Activity Complexes and A Prominent Poleward Surge During Solar Cycle 24
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Activity Complexes and A Prominent Poleward Surge During Solar Cycle 24
Zi-Fan Wang,
Jie Jiang,
3, 4
Jie Zhang, and Jing-Xiu Wang
2, 1 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, China School of Space and Environment, Beihang University, Beijing, China Key Laboratory of Space Environment Monitoring and Information Processing of MIIT, Beijing, China Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA
ABSTRACTLong-lasting activity complexes (ACs), characterised as a series of closely located, continuouslyemerging solar active regions (ARs), are considered generating prominent poleward surges from ob-servations. The surges lead to significant variations of the polar field, which are important for themodulation of solar cycles. We aim to study a prominent poleward surge during solar cycle 24 on thesouthern hemisphere, and analyse its originating ACs and the effect on the polar field evolution. Weautomatically identify and characterize ARs based on synoptic magnetograms from the Solar DynamicObservatory. We assimilate these ARs with realistic magnetic configuration into a surface flux trans-port model, and simulate the creation and migration of the surge. Our simulations well reproduce thecharacteristics of the surge and show that the prominent surge is mainly caused by the ARs belongingto two ACs during Carrington Rotations 2145-2159 (December 2013-January 2015). The surge hasa strong influence on the polar field evolution of the southern hemisphere during the latter half ofcycle 24. Without the about one-year-long flux emergence in the form of ACs, the polar field aroundthe cycle minimum would have remained at a low level and even reversed to the polarity at cycle 23minimum. Our study also shows that the long-lived unipolar regions due to the decay of the earlieremerging ARs cause an intrinsic difficulty of automatically identifying and precisely quantifying lateremerging ARs in ACs. INTRODUCTIONThe spatial and temporal proximity of active regions (ARs) on the Sun is an important feature of large-scalesolar magnetism (van Driel-Gesztelyi et al. 1992; Harvey & Zwaan 1993). A sequence of closely located, continuouslyemerging ARs is defined as a complex of activity (Gaizauskas et al. 1983), or activity complex (AC). This definitionagrees with the concept of “sunspot nests” (see Castenmiller et al. 1986), which last for several rotations and containover 30% ARs in total. ACs can also be associated with “active longitudes”, which date back to Carrington (1858).Consequently, ACs are foci of Sun’s toroidal magnetic fields, and an indicator of solar cycle development (Yazev 2015).The nesting tendency of ARs and physical interpretations are discussed in the review of van Driel-Gesztelyi & Green(2015).The decay of ARs over the solar surface determines the evolution of the large-scale field, including the polar field.According to the Babcock-Leighton (B-L) mechanism (Babcock 1961; Leighton 1964, 1969), the surface large-scalefield corresponds to the surface poloidal field of the dynamo loop and serves as the seed of the subsequent cycle(Cameron & Sch¨ussler 2015; Wang 2017; Jiang et al. 2018; Petrovay 2020). The polar field is also the source of thefast solar wind (Tu et al. 2005) and the interplanetary field (Balogh et al. 1995; Jiang et al. 2010), which modulatesthe density of cosmic rays (Cane et al. 1999; Potgieter 2013). Considering the continuous flux emergence in ACs, thedecay of ACs is possible to introduce strong variations to the surface large-scale field, and is supposed to be a causeof short-term variation and perturbation of the interplanetary field. Thus it is important to investigate the evolutionof ARs within ACs and its influence on the large-scale field.
Corresponding author: Jie [email protected]
The migration of ARs on the surface can be described by the surface flux transport (SFT) model (e.g. DeVore et al.1985; Wang et al. 1989; van Ballegooijen et al. 1998; Mackay et al. 2002; Jiang et al. 2014). The SFT model utilizesa set of transport parameters based on observations and estimations to solve the magnetic induction equation onthe surface, with the source of surface magnetic flux coming from emerging flux in ARs. The SFT model is able toreproduce the polar field evolution. Early SFT simulations use the bipolar magnetic region (BMR) approximation asthe source term. Wang et al. (1989) analysed the evolution of BMRs by comparing SFT simulations with observationallongitudinally averaged surface field during cycle 21, and found how the trailing polarity flux of BMRs built up thepolar field. Cameron et al. (2010) used BMRs constructed from observations in the SFT model to reproduce the solaropen flux and polar field of cycles 15-21.Recently, more SFT simulations have begun to use real configurations instead of the BMR approximation as sourceterms (e.g. Yeates et al. 2015; Virtanen et al. 2017; Whitbread et al. 2018; Jiang et al. 2019). Using real configurationof ARs is more precise in terms of polar field influence than using BMRs constructed from AR parameters, especiallyfor more complex ones like δ -type ARs (Jiang et al. 2019). The final dipole moment could deviate from or even beopposite to that determined by tilt angle and other AR parameters. Therefore, using real configurations of ARs isnecessary as we aim to simulate ARs emerging during a few Carrington Rotations (CRs) in detail.The poleward migration of flux is not uniform in time, but usually in the form of poleward surges (or polewardflux streams, plumes) seen on magnetic butterfly diagrams, i.e., longitudinally averaged radial magnetic field at thephotosphere (Howard & Labonte 1981). Poleward surges’ characteristics are related to originating ARs, whose axeshave tilts respect to the east-west direction. Typically, a tilted bipolar AR generates a poleward surge of the trailingpolarity. This results from the latitudinal separation of the two polarities because of the tilt angle, which leads toa more diffusive, less distinguishable poleward migration of the leading polarity (Mackay et al. 2002; Yeates et al.2015; Sun et al. 2015; Jiang et al. 2019). Surges are more concentrated if originating from higher latitudes, and morediffusive if originating from lower latitudes. The concentrated surges correspond to a short-term perturbation in thepolar field by ARs. On the other hand, ARs’ influences on the final polar field, i.e., the polar field at cycle minimum,decrease exponentially as their emergence latitudes increase, as revealed by the SFT simulations of Jiang et al. (2014);Whitbread et al. (2018), and by a mathematical explanation of Petrovay et al. (2020). Hence, a surge with long-lasting influence to the solar cycle development should originate from lower latitudes, especially with concentrated fluxemergence, e.g., ACs.Meanwhile, observations suggest the relation among ACs, the generated poleward surges, and the polar field rever-sal (Mordvinov et al. 2016; Mordvinov & Kitchatinov 2019). ARs with different tilt angles in ACs may form largeregions of single polarity as a result of flux cancellation between them, and create poleward surges (Gaizauskas 2008).Comparison of polar field reversal of cycles 21-24 shows that ACs with larger area and longer lifetime are associatedwith stronger poleward surges and more violent polar field reversal (Petrie & Ettinger 2017). This, however, was doneby stacking synoptic maps, as Gaizauskas et al. (1983) did, and by measuring observational magnetic flux at differentlatitudes, but no SFT simulations were applied. It is needed to tell whether such long-lasting ACs that are ableto cause violent polar field variation can have significant influence on the final polar field as well. The relationshipbetween poleward surges by ACs and their polar field influence should be evaluated in the data-driven SFT model totell the exact long-term influence of ACs.To learn the contribution of ACs to poleward surges and the final polar field, we simulate the production andmigration of the most prominent poleward surge on the southern hemisphere during cycle 24. As shown in Figure1, the surge of interest covers the time period of CRs 2145-2159 (DEC 2013-JAN 2015), carrying a large quantityof negative flux that reversed the polar field from positive to negative and further strengthened the field to -4 G onaverage. The surge of interest originates from long-lasting ACs, which will be shown in Subsection 2.2. We simulatethe overall development of the surge by assimilating the ARs with their real configurations during CRs 2145-2159 intoSFT simulations, and compare them with observations. Our simulation is able to reproduce the features of the surge,especially its dominant influence on the southern polar field. We present the simulation of a fraction of the ACs indetail, discussing the continuous flux emergence and cancellation occurring in ACs, in order to examine and discussthe associated intrinsic difficulty of automatic AR identification in ACs.The article is organized as follows. In Section 2 we describe the AR identification method based on synoptic maps.We then show the identified ARs and describe the ACs. In Section 3 we introduce the data driven SFT model thatwe use, and the assimilation technique of identified ARs. In Section 4 we present simulation results for the surge. Wediscuss and conclude in Section 5. Field Strength [G] -3 -2 -1 0 1 2 3 L a t i t u d e [ d e g ] Figure 1.
Magnetic butterfly diagram of cycle 24 generated from longitudinally averaged SDO/HMI synoptic maps describedin Subsection 2.1. The poleward surge studied in the article is marked with the black dashed ellipse in the figure.2.
ARS DURING CRS 2145-21592.1.
Method of identifying ARs
To obtain the input source term for the SFT model, an AR identification method is needed. Up to now, identificationof ARs for the source term of the SFT model has been done by smoothing the magnetograms and applying a threshold,as done by Yeates et al. (2015); Virtanen et al. (2017); Whitbread et al. (2017, 2018). The threshold is determinedby trial and optimization methods over a given cycle. However, as we aim to examine the properties of ACs within ashorter period of time than the whole cycle, where flux of different strengths and concentrations is mixed as a resultof continuous emergence, one threshold is not sufficient to obtain the needed AR properties. Instead, we apply anidentification method with the ability of morphological analysis to adapt to the complex environment in ACs.AR data are obtained from synoptic maps of radial magnetic field component from Helioseismic and Magnetic Imagerof Solar Dynamics Observatory (SDO/HMI) (Schou et al. 2012). The radial field component is derived from HMI line-of-sight 720 sec-cadence magnetograms by dividing cosine latitude. The synoptic maps have a size of 3600 × Identification results for ARs
Table 1.
Parameters of AR12222 identified by the standard set of control parameters and the correspondingvariationsIdentification parameters Latitude Longitude Area Positive flux Negative flux Tilt(degree) (degree) ( µ Hem) a (10 Mx) (10 Mx) (degree)Standard set -20.2 82.6 3021.9 183.9 -138.6 10.2Decreased kernel -20.2 82.6 3021.9 183.9 -138.6 10.2Decreased growth -20.2 82.6 3289.3 185.0 -141.3 10.2Increased erosion/dilation -20.2 82.6 3021.9 183.9 -138.6 10.2Special set -20.5 83.5 4968.4 194.4 -170.3 14.9 a Millionths of the solar hemisphere.
Field strength [G] -50 -40 -30 -20 -10 0 10 20 30 40 50
Longitude [DEG] Longitude [DEG] Longitude [DEG] L a t i t u d e [ D E G ] L a t i t u d e [ D E G ] (a) CR2156(b) CR2157 (c) AR12192 (d) ARs 12209,12213,12214 (AR12192)(e) AR12222 (f) AR12222 AR12192ARs 12209,12213,12214 (AR12192) UnipolarregionUnipolarregion Figure 2.
Identified ARs on synoptic maps. The left column shows synoptic maps of CR2156 (a), and CR2157 (b), with theARs (enclosed by black curves) identified by the automatic identification method using the standard set of control parameters.AR12192 and the unipolar region in proximity are indicated with black arrows. The middle and right columns show AR12192identified using the standard set of control parameters on CR2156 (c), and identified using the special set of control parameterson CR2157 (d), as well as AR12222 identified using the standard set of control parameters on CR2157 (e), and identified usingthe special set of control parameters on CR2157 (f).
Utilizing the identification methods described above, we identified 84 ARs in total. The time-latitude distributionis displayed in Figure 3(a). As shown, all identified ARs reside within ± ◦ latitude in both hemispheres, with themajority lying between -10 ◦ to -20 ◦ . The emergence latitudes of ARs do not follow a clear trend, since a relativelyshort time of period is considered here. The majority of emerging latitudes are lower than the source of the surgestudied by Yeates et al. (2015), which covers +20 ◦ to +40 ◦ . We expect the surge we study to produce large final polarfield influence.During CRs 2145-2159, more ARs are identified in the southern hemisphere than in the northern hemisphere, interms of region counts and total areas. Figure 3(b) and 3(c) show the numbers and total areas of ARs identifiedin both hemispheres on each CR, respectively. The difference of areas between two hemispheres is larger than thatof region numbers, indicating that the ARs of the southern hemisphere are also generally larger than regions of thenorthern hemisphere.The imbalance of flux in two polarities is common among the identified ARs. Figure 3(d) shows the total identifiedpositive and negative flux of each CR. The difference between two signs of polarities differs from rotation to rotation.We note that unbalanced large ARs affect the result of our SFT model simulations. Table 2.
Parameters of AR12192 identified on CR2156 and CR2157Carrington Rotation Identification parameters Latitude Longitude Area Positive flux Negative flux Tilt(degree) (degree) ( µ Hem) (10 Mx) (10 Mx) (degree)2156 Standard set -13.2 246.1 12779.4 631.2 -698.2 0.92157 Special set -15.0 249.9 21834.3 546.0 -523.3 5.7 -30-20-100102030 L a t i t u d e [ d e g ] A R n u m b e r F l u x [ M x ] (a)(c) (d)(b) A r e a [ μ H e m ] Figure 3.
Identified ARs’ parameters. (a) Time-latitude diagram of identified ARs with each diamond representing one AR,with the dashed horizontal line at -15 ◦ latitude indicating the median of latitudes of ARs on the southern hemisphere; (b)Number of identified ARs in each hemisphere on each CR, with solid line indicating southern hemisphere and dashed lineindicating northern hemisphere; (c) Total area of identified ARs on each CR, with solid line indicating southern hemisphereand dashed line indicating northern hemisphere; (d) Total flux of identified ARs on each CR, with solid (dashed) line indicatingnegative (positive) flux. Among all identified ARs, some ARs in the southern hemisphere fit the concept of ACs. We identify ACs accordingto standards similar to that of Gaizauskas et al. (1983); Petrie & Ettinger (2017). By stacking those identified regionsin the southern hemisphere rotation by rotation in Figure 4, we see that ARs between 180 ◦ and 270 ◦ longitudes belongto a long lasting AC. This major AC exists from CR2145 to CR2156, and ends as the AR12192 emerges; AR 12192 isthe largest AR in area and the most abundant in flux in solar cycle 24. This AC consists of 18 regions, over 30% ofall ARs in the southern hemisphere. From its rotation-to-rotation development, we can clearly observe the formationof unipolar magnetic regions, especially the region that exists for several rotations near AR12192. The formation ofsuch regions is a superposition of flux from several previous ARs emerging around. After one CR from its majorflux emergence, the diffusive AR12192 is mixed with the unipolar region, as well as new flux emergence. From thisperspective we consider AR12192 a member of the AC as well. Besides the most long-lasting AC mentioned above,the ARs between 50 ◦ and 135 ◦ during CRs 2145-2149 can also be identified as an AC, or a nest. The flux from theseARs also superposes during evolution, forming unipolar regions. In total, approximately 50% of all identified ARs areassociated with the two ACs. SFT MODEL WITH DATA DRIVEN SOURCE3.1.
Model description
Field strength [G] -50 -40 -30 -20 -10 0 10 20 30 40 50
Figure 4.
Stack plot of magnetograms during CRs 2145-2159 of the southern hemisphere, with the identified ARs outlined bythe black curves. Each magnetogram is displayed in equal sine-latitude in the latitudinal part. Black solid squares mark theARs that can be regarded as members of ACs. The black dashed square marks the ARs studied in Subsection 4.2. AR12192identified by the special set of control parameters on CR2157 is not marked here.
The SFT model is to solve the radial component of the magnetic induction equation with given differential rotation,meridional flow and supergranular diffusion at the solar surface to get the temporal evolution of radial magnetic fieldcomponent. The SFT simulation code is based on Baumann et al. (2004). The code has 360 ×
180 spatial resolutionand a time interval of one day. The spatial component is expanded in terms of spherical harmonics up to the order of63, in which case the resolution corresponds to the size of supergranulation. The temporal component is solved withthe 4th-order Runge-Kutta method.The differential rotation and meridional flow are determined empirically from historic observations. We adoptthe differential rotation profile of Snodgrass (1983), and the meridional flow of van Ballegooijen et al. (1998). Themeridional flow speed is set to 11 ms − . The supergranular diffusivity is set to 500 km s − . The model details aredescribed in Jiang et al. (2014).Besides aforementioned time-independent transport processes, inflows towards activity belts are another importantprocess that affects the result of SFT simulations (Haber et al. 2002; Zhao & Kosovichev 2004; Gizon 2004; Jiang et al.2010; Cameron & Sch¨ussler 2012). Inflows affect flux cancellation and the latitudinal separation of polarities of ARs(Martin-Belda & Cameron 2016). For simulations that implement BMRs into the SFT code, the effect of inflows canbe simplified as a factor that decreases all tilt angles of BMRs (Jiang et al. 2015). For ARs with real configurations, theeffect of inflows would be more complicated. At present we do not include inflows in our simulations. To compensatethe effect of inflows, we set the supergranular diffusivity to 500 km s − , larger than the diffusivity of Jiang et al.(2014). Still, inflows are expected to take part in the evolution of ACs, as ACs are characterized as a large amount offlux emergence and interaction in activity belts. The exact effect of inflows remains to be discussed.3.2. Source term
The ARs identified in Section 2 are assimilated into the simulation. We first balance the total flux of each AR byenlarging the flux of the weaker polarity on each pixel by a same ratio to balance positive and negative flux. Thisbalancing technique is identical to that of Jiang et al. (2019). Then we convert the ARs from equal sine latitudeto equal latitude, and rescale them to the resolution of the code. The insertion of ARs is done by replacing thecorresponding pixel in the simulation with new values of the ARs. Considering how synoptic maps are generated, theday of inserting each AR into the simulation is determined by the time when it crosses central meridian.Theoretically, ARs are intended to be assimilated into the SFT model when they reach the decay phase. ACsare characterized as intense flux emergence and cancellation, so decaying ARs within ACs may be mixed with newemerging flux and old flux from previous ARs. The observed flux is a superposition of flux from different emergingsources at different stages of evolution, so it is intrinsically hard to determine the exact decaying phase of ARs in anAC. As shown in Subsection 2.1, the recurring AR12192 on CR2157 has fairly different parameters and configurationfrom that of AR12192 on CR2156, possibly caused by flux emergence. Hence, we use the configuration of AR12192 onCR2157, while its previous occurrence is not assimilated. Such issue is a direct result of the identification problem inACs described in Subsection 2.1, and remains a possible problem for assimilation studies using real ARs. RESULTS4.1.
The overall properties of the simulated poleward surge
In order to simulate the poleward surge of interest, we first assimilate all identified ARs during CRs 2145-2159 (DEC2013-JAN 2015). We use the synoptic map of CR2144 as the initial magnetic field configuration, after converting it toequal latitude along the y-axis and rescaling it to the resolution of the code. The simulation ends at CR2220 (AUG2019), which was the latest CR with HMI synoptic maps available when the simulation was conducted.We generate the magnetic butterfly diagram for the whole simulated time range to display the simulated surge. Wealso demonstrate a butterfly diagram of one simulation without the identified ARs, solving the evolution of the initialfield only. They are shown in Figure 5(a) and 5(b), respectively. By comparing the diagrams we can show that thesurge is primarily generated by the ARs in the time period. Without such a surge and the originating ARs emergingduring the year 2014, the polar field reversal would not have been achieved. Instead it would remain at a low level,and even reverse to previous polarities. The validation of our SFT simulation results is presented in the Appendix A.In the following we present quantitative comparisons between the simulated results and observations.Polar fields are obtained by averaging from 60 ◦ to 75 ◦ latitudes for both hemispheres. Its evolution during CRs2145-2220 is shown in Figure 6. Observations (black lines) show that from the middle of 2014 to the end of 2015, thesouthern polar field quickly rises to maximum from near zero, and then decreases gradually as the flux of the leadingpolarity from the originating ARs begins reaching the south pole, while the northern polar field rises more steadilyand continuously. The simulated polar field of the southern hemisphere (red solid line) is close to observations duringthe majority of the latter half of cycle 24, though ARs after CR2159 are not assimilated into the simulation. Thisindicates that the rise to maximum and decrease from maximum of the southern polar field is mostly determined bythe ARs assimilated, while the ARs after CR2159 do not have a significant effect on the southern polar field. Thisconfirms the importance of the ARs during CRs 2145-2159 to the final polar field, hence to the long-term developmentof the solar cycle. According to Jiang et al. (2018); Jiang & Cao (2018), there are large ARs with abnormal tilt closeto the equator during the years 2016 and 2017, weakening the contribution of ARs after CR2159 to the final polarfield. As a result, the final polar field at cycle 24 minimum is largely determined by the ARs during CRs 2145-2159.Without ARs during the time period (blue lines), the final polar field would be extremely weak, leading to a possiblenext Maunder minimum. These ARs keep this from happening, and build up the final polar field, which has a similarstrength to that of cycle 23. Based on such strength of polar fields, we expect a moderate cycle 25.The surge we consider is stronger and more influential than other poleward flux migrations in the latter half ofcycle 24. We show the observed and simulated field strength at different latitudes in Figure 7. As shown by the blackcurves obtained from observational data, the surge maintains its width of approximately 0.7-1.0 yr until it reaches highlatitudes, that is, -55 ◦ (Figure 7(e)) to -60 ◦ (Figure 7(f)). With a strength larger than 3 G, the surge is significantlystronger than following surges, of which the strength does not exceed 1G. For intermediate latitudes that are not closeto the pole (where the net flux does not pile up), like latitudes -35 ◦ (Figure 7(a)) and -45 ◦ (Figure 7(b)), we can seefrom the black observational curves that the surges after the prominent surge we consider are of different signs, sotheir influence on the final polar field is fairly small. As shown by the red solid curves, our simulation of the surgeof interest maintains its key features, while being not as narrow as the observational surge. The simulated surge at35 ◦ is located somewhat away from the center of the observational surge, which is possibly a result of AR assimilationrandom error. The initial difference is, however, reduced by the transport of flux. The magnetic field evolution inthe simulation after CR2159, that is, after all AR assimilation, stays close to that of observations. This is similar tothe situation of polar field evolution. Thus we can conclude that the surge we consider defines the major evolution ofmagnetic field of the southern hemisphere since CR2145.The surge is primarily generated by ARs within ACs. To show this, we run a simulation with only ARs within thetwo ACs described in Subsection 2.2 and CR2144 as the initial field. The generated surge by only ARs in the twoACs is shown as the red dash-dot curves in Figure 7. The resulting surge is fairly close to the overall result of thesurge where all ARs are assimilated, with matching surge strength and width. The ARs in the two ACs generate theprominent surge, and in turn have a long-lasting influence on the southern polar field during the latter half of cycle24. 4.2. Evolution characteristics of ARs within ACs
ACs are characterized as consistent flux emergence as well as cancellation, which affects the configuration of surfaceflux. In order to discuss how this feature is simulated in the SFT model, we choose a sequence of ARs between180 ◦ and 270 ◦ longitudes during CRs 2152-2153 of the southern hemisphere to simulate their evolution together. Theparameters of these ARs are shown in Table 3. Most ARs listed in Table 3 have large and positive tilt angles, but witha wide range of variation. This is expected since statistical studies of tilt angles have shown that tilt angles of ARs havea large deviation from the Joy’s law (Hale et al. 1919). The scatter of the tilts is regarded as the result of the buffetingby convective turbulence during the rise of flux tubes through the convection zone to form ARs (Weber et al. 2013).The poleward flux originates from a part of the trailing polarity depending on the tilt angles and latitudes of ARs inthe AC. We note that, among the listed ARs, some are too close to be identified individually. Hence some identifiedregions may contain more than one NOAA AR, e.g., the pair of ARs 12104 and 12107. We start the simulation withoutinitial field and assimilate the ARs on their corresponding day. The simulation is run for 10 years for the field to reachtheir finial state.During the simulation, opposite polarities of close ARs cancel, which is also seen in observations. Figure 8 showsthe simulated synoptic maps for CRs 2153-2158. In the simulation, a large area of concentrated flux of the leadingpolarity, that is, positive polarity is formed at the edge of the AC, as the flux from ARs cancels out. Apparently thepolarities of the same sign from different ARs tend to merge into larger area of flux as a result of cancellation betweenARs, similar to the observations of Gaizauskas (2008). Eventually a long-lived unipolar region is formed, and affectsnearby ARs, as described in Subsection 2.1. The unipolar region of positive polarity still resides at low to intermediate0 Field Strength [G] -3 -2 -1 0 1 2 3 -90-4504590 L a t i t u d e [ d e g ] -90-4504590 L a t i t u d e [ d e g ] L a t i t u d e [ d e g ] (a)(b)(c) Figure 5.
Simulated magnetic butterfly diagrams for the simulation starting at CR2144 with ARs during CRs 2145-2159assimilated (a), the simulation starting at CR2144 without ARs assimilated (b), and the simulation with no starting field andwith ARs listed in Table 3 assimilated (c). latitudes after CR2156 for several rotations. Hence it exists close to AR12192 as it evolves for a considerably longtime. The extended coexistence of the unipolar region and the diffusive AR12192 affects the identification of AR12192and new weak flux emergence, as well as the analysis of the development of AR12192 in the following CRs. In the SFTmodel, ARs interact only in the form of cancellation from supergranular diffusion. Consequently, the observed processof gathering same sign polarities and the formation of unipolar regions is mostly a result of flux cancellation. Suchcancellation of ARs is common for ACs, as described in Subsection 2.2, and in the observations of Gaizauskas et al.(2001) and Gaizauskas (2008).We present the simulated magnetic butterfly diagram shown in Figure 5(c), for assimilating only a part of the ACs.The butterfly diagram shows that the part of ACs assimilated creates a section of the poleward surge of the trailingpolarity. As for the leading polarity, both poleward migration and transequatorial migration occur. This is the typicalevolution for a single AR at intermediate emerging latitudes. After the surge, the large unipolar region of the positive1 P o l a r fi e l d [ G ] Figure 6.
Time evolution of polar field. Solid lines indicate the southern hemisphere, and dashed lines indicate the northernhemisphere. Black lines are observational data. Red lines are results of the simulation with initial field CR2144 and withARs during CRs 2145-2159 assimilated. Blue lines are results of the simulation with initial field CR2144 and without ARsassimilated. The vertical black dashed line near year 2015 indicates CR 2159, the last CR with ARs assimilated. -5-4-3-2-1012 M a g n e t i c fi e l d [ G ] M a g n e t i c fi e l d [ G ] (a) (b) (c)(d) (e) (f) Figure 7.
Comparisons of longitudinally averaged magnetic field on different latitudes of the southern hemisphere, obtainedby slicing magnetic butterfly diagram on 35 ◦ (a), 40 ◦ (b), 45 ◦ (c), 50 ◦ (d), 55 ◦ (e), and 60 ◦ (f). The black solid curves areobservational, the red solid curves show the simulation including all ARs, the red dashed curves show the simulation includingARs listed in Table 3, and the red dash-dotted curves show the simulation including all ARs in ACs described in Subsection2.2. All curves are smoothed with a width of 3 rotations. The vertical black dashed lines indicate CR2159, the last CR withARs assimilated. DISCUSSION AND CONCLUSIONWe have applied a data-driven SFT model to simulate the formation and evolution of the prominent poleward surgeoriginating from ARs during CRs 2145-2159 on the southern hemisphere in solar cycle 24. We find the strength andshape of the surge is primarily determined by ARs within the two ACs, which consists of about half the number of allARs identified. Our simulations show that the ARs within the ACs generating the surge have a strong long-term effecton the final polar field at cycle minimum, while other surges during the latter half of cycle 24 only have considerably lesseffect on the final polar field. The development of the southern polar field of the latter half of cycle 24 is predominantlyshaped by ARs generating the surge. Without the ARs within the ACs generating the prominent surge, the final polarfield would be less than 1 G, and even reverse to previous polarities. The ARs within the ACs effectively build up thepolar field of cycle 24 minimum, thus determining the strength of cycle 25 in the framework of B-L-type dynamos,instead of entering a next Maunder minimum. The surge we consider is different from the surge studied by Yeates et al.(2015). Our surge is stronger and has longer persistence than the surge studied by Yeates et al. (2015). The ARsgenerating our surge mostly lie between -10 ◦ to -20 ◦ latitudes, which are lower than that of Yeates et al. (2015)’s,and our surge has significantly larger long-term polar field influence. This is consistent with the relationship betweenARs’ final polar field contributions and emerging latitudes proposed by Jiang et al. (2014). Since the strength andlong-term polar field influence of the surge is unique to cycle 24, it makes sense to refer to it as a “super surge”, similarto the idea of super ARs. This feature is a notable supplementary to the AC-surge-polar field relationship obtainedfrom previous observations.In SFT simulations, ARs within ACs are similar to a single, large AR in terms of surge generation and polar fieldinfluence, as the observed process of ARs’ emergence and cancellation creating large regions of leading and trailingpolarities can be simulated by SFT processes. For large ARs with large latitude coverage, the long-term polar fieldinfluence is focused on the flux located around lower latitudes. Thus it may deviate from estimations given by overallAR parameters. The concept was first proposed by Jiang et al. (2019) based on the evolution of a βγδ type AR. Theeffect of size asymmetry for two polarities of BMR type ARs examined in Iijima et al. (2019) is also consistent withthis concept. ACs and ARs with large latitude coverage can contribute to both surge and polar field, and it is likelythat the surge is not followed by prominent surge of the other polarity. Such a surge can be regarded as the cause oflong-term polar field change.Even for surges causing long-term polar field change, the contributed magnetic flux to the final polar field consistsof only a very small part of originating ARs’ total flux. The percentage depends on the tilt angle and latitude of theARs. The AR flux decreases monotonically as a result of diffusive cancellation at the neutral line. Poleward fluxesfrom separate ARs still cancel in the polar caps if they have different polarities. The axial dipole field, which resultsfrom AR tilt angles, has the longest lifetime among different orders of multipoles (Wang et al. 2000; Baumann et al. Table 3.
Parameters of the selected ARs within the ACDay of emergence a Latitude Longitude Area Positive flux Negative flux Tilt NOAA/AR number(degree) (degree) ( µ Hem) (10 Mx) (10 Mx) (degree)195 -15.2 262.9 4730.8 238.2 -154.6 47.0 12104,12107197 -8.5 237.8 3386.5 151.1 -179.9 1.8 12108,12110199 -8.1 218.9 2845.9 162.8 -128.4 5.0 12109224 -8.5 249.5 2198.8 88.8 -51.1 43.6 12127225 -18.5 238.5 1151.5 35.3 -33.4 7.2 12131227 -20.2 209.4 2368.9 84.5 -94.4 25.8 12132 a Since the end of CR2144 (2013 Dec 19). Field strength [G] -20 -15 -10 -5 0 5 10 15 20 -90-450-90-450-90-450-90-450-90-4500 45 90 135 180 225 270 315 360Longitude [deg]-90-450 L a t i t u d e [ d e g ] CR2153CR2154CR2155CR2156CR2157CR2158
Figure 8.
Stack plot created from the southern hemisphere of simulated synoptic maps of ARs assimilated in Subsection 4.2from CR2153 to CR2158. Each simulated synoptic map is displayed in equal space in latitude. A. VALIDATING THE SFT SIMULATION RESULTSIn order to examine the reliability of the SFT simulation results, we introduce two methods of validating the SFTsimulations.One method is to compare the one year evolution of the simulated polar field with observations. If the initial field andthe transport terms were ideal, the SFT simulated polar field would be comparable to observations for approximatelya year. This is because that the variation of the polar field is due to the magnetic flux originated from the activitybelt. It takes a few years for the flux to be transported to the poles. The red and blue lines in Figure 6, whichare represented in Appendix as Figure 9, are results of the simulations starting from CR2144 with and without ARsassimilated, respectively. In both cases, we find that they are consistent with observational data from HMI synopticmaps (black lines) for about 1 year since CR2145. Apart from these simulations described already in Subsection 4.1,we introduce another simulation with the initial field set as CR2159 and without ARs assimilated (orange lines inFigure 9). Its polar field evolutions also fit the standard of the method. These results show that the transport termsin the SFT model are generally reliable.The other validation is to compare two SFT simulations starting at different CRs while ending at the same CR. Stillif the initial field and the transport terms were ideal, the two SFT simulations would strictly follow each other duringthe overlapped time period. Here we compare the two simulations starting at CR2144 and CR2159, respectively. Weverify the consistency of the surface field’s development from CR2159 to the end of the simulations. We find fromFigure 9 that the red lines (starting at CR2144) and the orange lines (starting at CR2159) are fairly comparable. Thisresult further supports the reliability of the transport terms in the SFT model. The result also shows that the ARidentification and assimilation methods that we apply during CRs 2145-2159 produce source terms that are close tothe realistic flux emergence. The results of the two methods confirm the reliability of our simulation results.REFERENCES
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