The Formation and Decay of Sunspot Penumbrae in Active Region NOAA 12673

Qiaoling Li; Xiaoli Yan; Jincheng Wang; DeFang Kong; Zhike Xue; Liheng Yang

doi:10.3847/1538-4357/ab4f84

1. Introduction

Sunspots are the most noticeable manifestation of solar magnetic field concentrations in the photosphere. A typical mature sunspot has an umbra and a penumbra. The presence of a penumbra distinguishes a mature sunspot from a small pore. The formation and decay of a sunspot penumbra are a considerably complex process. Although the formation and decay of sunspot penumbrae occur frequently in the active region (AR), the formation mechanism and the origination of the penumbral magnetic field are poorly understood, due to the lack of observations that fully cover the penumbral evolution process with high spatial, spectral, and temporal resolution.

When a sunspot penumbra begins to form, the transitions in the area and the magnetic field from umbra to penumbra seem to have an effect on the development of penumbral filaments. As the total magnetic flux of a pore increases, the outermost magnetic field lines of the pore become more horizontal because of the demand of force balance. Once these field lines incline to a critical angle, a convectively driven filamentary instability sets in (Hurlburt & Rucklidge 2000; Tildesley & Weiss 2004). Then the field lines at the boundary of the pore are so horizontal that they are grabbed and pumped downward by the surrounding granular convection. The development of this process leads to the formation of the penumbra with its interlocking-comb field. This mechanism for penumbral formation is referred to as "flux pumping" (Thomas et al. 2002; Weiss et al. 2004; Brummell et al. 2008). Using the Fe i 630.25 nm spectral line, Romano et al. (2014) detected some patches around a pore that showed upward motions and radially outward displacement. These features were interpreted as the footpoints of the pore magnetic field lines. They suggested that the magnetic field lines rooted in the pore were forced to return to the photosphere by the chromospheric magnetic fields and were progressively stretched and pushed down by granular convection. The penumbra forms as a result of the change in inclination of the magnetic field lines of an umbra (from a vertical to horizontal configuration), as supported by the investigation of Murabito et al. (2016).

Based on a study of 10 sunspots, Jurčák (2011) analyzed the umbra–penumbra boundary and concluded that the inner stable penumbral boundary is defined by the critical value of the vertical component of the sunspot magnetic field ( ${B}_{\mathrm{stable}}^{\mathrm{ver}}$ = 1.8 KG). If the vertical component of the magnetic field (B_ver) in the pore was smaller than ${B}_{\mathrm{stable}}^{\mathrm{ver}}$ , the penumbral magnetoconvective mode in the pore would not be hindered and a stable pore–penumbra boundary would not be established. Jurčák et al. (2017) further analyzed the penumbral formation of a pore and confirmed the necessity of ${B}_{\mathrm{stable}}^{\mathrm{ver}}$ for establishing a stable umbra–penumbra boundary (Jurčák et al. 2015). They found that the penumbra grew at the expense of the magnetic flux of the pore, which supports the result proposed earlier by Watanabe et al. (2014). When the rudimentary penumbral filaments formed, Watanabe et al. (2014) observed that the area of the dark umbra gradually decreased. However, during the process of penumbral decay, they found that the horizontal penumbral field became vertical, resulting in the recovery of the umbral area. Conversely, Schlichenmaier et al. (2010a) found that the umbral area remained a constant value while a sunspot penumbra formed.

According to some studies on penumbral formation, the magnetic field in the nearby sunspots, such as flux emergence and the preexisting overlying magnetic field, plays a pivotal role in the formation of a penumbra. The emergence of magnetic flux in the vicinity of a sunspot can lead to a critical point in penumbral formation (Zwaan 1992; Leka & Skumanich 1998; Yang et al. 2003; Zuccarello et al. 2014). Leka & Skumanich (1998) suggested that the emerging horizontal field lines would be trapped in the photosphere and form penumbral filaments rather than continuing to rise to higher layers. However, how the emerging field is trapped in the photosphere is still not clear. Shimizu et al. (2012) suggested that the magnetic structure of the chromosphere may play an important role in the process of emerging horizontal fields trapped in the photosphere. They noticed the presence of an annular zone of 3''–5'' width in Ca ii H images around a pore before the formation of its penumbra. The annular zone reflects the formation of a magnetic field overlying the surrounding of the pore at the chromosphere. Lim et al. (2013) observed some chromospheric threads above the forming penumbral filaments in an emerging flux region. They thought the chromospheric threads represent the preexisting chromospheric horizontal field during the formation of penumbra filaments and suggested the emerging flux is trapped at the photosphere by the overlying chromospheric canopy fields. The presence of magnetic canopy fields in the chromosphere before penumbra formation may be crucial for the development of penumbra evidenced by chromospheric observations (Romano et al. 2013, 2014; Guglielmino et al. 2014) and simulations (Rempel 2011, 2012; MacTaggart et al. 2016). However, not all events of penumbral formation are accompanied by an overlying magnetic field before their formation. The effect of an overlying magnetic field on penumbral filaments deserved further study.

Though the emerging magnetic flux may supply additional magnetic flux to the penumbra, some investigations have an opposite point of view. The emerging flux seems to prevent the formation of a steady penumbra. Schlichenmaier et al. (2010b) and Rezaei et al. (2012) studied the same sunspot in the AR NOAA 11024 and noted that a stable penumbral sector formed on the side away from the flux emergence region. Both studies agreed that the ongoing flux emergence around the sunspot inhibited the formation of a stable penumbra, and they suggested that "quiet" magnetic surroundings in the vicinity of a sunspot seem to facilitate the formation of a stable penumbra on a dynamical timescale. In contrast, Louis et al. (2013) found that some stable penumbral filaments of a decaying sunspot formed after the newly emerged patch coalesced with the sunspot. Likewise, Murabito et al. (2017) observed that the first stable penumbral sector around a pore formed in the flux emergence region. By analyzing penumbral formation in 12 ARs, Murabito et al. (2018) reported that eight sunspots formed the first stable penumbral sector in the flux emergence and nine sunspots formed on the side away from the flux emergence. Consequently, these contradictory results on penumbral formation in flux emergence lead to an open question: What role does an emerging flux play in penumbral formation?

Penumbral decay is a relatively slow process compared with the process of penumbral formation. In particular, there are many events in which the penumbra quickly disappears. These events mostly are related to solar flares or other eruptive phenomena. Some studies found the penumbra to rapidly decay after some X-class solar flares because the magnetic fields of the penumbra turned from horizontal to vertical (Wang et al. 2004; Deng et al. 2005). Bellot Rubio et al. (2008) observed a sunspot that gradually lost its penumbra in three days and discovered some finger-like structures near the decaying sunspot. These features were characterized by a weak horizontal magnetic field and blueshift. The authors speculated these structures may be related to penumbral magnetic field lines, which rise to the chromosphere by buoyancy and result in the disappearance of the penumbra in the photosphere. By using the high-resolution observations of a decaying sunspot, Verma et al. (2018) found that the horizontal magnetic fields in a penumbra became vertical when the sunspot decayed. This conclusion is the same as the explanation of flare-induced rapid penumbral decay.

Except for the changes in the magnetic field of a penumbra, the magnetic flux removal of a sunspot is an explanation of sunspot decay. Moving magnetic features (MMFs) are a key feature of the magnetic flux dispersal process and are only associated with decaying sunspots (Harvey & Harvey 1973). Martínez Pillet (2002) analyzed the decay of leading sunspots and trailing sunspots and explained how the magnetic flux of a sunspot was spread over a larger area when the sunspot was decaying, but they failed to satisfactorily describe the origin of the flux removal process. It has been shown that the sunspot flux-removal process mainly includes fragmentation of the umbra, flux cancellation of MMFs, and flux transport by MMFs to the surrounding region, as suggested by Deng et al. (2007). Similarly, Verma et al. (2012) found that magnetic flux was carried by MMFs from the decaying sunspot. However, the relation between MMFs and the decay of a penumbra is still a matter of debate (Cabrera Solana et al. 2006).

Rempel (2015) have analyzed how a sunspot decays by numerical simulation. In his simulations, he found two factors that inhibited sunspot decay. One is a strong reduction of the downflow filling factor and convective rms velocity underneath the sunspot penumbra. The other is the outer boundary of the naked pore. The reduction of the downflow filling factor prevents the submergence of the horizontal magnetic field, which turns out to be the dominant decay process in the simulations. In addition, they noted that the deeper-seated convective motions perhaps can erode the "footpoint" of the sunspot and lead to flux separation, resulting in the decay of the sunspot.

In this paper, we study the evolution of sunspots in three regions of AR NOAA 12673. We focus on how the emerging flux affects penumbral formation and decay. The paper is organized as follows. The observations are described in Section 2. The details of the results are presented in Section 3. The conclusions are given in Section 4, and in Section 5 we discuss some of the findings.

2. Observations

The main data used in this paper are the full-disk continuum intensity images and line-of-sight (LOS) magnetograms with a 45 s cadence and a pixel scale of 0 farcs 5 taken by the Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) on board the Solar Dynamic Observatory (SDO; Scherrer et al. 2012). The continuum intensity images and LOS magnetograms are used to show the temporal evolution of sunspots in AR NOAA 12673 from 2017 September 2 to 6.

To study the evolution of the magnetic field, we also analyzed the Space-weather HMI Active Region Patches (SHARP) vector magnetogram data (Bobra et al. 2014; Centeno et al. 2014). The SHARP data are generated from the polarization measurements at six wavelengths along the Fe i 617.3 nm spectral line (Hoeksema et al. 2014) and are inverted using the Very Fast Inversion of the Stokes Vector algorithm (Borrero et al. 2011) based on the Milne–Eddington approximation. The 180° ambiguity is resolved by using the minimum-energy code (Metcalf 1994; Leka et al. 2009). The inversion provided several physical parameters, including maps of continuum intensity, LOS velocity, and magnetic field inclination. The data series have a pixel scale of about 0 farcs 5 and a cadence of 12 minutes. These data can show the change in longitudinal and transverse magnetic fields during the evolution of sunspots.

To show the fine structure of the sunspot, we present some TiO images observed by the New Vacuum Solar Telescope (NVST; Liu et al. 2014). The TiO images were taken with a cadence of 12 s and a pixel size of 0 farcs 04. The data were calibrated from Level 0 to Level 1 with the dark current subtracted and flat-field corrected. To acquired better image quality, the calibrated images were reconstructed with the speckle masking method from Level 1 to Level 1+ (Xiang et al. 2016).

By using the standard procedure in SolarSoftWare (SSW), the continuum intensity and LOS magnetogram data were rotated differentially to a reference time at 18:00:00 UT on 2017 September 3. The SDO and NVST images were coaligned by the cross-correlation method.

All of the continuum intensity images were normalized to the quiet Sun continuum intensity (I₀). The quiet Sun continuum intensity is the average value of continuum intensity in the region of the quiet Sun. Each of the continuum intensity images were divided into three regions to precisely identify the umbra and penumbra. The umbra area is defined as the area of a continuum image having an intensity darker than 0.48 I₀ (I_umbra ≤ 0.48I₀; Yang et al. 2018). The penumbra area is defined as the area of a continuum image with on intensity brighter than 0.48 I₀ and darker than 0.85 I₀ (0.48I₀ < I_penumbra ≤ 0.85I₀). The gravity center of a sunspot (X_c, Y_c) is defined as

$\begin{eqnarray}&&{X}_{c}=\displaystyle \frac{\sum {I}_{i}{x}_{i}}{\sum {I}_{i}},\qquad {Y}_{c}=\displaystyle \frac{\sum {I}_{i}{y}_{i}}{\sum {I}_{i}}.\end{eqnarray} \tag{ 1 }$

The data provided in the hmi.Sharp-cea-720s were used to produce the magnetic quantities (the integrated positive (ϕ_zp) and negative (ϕ_zn) magnetic flux, the transverse magnetic field strength (B_t), and the magnetic field inclination angle (γ)). The SHARP data are as follows: B_P, which gives the component of the magnetic field, positive westward; B_T, which gives the component of the magnetic field, positive southward; B_R, which gives the radial component of the magnetic field, positive upward; and their errors B_P-ERR, ${B}_{T \mbox{-} \mathrm{ERR}}$ , and ${B}_{R \mbox{-} \mathrm{ERR}}$ (Hoeksema et al. 2014).

The B_P, B_T, and B_R in the cylindrical equal area (CEA) coordinate system were converted to B_x, B_y, and B_z in plate coordinates (B_x = B_P, B_y = −B_T, B_z = B_R). The ${\sigma }_{{B}_{x}}$ , ${\sigma }_{{B}_{y}}$ , and ${\sigma }_{{B}_{z}}$ are the errors of B_x, B_y, and B_z ( ${\sigma }_{{B}_{x}}={B}_{P \mbox{-} \mathrm{ERR}}$ , ${\sigma }_{{B}_{y}}={B}_{T \mbox{-} \mathrm{ERR}}$ , ${\sigma }_{{B}_{z}}={B}_{R \mbox{-} \mathrm{ERR}}$ ). The integrated positive (ϕ_zp) and negative (ϕ_zn) magnetic fluxes in a sunspot are found according to the following equations:

$\begin{eqnarray}&&{\phi }_{{zp}}=\int {B}_{z+}{dA},\qquad {\phi }_{{zn}}=\int {B}_{z-}{dA},\end{eqnarray} \tag{ 2 }$

where ${B}_{z+}$ / ${B}_{z-}$ is the positive/negative longitudinal magnetic field and the dA denotes the integrated area (sunspot area).

The transverse magnetic field strength (B_t) is calculated by the following equation:

$\begin{eqnarray}&&{B}_{t}=\sqrt{{{B}_{x}}^{2}+{{B}_{y}}^{2}}\end{eqnarray} \tag{ 3 }$

where B_x and B_y are the horizontal components of a magnetic field in plate coordinates.

The magnetic field inclination angle $(\gamma ,\ \mathrm{unit}\ \mathrm{is}\ \mathrm{degree})$ is calculated by the following equation:

$\begin{eqnarray}&&\gamma =\arctan \left(\displaystyle \frac{{B}_{t}}{| {B}_{z}| }\right)\cdot \left(\displaystyle \frac{180}{\pi }\right),\end{eqnarray} \tag{ 4 }$

where B_t is the transverse magnetic field and B_z is the longitudinal magnetic field.

According to error propagation, the error of a magnetic flux is given by

$\begin{eqnarray}\begin{array}{rcl}{\sigma }_{{\phi }_{z+}} & = & \left(\displaystyle \frac{\partial {\phi }_{z+}}{\partial {B}_{z+}}\right)\cdot {\sigma }_{{B}_{z+}}=\displaystyle \sum {\sigma }_{{B}_{z+}},\\ {\sigma }_{{\phi }_{z-}} & = & \left(\displaystyle \frac{\partial {\phi }_{z-}}{\partial {B}_{z-}}\right)\cdot {\sigma }_{{B}_{z-}}=\displaystyle \sum {\sigma }_{{B}_{z-}},\end{array}\end{eqnarray} \tag{ 5 }$

where ${\sigma }_{{B}_{z+}}$ / ${\sigma }_{{B}_{z-}}$ is the error of the positive/negative longitudinal magnetic field in the sunspot area.

The error of the transverse magnetic field strength $({\sigma }_{{B}_{t}})$ is given by

$\begin{eqnarray}&&{\sigma }_{{B}_{t}}=\left(\displaystyle \frac{\partial {B}_{t}}{\partial {B}_{x}}\right)\cdot {\sigma }_{{B}_{x}}+\left(\displaystyle \frac{\partial {B}_{t}}{\partial {B}_{y}}\right)\cdot {\sigma }_{{B}_{y}}.\end{eqnarray} \tag{ 6 }$

The error of the magnetic field inclination angle (σ_γ) is given by

$\begin{eqnarray}&&{\sigma }_{\gamma }=\left(\displaystyle \frac{\partial \gamma }{\partial {B}_{z}}\right)\cdot {\sigma }_{{B}_{z}}+\left(\displaystyle \frac{\partial \gamma }{\partial {B}_{t}}\right)\cdot {\sigma }_{{B}_{t}},\end{eqnarray} \tag{ 7 }$

where ${\sigma }_{{B}_{z}}$ is the error of the longitudinal magnetic field and ${\sigma }_{{B}_{t}}$ is the error of the transverse magnetic field.

In addition, we traced the photospheric horizontal motions of the plasma flow around the sunspots by the differential affine velocity estimator for vector magnetograms (DAVE4VM) method (Schuck 2008). The SDO/AIA 1600 Å images and the Geostationary Operational Environmental Satellites (GOES) X-ray flux profile of 0.1–0.8 nm are utilized to investigate the role of the solar flare in penumbral decay.

3. Results

3.1. Evolution of AR NOAA 12673

AR NOAA 12673 appeared at the east solar limb on 2017 August 30 and disappeared at the west solar limb on 2017 September 9. AR 12673 was classified as an α magnetic field configuration of the sunspot group and consisted of a simple mature sunspot (S1) with a fully extended penumbra from 2017 August 30 to September 2. Sunspot S1 with positive polarity was located on S08 E11 at 18:46 UT on 2017 September 2 (see Figure 1(a1)).

Figure 1. Evolution of AR NOAA 12673. (a1)–(a8) Continuum intensity images observed by SDO/HMI. The red and blue contours represent the LOS magnetic fields at −800 G and +800 G, respectively. The boxes (black dashed line) in Figure 1(a2), in Figure 1(a4), and in Figure 1(a7) outline the field of view of Figures 2, 9, and 15, respectively. (b1)–(b2) High-resolution TiO images observed by the NVST. An animation of the top SDO/HMI panels is available. The video begins at 2—2017 September 02:00 UT and covers the next five days. The real-time video duration is 18 s. The left panel of the video is the SDO/HMI continuum intensity evolution, while the right panel is of the LOS magnetogram evolution.

(An animation of this figure is available.)

Download figure:

Video Standard image High-resolution image

On 2017 September 3, some new flux emerged as bipoles (labeled "Bipole A" and "Bipole B") near sunspot S1. The small patches in the continuum intensity images showed the footpoints of the emerging magnetic flux. The negative patches of Bipole A and Bipole B moved eastward, and the positive ones moved westward (see Figure 1(a2)). The westward patches gradually combined, and then a C-shaped sunspot (Sc) formed (see Figure 1(a3)). In particular, the penumbra of the C-shaped sunspot appeared in the side toward the magnetic flux emergence. As sunspot Sc gradually got closer to S1, the penumbra of sunspot S1 near the emerging region disappeared. This region was labeled as Region 1 (see the black dashed box in Figure 1(a2)).

In next few hours, AR NOAA 12673 changed rapidly, and the magnetic configuration of the sunspot group gradually developed into a βγ-type. AR 12673 began to erupt in a series of flares on September 4. When AR 12673 went across the visible solar disk, it produced several M-class and X-class flares. Two X-class flares occurred on 2017 September 6. More detailed descriptions of AR 12673 are given by Yang et al. (2017), Verma (2018), Yan et al. (2018), Hou et al. (2018), Shen et al. (2018), and Jiang et al. (2018a, 2018b, 2019).

Around 22:00 UT on 2017 September 3, another small bipole (labeled "Bipole C") emerged around sunspot S1. The patches of Bipole C with negative polarity gradually moved to the northwest and coalesced with the preemerging negative patches of Bipole B (see Figure 1(a3)). These small patches gradually developed into a bigger sunspot (S2) with full penumbra filaments (see Figures 1(a4) and (a5)). After 2017 September 5, sunspot S2 started to decay and gradually lost its penumbra (see Figures 1(a6)–(a8)). The penumbra of S2 on the side away from the flux emergence disappeared earlier than on the other side. This region was labeled "Region 2" (see the black dashed box in Figure 1(a4)).

At around 11:00 UT on 2017 September 4, two new bipoles appeared (labeled "Bipole D" and "Bipole E"; see Figure 1(a4)). The positive footpoints of Bipole D gradually moved southward and combined to form a small positive sunspot (S3p; see high-resolution observations of TiO images in Figures 1(b1)–(b2)). The southward motion of Bipole D was blocked by the negative sunspot S3n. Then the negative sunspot S3n gradually disappeared, and the penumbra of sunspot S3p began to decay. In the end, the negative sunspot S3n almost completely disappeared, and the positive sunspot S3p became a naked pore (see Figures 1(a5)–(a8)). This region was labeled as "Region 3" (see the black dashed box in Figure 1(a5)).

The following sections discuss the evolution of sunspot penumbrae in these three regions. In Region 1, we study the formation of the penumbra in sunspot Sc and the disappearance of the penumbra in sunspot S1. In Region 2, we present the evolution of sunspot S2, including its penumbra formation and decay. In Region 3, we discuss the penumbra decay of sunspots S3n and S3p. For comparison, we also discuss the photospheric magnetic field properties in the umbra during the evolution of these sunspots.

3.2. Evolution of Sunspots in Region 1

Figure 2 shows the formation of the penumbra in Sc and the disappearance of the penumbra in S1 with continuum intensity images ((a1)–(a4)), longitudinal magnetic field maps ((b1)–(b4)), transverse magnetic field maps ((c1)–(c4)), and magnetic inclination angle maps ((c1)–(c4)).

From the continuum intensity images and the longitudinal magnetic field maps (see in Figures 2(a1)–(a4) and (b1)–(b4)), we see that the patches of Bipoles A and B with positive polarity merged and formed a C-shaped sunspot, Sc. Before the appearance of the penumbra in Sc, there were some elongated granules along the direction connecting two opposite polarities of Bipoles A and B (see the black arrows in Figure 2(a2)). At around 18:00 UT, sunspot Sc formed a relatively stable structure, including an umbra and a penumbra. During this process, the magnetic field strength of the patches gradually increased with time, especially the side toward sunspot S1. It is noticed that Sc did not have any penumbra on the side toward S1. When sunspot Sc gradually approached S1, the left (east) penumbra of S1 gradually disappeared.

From the maps of the transverse magnetic field (see Figures 2(c1)–(c4)), we see that the transverse magnetic field strength of Sc increased with time during the formation of Sc, especially on the side away from S1. The penumbra had a stronger transverse magnetic field than the umbra. From the maps of magnetic inclination angle (see Figures 2(d1)–(d4)), the magnetic inclination angle in the umbra was small and changed little. However, the magnetic inclination angle in the penumbra was big and gradually increased with time. During the formation of Sc, a more and more horizontal magnetic field appeared in the penumbra.

Figure 3 shows the variations of the area, the total positive magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the penumbra and umbra during the formation of Sc. The black and blue solid curves show the variations in the umbra and penumbra of Sc, respectively.

From 09:00 UT to 12:48 UT on September 3, Sc had a small umbra. After 12:48 UT, the umbra gradually grew in area. During the formation of Sc, the area, the total positive magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the umbra of Sc increased with time. The mean transverse magnetic field strength in the umbra increased from 500 G at 12:48 UT to 700 G at 14:36 UT. After that, the value of the mean transverse magnetic field strength in the umbra remained at around 650–700 G. Similarly, the magnetic inclination angle in the umbra increased from around 15° at 12:48 UT to 20° at 14:36 UT. Then the magnetic inclination angle in the umbra remained at 20° (see black curves in Figure 3). The growth range of the mean magnetic inclination angle in the umbra is within the errors (the error of the mean magnetic inclination angle is about 2°–5°). The increase is uncertain owing to the errors of the magnetic inclination angle. The mean magnetic inclination angle in the umbra may remain constant during the formation of the penumbra.

The area, the total positive magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the penumbra increased with time during the formation of Sc. As the formation of the penumbra was accompanied by the ongoing emerging flux, the penumbra of Sc did not develop at the expense of the umbral magnetic flux. The continuous emerging flux can provide enough magnetic flux for penumbral formation. During the formation of Sc, the mean transverse magnetic field strength in the penumbra increased from about 600 G at 09:00 UT to around 800 G at 14:36 UT, and then slowly increased to above 1000 G at 20:00 UT. The mean magnetic inclination angle in the penumbra increased from below 30° at 09:00 UT to about 45° at 14:36 UT, and then remained at around 50° (see blue curves in Figure 3). The magnetic field in the penumbra became more horizontal during the formation of Sc.

Figure 4 shows the dependencies of the area and the total magnetic flux/mean longitudinal magnetic field strength/mean transverse magnetic field strength, the mean magnetic inclination angle, and the mean total magnetic field strength during the formation of Sc. The upper and lower panels in Figure 4 show these correlations in the penumbra ((a1)–(a4)) and umbra ((b1)–(b4)), respectively. The dashed lines in each panel represent the linear fitting results of minimizing the chi-squared error statistic. The letter "R" represents the linear correlation coefficient of two parameters. The color of the symbol represents the evolution with time. The blue and red symbols respectively indicate the start and end times. Note that the dashed lines, the letter "R," and the colors in Figures 12, 13, and 18 have the same meaning as in Figure 4.

In the penumbra of Sc, the magnetic flux and the mean transverse magnetic field strength increased with the increasing penumbral area (Figures 4(a1) and (a3)). The mean longitudinal field strength (Bz) in the penumbra decreased with increasing penumbral area (Figure 4(a2)). During the formation of sunspot Sc, the mean total magnetic field strength (B) in the penumbra almost kept a constant value with the increasing magnetic inclination angle (Figure 4(a4)). The constant mean magnetic field strength is about 1.3 KG. The increase of the mean magnetic inclination angle in the penumbra is from 30° to 55°. These results imply that some of the relatively vertical magnetic lines in the penumbra became more horizontal during the process of penumbral formation.

For the umbra, the magnetic flux and the mean longitudinal/transverse magnetic field strength increased with the increasing umbral area (Figures 4(b1)–(b3)). The mean total magnetic field strength increased with the increasing mean magnetic field inclination in the umbra (Figure 4(b4)). The mean total magnetic field strength increased from around 1.5 to 1.8 KG, and the growth range of the mean magnetic inclination angle in the umbra is around 15°–20°. The increase in the mean magnetic inclination angle in the umbra is small. During the formation of Sc, the dependence of the area and the mean longitudinal field strength in the umbra is different from that in the penumbra. The growth range of the mean magnetic inclination angle in the umbra (5°) is smaller than that in the penumbra (25°). The mean total magnetic field strength in the penumbra almost kept a constant value (1.3 KG); however, the mean total magnetic field strength in the umbra increased around 300 G.

As shown in Figures 2(a1)–(a4), when Sc gradually approached S1, the left (east) penumbra of S1 gradually disappeared. The disappearance of the penumbra of S1 has a close relationship with the evolution of Sc. Figure 5(a) shows the time–distance diagram by using the continuum intensity images along the slit across S1 marked by the black line in Figure 2(a4). As seen in the time–distance diagram, Sc approached S1 at a rate of about 486 m s⁻¹ during 11:00 UT to 20:00 UT on September 3. The left penumbra of S1 started to get shorter at around 13:00 UT. After 18:00 UT, the left penumbra of S1 almost disappeared. Interestingly, the umbra in the left side of S1 and the penumbra in the right side of S1 seem to increase in area.

In order to address the area change of S1 in detail, sunspot S1 was divided into left and right sectors according to its gravity center with the red vertical dashed line shown in Figure 2(a1). Figures 5(b1)–(b3) show the relationships between the total area of Sc and the area in each sector of S1. The total area of the sunspot is defined as the area in the continuum intensity images darker than 0.85 I₀.

Although the total area of S1 changed little when the total area of Sc increased (+ symbols in Figure 5(b1)), the sunspot S1 indeed lost a part of its penumbra with the development of Sc. During the formation of Sc, the area in the left sector of S1 decreased (∗ symbols) and in the right sector of S1 increased (× symbols) with the increasing total area of Sc. This opposite change in the left and right sectors may be the reason why the total area of S1 kept a constant value.

Figure 5(b2) shows the relationships between the total area of Sc and the penumbral area in each sector of S1. The total penumbral area of S1 decreased a little when the area of Sc increased (+ symbols). The penumbral area in the left sector decreased (* symbols) and in the right sector increased (× symbols) with the increasing total area of Sc. Figure 5(b3) shows the relationships between the total area of Sc and the umbral area in each sector of S1. The umbral area in each sector of S1 has no notable change with the increasing total area of Sc (Figure 5(b3)). The total umbral area of S1 (+ symbols), the umbral area in the left sector (∗ symbols), and the umbral area in the right sector (× symbols) of S1 increased a little when the area of Sc increased. With the growth of area in Sc, the closer Sc got to S1 and the more penumbral area in the left sector of S1 disappeared. Meanwhile, the penumbra in the right sector of S1 and the umbra in the whole S1 grew.

Figure 6 shows the variations of the mean magnetic inclination angle, mean transverse magnetic field strength, and mean longitudinal magnetic field strength in the penumbra (a1)–(a3) and umbra (b1)–(b3) during the disappearance of the penumbra of S1. The black and blue curves show the variations of the left sector and right sector of S1, respectively.

In the penumbra of S1, the mean longitudinal magnetic field strength in the left sector increased from 800 G at 09:00 UT to 1100 G at 20:00 UT; however, it decreased from 700 G at 09:00 UT to 550 G at 20:00 UT in the right sector (see Figure 6(a1)). The mean transverse magnetic field strength/mean magnetic inclination angle in the penumbra of the left sector decreased from around 1000 G/57° at 09:00 UT to 900 G/40° at 20:00 UT, but it increased from around 1000 G/60° at 09:00 UT to 1050 G/65° at 20:00 UT in the penumbra of the right sector (see Figures 6(a2) and (a3)). Although the increase of the mean transverse magnetic field strength/mean magnetic inclination angle in the penumbra of the right sector is within their errors, it is notable that the mean longitudinal magnetic field in the right sector is decreasing. The magnetic field of the penumbra became more vertical in the left sector and became more horizontal in the right sector during the disappearance of the penumbra of S1.

In the umbral region, the mean longitudinal magnetic field strength in the left sector/right sector increased from 2040 G/2060 G at 09:00 UT to 2080 G/2120 G at 20:00 UT (see in Figure 6(b1)). The mean transverse magnetic field strength/mean magnetic inclination angle decreased from 840 G/23° at 09:00 UT to 675 G/19° at 20:00 UT in the umbra of the left sector; however, it increased from 700 G/19° at 09:00 UT to 1025 G/26° at 20:00 UT in the umbra of the right sector (see Figures 6(b2) and (b3)). Although the variations of the mean magnetic inclination angles and the mean longitudinal magnetic field strength in the umbra are within the errors, the trend of the mean transverse magnetic field strength in the umbra is clear. The mean transverse magnetic field strength decreased in the left umbra while it increased in the right umbra. In summary, the magnetic field in the left sector of S1 became more vertical and it became more horizontal in the right sector of S1, especially in the penumbra. The rearrangement of the magnetic field occurred not just in the left sector but in the entire sunspot S1 simultaneously. Furthermore, the rearrangement in the magnetic field of sunspot S1 caused the disappearance of the penumbra in the left sector and the growth of the penumbra in the right sector.

Figure 7 shows the variations of the mean longitudinal magnetic field strength, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the blue-dotted region and the red-dotted region during the disappearance of the left penumbra. The blue-dotted region denotes the area where the penumbra disappeared in the left sector of S1 at 20:00 UT (see the blue dots in Figure 7(a3)). The red-dotted region is the place where the penumbra in the left sector of S1 still remained at 20:00 UT (see the red dots in Figure 7(a3)).

In the blue-dotted region, the mean longitudinal magnetic field strength increased from 300 G at 09:00 UT to 400 G at 20:00 UT, and the mean transverse magnetic field strength/mean magnetic inclination angle decreased from 850 G/70° at 09:00 UT to 450 G/45° at 20:00 UT (see the blue curves in Figures 7(b)–(d)). In the red-dotted region, the mean longitudinal magnetic field strength increased from 700 G at 09:00 UT to 1200 G at 20:00 UT, and the mean transverse magnetic field strength/mean magnetic inclination angle decreased from 1050 G/60° at 09:00 UT to 850 G/35° at 20:00 UT (see the red curves in Figures 7(b)–(d)). The varying trend of the blue-dotted region is consistent with that of the red-dotted region. During the whole process of penumbral disappearance, the mean magnetic inclination angle in the blue-dotted region is larger than that in the red-dotted region. The strength of the mean transverse magnetic field and the mean vertical magnetic field in the blue-dotted region is weaker than in the red-dotted region. These results indicate that the magnetic field in the left penumbra of sunspot S1 gradually became more and more vertical from east to west during the disappearance of the left penumbra.

Figure 8 shows the horizontal motion around sunspots (S1 and Sc) derived by DAVE4VM. The prominent flow features around the sunspot were a strong outward flow. Before the new flux emerged, the outward flow (moat flow) encircled sunspot S1 (see Figure 8(a1)). With the approach of emerging patches, the outward flow in the left side of S1 was diminished. However, the outward motions continued in the other side (see Figures 8(a2)–(a5)). When sunspot Sc got closer to S1, the outward flow in the left side of S1 gradually vanished (see Figure 8(a6)).

3.3. Evolution of a Sunspot in Region 2

Figure 9 shows the evolution of sunspot S2 in Region 2 in the continuum intensity images and the longitudinal magnetic field maps. The blue and black contours represent the boundaries of the penumbra and umbra. SDO observations covered the evolution of S2 from its formation to its decay because S2 evolved quickly.

The formation of S2 originated from the combination of small pores, which was due to the movement of the footpoints of the newly emerging magnetic bipoles. These magnetic bipoles connected the negative sunspot S2 and the positive region near sunspot S1. Some elongated granules were observed between two separating polarities (see the black arrows in Figure 9(a1)). The growth of sunspot S2 was accompanied by the emerging magnetic flux. The penumbra first formed facing the side of flux emergence (see the red arrows in Figure 9(a2)). At around 11:00 UT on September 4, a complete sunspot S2 surrounded by a full penumbra had formed. There were still some emerging patches around the complete sunspot S2 (see the black arrows in Figure 9(a4)). The polarities of these patches are opposite (see Figure 9(b4)). The bipolar patches can be interpreted as being produced by sea serpent field lines (Sainz Dalda & Bellot Rubio 2008). With the approach of these patches, a part of the penumbra of S2 disappeared. Then the emerging patches gradually merged with the umbra, and the shape of the umbra changed (see the black arrows in Figures 9(a4)–(a6)).

As a light bridge appeared in the middle of the umbra of S2 at around 05:00 UT on September 5, the sunspot S2 started to decay (see the red arrows in Figure 9(a7)). S2 was completely divided into two parts (north part and south part) at 17:00 UT on September 5 (see Figure 9(a9)). Then the south and north parts of S2 gradually lost their penumbra. The penumbra of S2 on the opposite side of the flux emergence disappeared first (see Figure 9(a10)).

Figure 10 shows the variations of the area, the total negative magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the umbra (black solid curves) and penumbra (blue solid curves) during the evolution of sunspot S2.

The formation phase of S2 occurred from 20:00 UT on September 3 to 06:00 UT on September 5. According to the growth trend of the penumbral area, the penumbral formation process can be divided into two stages: a rapidly growing stage and a relatively slow development stage. In the rapidly growing stage, the area of the penumbra increased from 70 Mm² at 20:00 UT on September 3 to around 200 Mm² at 06:00 UT on September 4 (170 Mm² in 10 hr). In the slow development stage, the area of the penumbra increased from 200 Mm² at 06:00 UT on September 4 to around 380 Mm² at 06:00 UT on September 5 (180 Mm² in 24 hr).

In the rapidly growing stage (from 20:00 UT on September 3 to 06:00 UT on September 4) in the region of the umbra, the area, the magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle rapidly increased with time (see the black curves in Figures 10(a)–(d)). Similarly, the area, the magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the penumbra also rapidly increased (see the blue curves in Figure 10(a) and (d)).

In the slow development stage (from 08:36 UT on September 4 to 06:00 UT on September 5), the area, the magnetic flux, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the umbra and penumbra changed with a relatively slow rate, especially the mean transverse magnetic field strength and the mean magnetic inclination angle. During the slow development stage, the mean transverse magnetic field strength in the penumbra remained at around 900–1000 G, and the mean magnetic inclination angle in the penumbra remained at around 56°–60°. The mean transverse magnetic field strength in the umbra remained at around 800 G, and the mean magnetic inclination angle in the umbra remained at around 23° from 08:36 UT on September 4 to around 00:00 UT on September 5. Then the mean transverse magnetic field strength and the mean magnetic inclination angle in the umbra decreased from 800 G at 00:00 UT to 650 G at 06:00 UT on September 5.

The decay phase of sunspot S2 occurred from 08:36 UT on September 5 to 04:00 UT on September 6. From 08:36 UT to 17:00 UT on September 5, the area and total negative magnetic flux of the umbra decreased with time. However, at the same time, the area and total negative magnetic flux in the penumbra continued to increase. During this period, the flux emergence was not as active as the period of penumbral formation. The penumbra may develop at the expense of the umbral magnetic flux. When the umbra completely split into two parts at 17:00 UT, the area and total negative magnetic flux of the umbra picked up. In the meantime, the area and total negative magnetic flux of the penumbra began to decrease. The umbra may recover at the cost of the penumbral magnetic flux. The mean transverse magnetic field strength and the mean magnetic inclination angle both in the umbra and penumbra gradually decreased during the whole decay phase. The magnetic field of the umbra and penumbra became more horizontal during the decay of S2.

Figure 11 simply shows the relationship between the evolution of S2 and the flare in AR. The blue curve in Figure 11(a) indicates the GOES X-ray flux profile of 0.1–0.8 nm from 20:00 UT on September 3 to 04:00 UT on September 6. The information on solar flares can be extracted from the GOES flare catalog. The black curve shows the evolution of total area in S2. Although a series of flares occurred in AR NOAA 12673 during the evolution of S2, the evolution of total area in S2 had no abrupt change after the flares. Some brightening can be found in the vicinity of S2 during flares, like the M5.5 flare (see 11(b2)), and the flares may affect the magnetic field in the vicinity of S2. Because of the active surroundings, the sunspot cannot be stable. The lifetime of S2 is obviously shorter than that of a typical mature sunspot. Sunspot formation typically takes hours to days, while sunspot decay takes longer, typically weeks to months (Hathaway & Choudhary 2008).

Figure 12 shows the correlations of the area and the total magnetic flux/mean longitudinal magnetic field strength (Bz)/mean transverse magnetic field strength (Bt), the mean magnetic inclination angle, and the mean total magnetic field strength during the formation of S2. The upper panels ((a1)–(a4)) and lower panels ((b1)–(b4)) in Figure 12 show these correlations in the penumbra and umbra of S2, respectively.

In the penumbra of S2, the magnetic flux increased with increasing penumbral area (Figure 12(a1)). The mean longitudinal field strength (Bz) in the penumbra decreased with increasing penumbral area (Figure 12(a2)). The relationship between the mean transverse magnetic field strength and the area in the penumbra was divided into three stages. The first one is from 20:00 UT on September 3 to 06:00 UT on September 4, the rapidly growing stage of S2. The second one is from 08:36 UT on September 4 to 00:00 UT on September 5. The third one is from 00:00 UT on September 5 to 06:00 UT on September 5. The mean transverse magnetic field strength increased with the increasing penumbral area during the first stage, decreased during the second stage, and increased during the third stage (Figure 12(a3)). This transition of the tendency in transverse magnetic field may be influenced by the emerging intensity of the magnetic flux. At the initial stage, a lot of new flux emerged near sunspot S2, and the transverse magnetic field in S2 increased rapidly. However, subsequently, the new emerging magnetic flux became less and the transverse magnetic field in S2 started to decrease. At around 00:00 UT on September 5, some emerging paths merged with S2, and then the mean transverse magnetic field strength increased. The relationship between the mean total magnetic field strength (B) and the magnetic inclination angle in the penumbra was divided into two stages. The first one is from 20:00 UT on September 3 to 06:00 UT on September 4, the rapidly growing stage of S2. The second one is from 08:36 UT on September 4 to 06:00 UT on September 5, the slow development stage. The mean total magnetic field strength in the penumbra decreased a little with the increasing magnetic inclination angle in the rapidly growing stage of S2. It remained at around 1.09 KG, and the magnetic inclination also remained around 55°–60° during the slow development stage (Figure 12(a4)).

In the umbra of S2, the magnetic flux increased with the increasing umbral area (Figure 12(b1)). The time division in Figures 12(b2)–(b4) is the same as in Figure 12(a3). The mean longitudinal field strength in the umbra increased with the increasing umbral area in the first stage, remained constant (1.97 KG) in the second stage, and decreased in the third stage (Figure 12(b2)). Similarly, the mean transverse magnetic field strength in the umbra increased with the increasing umbral area in the first stage, remained constant (0.88 KG) in the second stage, and decreased in the third stage (Figure 12(b3)). It was the same as the dependence of the penumbral area and the mean transverse magnetic field strength in the penumbra of S2, except in the third stage. The mean total magnetic field strength in the umbra increased with the increasing mean magnetic inclination angle of the umbra in the first stage and decreased in the third stage (Figure 12(b4)).

Figure 13 shows the relationships between the area and the total magnetic flux/mean longitudinal magnetic field strength (Bz)/mean transverse magnetic field strength (Bt), the mean magnetic inclination angle, and the mean total magnetic field strength during the decay of S2. The upper panels ((a1)–(a4)) and lower panels ((b1)–(b4)) in Figure 13 show these relationships in the penumbra and umbra of sunspot S2, respectively. It is worth noting that the area of S2 decreased during its decay, and the values of the X-axis in Figure 13 go from big to small.

In the penumbra of S2, the relationship between the magnetic flux and the area in the penumbra was divided into two stages: the first one is from 08:36 UT on September 5 to 14:00 UT on September 5, and the second one is from 14:00 UT on September 5 to 04:00 UT on September 6. The magnetic flux increased with the increasing penumbral area in the first decay stage, and decreased with decreasing penumbral area in the second decay stage (Figure 13(a1)). Although the area of the umbra in S2 began to decrease in the first stage, the area of the penumbra of S2 still increased. The mean longitudinal field strength in the penumbra gradually increased with the decreasing penumbral area (Figure 13(a2)). The same occurred in Figure 13(a1): the mean transverse magnetic field strength in the penumbra increased with the increasing penumbral area in the first stage. Then it decreased with the decreasing penumbral area in the second stage (Figure 13(a3)). During the decay of sunspot S2, the mean total magnetic field strength (B) in the penumbra changed little with the decreasing magnetic field inclination (Figure 13(a4)). The mean magnetic field strength remained at 1.1 KG. During the decay of the penumbra, some of the horizontal magnetic lines in the penumbra became more vertical.

During the decay of S2, the magnetic flux in the umbra decreased with decreasing umbral area (Figure 13(b1)). The relationship between the umbral area and the mean longitudinal/transverse magnetic field strength and between the mean total magnetic field strength and the mean magnetic inclination angle of umbra are not notable. Their correlation coefficients are small (Figures 13(b2)–(b4)).

Figures 14(a1)–(a5)) show the variety of the horizontal motion around S2 during the formation of S2. Sunspot S2 formed in flux emergence. When S2 was a pore (the penumbra of S2 did not form), the moat flow of S2 was absent (see Figure 14(a1)). There was a strong flow in S2, which was mainly caused by the strong flux emergence. During the formation of S2, the outward flow of S2 gradually appeared at the nearest sunspot–granular boundary, and its velocity was gradually increased (see Figures 14(a1)–(a5)). When S2 was basically formed, the outward flow partly encircled S2. However, the outward flow was absent in the flux emergence (see the yellow arrow in Figure 14(a3)). With the development of S2, the outward flow did not appear at the side facing the emerged flux. In addition, the typical line, which demarcated radial inflows in the inner and outflow in the outer penumbra (Sobotka et al. 1999), was absent in that side. The strong emerging flow was dominant in this side of S2 (see the yellow arrow in Figure 14(a4)). Figures 14(a6)–(a8)) show the horizontal motion around S2 during the decay of S2. During the decay of S2, the dividing line between inward and outward proper motions in the penumbra (Deng et al. 2007) was not found either in the side of flux emergence (see the yellow arrow in Figure 14(a6)). The newly emerging flux destroyed the moat flow around S2 (see the green arrow in Figure 14(a6)). On the other side away from the flux emergence, the outward flow seemed to continue but the flow speed was lower (see Figures 14(a6)–(a8)).

**Figure 14.** Horizontal velocity in the photosphere in Region 2 derived by DAVE4VM. The background image shows the vertical magnetic field with the positive field in white and negative field in black. The arrows represent horizontal velocity. Blue (red) arrows indicate that the vertical magnetic fields in the pixels are positive (negative).
Download figure:
Standard image High-resolution image

3.4. Decay of Sunspot Penumbra in Region 3

Figure 15 shows the decay process of sunspots in Region 3 from 03:00 UT on September 6 to 02:00 UT on September 7. Figures 15(a1) and (b1) show the location of Region 3 in AR NOAA 12673. There were two opposite-polarity developing sunspots (S3p and S3n) in Region 3 (see Figures 15(a2) and (b2)). When the positive patches of Bipole D moved toward the preexisting negative one, S3n, the negative sunspot S3n lost its penumbra and disappeared (see Figures 1(a4)–(a8)). The positive sunspot S3p eventually became a small pore (see Figures 15(a3) and (b3)). During this process, the positive and negative magnetic flux in the sunspot group (S3p and S3n) decreased with time (see in Figure 15(c)). The result implies that the decay of this sunspot group was accompanied by magnetic cancellation.

Figure 16 shows the variations of the area, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the umbra (the black solid curves) and penumbra (the blue solid curves) of the sunspot group during the decay of the sunspot group. Because it is difficult to distinguish the boundary between the positive and negative sunspots in the continuum intensity images, the umbral area represents the total area of the two sunspots' umbrae. The penumbral area is the same as the umbral area, but for the total area of the two sunspots' penumbrae.

During the decay of the sunspot group, the area, the mean transverse magnetic field strength, and the mean magnetic inclination angle in the umbra and penumbra all decreased with time. The area in the umbra remained constant (around 23 Mm²) from 03:00 UT to 12:00 UT on September 6. During this period, the mean transverse magnetic field strength in the umbra remained at 600 G, and the mean magnetic inclination angle remained at 20°. After 12:00 UT, the area in the umbra rapidly decreased from 20 Mm² at 12:00 UT on September 6 to around 5 Mm² at 01:00 UT on September 7. The mean transverse magnetic field strength in the umbra decreased from 600 G at 12:00 UT on September 6 to 400 G at 01:00 UT on September 7. The mean magnetic inclination angle decreased from 20° at 12:00 UT on September 6 to 10° at 01:00 UT on September 7. For the penumbra, the area decreased from 160 Mm² at 03:00 UT to 120 Mm² at 06:00 UT on September 6. Then it remained at 120 Mm² until 12:00 UT. Then the area of the penumbra rapidly decreased from 120 Mm² at 12:00 UT on September 6 to around 20 Mm² at 01:00 UT on September 7. The mean transverse magnetic field strength in the penumbra remained at 900 G, and the mean magnetic inclination angle remained at 32° during 03:00 UT to 12:00 UT on September 6. After 12:00 UT, their values decreased (see Figures 16(a)–(c)).

Figure 17 simply shows the relationship between the evolution of S3 and the flare in the AR. The blue curve in Figure 17(a) indicates the GOES X-ray flux profile of 0.1–0.8 nm during the evolution of S3. There were two X-flares in NOAA 12673 during 08:36 UT to 12:10 UT. Although the big flare did not erupt in Region 3 (see the red box in Figure 17(b0)), the rapid variation in the area and transverse magnetic field of the sunspot group occurred after the flare (after 12:00 UT as shown in Figure 16). The rapid decay of S3 may be related to the flare.

Figure 18 shows the correlations of the area and the total magnetic flux/mean longitudinal magnetic field strength (Bz)/mean transverse magnetic field strength (Bt), the mean magnetic inclination angle, and the mean total magnetic field strength in the penumbra ((a1)–(a4)) and umbra ((b1)–(b4)) during the decay of the sunspot group.

Although the sunspots in Region 3 cannot be distinguished in the continuum intensity images, the positive and negative magnetic fluxes of the sunspot group can be calculated separately. The "+" symbols and "△" symbols in Figure 18(a1)/(b1) respectively represent the positive and negative magnetic flux in the penumbra/umbra of the sunspot group. The "×" symbols and " $\diamond$ " symbols in Figure 18(a2)/(b2) respectively represent the mean positive and negative longitudinal field strength in the penumbra/umbra of the sunspot group.

During the decay of S3, the negative/positive magnetic flux in the penumbra decreased with decreasing penumbral area (see Figure 18(a1)). In the penumbra, the mean positive longitudinal magnetic field strength increased and the mean negative longitudinal magnetic field strength decreased with the decreasing penumbral area (see in Figure 18(a2)). The smallest value of the mean negative longitudinal magnetic field strength was 0 KG, which we did not plot in the figure. This change tendency of the mean longitudinal magnetic field strength is consistent with the fact that the negative sunspot S3n almost completely disappeared and the positive S3p became a small naked pore at the end of the observational time. The mean transverse magnetic field strength decreased with the decreasing penumbral area (see Figure 18(a3)). The magnetic field line in the penumbra became more vertical during the decay of S3. The relationship between the mean total magnetic field strength and the magnetic inclination angle in the penumbra is not notable; the correlation coefficient is small (Figure 18(a4)).

The negative/positive magnetic flux in the umbra of S3 decreased with the decreasing umbral area (see Figure 18(b1)). The mean positive/negative longitudinal magnetic field strength decreased with the decreasing umbral area. The correlation coefficient of the mean positive longitudinal magnetic field strength and the umbral area is higher than that of the mean negative longitudinal magnetic field strength and the umbral area (see Figure 18(b2)). The mean transverse magnetic field strength in the umbra decreased with the decreasing umbral area during the decay of S3 (see Figure 18(b3)). The correlation between the mean total magnetic field strength and the magnetic inclination angle in the umbra was not significant; the correlation coefficients are small (see Figure 18(b4)). Basically, the mean total magnetic field strength and the magnetic field inclination in the umbra were gradually reduced during the decay of S3.

Figures 19(a1)–(a4)) show the variety of the horizontal motion around S3 during the decay of S3. The prominent outward flow around the sunspot was not found in the surroundings of S3. In addition, the typical inflows in the inner and outward flows in the outer penumbra were absent in the region of S3. The strong emerging flow around S3 was dominant.

**Figure 19.** Horizontal velocity in the photosphere in Region 3 derived by DAVE4VM. The background image shows the vertical magnetic field with the positive field in white and negative field in black. The arrows represent horizontal velocity. Blue (red) arrows indicate that the vertical magnetic fields in the pixels are positive (negative).
Download figure:
Standard image High-resolution image

4. Conclusion

Three regions in AR NOAA 12673 were chosen to analyze the formation and decay of a sunspot penumbra and umbra. The main results are as follows:

1.
The formation of a penumbra in Sc and S2 was accompanied by a continuous emerging flux. The penumbra of Sc and S2 first formed facing the side of flux emergence. The formation of the penumbra was involved in two magnetic field systems: the continuous emerging magnetic field and the preexisting magnetic field. The new emerging flux was trapped at the photosphere by the preexisting magnetic field.
2.
The magnetic field in the left penumbra of S1 gradually became more and more vertical during the disappearance of its left penumbra. The rearrangement in magnetic field caused the disappearance of the left penumbra of S1 and the growth of the right penumbra.
3.
The penumbra of S2 on the side opposite to flux emergence disappeared first. The mean longitudinal magnetic strength in the penumbra increased and the mean transverse magnetic strength in penumbra decreased with decreasing penumbral area during the decay of S2. When sunspot S2 decayed, some of the horizontal magnetic lines in the penumbra became more vertical.
4.
The decay of S3 was accompanied by magnetic cancellation. The abrupt variation in the area and transverse magnetic field strength of S3 occurred after the X9.3 flare.
5.
The dominant moat flow around sunspot S2 appeared gradually with the formation of the penumbra. During the decay of the penumbra, the outward flow first vanished on the side of the magnetic emergence region, and its speed gradually decreased.

5. Discussion

Many previous results demonstrated that the formation of a penumbra may be due to the emerging magnetic flux trapped at the photosphere. The preexisting horizontal field in the chromosphere acts as a suppressor of the emerging flux (Leka & Skumanich 1998; Shimizu et al. 2012; Romano et al. 2013). The importance of the overlying chromospheric field for the formation of the penumbra was demonstrated in observations (Lim et al. 2013) and in numerical simulations (Rempel 2012). Our observations show that the penumbral formation in sunspots may be formed by the interaction of two magnetic field systems. The penumbral filaments of sunspots formed from the later-emerging magnetic flux that was trapped in the photosphere. The magnetic pressure from the already emerged magnetic field suppressed the later emerging flux.

For our studied cases, the formation of the penumbra in Sc and S2 was accompanied by a continuous emerging flux. The formation of Sc was involved in the continuous emerging magnetic field (Bipole A and Bipole B) and the preexisting sunspot's magnetic field (S1). The magnetic pressure from the existence of the magnetic field hindered the upward motion of the later-emerging magnetic field. The ongoing emerging magnetic flux was trapped in the photosphere, resulting in the penumbral formation of Sc. A cartoon is drawn to show the penumbral formation of Sc and the penumbral disappearance of S1. The blue and red patches indicate the positive and negative polarities. The dark and the gray area indicate the umbra and penumbra of the sunspot (see Figures 20(a1)–(a3)). The penumbral formation of sunspot S2 was also related to two magnetic field systems: the already emerged magnetic field systems (Bipole B) and the later-emerging magnetic field (Bipole C; see Figure 20(b1)). As the later-emerging magnetic flux of Bipole C merged with the preexisting small patches of Bipole B, the total magnetic flux of the pore gradually increased, and the outermost magnetic field lines of the pore changed from vertical to horizontal. And then the later-emerging magnetic field was gradually trapped in the photosphere by the already emerged magnetic field systems. Cartoons in Figures 20(b1)–(b3) show the formation of the penumbra in S2.

**Figure 20.** Sketch of the magnetic field configuration during the evolution of sunspots in the three regions. (a1)–(a2) Region 1, the disappearance of the penumbra in S1 and the formation of the penumbra in Sc. (b1)–(b3) Region 2, the formation of the penumbra in S2. (c1)–(c3) Region 3, the penumbral decay of sunspots S3n and S3p.
Download figure:
Standard image High-resolution image

According to the results of Kitai et al. (2014), the sunspot penumbra can be formed by active accumulation of magnetic flux (the moving magnetic flux concentrations combined to form a denser magnetic concentration), rapid emergence of magnetic fields (new magnetic flux of the same polarity), and twisted or rotating magnetic flux tubes (the penumbrae are seen to be rotating with respect to the radial direction from the umbra center). AR NOAA 12673 belongs to the category of rapid emergence of magnetic field accumulation to form a sunspot: the rapid emergence of the small-scale bipole flux. The small-scale bipole that appears around the sunspot can make a significant contribution to the formation of the sunspot penumbra. Due to the ongoing emerging flux of the bipole, the magnetic flux in the sunspot umbra and penumbra increased with evolution time. As the two polarities of the bipole move away from each other, the magnetic lines connecting the bipole are elongated and become more and more horizontal. The penumbra can easily form in the region between the bipoles.

The role of the newly emerging bipole flux in penumbral formation and decay may depend on its polarities and the polarity of the adjacent sunspot. There are three different situations. First, if the polarity of one of the bipoles approaching the adjacent sunspot is the same as that sunspot and they do not merge together, the penumbra filaments of the emerging polarity first appear along the direction of its movement. The penumbra of the adjacent sunspot facing the emerging bipole will disappear (like the case in Region 1). Second, if the polarity of one of the bipoles approaching the adjacent sunspot is the same as that sunspot and they merge, the penumbra filaments of the adjacent sunspot first appear at the merging place (like the case in Region 2). Third, if the polarity of one of the bipoles approaching the adjacent sunspot is opposite that of the sunspot, it will cause the disappearance of the penumbra between the emerging magnetic bipole and the adjacent sunspot (like the case in Region 3). Whatever the case, the ongoing flux around the sunspot indeed affects the evolution of the penumbra. For sunspot S2, the penumbra only partly encircled its umbra, and the penumbra and moat flow in the side near the flux emergence were absent. It was hard for S2 to sustain its stability without a stable penumbra.

Rapid penumbral decay and umbral strengthening after a solar flare are often observed (Wang et al. 2004, 2012; Deng et al. 2005 ). The effect of a flare on the sunspot is rapid and could change the sunspot's area suddenly. The rapid rearrangement of a sunspot's magnetic field could induce the disappearance of the sunspot's penumbra after the solar flare. Verma et al. (2018) focused on a decaying sunspot with high-resolution observations. A darkened area with the same properties as an umbra was found in the decaying penumbra. They proposed that the horizontal magnetic fields in a decaying penumbra became vertical. This process is the same as the flare-induced rapid penumbral decay, only on a different timescale. In our studies, the decay of a penumbra is closely related to the rearrangement of its magnetic field lines.

For sunspot S1, the disappearance of the penumbra in S1 stems from the change in magnetic field direction. When the newly emerging flux collided with S1, the leftmost magnetic field lines of S1 became more and more vertical from east to west. While the magnetic field lines in the left sector of S1 became more vertical, they became more horizontal in the right sector of S1. The changes in magnetic field in the sunspot's penumbra that are induced by the flux emergence affect the development of the sunspot. For sunspots S2 and S3, the penumbral magnetic field also became more vertical during their decay. During the course of the penumbral disappearance, the mean magnetic inclination angle in the penumbra of S2 decreased from 60° to around 45° and that of S3 decreased from 55° to around 35°. A cartoon in Figures 20(c1)–(c3) shows the disappearance of the penumbra of S3.

Moreover, the evolution tendency of area in S2 had no abrupt change after the series of flare eruptions. However, the flares could affect the magnetic field surrounding the sunspots, and then it may affect the evolution of sunspots. Normally, a mature sunspot with an umbra and penumbra lives for hours to months (Hathaway & Choudhary 2008). Sunspot S2 has a shorter lifetime. As soon as the rudimentary structure of S2 was formed, S2 began to decay. The flares may affect the lifetime of sunspots, but more studies are needed to address this issue. After all, the ongoing flux emergence may also affect the lifetime of S2. It is hard to differentiate the effects of the flux emergence and the surrounding magnetic field on the decay of S2. These unstable factors around sunspots likely change the conditions that are needed to sustain a stable sunspot.

Leka & Skumanich (1998) found a self-similarity between a growing pore and a small mature sunspot with respect to the magnetic field strength and the magnetic inclination angle distribution. In their study, the formation of the penumbra was preceded by an increase in the pore's magnetic field strength, and the flux history of the pore-to-sunspot transition was not solely a function of the pore's size, but of initial intensification of the magnetic fields. Jurčák (2011) discussed the distributions of the magnetic inclination angle and the magnetic field strength, the sunspot area and the magnetic field strength, and the sunspot area and the magnetic inclination angle on the penumbral boundaries of mature sunspots. The magnetic field strength and inclination on the outer penumbral boundary decreased with decreasing sunspot area. The vertical component of the magnetic field is independent of the sunspot area. Along the inner penumbral boundary, both the magnetic field strength and inclination on average decreased with the decreasing umbral area. Compared to large umbrae, the boundaries of small umbrae have weaker and more vertical magnetic fields.

In our study, we presented the area and the magnetic flux, the area and the longitudinal magnetic field strength, the area and the transverse magnetic field strength, and the magnetic inclination angle and the magnetic field strength distributions in a penumbra and umbra during the evolution of three sunspots. During the formation of a sunspot, both the mean magnetic flux and the mean transverse magnetic field strength in the penumbra and umbra increased with increasing area. The increase in penumbral area was accompanied by a gradual decrease in longitudinal magnetic field. Instead, the growth of the umbra was accompanied by an increasing longitudinal magnetic field. The total magnetic field strength in the penumbra almost remained constant with the increasing mean magnetic inclination angle. The total magnetic field strength in the umbra increased with the increasing mean magnetic inclination angle. For the case of decaying sunspots, the mean magnetic flux and the mean transverse magnetic field strength in the penumbra and umbra decreased with the decreasing area. The decay of the penumbra was accompanied by an increasing longitudinal magnetic field. The decay of the umbra occurred with a gradually decreasing longitudinal magnetic field.

Conclusions on whether the penumbra developed at the expense of the umbral magnetic flux remain contradictory. Jurčák et al. (2015) proposed that the penumbra developed at the cost of the pore magnetic flux, which supports the result suggested earlier by Watanabe et al. (2014). They found that the umbral area of a sunspot decreased during the formation of its penumbra. However, Schlichenmaier et al. (2010b) found that the umbral area remained a constant value during the formation of a sunspot penumbra. In our study, both the umbral area and the penumbral area of sunspots increased during the penumbral formation of the sunspot. The development of a penumbra was not at the expense of the umbral magnetic flux because the continuous flux emergence can provide sufficient magnetic flux for the development of the penumbra. However, the magnetic flux in the umbra of S2 decreased while the magnetic flux in the penumbra increased during the decay of S2. Simultaneously, the umbral area decreased but the penumbral area developed into its maximum. The penumbra may develop at the expense of the umbral magnetic flux. After the umbra was completely separated into two parts by the light bridge, the area and the magnetic flux of the umbra recovered a little when the area and magnetic flux in the penumbra decreased. The recovery of the umbra may be at the cost of the penumbral magnetic flux. The transformation of magnetic flux between umbra and penumbra is found at the beginning of sunspot decay.

Murabito et al. (2017) suggested that the rising velocity of the magnetic flux bundle may affect sunspot structure and evolution. The complexity of the emerging magnetic field in the pore's surroundings may also influence the development of the penumbra. Botha et al. (2011) presented a study of the decay process of large magnetic flux tubes and found that the decay of the central flux tube relies on its surrounding convection. The convection around large sunspots can change the shape of the central flux tube. The convection and the rising velocity and complexity of the emerging magnetic flux may influence the formation and decay of sunspots. However, how does the emerging magnetic flux or convection affect the penumbral evolution? The answer is still open. We need more observations to confirm the correlation between penumbra formation and the surrounding flux emergence. In the future, we will analyze more examples to address this issue by using high-resolution observations from the NVST and other instruments.

We would like to thank the NVST, SDO/AIA, and SDO/HMI teams for the high-cadence data support. This work is sponsored by the National Science Foundation of China (NSFC) under grant Nos. 11873087, 11603071, 11503080, and 11633008, by the Youth Innovation Promotion Association CAS (No. 2011056), by the Yunnan Science Foundation of China under No. 2018FA001, by the project supported by the Specialized Research Fund for State Key Laboratories, and by the grant associated with the project of the Group for Innovation of Yunnan Province. X.L.Y. thanks ISSI-BJ for supporting him to attend the team meeting led by J. C. Vial and P. F. Chen.

The Formation and Decay of Sunspot Penumbrae in Active Region NOAA 12673

Article metrics

Permissions

Author e-mails

Author affiliations

ORCID iDs

Dates

Abstract

1. Introduction

2. Observations