High-resolution Observation of Moving Magnetic Features

Moving magnetic features (MMFs) are small dynamic magnetic features moving from sunspots toward the boundary of the moat (an annular region surrounding the sunspot; Hagenaar et al. 2012). They were first found by Sheeley (1969), and then named and summarized by Harvey & Harvey (1973). MMFs are believed to be the intersection of magnetic flux tubes with the solar photosphere, and are often explained with the "sea-serpent" magnetic structure near the solar surface.

Previous studies have shown two types of MMFs: unipolar MMFs with the same/opposite polarity to the parent spot (Type II/Type III) and bipolar pairs of MMFs (Type I). Each type has a different sketch: unipolar MMFs are considered as the movement of single magnetic elements, while bipolar MMFs are the manifestation of Ω-shaped or U-shaped loops traveling along penumbral filaments (Zhang et al. 2003; Criscuoli et al. 2012). Type II MMFs formed as a result of the detached penumbral spines, and Type III MMFs are the results of intersections of the submerged penumbral flux (Thomas et al. 2002). They are modeled as manifestations of shocks and solitons propagating along the penumbral filaments (Ryutova & Hagenaar 2007). Their horizontal velocities are usually ≤1 km s⁻¹ (Zhang et al. 2007; Criscuoli et al. 2012; Hagenaar et al. 2012). Bipolar MMFs may participate in the formation of a moat region, while unipolar MMFs are believed to be associated with chromospheric jets and microflares (Ryutova & Hagenaar 2007). Dynamic unipolar MMFs can interact with the opposite unipolar network magnetic features (NMFs) and cause cancellation and sequential solar jets (Yang et al. 2013; Chen et al. 2015). Compared to unipolar MMFs, bipolar ones have additional orientational parameters with respect to the sunspot. The boundary between unipolar and bipolar pairs are usually unclear. They can be mistaken for the other due to an improper threshold of chosen separation and unbalanced magnetic flux, especially when the opposite polarity feature is close to the sunspot, around which ambient flux is strong (Lee 1992).

In more recent observations, MMFs are found to originate from the mid-penumbra (Sainz Dalda & Bellot Rubio 2008). The magnetic features are intersections of horizontal fields extended from the penumbra with the photospheric surface in highly inclined fields (Kubo et al. 2003). The inclination of MMFs tends to be more and more vertical with MMF propagation due to the interaction with the magnetic canopy (Kaithakkal et al. 2017). Zhang et al. (2003) demonstrated the geometry and motion of MMFs between the main spot and the smaller opposite polarity spot, yet with an open question on whether MMF clustering depends on details of the magnetic and velocity fields.

MMFs can be related to the decay of sunspots (Harvey & Harvey 1973). As Meyer et al. (1974) suggested, the growth and decay of sunspots can be related to supergranular convection, and corresponding photospheric fields outside sunspots are concentrated into knots in a comparable size as that of granulation. Small flux tubes are transported away by the large-scale supergranulation from a sunspot, which are seen as MMFs in the moat. Martínez Pillet (2002) estimated that the rate of flux transport by appearance of Type II MMFs is 3–8 times larger than the flux decay rate of the sunspot. Kubo et al. (2003) agreed that Type II MMFs are responsible for the disintegration of the sunspot because the number of Type II MMFs is much larger than Type III MMFs. One reason for this conclusion is due to the lack of high spatial resolution vector magnetograms; the detection of Type III MMFs is influenced by strong ambient magnetic flux.

In this paper, photospheric vector magnetograms are obtained from the 1.6 m Goode Solar Telescope (GST; Cao et al. 2010; Goode et al. 2010) at Big Bear Solar Observatory (BBSO). The bipolar MMFs around a stable sunspot can be identified unambiguously. We studied the physical properties of all MMFs and their role in the sunspot flux evolution.

The main data source is the vector magnetograms from the Near InfraRed Imaging Spectropolarimeter (NIRIS) of GST (Cao et al. 2012). GST is operated with a 308 element high-order AO system (Goode et al. 2010). In the visible wavelengths, the data acquired at GST achieve a spatial resolution around 005 after using 100 frames for speckle reconstruction. The cadence of the data is 15 s. NIRIS was upgraded from the first-generation near-infrared imaging spectropolarimeter of BBSO. It offers unprecedented high-resolution spectroscopic and polarimetric imaging data of the solar atmosphere from the deepest photosphere through the base of the corona. NIRIS covers a broad spectral range from 1.0 to 1.7 μm, with particular attention to two main spectral lines: the Fe i 1565 nm line, which probes the magnetic field in the deepest photosphere, and the He i 1083 nm line, which is useful for mapping the vector field at the base of the corona (Cao et al. 2012). The sunspot under investigation was approximately located in the heliocentric coordinate (4'', −1'') on 2016 July 14, 16:19 UT. The cosine of the heliocentric angle is about 0.87 at that time. The data during our observation period (16:19 UT–22:53 UT) were used to conduct the study. In the observation, the field of view (FOV) of NIRIS covered the sunspot and the partial moat region from the outer penumbra of AR 12565, as illustrated in Figure 1. Polarimetric measurements of Stokes I, Q, U, V profiles ran at a 10 s cadence. Images were corrected for dark current, flat field, interference fringe, and polarization crosstalk. The diffraction-limited spatial resolution of vector magnetograms reached 024. The polarization noise was ∼10⁻³ I_c, where I_c is the continuum intensity (Cao et al. 2012). The Stokes vectors were inverted using the Milne–Eddington inversion method (Orozco Suárez et al. 2010), which solves the polarized radiative transfer equation and fits the Stokes line profiles. The inversion procedure returned parameters including magnetic field, inclination, azimuth angle, and Doppler center shift. The inverted data then underwent the 180° azimuth ambiguity correction by using the minimum-energy method (Leka et al. 2009), which simultaneously minimizes the electric current density and the field divergence. Because the azimuth ambiguity is not fully resolved in other regions, we only study a central subregion of data (as denoted by the dashed box in Figure 1) within the original FOV (as denoted by the solid box in Figure 1) mainly covering the sunspot and northwestern region. The noise of NIRIS varied with locations in the FOV. A denoise algorithm was implemented to assign a denoise mask. In the surrounding 5 × 5 × 5 pixel³ cube, isolated pixels as singularities were detected and smoothed out by the linear least-squares interpolation.

To validate the NIRIS data, we compared the B_los, B_transvers, and azimuth obtained with NIRIS and the Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) vector magnetograms. Visual inspection of images in Figure 2 shows that magnetograms derived from SDO/HMI and NIRIS data show a good agreement. This is also confirmed through the calculation of the Pearson correlation coefficient. The NIRIS data products measured at 17:35 UT were compared to the cotemporal SDO/HMI data products over a common area marked by the yellow box in Figure 2. 10⁵ pixel pairs were used to obtain the regression relationship between NIRIS and SDO/HMI data products. The linear regression coefficients of B_los, B_transvers, and azimuth between SDO/HMI and NIRIS magnetograms are close to 1.0, while the Pearson correlation coefficients are larger than 0.94, indicating a strong correlation between the pair of data products.

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Type II and III MMFs around the sunspot are identified by the Yet Another Feature Tracking Algorithm (YAFTA; Welsch & Longcope 2003). Type I MMFs are classified as Type II and III MMFs, and will be discussed in Section 4.3. The intensity and size threshold levels are set to be ±100 Gauss and 0.07 Mm². As suggested by DeForest et al. (2007), feature identification uses a clumping algorithm to keep tracking flux clusters. Differences among the identification methods, such as clumping, the downhill, and curvature have been discussed in DeForest et al. (2007). The clumping algorithm may merge MMFs in the same polarity, but it does not affect the separation of Type II and III MMFs. The code returns the spatial location of features, each of which is masked with a specific identification number. Values of all relevant parameters such as flux density, inclination, and azimuthal angle can be obtained. MMFs are tracked over consecutive B_z maps based on the estimated centroid positions. Considering the differences of physical properties between MMFs and NMFs, they are distinguished based on the following facts: (1) MMFs tend to move outward away from the sunspot, while NMFs drift inward. (2) The velocity of NMFs is less than 0.5 km s⁻¹. (3) MMFs are inside the moat, while NMFs are outside the moat. Some large network patches within the moat are excluded from MMFs manually. In total, 268 MMFs and 16 NMFs are found around the sunspot. There are 137 negative MMFs, 131 positive MMFs, 15 negative NMFs, and 1 positive NMF.

The tracking results of all magnetic features by using YAFTA over 6.5 hr of observation in B_z can be seen in Figure 3(a). The original positions (roots of the arrows) and the moving direction of the centroid of MMFs over 6.5 hr are shown in Figure 3(b). MMFs are distributed mostly from the outer penumbra to the boundary of the moat region. NMFs are mostly rooted around the boundary of the moat region and slowly drift around.

The distribution of overall magnetic features excluding sunspot umbra and penumbra and isolated MMFs only are shown in Figure 4. In Figure 4(a), three lines from top to bottom represent overall magnetic features (F_all), the magnetic features excluding MMFs (F_all–F_MMF), and the magnetic features excluding 2.5 times MMFs (F_all − 2.5 × F_MMF). The overall magnetic features have a tendency to yield power-law distribution. The low flux tail of the distribution falls off because fluxes below the threshold are ignored. The linear fitting line has a broken slope of 0.4 before 6 × 10¹⁸ Mx and 1.81 after 6 × 10¹⁸ Mx. This does not agree well with Parnell et al. (2009), which suggested a scale-free power-law distribution with slope of 1.85 for all surface magnetic features. After removal of MMFs (middle dotted line), the turning point at 6 × 10¹⁸ Mx becomes smoother. Multiplying the total flux of MMFs by a factor of 2.5 makes the slope to be 1.81 as shown in the bottom dashed line. This may hold true due to the lack of observations of the west and east sides of the sunspot. Unlike most of the surface magnetic features, the characteristic flux of MMFs is ∼10¹⁸ Mx. Considering the Gaussian form of the MMF flux distribution, lowering the threshold to include more flux of MMFs will not change the result, as it will only expand the peripheral flux while the center part of the flux density still remains ∼1500 G. The difference between overall magnetic features and MMFs was first shown in the Hinode/SOT observation in 2007 by Hagenaar et al. (2012), in which the overall magnetic features yield a simple power-law distribution, while MMFs do not follow this distribution.

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4.1. Physical Properties of MMFs

Distributions of MMFs' size, lifetime, inclination, velocity, and magnetic flux are shown in Figure 5. NMFs are removed from the data sets. For Type II and III MMFs, their sizes are all below 2.0 Mm² with a median of 0.4 Mm². They show very similar distribution, which may imply the balance of two polarities.

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The mean lifetime of Type II and III MMFs is 43 min, comparable to the 1 hr found by Hagenaar & Shine (2005), but less than the 4 hr found by Zhang et al. (2003). Note that the clumping method is implemented to identify and track MMFs. Surface process, such as fragmentation, coalescence, and cancellation, which mostly happens at the boundary of the moat region, will create new feature masks.

Panel (c) shows the inclination of MMFs. The mean inclination of Type III MMFs is about −57° and that of Type II MMFs is about 56°. A portion of MMFs can be highly inclined. As suggested by previous studies (Criscuoli et al. 2012; Kaithakkal et al. 2017), with an increasing distance from the sunspot, magnetic fields of MMFs tend to be more vertical. This is shown clearly in Figure 7.

In panel (d), the horizontal velocity in MMFs ranges from 0.0 to 2.0 km s⁻¹. Mean velocity of MMFs is 0.5 km s⁻¹.

As shown in Figure 5(e), the total signed flux of MMFs ranges between 10¹⁷ ∼ 10¹⁹ Mx, with an average value of 1.1 × 10¹⁸ Mx. This agrees well with an average flux of 3.6 × 10¹⁸ Mx deduced from MDI (Zhang et al. 2003), 2.5 × 10¹⁸ Mx also from MDI (Hagenaar & Shine 2005), but much larger than 1.16 × 10¹⁷ Mx deduced from SUNRISEII/IMaX around a pore (Kaithakkal et al. 2017). As suggested by Kaithakkal et al. (2017), the flux density of MMFs around a pore may be as small as 1000 G, whereas in our study most of them are around 1500 G. The flux density of a unipolar MMF may fluctuate randomly during its motion to the boundary of moat. Note that the lower limit of the magnetic strength of identified MMFs is 6.5 × 10¹⁶ Mx, which is sufficient to detect MMFs.

4.2. Variation of MMFs as a Function of Distance from Sunspot Center

In Figure 6, we show the NIRIS continuum intensity and vertical field around the sunspot from NIRIS data. East–west regions are cut off due to missing data when conducting the 180 disambiguity procedures. Four concentric circles marked in dashed lines have a radius r = 11.0, 18.5, 23.5, 31.0 Mm, corresponding to the boundary of umbra, outer penumbra, moat region, and FOV, respectively. Azimuthal and temporal averages of the intensity, inclination, Flux_signed/Flux_unsigned, and radial velocity as a function of distance from the center of the sunspot are shown in Figure 7.

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In Figure 7(a), the azimuthally averaged inclination around the sunspot shows a magnetic dome structure, which can also be seen in the sunspot simulation study by Rempel (2012). Both positive and negative MMFs originate with a highly inclined field topology, and become more and more vertical along the way to the boundary of the moat at a rate of 7° Mm⁻¹. The origin of Type III MMFs can be intraspines in a penumbral uncombed structure, where a more horizontal magnetic component is present (Deng et al. 2010; Wang et al. 2012). Such a tendency for inclination angle to become more vertical was also confirmed by Criscuoli et al. (2012).

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In Figure 7(b), both Type II and III MMFs show strong downflows, with a mean V_los of 0.7 and 1.5 km s⁻¹, respectively. The V_los values of the Type III MMFs are similar to previous results, e.g., 1.0 km s⁻¹ reported by Criscuoli et al. (2012), but the direction of the flow is opposite. A strong upflow trend for Type III MMFs is presented by Criscuoli et al. (2012) and Kaithakkal et al. (2017).

To determine the origin of Type III MMFs, we present the ratio of Flux_signed/Flux_unsigned shown in Figure 7(c). Gradual polarity reversal of the magnetic flux can be found in mid-penumbra, at r = 12 Mm in this case, where the total signed flux becomes less than the total unsigned flux within the same circular region. Inverse polarity flux was also observed in Hinode for a larger positive polarity sunspot (Sainz Dalda & Bellot Rubio 2008). In a sunspot simulation modeled by Rempel (2012), inverse polarity flux occurs between 10 and 15 Mm away from the sunspot center for the optical depth from τ = 1 to τ = 0.001. Resolution may also lead to a shift of inverse polarity flux in ∼2 Mm.

The azimuthally averaged velocity is shown in Figure 7(d). Radial components of horizontal velocity V_r of Type II MMFs begin with 3.0 km s⁻¹, which is highly affected by the evershed flow velocity. It decreases to 0.15 km s⁻¹ at the boundary of the moat. The slope of linear regression for Type II MMFs is around −4.4 along with the penumbral evershed flow, −0.18 in the penumbra, and 0.03 in the moat. V_r of Type III MMFs keeps relatively stable. The bump at Mm = 27 is mainly due to the instability of the feature identification, as frequent cancellation occurs at the boundary of the moat.

4.3. Flux Transport of MMFs and Sunspot

The tempo-spatial evolution of the magnetic flux and flux transport rate is shown in Figure 8. The flux transport rate is calculated in an angle range of the θ = 25° region shown in Figure 6(b). The flux transport rate as a function of distance from the sunspot center (Kubo et al. 2008) is

$$\begin{eqnarray*}&&{F}_{v}=\displaystyle \frac{\sum F(r)\cdot {V}_{r}(r)}{\pi ({r}_{2}^{2}-{r}_{1}^{2})}\cdot \displaystyle \frac{2\pi ({r}_{1}+{r}_{2})}{2}\cdot \displaystyle \frac{\pi }{\theta }.\end{eqnarray*}$$

Here, r₁ and r₂ are inner and outer annular radius, θ = 25°.

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From Figure 8(a), negative and positive MMFs show very strong serpent wave spatial distribution when they moved out from the sunspot. Dominant MMFs are about ±2.0 × 10¹⁹ Mx. Separation of their centroid increases from around 1.8 Mm to 3.0 Mm. In Figure 8(b), the dominant flux transport rate for Type II MMFs is ∼−2.0 × 10²⁰ Mx h⁻¹, with a median flux rate ∼−1.64 × 10¹⁹ Mx h⁻¹. Type III MMFs have a similar value of dominant flux transport rate, but with a larger median flux rate ∼2.47 × 10¹⁹ Mx h⁻¹. The flux transport rate of the Type II MMFs found in this study agrees well with that found by Kubo et al. (2003). However, Kubo et al. (2003) also find that the transport rate of the Type II MMFs is 50 times larger than that of the Type III MMFs, which is not the case in our study. Note that only the flux transport rate of the vertical MMFs is considered. The flux transport rate of the vertical MMFs should be more important than horizontal ones because horizontal MMFs sometimes correspond to the local fluctuation of the magnetic field (Kubo et al. 2003). Our sunspot is in a stable phase, with a flux evolution rate of vertical field ∼1.79 × 10¹⁹ Mx h⁻¹. The median net flux transport of MMFs agrees well with the flux evolution of the sunspot.

The physical properties of Type II and III MMFs on subarcsecond size are studied. In previous studies, Type II and III MMFs are imbalanced, due to the limitation of observations (Kubo et al. 2003; Hagenaar et al. 2012). In our study, Type II and III MMFs have a similar distribution of size, lifetime, inclination, horizontal velocity, and balanced flux strength, which implies the same origin and symmetric properties of MMFs in both polarities.

The overall distribution of magnetic features confirms that the scale-free power-law distribution between 3.0 × 10¹⁶–2.0 × 10¹⁹ Mx tends to hold after the removal of the MMFs. MMFs have a characteristic flux ∼10¹⁸ Mx, which does not follow the scale-free power-law distribution. It may imply a different mechanism upon the generation of MMFs compared to other global surface magnetic features.

Type III MMFs may originate from mid-penumbra, where the fields of penumbral filaments are the most inclined. Same as Type II MMFs, Type III MMFs are shredded from the extension of the penumbral filaments with highly inclined fields. With the distance from the sunspot, all MMFs tend to become more and more vertical as the result of the interaction with magnetic canopy, and the velocity of Type II MMFs decreases until reaching the boundary of the moat. Type III MMFs are associated with downflows instead of upflows, which is contrary to previous studies (Criscuoli et al. 2012; Kaithakkal et al. 2017). Though they show stronger line-of-sight velocity than Type II ones.

For all MMFs that originate from the mid-penumbra to the boundary of the moat, Type I MMFs dominate. Type II and III MMFs may carry a similar amount of the opposite flux. Resolvable separation of 2 Mm is needed to find out the bipolar structure near the outer penumbra. As Type III MMFs can be found in mid-penumbra, even at a shorter distance than Type II ones, they should also be accountable for sunspot flux evolution. In previous studies, only Type II MMFs are thought to be responsible for sunspot flux loss (Kubo et al. 2003), as Type III MMFs had seldom been found near the outer penumbra. The net flux transport rate for MMFs with both polarities is derived. The sunspot flux evolution rate is much smaller than the flux transport rate of the Type II MMFs, but is comparable with the net flux transport rate. Therefore, MMFs do not have to be associated with sunspot decay. The transition from balance to imbalance of the flux transport rate of Type II and III MMFs may be associated with sunspot decay.

We thank the BBSO team for the excellent data of this event. We also thank the Southwest Research Institute for the tracking code. The BBSO operation is supported by NJIT and US NSF AGS 1821294 grant. The GST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University, and by the strategic priority research program of CAS with grant No. XDB09000000. This work was supported by NASA grants NNX16AF72G, 80NSSC17K0016, 80NSSC18K0673, 80NSSC18K1705, and 80NSSC19K0257 and by NSF grants AGS 1408703 and 1821294.