Magnetic Helicity Flux across Solar Active Region Photospheres: II. Association of Hemispheric Sign Preference with Flaring Activity during Solar Cycle 24
aa r X i v : . [ a s t r o - ph . S R ] F e b Draft version March 1, 2021
Typeset using L A TEX preprint style in AASTeX63
Magnetic Helicity Flux across Solar Active Region Photospheres: II. Association ofHemispheric Sign Preference with Flaring Activity during Solar Cycle 24
Sung-Hong Park, K. D. Leka,
1, 2 and Kanya Kusano Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan NorthWest Research Associates, Boulder, CO, USA (Received January 6, 2021; Revised February 23, 2021; Accepted February 24, 2021)
Submitted to ApJABSTRACTIn our earlier study of this series (Park et al. 2020, Paper I), we examined thehemispheric sign preference (HSP) of magnetic helicity flux dH/dt across photosphericsurfaces of 4802 samples of 1105 unique active regions (ARs) observed during solar cycle24. Here, we investigate any association of the HSP, expressed as a degree of compliance,with flaring activity, analyzing the same set of dH/dt estimates as used in Paper I. TheAR samples under investigation are assigned to heliographic regions (HRs) defined inthe Carrington longitude-latitude plane with a grid spacing of 45 ◦ in longitude and 15 ◦ in latitude. For AR samples in each of the defined HRs, we calculate the degree ofHSP compliance and the average soft X-ray flare index. The strongest flaring activityis found to be in one distinctive HR with an extremely low HSP compliance of 41%as compared to the mean and standard deviation of 62% and 7%, respectively, overall HRs. This sole HR shows an anti-HSP (i.e., < Keywords: methods: data analysis — methods: observational — Sun: activity — Sun:flares — Sun: magnetic fields — Sun: photosphere INTRODUCTIONSolar flares are known as the sudden and rapid release of magnetic energy stored in the so-lar atmosphere, producing electromagnetic radiation from radio waves to gamma rays. Thevast majority of large flares occur in active regions (ARs) where intense magnetic fields mani-
Corresponding author: Sung-Hong [email protected]
Park et al. fest as dark sunspots in the photosphere. Many studies have been conducted to find out sig-nificant statistical differences of magnetic field properties between flaring and flare-quiet ARs(e.g., see Zirin & Liggett 1987; Livi et al. 1989; Zhongxian & Jingxiu 1994; LaBonte et al. 2007;Leka & Barnes 2007; Georgoulis & Rust 2007; Park et al. 2008; Toriumi & Wang 2019, and refer-ences therein). It is now generally accepted that flares are more likely to occur in ARs with magneticfields exhibiting (1) more complex morphologies (e.g., δ -sunspots), (2) higher degrees of magneticnon-potentiality in a wide variety of forms (e.g., magnetic twist or shear), and (3) more drasticchanges in the photosphere near magnetic polarity inversion lines (e.g., magnetic flux emergence orcancellation). Even though these comparison studies have broadly advanced our understanding offlare-productive ARs, contemporary usage in the context of forecasting solar flares demonstrates thatthere are still fundamental aspects yet to be understood (e.g., Barnes et al. 2016; Nishizuka et al.2017; Leka et al. 2019; Kusano et al. 2020). For example, it is still not clear whether one or manydifferent critical conditions exist for triggering flares and driving eruptive instabilities, not to mentionour continuing quest to understand the physical processes of flare energy build-up and release in thecorona.Magnetic helicity has received substantial attention over the past few decades, mainly due to itspractical use in quantitatively measuring twists, kinks, and inter-linkages of magnetic field lineswithin a volume enclosed by a boundary surface S (e.g., Berger & Field 1984; Berger & Prior 2006;Longcope et al. 2007; D´emoulin & Pariat 2009). Magnetic helicity is gauge invariant only in the caseof a closed volume satisfying that the normal component B n of the magnetic field vanishes at everypoint on S . In an open volume (i.e., B n = 0 at any point on S ), on the other hand, a gauge-invariantform of the so-called relative magnetic helicity was introduced with the choice of a reference magneticfield having the same B n at S . The relative magnetic helicity is defined as subtracting magnetichelicity of the reference field from the total (refer to Berger & Field 1984; Finn & Antonsen 1985).For notational simplicity, hereafter, we refer to the relative magnetic helicity as magnetic helicity.Since magnetic helicity flux dH/dt across photospheric surfaces of ARs was first estimated fromobservations of the solar magnetic field (e.g, Chae 2001), there have been many attempts to investigate dH/dt in the context of understanding the energy build-up process and initiation mechanism of flares.For example, Park et al. (2010) examined the temporal variation of dH/dt over 24 hr for each of 378unique ARs observed during solar cycle 23. They found a tendency that ARs with larger values of | dH/dt | are more flare-productive. Meanwhile, temporal variations of dH/dt over different timescalesof a few hours to days before flare occurrence have been also investigated; consequently, some flare-associated variations of dH/dt were found, including a large increase or sign reversal of dH/dt (e.g.,Park et al. 2008; Romano et al. 2014; Vemareddy & D´emoulin 2017). It should be noted, however,that all these studies were carried out based on estimates of dH/dt for a set of individual ARs.However, so far, no studies have tackled the question of whether the level of flaring activity has anyassociation with the distribution of dH/dt for a group of ARs located at the same region arbitrarilydefined in the Carrington longitude-latitude heliographic plane.In our earlier study of this series (Park et al. 2020, Paper I), we explored the well-known hemisphericsign preference (hereafter referred to as HSP) of magnetic helicity: i.e., a dominance of negative(left-handed) helicity in the northern hemisphere and positive (right-handed) helicity in the southernhemisphere, independent of the solar cycle. More specifically, we examined the HSP, expressed as adegree of compliance that ARs follow the expected preference, analyzing dH/dt across photospheric emispheric Sign Preference and Flaring Activity dH/dt was found to be stronger in the case of ARs that (1) appear at higherlatitudes during the rising phase of the solar cycle; (2) have larger values of | dH/dt | , the total unsignedmagnetic flux Φ, and the average plasma-flow speed < | v | > = < p v x + v y + v z > through the givenAR surface, where v x , v y and v z are all three components of the photospheric magnetized plasmavelocity derived from HMI vector magnetograms with the Differential Affine Velocity Estimatorfor Vector Magnetograms (DAVE4VM; Schuck 2008). These observed HSP dependencies suggestthat the Coriolis force acting on a rising and expanding flux tube in the convection zone may playan important role in enhancing the HSP. Moreover, the HSP for ARs at higher latitudes may bestrengthened by the differential rotation on the solar surface as well as the tachocline α -effect of aflux-transport dynamo. With the same set of dH/dt estimates as used in Paper I, here we studywhether there is any relation between the HSP of dH/dt and flaring activity. The dH/dt data set isdescribed in Section 2.1, the association of flares with their source ARs is presented in Section 2.2,and analysis results in Section 3. Finally, in Section 4, we summarize and discuss our main findings. DATA ANALYSIS2.1.
Description of the Data Set
In this study, we analyze the same data set as in Paper I, which contains estimates of dH/dt , Φ and < | v | > for all 4802 samples of 1105 unique NOAA-numbered ARs. The AR samples comprise pairs ofvector magnetograms acquired from HMI AR Patches (HARPs; Hoeksema et al. 2014, as recordedin the hmi.M 720s series), and observed daily at 00:36 and 00:48 TAI over an 8 yr period from 2010May 1 to 2017 December 3, satisfying the following criteria: (1) the longitudinal boundaries of thegiven HARP are located within ± ◦ from the central meridian of the solar disk, and (2) the HARPcontains only a single NOAA-numbered AR with at least one sunspot visible in white-light. Detailsof HMI vector magnetic field data and methods used to obtain dH/dt estimates as well as theiruncertainties can be found in Paper I and references therein. We note that the results in Section 3are only minimally affected by the uncertainties in dH/dt , because the uncertainties were found tobe insufficient to cause the misidentification of the sign of dH/dt , as discussed in detail in Paper I.For all of the AR samples, we find that 28%, 57%, and 15% are α -class, β -class, and the othercomplex-class ARs, respectively, according to their Mount Wilson (or Hale) magnetic classificationsfor sunspot groups. It is also found that 63% of 2530 AR samples in the northern hemisphere and65% of 2272 samples in the southern hemisphere comply with the HSP of dH/dt . These observeddegrees of HSP compliance are within the range reported in previous studies (e.g., Longcope et al.1998; Pevtsov et al. 2001; Hagino & Sakurai 2005; Zhang 2006; Liu et al. 2014). We refer the readerto Paper I for the HSP dependencies identified with respect to various properties of ARs as well assome relevant physical mechanisms for adherence to the observed HSP.2.2. Assignment of Flares to the Active Region Samples
The NOAA/Space Weather Prediction Center (SWPC) provides historical flare event list data(ftp://ftp.swpc.noaa.gov/pub/warehouse), obtained by the Geostationary Operational Environmen-tal Satellites (GOES), along with a network of ground-based solar observatories. The SWPC flareevent list contains relevant information, such as flare start times, magnitudes, source regions andlocations, in order to find GOES soft X-ray flares that occurred in a given AR within an interval
Park et al. τ = 24 hr following the AR observation time (00:36 TAI). For each of our AR samples, the flare as-signment is done basically searching for flares within τ , of which source regions are assigned with thesame NOAA region number as the AR sample. In the SWPC list, there are however some flares forwhich no information is available on their source regions (i.e., no NOAA region number is given), buttheir heliographic locations (i.e., longitudes and latitudes) are available. Among such flares within τ , those which are located within the derotated HARP field of view (FOV) of the given AR sampleat the flare start times are assigned to that AR sample.To quantify flaring activity of each AR sample under consideration, we define the 24 hr flare index(hereafter shortly indicated as F idx ) as F idx = 100 × S X + 10 × S M + 1 × S C + 0 . × S B , (1)where S j = P N j i =1 M ji . Here N j is the total number of j -class flares assigned to the given AR sampleduring τ , and M ji is the magnitude (i.e., digit multipliers from 1.0 to 9.9) of the j -class flares. Simplyput, F idx refers to the sum of GOES soft X-ray peak fluxes of all flares assigned to the given ARduring τ , and it is often considered to measure flare productivity of an AR for a target interval (e.g.,Abramenko 2005; Park et al. 2010; Lee et al. 2018).2.3. Calculation of the HSP for Defined HRs
We define heliographic regions (HRs) in the Carrington longitude-latitude plane, each of whichhas the longitudinal and latitudinal extents of 45 ◦ and 15 ◦ , respectively. The AR samples are thenassigned to the defined HRs, based on where the center coordinates of the AR samples are located.In the case that the AR sample’s HARP FOV spans two or more HRs, the assignment is to thatwhich includes the largest fraction of the HARP. For each HR, the degree of HSP compliance is thencalculated as the fraction of AR samples that have negative/positive values of dH/dt if the given HRis located in the northern/southern hemisphere. RESULTS3.1.
HSP versus Anti-HSP Active Region Properties
With the given set of our dH/dt estimates, we first examine whether the level of flaring activityis different between two separate groups of AR samples: i.e., 3007 HSP AR samples with dH/dt estimates following the HSP versus 1795 anti-HSP AR samples with dH/dt estimates against theHSP. In panel (a) of Figure 1, the relative frequency distribution of F idx values is shown for the HSPsamples (red curve) and anti-HSP samples (blue curve), respectively, with the mean (vertical line)and mean ± IQR (tilted lines), where IQR is the interquartile range defined as the 75th percentileminus 25th percentile. We find that the mean of F idx values for the anti-HSP AR samples is largerthan that for the HSP samples. The difference between them is however not significant accordingto the two-sided p -value of 0.097 from the Student’s t-test. In each case of the parameters | dH/dt | (panel (b)) and Φ (panel (c)), the mean value for the HSP samples is found to be similar to that forthe anti-HSP samples in the context that: (1) p -value is much larger than 0.1, and (2) the mean valuefor the HSP samples is well constrained within the range of the mean ± × IQR for the anti-HSPsamples, and vice versa. Meanwhile, as shown in panel (d) of Figure 1, the anti-HSP samples havelarger values of < | v | > generally compared to the HSP samples with the p -value of 0.004, but thedifference between the mean values is within 0.1 × IQR for either the HSP samples or the anti-HSPsamples. emispheric Sign Preference and Flaring Activity Significance of t−test: 0.097 idx F re qu e n c y [ % ] Significance of t−test: 0.450 Mx /s]0.11.010.0100.0 F re qu e n c y [ % ] Significance of t−test: 0.589 Φ [10 Mx]0.11.010.0100.0 F re qu e n c y [ % ] Significance of t−test: 0.004 F re qu e n c y [ % ] (a) (b)(c) (d) Figure 1.
Frequency distributions of 3007 HSP AR samples (red curve) and 1795 anti-HSP AR samples(blue curve) considered in this study, with respect to (a) the flare index F idx , (b) the absolute value of dH/dt ,(c) the total unsigned magnetic flux Φ, and (d) the AR samples’ average plasma-flow speed < | v | > . In eachpanel, the mean (vertical line) and mean ± IQR (tilted lines) are marked for the HSP and anti-HSP samples,respectively, where IQR is the interquartile range defined as the 75th percentile minus 25th percentile.
Flares are known to occur more frequently in ARs that include complex magnetic fields, suchas δ -sunspots (e.g., Zirin & Liggett 1987; Livi et al. 1989; Zhongxian & Jingxiu 1994; Sammis et al.2000; Lee et al. 2012). In this respect, we investigate what percentage of the HSP and anti-HSPAR samples, respectively, belong to δ -class, and whether there is a notable difference of the δ -classpercentages between the two AR groups. We find 4.9 ± δ -sunspots, while for the anti-HSP AR samples it is 5.0 ± δ -class percentage is estimated by the Poisson uncertainty of 1 / √ N , where N is the totalnumber of the given samples. We find that the δ -class percentage shows no significant differencebetween the two groups, even though the mean of F idx is slightly larger for the anti-HSP samplescompared to the HSP samples.3.2. Association of the HSP with Flaring Activity in Heliographic Regions
Here, we aim to find any association of the HSP with flaring activity in the HRs defined in Sec-tion 2.3. In Figure 2, each of the defined HRs is color-coded by the degree of HSP compliance for thesubset of our AR samples contained therein. The number of AR samples located within a given HRis indicated by the side length of the color-coded square in that HR. In this HSP diagram, higher
Park et al. −180 −135 −90 −45 0 45 90 135 180Carrington Longitude [deg]−30−1501530 H e li og r a ph i c L a t i t ud e [ d e g ]
40 45 50 55 60 65 70HSP of dH/dt [%] N u m b er o f AR s Figure 2.
Each heliographic region (HR) defined in this study is color-coded by the degree of HSP compli-ance of dH/dt . The side length of the squares represents the number of AR samples located at the definedHRs. degrees of HSP compliance (i.e., ∼
60 – 70%) are found in the regions at higher latitudes in the ranges[ − ◦ , − ◦ ] and [15 ◦ , 30 ◦ ], compared to lower degrees of HSP compliance (i.e., ∼
40 – 60% in mostcases) in the regions at lower latitudes [ − ◦ , 0 ◦ ] and [0 ◦ , 15 ◦ ]. Such latitudinal dependence of theHSP was reported in Paper I. More interestingly, we find a notable HR at [ − ◦ , − ◦ ] in Carringtonlongitude and [ − ◦ , 0 ◦ ] in latitude, exhibiting an extremely low HSP compliance of 41% as comparedto the mean and standard deviation of 62% and 7%, respectively, for all HRs. It should be also notedthat this HR is the only one that definitively shows an anti-HSP (i.e., less than 50% compliance).Figure 3 shows the average F idx values for the same subset of AR samples assigned to each of theHRs as in Figure 2. We find that the anti-HSP HR with the remarkably low HSP compliance showsthe strongest flaring activity, having the largest value of the average F idx = 22. This is extremelylarge relative to the mean and standard deviation (i.e., 3.8 and 4.3, respectively) of the average F idx values for all HRs. This anti-HSP HR contains the highly flare-productive AR NOAA 12673.However, even when NOAA 12673 is excluded, this HR still shows an anti-HSP with the lowest HSPcompliance of 44% as well as a high level of flaring activity with the average F idx = 6 ranked in thetop three. Another large flare-productive HR with the average F idx = 15, including the largest ARNOAA 12192 observed in cycle 24, is found at [45 ◦ , 90 ◦ ] in Carrington longitude and [ − ◦ , 0 ◦ ] inlatitude. This region has a low HSP compliance of 56% that is smaller than the mean minus onestandard deviation. In addition, as shown in Figure 4, those two specific HRs have the average Φvalues ranked in the top two (i.e., greater than 1.9 × Mx).Now we turn to the question of whether there are any general trends or strong correlations betweenthe degree of HSP compliance, the average F idx , and the average Φ derived from the AR samples emispheric Sign Preference and Flaring Activity −180 −135 −90 −45 0 45 90 135 180Carrington Longitude [deg]−30−1501530 H e li og r a ph i c L a t i t ud e [ d e g ] idx N u m b er o f AR s Figure 3.
Same as Figure 2, but showing the average value of the 24 hr flare index F idx for AR samplesassigned to each of the defined HRs. −180 −135 −90 −45 0 45 90 135 180Carrington Longitude [deg]−30−1501530 H e li og r a ph i c L a t i t ud e [ d e g ] Φ [10 Mx] N u m b er o f AR s Figure 4.
Same as Figure 2, but showing the average value of the total unsigned magnetic flux Φ for ARsamples assigned to each of the defined HRs.
Park et al.
Linear PCC: −0.55
40 45 50 55 60 65 70HSP of dH/dt [%]0510152025 A v er ag e F i d x Linear PCC: 0.65 Φ [10 Mx]0510152025 A v er ag e F i d x A v er ag e F i d x Linear PCC: −0.36
40 45 50 55 60 65 70HSP of dH/dt [%]0.51.01.52.02.5 A v er ag e Φ [ M x ] (a) (b) (c) Figure 5.
Scatter plots of (a) the average F idx versus the HSP, (b) the average F idx versus the averageΦ, and (c) the average Φ versus the HSP for the defined HRs in the northern (stars) and southern (circles)hemispheres. In panel (c), the symbols are color-coded by the average F idx . Data points of the five lowestHSP, the five largest average Φ, or the five largest average F idx , respectively, are separated from the othersby the dashed lines in each panel. contained in the defined HRs. As shown in the scatter plot of the average F idx versus the HSP (panel(a) of Figure 5), we find a weak tendency that HRs with lower degrees of HSP compliance showlarger values of the average F idx , with the linear Pearson correlation coefficient (PCC) of − F idx can be considered as an extremecase, which lies far away from both the vertical and horizontal dashes lines used to separate datapoints of the five lowest HSP and the five largest average F idx , respectively. On the other hand, apositive correlation exists between the average Φ and the average F idx with the linear PCC = 0.65(refer to panel (b) of Figure 5). Such correlation of Φ with flaring activity in “individual” ARs hasbeen reported in many previous studies (e.g., Leka & Barnes 2003, 2007; Park et al. 2010; Liu et al.2017; Lee et al. 2018), but it is reported here for the first time on this larger spatial scale of the HRsover a much longer period of solar cycle 24. As shown in Figure 5(c), a negative, although weak,correlation appears between the HSP and the average Φ with the linear PCC = − F idx ≥
15 have the average Φ values ranked in the top two as well as lower degrees of HSP compliance(i.e., one with the lowest HSP and the other with the HSP in the bottom 20%). Meanwhile, thetwo highly flare-productive regions can be considered as obvious outliers, compared to the positivetrend of the HSP with respect to the average Φ in Paper I. This may indicate that the HSP for thoseregions is obscured by vigorous turbulent convective flows interacting with rising flux tubes therein.As mentioned earlier, the two X-class flaring ARs, NOAA 12673 and NOAA 12192, are located atthe two HRs, respectively. Even excluding these two influential ARs, however, all of the trends asdescribed in Figure 5 remain the same, although the correlations become less strong (i.e., the linearPCCs of − − emispheric Sign Preference and Flaring Activity North-south Asymmetry of the HSP
We explore the north-south hemispheric asymmetry of solar activity during solar cycle 24. Thenorth-south asymmetry has been studied with respect to various solar activity indices for cycle24, including the total number of flares for a given GOES class (e.g., Bruevich & Yakunina 2017;Joshi & Chandra 2019), and sunspot areas (e.g., Li et al. 2019). The scatter plots in Figure 5 areused to examine any notable asymmetry in the distributions of the HSP, the average Φ and theaverage F idx between the HRs in northern (stars) and southern (circles) hemispheres. For the HSP,as shown in Figure 5(a), we find that four out of the five HRs with the HSP ranked in the bottomfive (i.e., bottom 15%) are located in the southern hemisphere. A similar north-south asymmetryis found in the average Φ (see Figure 5(b)), but for the HRs with the five largest average Φ (i.e.,top 15%). In the case of the average F idx , all of the HRs in the top five are placed in the southernhemisphere.These observational findings lend support to the presence of the north-south asymmetric behavior ofsolar activity in cycle 24, as discussed above, in which the southern hemisphere is more active overallthan the northern hemisphere. In the present analysis, this asymmetry is most clearly visible with theactivity metrics used here (i.e., the HSP, the average F idx , and the average Φ) between the HRs lyingwithin [ − ◦ , 0 ◦ ] versus those lying within [0 ◦ , 15 ◦ ] (refer to Figures 2–4). The observed asymmetry infavor of stronger activity in the southern hemisphere during cycle 24 agrees with other observationsof more frequent flare events at C- or M-class by Joshi & Chandra (2019) as well as larger values ofthe yearly mean sunspot area by Li et al. (2019). In addition, the southern hemisphere is expectedto be more active based on the previously reported periodicities of the north-south asymmetry longerthan a few solar cycles (e.g., periodic behaviors of ∼ ∼
12 cycles shown in Ballester et al. (2005)and Li et al. (2002), respectively). SUMMARY AND CONCLUSIONSIn this paper we have investigated the hemispheric sign preference (HSP) of magnetic helicity flux dH/dt for 4802 samples of 1105 unique active regions (ARs), in the context of whether and how theHSP is associated with flaring activity of the AR samples observed from 2010 to 2017 of solar cycle24. The AR samples were first categorized into two separate groups of 3007 HSP AR samples with dH/dt estimates following the HSP and 1795 anti-HSP AR samples with dH/dt estimates againstthe HSP. Comparing values of the 24 hr flare index F idx between the HSP and anti-HSP AR samples,we found that the mean F idx for the anti-HSP samples is larger than that for the HSP samples, albeitwith minimal statistical significance. Next, heliographic regions (HRs) were defined in the Carringtonlongitude-latitude heliographic plane, each of which has the longitudinal and latitudinal extents of45 ◦ and 15 ◦ , respectively. We then examined the relations between the degree of HSP compliance,the average total unsigned flux Φ and the average F idx for a subset of AR samples placed in each ofthe defined HRs. Our main findings can be summarized as follows:1. Among the HRs is a distinctive one with the strongest flaring activity that exhibits an extremelylow HSP compliance of 41% as compared to the mean and standard deviation of 62% and 7%,respectively, for all the regions. This HR includes the highly flare-productive AR NOAA 12673.Note that even if NOAA 12673 is excluded, the HR still remains an anti-HSP with the lowestHSP compliance of 44%.0 Park et al.
2. There is a weak tendency for HRs with larger values of the average F idx to have lower degreesof HSP compliance with the the linear Pearson correlation coefficient (PCC) of − F idx values rank in the top 15% are located in the southern hemisphere.Such hemispheric asymmetry is also found in favor of lower degrees of HSP compliance as wellas larger values of the average Φ in the southern hemisphere.In summary, all these observational findings lend support to the general trend of stronger flaringactivity in a given HR with a lower degree of HSP compliance during cycle 24. We now attemptto tackle the question of why there may exist such association of the HSP with flaring activity.LaBonte et al. (2007) compared dH/dt estimates between 48 X-class flaring ARs and 345 ARs withoutX-class flares. Separating the components of dH/dt into the one dH/dt rot by the differential rotationon the solar surface and the rest dH/dt rest , they found that on average, the X-class flaring ARs havea larger ratio of | dH/dt rest | to | dH/dt rot | , i.e., ∼ ∼ dH/dt rest can be more disorganized and of opposite signcompared to the HSP, so that the HSP is effectively obscured by dH/dt rest .These results suggest that the surface differential rotation is less likely to be a crucial mecha-nism to cause the observed X-class flares, but the other components contributing to dH/dt , suchas an emerging twisted magnetic flux tube across the photosphere, may be more related to flareenergy build-up and triggering mechanisms. In this respect, it is noteworthy to consider the “Σ-effect” (Longcope et al. 1998), which acts on a buoyantly rising and expanding flux tube throughthe turbulent convection zone. Through numerical simulations of the Σ-effect on rising flux tubes,Longcope et al. (1998) found that a lower degree of HSP compliance can be obtained mainly dueto the interaction of a flux tube with increased magnitudes of turbulent velocities in the convectionzone. Based on the Σ-effect simulations, we conjecture that the distinctive anti-HSP heliographicregion found in the present study may have highly turbulent localized flows through its layers fromthe deep convection zone to the photosphere. Such localized, amplified turbulence in the convectionzone may play a crucial role for rising flux tubes as their magnetic fields get more complex withlarger magnetic non-potentiality, and eventually produce large flares.As shown in Figure 5(c), the inverse correlation between the HSP and the average Φ may also sup-port the conjecture that the expected high-HSP for a rapidly expanding flux tube (with large magneticflux) therein by the Coriolis force would be obscured by highly turbulent convective flows in suchlow-HSP HRs. Moreover, a number of numerical simulations showed that ARs with complex mag-netic structures (e.g., γ - or δ -class) are formed by multiple buoyantly emerging segments of a singlesubsurface flux tube (e.g., Toriumi et al. 2014; Fang & Fan 2015; Toriumi & Takasao 2017), confirm-ing prior observational studies (e.g., Leka et al. 1996; Chintzoglou & Zhang 2013). Such multiplebuoyant segments of a single subsurface flux tube may be produced by intense turbulence of localizedregions in the convection zone. Meanwhile, examining Carrington longitudes of recurrent magneticflux emergence for several solar rotations (called “long-lived activity complexes”), Komm & Gosain(2015) revealed that each such activity complex typically has a mixture of positive and negativecurrent helicity over its lifetime. In these activity complexes, newly emerging magnetic flux interactswith pre-existing flux of prior ARs, which may cause an increase in magnetic field complexity andlead to flares at an enhanced rate. emispheric Sign Preference and Flaring Activity Facilities:
SDO (HMI)
Software:
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