \end{equation} \tag{ 4 }$$

where $w_{x^{\prime }}$ and $w_{y^{\prime }}$ are, respectively, the length and width of the rectangle which were selected to measure the magnetic object, $\gamma _{x^{\prime }}$ ($\gamma _{y^{\prime }}$) is the ratio between the rectangle's half-width $w_{x^{\prime }}$ ($w_{y^{\prime }}$) and the bulb's spread $\sigma _{x^{\prime }}$ ($\sigma _{y^{\prime }}$), and erf is the error function $(2/{\sqrt{\pi }})\int _0^x\mathrm{exp}(-{t}^2){d}t$. The real flux of the magnetic object should be the entire volume of the bulb,

$$\begin{equation} \phi _{\gamma _{x^{\prime }},\gamma _{y^{\prime }}\rightarrow \infty } = 2\pi A\sigma _{x^{\prime }}\sigma _{y^{\prime }}. \end{equation} \tag{ 5 }$$

For each identified MMF on each frame, a Gaussian fit is performed on the local region, which yields A, $\sigma _{x^{\prime }}$, and $\sigma _{y^{\prime }}$. These coefficients provide the magnetic flux using the formulation (5). The Gaussian fit procedure also measures the MMF's rotation, location, and background field strength Bⁿ.

For those magnetic objects where the Gaussian fitting calculations do not converge, their real fluxes can be estimated by correcting the values measured through integration

$$\begin{equation} \phi _{\gamma _{x^{\prime }},\gamma _{y^{\prime }}\rightarrow \infty } = \frac{\phi (w_{x^{\prime }},w_{y^{\prime }})}{\mathrm{erf} \left(\sqrt{\mathrm{ln}2}\frac{w_{y^{\prime }}}{r_{y^{\prime }}} \right)\cdot \mathrm{erf} \left(\sqrt{\mathrm{ln}2}\frac{w_{x^{\prime }}}{r_{x^{\prime }}} \right)}, \end{equation} \tag{ 6 }$$

where $r_{x^{\prime }} = \sqrt{2\ln 2}\cdot \sigma _{x^{\prime }}$ and $r_{y^{\prime }} = \sqrt{2\ln 2}\cdot \sigma _{y^{\prime }}$ are the Gaussian bulb's half-width at half-maximum (HWHM) whose determination does not require the Gaussian fit routine. Thus, the errors of the flux measurement caused by the uncertainties of the selection of the rectangles are compensated.

Figure 3(d) shows the result of this procedure on a magnetogram frame, in which the information of MMFs' magnetic and geometric properties is extracted from the complex magnetogram and is ready to be used for statistical study.

For each identified MMF, we record its appearance and disappearance. Since the observation of those MMFs with longer lifetimes is more likely to be interrupted by the ends of the time sequences than that of short-lived ones, selection of the samples is not objective. Thus, arithmetic calculations of characteristic values such as lifetime, population, and production rate would certainly be biased by the limited time duration of observation. We propose the following method to compensate for this bias. The method yields relatively good estimations on artificial data.

The frequency distribution of MMFs' lifetimes, F(T), can be estimated by

$$\begin{eqnarray} F(T) & = & \frac{F_o(T)\cdot D}{D-T}, \quad (0<T\leqslant D), \end{eqnarray} \tag{ 7 }$$

in which T is MMFs' lifetime, D is the duration of observation, and F_o(T) is the observed frequency of those MMFs whose entire lifetime is within the duration of observation. Thus, the estimated population of newly produced MMFs during the observation is

$$\begin{eqnarray} &&N=\int _{0}^{D}F(T){d}T =\int _{0}^{D}\frac{F_o(T)\cdot D}{D-T}{d}T. \end{eqnarray} \tag{ 8 }$$

We calculate composite evolution functions to study the evolution of the magnetic flux, central flux density, and area of all the MMFs observed in the region of interest. These functions merge the individual characteristics of a set of MMFs, describe the most common pattern of their evolution, and inherit their average magnitude and lifetime. Here we take MMFs' magnetic flux as an example to present our formulation of the composites.

The whole MMF population is divided into n_g × n_τ subsets by their location and type. n_g is the total number of observed active regions, and n_τ is the number of nominal categories specifying the types of the MMFs. In our observation, n_g = 1 and n_τ = 4.

For each identified MMF, on each frame of the time sequence, its magnetic field is measured using methods described in Section 3.3. Its flux as a function of time is denoted by the symbol

$$\begin{eqnarray} &&\phi _{si}^\tau (t), \quad \left(0\leqslant t \leqslant T_{si}^\tau \right), \end{eqnarray} \tag{ 9 }$$

where the MMF's type τ ∈ {α, β, γ, θ} (see Table 1), index number i ∈ {1, 2, ..., N(τ, s)}, the region of observation s ∈ {1, 2, ..., n_g}, N(τ, s) is the subset population, and $T_{si}^\tau$ is the MMF's lifetime. Thus, $\phi _{si}^\tau (t)$ stands for the flux of type τ MMF numbered i in region s measured at moment t.

The composite evolution function of a subset, $\hat{\phi _s^\tau }(t^{\prime })$, shows the most common pattern of flux evolution of type τ MMFs in region s.

$$\begin{eqnarray} &&\hat{\phi _s^\tau }(t^{\prime })=\frac{1}{N(\tau,s)}\sum _{i=1}^{N(\tau,s)} \left (\! \frac{\widetilde{\phi _{s}^\tau }}{\bar{\phi }_{si}^\tau }\cdot \phi _{si}^\tau \left(t^{\prime }\cdot \frac{T_{si}^\tau }{\widetilde{T_{s}^\tau }} \right) \! \right)\!, \quad \left(0\leqslant t^{\prime } \leqslant \widetilde{T_{s}^\tau } \right), \nonumber\\ \end{eqnarray} \tag{ 10 }$$

where $\bar{\phi }_{si}^\tau$ is an MMF's weighted average flux on the n frames it appears $((1/T_{si}^\tau)\cdot \sum _{j=0}^{n-2}(({1}/{2})(\phi _j+\phi _{j+1})(t_{j+1}-t_j)))$. $\widetilde{\phi _{s}^\tau }$ and $\widetilde{T_{s}^\tau }$ are, respectively, the average flux ($\mathtt {median}\lbrace \bar{\phi }_{si}^\tau \rbrace$) and average lifetime ($\mathtt {median}\lbrace T_{si}^\tau \rbrace$) of the subset.

The composite evolution function of all the observed type-τ MMFs is calculated from the n_g subset composites,

$$\begin{eqnarray} \widehat{\phi ^\tau }(t^{\prime \prime }) &=& \frac{{\langle }\phi ^\tau {\rangle }}{n_\mathrm{g}}\sum _{s=1}^{n_\mathrm{g}} \left (\frac{1}{N(\tau,s)} \sum _{i=1}^{N(\tau,s)}\left (\frac{1}{\bar{\phi }_{si}^\tau }\cdot \phi _{si}^\tau \left(t^{\prime \prime } \cdot \frac{T_{si}^\tau }{{\langle }T^\tau {\rangle }} \right)\right)\right)\!, \nonumber\\ && (0\leqslant t^{\prime \prime } \leqslant {\langle }T^\tau {\rangle }), \end{eqnarray} \tag{ 11 }$$

where 〈ϕ^τ〉 and 〈T^τ〉 are, respectively, the average flux ($\mathtt {mean}\lbrace \widetilde{\phi ^\tau _s}\rbrace$) and average lifetime ($\mathtt {mean}\lbrace \widetilde{T^\tau _s}\rbrace$) of the n_g subsets. Each MMF subset has equal weight on the overall composite.

The magnetic flux of the observed MMFs ranges from 0.3 × 10¹⁸ to 55 × 10¹⁸ Mx. Figure 5(a) shows a histogram of their fluxes. The smallest distinguishable magnetic elements have fluxes of about 0.05× 10¹⁸ Mx. At the right end of the distribution are a few large MMFs which developed into pores. This distribution can be fitted with a lognormal model:

$$\begin{equation} F=a_0+a_{1}\mathrm{log}(x) \end{equation} \tag{ 12 }$$

The dashed line in Figure 5(a) is fitted with Equation (12), where a₀ = 13.54 and a₁ = −4.76. The number of small magnetic elements can be estimated by Equation (12). The median of this distribution model is 3.2 × 10¹⁸ Mx, i.e., in an exhaustive observation of MMFs, the population of MMFs with flux less than 3.2 × 10¹⁸ Mx should be approximately equal to the total number of those that have a flux greater than 3.2 × 10¹⁸ Mx. After similar calculations, it is found that the frequency distributions of MMFs' area, lifetime, and displacement are all similar to Figure 5(a) and therefore can be fitted by Equation (12). These suggest the existence of a large number of small short-lived MMFs.

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We have investigated the two-dimensional distribution of flux density inside the MMFs on Stokes V/I line-of-sight magnetograms. For each MMF's appearance on each frame of a magnetogram, we locate its flux center, determine its HWHM r_o, and measure its flux density profile B(r) as a function of distance to the flux center. On average, each MMF is measured on 72 frames. Then, these profiles are normalized to filter the amplitudes of each individual MMF's radius and flux density. The normalized profiles have been further combined into one single composite profile $\widehat{B(r)}$, as plotted in Figure 5(b) (solid curve). The error bars show the standard deviations. The dashed curve shows Gaussian fit using the equation

$$\begin{eqnarray} B(r) & = & a_0\cdot \mathrm{exp}\left (-\frac{1}{2}\left(\frac{r}{a_1} \right)^2\right)+a_2, \end{eqnarray} \tag{ 13 }$$

where a₀ = 0.6531, a₁ = 0.6159, and a₂ = 0.3342. The almost seamless fit of the Gaussian function could mean that the distribution of MMF's flux density is Gaussian along its radius. Figure 5(b) also compares the profile of MMF's flux density with that of sunspots. The dash-dotted curve is the flux density profile measured on the major sunspot of AR 10930.

We categorize MMFs into two categories and four types according to the location of their first appearances and the source of their initial magnetic flux.

•   
  Penumbral MMFs. They originate inside or immediately outside the outer penumbral boundary, separate from penumbra fibrils, and move outward. They are differentiated into two types by their polarities.

  •   
    α-MMF. Having the polarity opposite to the parent sunspot.
  •   
    β-MMF. Sharing the parent sunspot's polarity.
•   
  Moat MMFs. They originate outside the penumbra outer boundary, and first appear among moat granulations, with no obvious connection with penumbra fibrils. They are also differentiated into two types according to whether they are attached to other MMFs when they first appear.

  •   
    γ-MMF. Emerge in the moat, with no obvious affiliation to other magnetic objects.
  •   
    θ-MMF. A fragment separated from a magnetic object in the moat.

As shown in Table 1, β- and θ-MMFs are products of fragmentation, and their initial fluxes come from their parent magnetic objects. α- and γ-MMFs are newly emerged magnetic objects.

MMFs can disappear by fragmenting into smaller magnetic elements, merging into other magnetic objects, or diminishing below the threshold of observation. However, the extinction of MMFs is not considered in this categorization.

Penumbral MMFs first appear inside or near the periphery of penumbra. Precursors of penumbral MMFs sometimes can be identified inside the penumbral boundary on edge-enhanced magnetograms (Figure 3(c)). Once they leave the penumbra, penumbral MMFs move outwardly along the radial direction into the moat (Figure 4(a)). β-MMFs are produced close to the penumbral boundary and carry a large amount of flux, while α-MMFs emerge farther from the penumbra, and are small in size and weak in flux (Table 2). This agrees with Li et al.'s (2009) observation.

Figure 6 shows time series of magnetograms with two examples of penumbral MMFs. The top two rows (Figure 6(a)) show the motion of a positive polarity α-MMF, which emerged among magnetic negative penumbral fibrils. The bottom two rows (Figure 6(b)) are the serial images of a β-MMF which is a parcel of the penumbra that separated from the fibrils and moved outward.

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These two penumbral MMFs' fluxes as functions of time are plotted in the top row of Figure 7. The α-MMF's flux (Figure 7(a)) was weak when it first appeared; it increased as the MMF left the penumbra and moved into the moat, then it decreased when the MMF encountered magnetic elements of the opposite polarity. The β-MMF (Figure 7(b)) had its maximum flux when it left the penumbral fibrils, then its magnetic flux and size kept decreasing until it was no longer visible.

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The evolution curves of all the identified α- and β-MMFs are merged into two composite functions, applying the method described in Section 3.5. Figures 7(e) and (f) show the evolution of α- and β-composites. The β-composite (dashed curve) first appears with its maximum area and flux density, and it moves at a rather stable speed, but its magnetic field decreases all through its lifetime, until in the end it becomes too weak and small to be detected. On the other hand, the α-composite (dotted curve) evolves in a different way. Its initial magnetic flux is weak; in the first half of its life it increases in both flux density and area, and gains flux; after reaching its maximum flux it begins to diffuse. In the latter half of its life, although its area still increases gradually, the flux density keeps decreasing until the MMF disappears. The α-composite's velocity decreases faster than the β-composite's (Table 2).

Comparing the origins and displacements of penumbral MMFs (Figure 4(a)) to those of moat MMFs (Figure 4(b)) shows that, while the penumbral MMFs generally move along the radial direction, the moat MMFs' directions of motion are dispersed. Many of them move almost along the azimuthal direction; some γ-MMFs even move toward the parent sunspot instead of moving away from it as MMFs are traditionally defined.

Figure 8(a) shows a γ-MMF emerging in the moat, with no immediate connection to penumbral fibrils or other MMFs. Its initial magnetic flux was weak, as plotted in Figure 7(c). It moved southward along the azimuthal direction and gained flux. In about 1.5 hr, it moved 7'' on the solar surface at a speed of nearly 1 km s⁻¹. Finally, it merged into another MMF with the same polarity. Similar to α-MMFs, γ-MMFs usually have weak initial flux, they gain flux in the rise phase and lose flux in the decline phase, as demonstrated by γ-MMF's composite evolution functions plotted in Figures 7(e) and (f) (solid curve).

The flux evolution of the θ-MMF in Figure 7(d) is opposite to that of the γ-MMF in Figure 7(c). As shown in Figure 8(b), it first separated from another MMF, then it lost flux as it moved slowly and eventually vanished in the moat. Similar to β-MMFs, strong initial flux, decreasing magnetic strength, and long lifetime are typical among θ-MMFs, as shown by the evolution of their composites (Figures 7(e) and (f), dash-dotted curve). θ-MMFs' speed and deceleration are the lowest among the four types (Table 2).

Types α, β, and γ each constitute about 30% of the total MMF flux, while θ-MMFs account for about 10%, as listed in Table 2. Figure 9(a) plots the amount of magnetic flux contributed by MMFs as functions of radial distance to penumbra. About 63% of the moat MMF fluxes are input by new emergence fluxes (α- and γ-MMFs). The remaining 37% are brought in by fragments from the penumbra (β-MMFs). θ-MMFs are results of fragmentation in the moat; they generally do not produce new flux input. Table 2 also lists the average values of several basic physics quantities of the four MMF sets. Comparing α- and γ-MMFs to β- and θ-MMFs, respectively, it can be noticed that MMFs produced by emergence have shorter lifetime and displacement, and are smaller in size and flux.

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Nearly half of the MMF population are γ-MMFs. Their paths cover a large part of the observed moat region (Figure 4(b)). Their average speed and deceleration are the highest among the four types. Some pairs of opposite-polarity γ-MMFs emerge in a relatively quiet vicinity, and move in opposite directions. Some of them emerge next to a relatively stationary magnetic feature of the opposite polarity, and move quickly toward another stationary feature of the same polarity. In several places, γ-MMFs are observed to emerge continuously and move on repeated paths. Section 4.7 introduces our observation of some moat flux emergences that are visible in low chromospheric filtergrams.

Within the moat region, the merging and flux cancellation between MMFs are frequent. For many MMFs, these are the dominant factors in their evolution. Their lifetime and flux growth/decay are determined not by the amount of initial flux, but by the number and flux of the magnetic elements they encounter. Among the MMFs that we traced, 41% disappeared due to flux cancellation with opposite-polarity magnetic elements, 37% merged with other same-polarity elements; only 22% of the MMFs disappeared without visible interaction with other magnetic elements. The total flux of positive MMFs (514 × 10¹⁸ Mx) is approximately equal to the total flux of negative MMFs (568 × 10¹⁸ Mx). This also indicates that flux cancellation is the main mechanism to make MMFs disappear and to maintain the flux balance of the moat. It is also possible that some flux diffused into tiny magnetic elements that are below the threshold of observation.

To demonstrate the dynamic nature of the moat, we examined the contacts made by a particular MMF with neighboring magnetic elements. Figure 10(a) shows the evolution of a big, negative polarity β-MMF. When it left the penumbra, its initial flux was only 3.2 × 10¹⁸ Mx. During its 14 hr long lifetime, it gained flux mostly by merging magnetic elements of the same polarity. It lost flux partly by fragmentation and partly by cancellation with opposite-polarity magnetic elements. We count 59 contact events during which the MMF gained flux. The total flux gained (56.9 × 10¹⁸ Mx) more than doubles the MMF's maximum flux (25.1 × 10¹⁸ Mx). These events are indicated by the black, inward pointing arrows in Figure 10(b). There were also 53 contact events in which the MMF lost 49.8 × 10¹⁸ Mx of flux in total. In Figure 10(b), they are indicated by the white arrows that point outward. The lower panel of Figure 10(c) compares the MMF's evolution of flux (solid curve) and flux density (dotted curve) with the Ca ii H light flux (dashed curve), where the light flux is the two-dimensional integration of image intensity in arbitrary units. The upper panel plots the amounts of flux gained (plus sign) and lost (minus sign) in the contact events. Some of the flux cancellation events appear as bright points on Ca ii H images. During the MMF's rise phase, the conglomeration process was the dominant mechanism, while flux cancellation was dominant in the decline phase.

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A massive magnetic area left the major sunspot from the southwest side, as shown in Figure 6(a). It is a compact group of magnetic elements of various sizes. Due to the size and complexity of this region, the local magnetic elements are not counted as MMFs in this research.

Figure 11 shows some sub-regions of the vector magnetograms obtained by SOT/SP spectrograph during the time of observation. The arrows are the transverse component of magnetic field vectors overlaying the vertical flux density. In Figure 11(a), at the places where MMFs meet with magnetic regions of opposite polarity, the transverse fields deviate from their directions in the neighboring regions and point to the contact area where the polarities meet.

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On SP vector magnetograms, we have selected a few isolated round-shaped magnetic elements. Their transverse field points to the flux center, as plotted in Figure 11(b), indicating that the magnetic field inside these MMFs is directed inward. The inclination angle i of their magnetic field to the photosphere has been measured along their diameters. At the MMFs' boundaries, the amplitude of the inclination angle |i| is between 10° and 40°. |i| increases as the field strength increases, while at the flux center the field is almost vertical. This profile is similar to the field orientation of sunspots. A sunspot's magnetic field also inclines toward the spot center, the zenith angle increases with the radial distance to spot center, and the magnetic field at the sunspot center is almost vertical (Lites & Skumanich 1990; Skumanich et al. 1994). As an example, the periphery and flux center of the MMF in the lower panel of Figure 11(b) are marked with a circle and a cross. The field inclination angle measured along its east–west diameter is plotted in Figure 9(b) (solid curve). The dashed and dotted curves show the variation of |i| along the major axes of two of AR 10930's sunspots.

Horizontal flow velocity field was computed with the local correlation tracking (LCT) technique using Stokes V/I line-of-sight magnetograms. A comparison between the time-averaged flow map (Figure 4(d)) and the G-band filtergrams shows that the flow basically follows the extension of penumbral fibrils, especially near the highly sheared polarity inversion lines (solid curve). In the regions where the flow speed is relatively high (delineated with dashed contours), the production of penumbral MMFs is intense (cf. Figures 4(a) and (b)).

Figure 9(c) compares the average radial velocity of the MMFs (dashed curve) with that of the moat flow field (solid curve), both as functions of the distance to penumbra outer boundary. It can be seen that the speed of MMFs (∼0.5 km s⁻¹) is higher than the background flow speed (∼0.2 km s⁻¹). The former is taken statistically by following individual features, while the latter by the local correlation technique. Although both methods provide a basic estimation on the outflow of magnetic flux from sunspots, the average speed measured from the manually selected MMF set is subject to bias in sample selection, because it is natural for the human eye to be "drawn to large, intense, rapidly moving features" (Brickhouse & Labonte 1988) and those leading ones in MMF groups. Also, the variances of MMFs' radial velocity (dashed error bars) are quite large, which is caused partly by the broad distribution of MMFs' speed, and partly by the randomness of γ-MMFs' directions of motion. At 0''–4'' outside of the penumbral boundary, the speed of MMFs is the highest; this agrees with Hurlburt & Rucklidge's (2000) observation of a "collar flow" right outside the penumbra. MMF's radial velocity reaches a minimum at about 17'' outside the penumbra.

Four hundred chromospheric bright points have been observed over the Ca ii H time series. Their locations have been marked in Figure 4(c). More than 80% of the observed bright points are associated with mixed-polarity groups of magnetic elements. The places where bright points frequently appear are close to the penumbral boundaries and have high-speed flow (cf. Figure 4(d)). Moreover, many MMFs are produced here and they frequently cancel with opposite-polarity elements.

The distribution of bright points' observed Ca ii H light flux is plotted in Figure 9(d). The histogram (solid curve) can be fitted with a logsquare model (dashed curve). The left end of the distribution function represents a large number of small bright points that release little light flux and energy.

In Ca ii H images, many MMFs do not appear as identifiable features. However, quick emergence and fast motion of γ-MMFs are often visible. For example, the γ-MMF displayed in Figure 12(a) is small in size (∼1'') and flux (∼2 × 10¹⁸ Mx), but it can be clearly identified on Ca ii H and G-band filtergrams as a fast-moving bright point. It emerged next to one negative-polarity feature at the southwest corner of the small field of view, then it moved quickly toward a stationary positive polarity feature at the northeast corner, and finally merged with it. On the other hand, some big magnetic elements appear as dark patches on filtergrams, as displayed in Figure 12(b). On magnetograms they are about 4'' in size, and some of them became pores.

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The separation of magnetic elements of different polarities triggers short-timescale Ca ii H bright points, as illustrated by Figure 13(a). The elements' opposite directions of motion are illustrated by arrows. Bipolar flux emergence can also form mini dark filaments. In Figure 13(b), as the opposite-polarity MMF pairs emerge and move away from each other, small dark structures are formed and elongated.

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The formation of penumbral MMFs is accompanied by Ca ii H bright points. Bright points are especially frequent and intense when a mixed group of α- and β-MMFs separate from the mother sunspots. Figure 14(a) is an example: as two bipolar MMFs leave the penumbra, more than ten Ca ii H bright points appeared within 2 hr. These bright points could be microflares.

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Dark chromospheric loop structures are observed when some penumbral MMFs move away from the penumbra. For each filament, one footpoint is on the parent sunspot, the other on a departing penumbral MMF. The filaments are stretched and elongated as the MMFs move away. Figure 14(a) shows the formation and elongation process of several dark filaments as bipolar penumbral MMFs left the penumbra. These filaments lasted for about 3 hr. The filament in Figure 14(b) was formed when a fast-moving β-MMF moved away from the penumbra to join with a magnetic element of opposite polarity. The lifetime of this filament is less than ten minutes.

The collisions of opposite-polarity magnetic elements frequently produce bright points. For instance, in Figure 15(a), as a negative-polarity MMF moved westward, it encountered several positive-polarity MMFs and triggered several microflares. During this process the flux of this negative-polarity MMF decreased rapidly and finally disappeared. Flux cancellation events are probably responsible for most of the bright points in the moat.

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In some cases, collisions of opposite-polarity magnetic elements form chromospheric dark structures. Figure 15(b) shows five horn-shaped dark chromospheric structures. They were formed during the collision between a moving negative polarity MMF and a neighboring positive polarity magnetic element. These micro-filaments usually have uneven footpoints: one is substantially bigger than the other.

Granules and filigrees can be clearly identified in edge-enhanced G-band time sequences. However, their form and location frequently change on a timescale shorter than the time cadence of the instrument (120 s), which makes it difficult to follow their evolution. Also, their vast numbers suggest that, in order to study these features statistically, an automated feature-recognition procedure should be utilized.