Statistical investigation on the formation of sunspot light bridges

Light bridges (LBs) are among the most prominent sub-structures in sunspots. In photospheric observations of some sunspots, LBs usually appear as bright elongated structures across an umbra and divide the umbra into multiple parts. Observations have revealed different types of LBs. One type of LBs shows granule-like convective cells, called granular LBs (Lagg et al. 2014). There is another type of LBs named penumbral LBs, which resemble penumbral filaments and often show barb-like features aside (Louis et al. 2008; Rimmele 2008; Bharti 2015; Wang et al. 2018; Hou et al. 2020). Signatures of magnetoconvection, such as dark lanes and dark knots, have been frequently found in some narrow LBs based on recent high-resolution observations (Berger & Berdyugina 2003; Lites et al. 2004; Felipe et al. 2016; Zhang et al. 2018). The magnetic field on LBs is generally believed to be weaker and more inclined compared to the surrounding umbra (Leka 1997; Rimmele 1997, 2004; Falco et al. 2016). However, very strong magnetic field has been occasionally found on LBs. For instance, Castellanos Durán et al. (2020) detected the strongest magnetic field with a strength of 8.2 kG in an LB.

From chromospheric and transition region observations, several types of small-scale dynamic phenomena have been reported on LBs. One prominent phenomenon is the surge-like activity repeatedly occurring above LBs, called Hα surges, light wall oscillations, plasma ejections or chromospheric jets by various authors (Asai et al. 2001; Shimizu et al. 2009; Yang et al. 2015; Toriumi et al. 2015a; Su et al. 2016; Robustini et al. 2016; Reid et al. 2018; Humphries et al. 2020; Li et al. 2020; Kotani & Shibata 2020; Shen 2021). The surge-like activity appears to have at least two components: persistent up-and-down motions driven by the upward leakage of magnetoacoustic waves, and intermittent high-speed jets triggered by magnetic reconnection (Zhang et al. 2017; Hou et al. 2017; Tian et al. 2018). Lim et al. (2020) detected opposite magnetic polarities emerging and canceling on an LB. Such an observational signature might suggest the occurrence of magnetic reconnection between small-scale emerging flux and pre-existing field on the LB, which could result in intermittent jets (Louis et al. 2015; Yuan & Walsh 2016; Hou et al. 2017; Tian et al. 2018; Bai et al. 2019). In addition, photospheric vortices occurring at the edge of an LB were reported to be associated with subsequent ejections of chromospheric surges (Yang et al. 2019). Light bridges are also known to host sub-arcsecond transient bright dots with transition region temperatures, which are likely related to coronal rain or small-scale energy release events around the loop footpoints (Tian et al. 2014; Kleint et al. 2014). More recently, Li et al. (2021) reported blob-like plasma ejections with a speed of ∼80 km s⁻¹ from an oscillating bright front above an LB. Observations of these different types of dynamics on LBs have significantly advanced our understanding of magneto-convection under the condition of strong magnetic field (Schüssler & Vögler 2006) and magnetic reconnection in the partially ionized lower atmosphere of sunspots (Ni et al. 2020).

Though frequently observed in sunspots, the formation mechanisms of LBs have rarely been studied. Only a few case studies exisit in the literature. There are suggestions that LBs can form through field-free hot plasma intruding into the gappy umbral magnetic field or through large-scale magnetoconvection (Parker 1979; Rimmele 2004; Toriumi et al. 2015b). Katsukawa et al. (2007) suggested that the emergence of umbral dots (UDs) near the edges of penumbral filaments and the inward motion of these UDs to the umbral center are triggered by a buoyant penumbral flux tube as well as subphotospheric flows across the sunspot. They claimed that the intrusion of penumbral filaments can facilitate the emergence of a buoyant flux tube and ultimately form an LB. Louis et al. (2020) reported the formation of one LB associated with large-scale emerging flux, of which one end was outside the sunspot and the other one was gradually crossing the umbra. Besides penumbral intrusion, merging of sunspots can also lead to the formation of LBs. Zirin & Wang (1990) studied several LBs and found that a transient thin LB can form through merging of two spots with the same polarity or opposite polarities (forming δ-spots).

With only a few case studies, the formation mechanisms of LBs are not well understood. Here we present analysis results from the first statistical investigation on the formation of LBs. Our analysis reveals three types of LB formation processes.

Uninterrupted observations provided by the Helioseismic and Magnetic Imager (HMI, Schou et al. 2012) on board the Solar Dynamics Observatory (SDO, Pesnell et al. 2012) allow us to investigate in detail the formation and evolution of LBs. We thus took the HMI continuum images and magnetograms for our statistical analysis. We examined the data in the whole year of 2014, when the Sun was active. We used the JHelioviewer software (Müller et al. 2017) (also see the website at: https://www.helioviewer.org) and inspected HMI images with a cadence of 1 hour to select events of LB formation. The following criteria were used for event selection: (1) the forming LB should be well isolated from other LBs; (2) the whole LB formation process should be clearly visible on the front side of the solar surface. The second criterion has excluded many events that occur at locations close to the solar limb. Based on these criteria, we have selected 144 LBs in 71 ARs and characterized their formation processes.

For a subset of these selected events, we also plotted image sequences using the data in the 'hmi.Ic_720s' and hmi.M_720s' series. The time cadence and spatial resolution of the data are 720 s and 1'', respectively. Some images generated from these data are shown in Figures 1–3.

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By examining the HMI continuum images, we found that the formation processes of these LBs can be categorized into three groups: penumbral intrusion (type-A), sunspot merging (type-B) and umbral-dot emergence (type-C). The numbers of events in these three categories are 74, 57 and 13, respectively. Observational details such as the NOAA number of the resident AR, starting and ending times of the formation process, are shown in Table 1. For type-A events, the starting time was defined as the time when a bright structure starts to intrude from the penumbra to the umbra. For type-C events, the starting time refers to the time when the first UD associated with the subsequently formed LB appears. We did not write down the starting times for type-B events, since it is difficult to determine them. The ending time of the formation process refers to the time when both ends of an LB connect with the penumbra or the length of an LB stops increasing. Table 1 also lists the duration of the LB formation process, the length and width of each LB, and the sunspot group classification of the resident AR. The length and width of an LB were calculated at the ending time of its formation process. The length was defined as the distance between two ends of the LB. The width was calculated at its middle location.

3.1. LB Formation through Intrusion of Penumbra

3.2. LB Formation through Sunspot Merging

3.3. LB Formation through Umbral-dot Emergence

3.4. Statistic Analysis

Figure 4 presents the distributions of the sunspot group classification, LB length, and total duration of the LB formation process (see the details in Table 1). From the left panel of Figure 4, we can see that most LBs are formed in complicated ARs that are associated with βγ or βγδ sunspot groups. Only 11 events are identified in unipolar ARs with α sunspot group. Out of these 11 events, nine belong to type-A.

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The average lengths of the LBs are 9.8''±3.0'', 10.7''±3.8'' and 9.9''±2.2'' for type-A, type-B and type-C events, respectively. After dividing the lengths into three intervals (0''–10'', 10''–20'' and 20''–30''), we present in the middle panel of Figure 4 the distributions of the lengths for different types. We found that for each type more than half LBs are shorter than 10'', and only a few LBs are longer than 20''.

The distributions of the LB formation duration for type-A and type-C events are presented in the right panel of Figure 4. The average formation durations for the type-A and type-C events are 20 ± 12 and 18 ± 10 hours, respectively. Most LBs form within 40 hours, and the number of events obviously decreases with the increased formation duration.

We also investigated the relationships between different parameters for type-A and type-C events. Two scatter plots are shown in Figure 5. There appears to be a positive correlation between the LB length and formation duration. For type-A events their correlation coefficient is about 0.53, which is significant at the 99.9% confidence level (Bevington & Robinson 2003). This correlation suggests that the speed of penumbral intrusion is nearly the same in different sunspots. For the type-C events, this correlation is not as significant as that for the type-A events.

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Based on SDO/HMI observations in the year of 2014, we have performed a statistical investigation on the formation of sunspot LBs for the first time. We have categorized the formation processes of 144 LBs into three groups: penumbral intrusion (type-A), sunspot merging (type-B) and umbral-dot emergence (type-C). The percentages of these three groups are 51%, 40% and 9%, respectively.

Most of the identified LBs are formed in ARs with βγ and βγδ sunspot groups. The duration of the LB formation process is less than 40 hours for most LBs, and the average is about 20 hours. The maximum lengths of most identified LBs are less than 20''. For type-A events, we found a positive correlation between the formation period and length, suggesting that the speed of penumbral intrusion is almost the same for different LBs. The correlation is less obvious for type-C events.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11803002, 11825301 and 11790304) and the Strategic Priority Research Program of Chinese Academy of Sciences (XDA17040507). HMI is an instrument onboard the Solar Dynamics Observatory, a mission for NASA's Living With a Star program.