Bipolar Magnetic Regions Research Articles

The Role of Meridional Flow in the Generation of Solar/Stellar Magnetic Fields and Cycles

Meridional flow is crucial in generating the solar poloidal magnetic field by facilitating poleward transport of the field from decayed bipolar magnetic regions (BMRs). As the meridional circulation changes with the stellar rotation rate, the properties of stellar magnetic cycles are expected to be influenced by this flow. In this study, we explore the role of meridional flow in generating magnetic fields in the Sun and Sun-like stars using the STABLE (surface flux transport and Babcock–Leighton) dynamo model. We find that a moderate meridional flow increases the polar field by efficiently driving the trailing polarity flux toward the pole, while a strong flow tends to transport both polarities of BMRs poleward, potentially reducing the polar field. Our findings are in perfect agreement with what one can expect from the surface flux transport model. Similarly, the toroidal field initially increases with moderate flow speeds and then decreases beyond a certain value. This trend is due to the competitive effects of shearing and diffusion. Furthermore, our study highlights the impact of meridional flow on the strength and duration of stellar cycles. By including the meridional flow from a mean-field hydrodynamics model in STABLE, we show that the magnetic field strength initially increases with the stellar rotation rate and then declines in rapidly rotating stars, offering an explanation of the observed variation of stellar magnetic field with rotation rate.

Toward a Live Homogeneous Database of Solar Active Regions Based on SOHO/MDI and SDO/HMI Synoptic Magnetograms. II. Parameters for Solar Cycle Variability

Solar active regions (ARs) determine solar polar fields and cause solar cycle variability within the framework of the Babcock–Leighton dynamo. The contribution of an AR to the polar field is measured by its dipole field, which results from flux emergence and subsequent flux transport over the solar surface. The dipole fields contributed by an AR before and after the flux transport are referred to as the initial and final dipole fields, respectively. For a better understanding and prediction of solar cycles, in this paper, we provide a database including AR's initial and final dipole fields and the corresponding results of their bipolar magnetic region (BMR) approximation from 1996 onward. We also identify the repeated ARs and provide the optimized transport parameters. Based on our database, we find that although the commonly used BMR approximation performs well for the initial dipole field, it exhibits a significant deviation for the final dipole field. To accurately assess an AR’s contribution to the polar field, the final dipole field with its real configuration should be applied. Despite the notable contributions of a few rogue ARs, approximately the top 500 ARs ordered by their final dipole fields are necessary to derive the polar field at the cycle minimum. While flux transport may increase or decrease the dipole field for an individual AR, its collective impact over all ARs in a cycle is a reduction in their total dipole field.

Correction to: Variabilities in the polar field and solar cycle due to irregular properties of bipolar magnetic regions

Correction to: Variabilities in the polar field and solar cycle due to irregular properties of bipolar magnetic regions

Analysis of BMR Tilt from AutoTAB Catalog: Hinting toward the Thin Flux Tube Model?

One of the intriguing mechanisms of the Sun is the formation of bipolar magnetic regions (BMRs) in the solar convection zone (CZ), which are observed as regions of concentrated magnetic fields of opposite polarity on the photosphere. These BMRs are tilted with respect to the equatorial line, which statistically increases with latitude. The thin flux tube model, employing the rise of magnetically buoyant flux loops and their twist by Coriolis force, is a popular paradigm for explaining the formation of tilted BMRs. In this study, we assess the validity of the thin flux tube model by analyzing the tracked BMR data obtained through the Automatic Tracking Algorithm for BMRs. Our observations reveal that the tracked BMRs exhibit the expected collective behaviors. We find that the polarity separation of BMRs increases over their normalized lifetime, supporting the assumption of a rising flux tube from the CZ. Moreover, we observe an increasing trend of the tilt with the flux of the BMR, suggesting that rising flux tubes associated with lower flux regions are primarily influenced by drag force and Coriolis force, while in higher flux regions, magnetic buoyancy dominates. Furthermore, we observe Joy’s law dependence for emerging BMRs from their first detection, indicating that at least a portion of the tilt observed in BMRs can be attributed to the Coriolis force. Notably, lower flux regions exhibit a higher amount of fluctuations associated with their tilt measurement compared to stronger flux regions, suggesting that lower flux regions are more susceptible to turbulent convection.

Variabilities in the polar field and solar cycle due to irregular properties of bipolar magnetic regions

ABSTRACT Decay and dispersal of the tilted bipolar magnetic regions (BMRs) on the solar surface are observed to produce the large-scale poloidal field, which acts as the seed for the toroidal field and, thus, the next sunspot cycle. However, various properties of BMR, namely, the tilt, time delay between successive emergences, location, and flux, all have irregular variations. Previous studies show that these variations can lead to changes in the polar field. In this study, we first demonstrate that our 3D kinematic dynamo model, STABLE, reproduces the robust feature of the surface flux transport (SFT) model, namely the variation of the generated dipole moment with the latitude of the BMR position. Using STABLE in both SFT and dynamo modes, we perform simulations by varying the individual properties of BMR and keeping their distributions the same in all the cycles as inspired by the observations. We find that randomness due to the distribution in either the time delay or the BMR latitude produces negligible variation in the polar field and the solar cycle. However, randomness due to BMR flux distribution produces substantial effects, while the scatter in the tilt around Joy’s law produces the largest variation. Our comparative analyses suggest that the scatter of BMR tilt around Joy’s law is the major cause of variation in the solar cycle. Furthermore, our simulations show that the magnetic field-dependent time delay of BMR emergence produces more realistic features of the magnetic cycle, consistent with observation.

Inflows Towards Bipolar Magnetic Active Regions and Their Nonlinear Impact on a Three-Dimensional Babcock–Leighton Solar Dynamo Model

The changing magnetic fields of the Sun are generated and maintained by a solar dynamo, the exact nature of which remains an unsolved fundamental problem in solar physics. Our objective in this paper is to investigate the role and impact of converging flows toward Bipolar Magnetic Regions (BMR inflows) on the Sun’s global solar dynamo. These flows are large-scale physical phenomena that have been observed and so should be included in any comprehensive solar dynamo model. We have augmented the Surface flux Transport And Babcock–LEighton (STABLE) dynamo model to study the nonlinear feedback effect of BMR inflows with magnitudes varying with surface magnetic fields. This fully-3D realistic dynamo model produces the sunspot butterfly diagram and allows a study of the relative roles of dynamo saturation mechanisms such as tilt-angle quenching and BMR inflows. The results of our STABLE simulations show that magnetic field-dependent BMR inflows significantly affect the evolution of the BMRs themselves and result in a reduced buildup of the global poloidal field due to local flux cancellation within the BMRs, to an extent that is sufficient to saturate the dynamo. As a consequence, for the first time, we have achieved fully 3D solar dynamo solutions, in which BMR inflows alone regulate the amplitudes and periods of the magnetic cycles.

Observations key to understanding solar cycles: a review

A paradigm shift is taking place in the conception of solar cycles. In the previous conception, the changing numbers of sunspots over intervals of 9–14 years have been regarded as the fundamental solar cycle although two average 11-year cycles were necessary to account for the complete magnetic cycle. In the revised picture, sunspots are a phase in the middle of two 22-year overlapping solar cycles that operate continuously with clock-like precision. More than 20 researchers have contributed to the initial research articles from 2014 through 2021 which are dramatically altering the perception of solar cycles. The two 22-year cycles overlap in time by 11 years. This overlap is coincidentally the same average duration as the sunspot phase in each 22-year cycle. This coincidence and the relative lack of knowledge of the large numbers of small active regions without sunspots is what led to the previous paradigm in which the 11-year sunspot phases were misinterpreted as a single fundamental solar cycle. The combination of the two 22-year solar cycles, with their large numbers of short-lived active regions and ephemeral active regions are now understood to be the fundamental cycle with the proposed name “The Hale Solar Cycle.” The two 22-year solar cycles each occupy separate but adjacent bands in latitude. The orientations of the majority of bipolar magnetic regions in the two adjacent bands differ from each other by ∼180°. Both bands continuously drift from higher to lower latitudes as has been known for sunspot cycles. However, the polarity reversal occurs at the start of each 22-year cycle and at higher latitudes than it does for the sunspot cycles. This paradigm shift in the concept of solar cycles has resulted in major reconsiderations of additional topics on solar cycles in this review. These are 1) the large role of ephemeral active regions in the origin of solar cycles, 2) the depth of the origin of active regions and sunspots, 3) the mechanisms of how areas of unipolar magnetic network migrate to the solar poles every 11 years, and 4) the nature of the polarity reversal in alternate 22-year cycles rather than 11-year cycles.

Toroidal Magnetic Flux Budget in Mean-field Dynamo Model of Solar Cycles 23 and 24

We study the toroidal magnetic flux budget of the axisymmetric part of a data-driven 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes the effects of the formation and evolution of bipolar magnetic regions (BMRs) emerging on the solar surface. By applying Stokes’s theorem to the dynamo induction equation, we show that the hemispheric magnitude of the net axisymmetric toroidal magnetic field generation rate in the bulk of the convection zone can only partially be estimated from the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the radial integral along the equator, which is mostly due to the rotational radial shear at the bottom of the convection zone, has the same magnitude and is nearly in phase with the effect of the surface latitudinal differential rotation. Also, the toroidal field generation rate estimate strongly depends on the latitudinal profile of the surface radial magnetic field near the poles. This profile in our dynamo models significantly deviates from the polar magnetic field distribution observed during the minima of Solar Cycles 22, 23, and 24. The cause of this discrepancy requires further observational and theoretical studies. Comparing the 2D axisymmetric and the 3D nonaxisymmetric dynamo models, we find an increase in the toroidal field generation rate in the 3D model due to the surface effects of BMRs, resulting in an increase in the axisymmetric poloidal magnetic field magnitude.

The influence of small bipolar magnetic regions on basic solar quantities

Understanding the evolution of the solar magnetic field is of great importance for heliosphere, dynamo, and irradiance studies, for example. While the contribution of the field in active regions (ARs) hosting sunspots to the Sun's large-scale field has been extensively modelled, we still lack a realistic model of the contribution of smaller-scale magnetic regions such as ephemeral regions which do not contain any sunspots. For this work, we studied the effect of small and large bipolar magnetic regions (BMRs) on the large-scale solar magnetic field. The evolution of the total and open magnetic flux, the polar fields, and the toroidal flux loss since 1874 has been simulated with a surface flux transport model (SFTM) and the results were compared to analytical considerations and observational data. For this purpose, we constructed semi-synthetic BMR records using the international sunspot number as a proxy. We calculated the emergence rate of all BMRs from a single power-law size distribution, whose exponent varies with solar activity. The spatial distribution of the BMRs was calculated from statistical relationships derived from various solar observations. We included BMRs with a magnetic flux as low as $2 $ Mx in our SFTM, corresponding to regions with lifetimes down to one day. We found a good agreement between the computed total magnetic flux and observations, even though we do not have a free parameter to adjust the simulated total flux to observations, as in earlier versions of the employed SFTM. The open flux, the polar fields, and the toroidal flux loss are also consistent with observations and independent reconstructions. In our model, small BMRs contribute about one-third of the total and open flux at activity maximum, while their contribution increases to roughly half at activity minimum. An even greater impact is found on the polar fields and the toroidal flux loss, for which the contribution of small BMRs is comparable to that of spot-containing ARs at all activity levels. Even so, smaller regions, not included in our simulations, do not seem to play a significant role due to their high tilt angle scatter. Our simulation results suggest that most of the statistical noise is caused by large ARs, while small BMRs have a stabilising effect on the magnetic flux evolution, especially for the polar field reversals. We conclude that small BMRs (here, with magnetic fluxes between $2 $ Mx and $3 $ Mx) may also play an important role in the evolution of the solar magnetic field at large spatial scales. Their impact is largest at low solar activity, but it is also substantial during activity maxima, although the actual relative contributions by small and large regions depend on the steepness of their emergence rate distribution. The inclusion of small BMRs in SFTM simulations will allow the secular variability in solar irradiance to be better constrained and the generation of the poloidal field in the Babcock-Leighton dynamo to be better understood.

Solar Cycle Observations

We describe the defining observations of the solar cycle that provide constraints for the dynamo processes operating within the Sun. Specifically, we report on the following topics: historical sunspot numbers and revisions; active region (AR) flux ranges and lifetimes; bipolar magnetic region tilt angles; Hale and Joy’s law; the impact of rogue ARs on cycle progression and the amplitude of the following cycle; the spatio-temporal emergence of ARs that creates the butterfly diagram; polar fields; large-scale flows including zonal, meridional, and AR in-flows; short-term cycle variability; and helioseismic results including mode parameter changes.

AutoTAB: Automatic Tracking Algorithm for Bipolar Magnetic Regions

Bipolar magnetic regions (BMRs) provide crucial information about solar magnetism. They exhibit varying morphology and magnetic properties throughout their lifetime, and studying these properties can provide valuable insights into the workings of the solar dynamo. The majority of previous studies have counted every detected BMR as a new one and have not been able to study the full life history of each BMR. To address this issue, we have developed Automatic Tracking Algorithm for BMRs (AutoTAB) that tracks the BMRs for their entire lifetime or throughout their disk passage. AutoTAB uses the binary maps of detected BMRs and their overlapping criterion to automatically track the regions. In this first article of this project, we provide a detailed description of the working of the algorithm and evaluate its strengths and weaknesses by comparing it with existing algorithms. AutoTAB excels in tracking even for the small BMRs (with a flux of ∼1020 Mx), and it has successfully tracked 9152 BMRs over the last two solar cycles (1996–2020), providing a comprehensive data set that depicts the evolution of various properties for each BMR. The tracked BMRs exhibit the well-known butterfly diagram and 11 yr solar cycle variation, except for small BMRs, which appear at all phases of the solar cycle and show a weak latitudinal dependence. Finally, we discuss the possibility of adapting our algorithm to other data sets and expanding the technique to track other solar features in the future.

Probing the variations in the timing of the Sun’s polar magnetic field reversals through observations and surface flux transport simulations

ABSTRACT The polar field reversal is a crucial process in the cyclic evolution of the large-scale magnetic field of the Sun. Various important characteristics of a solar cycle, such as its duration and strength, and also the cycle predictability, are determined by the polar field reversal time. While the regular measurements of solar magnetic field have been accumulated for more than half a century, there is no consensus in the heliophysics community concerning the interpretation of the Sun’s polar field measurements and especially the determination of polar field reversal time. There exists a severe problem of non-reproducibility in the reported results even from studies of the same observational data set, and this causes an obstacle to make more accurate forecasts of solar cycle. Here, we analyze the solar magnetograms from four instruments for the last four cycles, to provide a more correct interpretation of the polar field observations and to find more accurate time of the reversals. We show the absence of triple (multiple) reversals in Cycles 21–24, significant variations in the time interval between reversals in the hemispheres and in the time interval between a reversal and a cycle beginning. In order to understand the origin of the reversal time variation, we perform Surface Flux Transport (SFT) simulations and find out that the presence of the ‘anomalous’ bipolar magnetic regions (BMRs) in different phases of a cycle can cause cycle-to-cycle variations of the reversal time within the similar range found in observations.

Effects of Emerging Bipolar Magnetic Regions in Mean-field Dynamo Model of Solar Cycles 23 and 24

We model the physical parameters of Solar Cycles 23 and 24 using a nonlinear dynamical mean-field dynamo model that includes the formation and evolution of bipolar magnetic regions (BMRs). The Parker-type dynamo model consists of a complete MHD system in the mean-field formulation: the 3D magnetic induction equation, and 2D momentum and energy equations in the anelastic approximation. The initialization of BMRs is modeled in the framework of Parker’s magnetic buoyancy instability. It defines the depths of BMR injections, which are typically located at the edge of the global dynamo waves. The distribution with longitude and latitude and the size of the initial BMR perturbations are taken from the NOAA database of active regions. The modeling results are compared with various observed characteristics of the solar cycles. Only the BMR perturbations located in the upper half of the convection zone lead to magnetic active regions on the solar surface. While the BMRs initialized in the lower part of the convection zone do not emerge on the surface, they still affect the global dynamo process. Our results show that BMRs can play a substantial role in the dynamo processes and affect the strength of the solar cycles. However, the data driven model shows that the BMR’s effect alone cannot explain the weak Cycle 24. This weak cycle and the prolonged preceding minimum of magnetic activity were probably caused by a decrease of the turbulent helicity in the bulk of the convection zone during the decaying phase of Cycle 23.

Observational Study of Recurrent Jets Confined by Active Region Loops

With high spatial and temporal resolution data from the Solar Dynamics Observatory and the New Vacuum Solar Telescope (NVST), we present observations of recurrent jets confined by coronal loops that occurred in the active region NOAA 11726 from 02:00 to 12:00 UT on 2013 April 21. Three jets are clearly observed by the NVST in Hα line. These recurrent jets originate from the emerging bipolar magnetic region at the north of the active region. Half of them are related to the magnetic flux emergence, and the others are associated with the magnetic flux cancellation. Their velocities range from 80.6 ± 1.3 km s−1 to 433.6 ± 20.1 km s−1. Though they eject from the same source region, their shapes, sizes, and eruptive trajectories are not exactly the same. Most of them consist of cool (dark) and hot (bright) components. The differential emission measure distributions of the recurrent jets suggest that they are multithermal structures. The rotation directions of the recurrent jets are not consistent. Eight of them have a counterclockwise rotation, and the others have a clockwise rotation. The 12 recurrent jets are classified as blowout (accounting for 33%) and standard (accounting for 67%) jets. The velocity and density range of the blowout jets are slightly wider than those of the standard jets. The blowout jets have lower temperatures than the standard jets. These observational results suggest that the recurrent jets are probably triggered by recurrent magnetic reconnection between the emerging bipolar magnetic region and its overlying large-scale active region loops.

Three-dimensional non-kinematic simulation of the post-emergence evolution of bipolar magnetic regions and the Babcock-Leighton dynamo of the Sun

Context. The Babcock-Leighton flux-transport model is a widely accepted dynamo model of the Sun that can explain many observational aspects of solar magnetic activity. This dynamo model has been extensively studied in a two-dimensional (2D) mean-field framework in both kinematic and non-kinematic regimes. Recent three-dimensional (3D) models have been restricted to the kinematic regime. In these models, the surface poloidal flux is produced by the emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy’s law. Aims. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. In particular, we examine the effect of the radial extent of the BMR. We also report our initial results based on a cyclic Babcock-Leighton dynamo simulation. Methods. We extended a conventional 2D mean-field model of the Babcock-Leighton flux-transport dynamo into 3D non-kinematic regime, in which a full set of magnetohydrodynamic (MHD) equations are solved in a spherical shell using a Yin-Yang grid. The large-scale mean flows, such as differential rotation and meridional circulation, are not driven by rotationally constrained convection, but rather by the parameterized Λ-effect in this model. For the induction equation, we used a Babcock-Leighton α-effect source term by which the surface BMRs are produced in response to the dynamo-generated toroidal field inside the convection zone. Results. We find that in the 3D non-kinematic regime, the tilt angle of a newly-emerged BMR is very sensitive to the prescription for the subsurface structure of the BMR (particularly, its radial extent). Anti-Joy tilt angles are found unless the BMR is deeply embedded in the convection zone. We also find that the leading spot tends to become stronger (higher field strengths) than the following spot. The anti-Joy’s law trend and the morphological asymmetry of the BMRs can be explained by the Coriolis force acting on the Lorentz-force-driven flows. Furthermore, we demonstrate that the solar-like magnetic cycles can be successfully obtained if Joy’s law is explicitly given in the Babcock-Leighton α-effect. In these cyclic dynamo simulations, a strong Lorentz force feedback leads to cycle modulations in the differential rotation (torsional oscillation) and meridional circulation. The simulations, however, do not include radiative effects (e.g., enhanced cooling by faculae) that are required to properly model the torsional oscillations. The non-axisymmetric components of the flows are found to exist as inertial modes such as the equatorial Rossby modes.

Observational Signature of Tilt Quenching of Bipolar Magnetic Regions in the Sun

AbstractIt is believed that the tilt in the bipolar magnetic regions (BMRs) is produced due to a torque induced by the Coriolis force, acting on the diverging flow from the apex of the rising flux tube of the toroidal field in the solar convection zone (SCZ).The BMRs with a strong magnetic field are expected to have reduced tilt as they rise very quickly in the SCZ. This effect can provide the required nonlinear quenching mechanism to suppress the growth of magnetic filed in the dynamo models. Here, we use the magnetograms of the Michelson Doppler Imager (1996–2011) and Helioseismic and Magnetic Imager (2010–2018) to automatically detect the BMRs and look for the signature of tilt quenching. Based on the Bayesian inference method, our results show that the posterior distribution of quenching parameters is Gaussian, and the mean of this distribution agrees with the earlier findings.

Automatic Algorithm for Tracking Bipolar Magnetic Regions

AbstractProperties of bipolar magnetic regions (BMRs), particularly, the tilt angle play critical roles in generating the observed polar magnetic field and its reversal. Hence, a long-term study of BMR over its lifetime is crucial not only to understand the solar dynamo but also to identify the origin of the properties of BMR. In our work, we have developed an automatic algorithm to detect and track the BMRs from the line-of-sight (LOS) magnetograms of Michelson Doppler Imager (MDI) for the period of Solar Cycle 23 over its lifetime/disk passage. Here, we present the details of our algorithm and the features of BMR, particularly the tilt angle, magnetic field strength and lifetime.

An ALMA Observation of Time Variations in Chromospheric Temperature of a Solar Plage Region

Nanoflares and the shock formation of magnetohydrodynamic waves in the solar chromosphere have been considered as key physical mechanisms of the heating of the chromosphere and corona. To investigate candidates of their signature in the mm-wavelength, a tiny active region located on the solar disk was observed with the Atacama Large millimeter and sub-millimeter Array (ALMA) at 3 mm, coordinated with observatories on orbit including Hinode SOT spectro-polarimeter in the Cycle 4 solar campaign (19 March 2017). ALMA’s spatial resolution was moderate, far from the best performance, but it provided stable conditions that are suitable to investigate temporal variations in the mm-wavelength. We determined that the noise level is less than 20 K (σ) over 1 hour in the 20-s cadence time series of synthesized ALMA images. The time variations with amplitudes above the noise level were observed throughout the field of view, but variations exceeding 200 K, corresponding to energy input to the chromosphere on the order of 1020-22 erg, were localized in two locations. One location was on the polarity inversion line, where tiny concentrated magnetic patches exist in weak field and a tiny magnetic flux may be emergent. The other location was at the outer edge of a bipolar magnetic region, which was under development with a successive series of magnetic flux emergence. This observation suggests that nanoflare-class energy inputs in the chromosphere can occur associated with emerging flux activities.

On the effect of surface bipolar magnetic regions on the convection zone dynamo

ABSTRACTWe investigate the effect of surface bipolar magnetic regions (BMRs) on the large-scale dynamo distributed in the bulk of the convection zone. The study employs the non-linear three-dimensional mean-field dynamo model. We model the emergence of the BMRs on the surface through the non-axisymmetric magnetic buoyancy effect, which acts on the large-scale toroidal magnetic field in the upper half of the convection zone. The non-axisymmetric magnetic field that results from this mechanism is shallow. On the surface, the effect of the BMRs on the magnetic field generation is dominant. However, because of the shallow distribution of BMRs, its effect on the global dynamo is less compared with the effect on the convective zone dynamo. We find that the mean-field α-effect, which acts on the non-axisymmetric magnetic field of the BMRs, provides the greater contribution to the dynamo process than the tilt of the BMRs. Even so, the fluctuations of the tilt of the BMRs lead to parity braking in the global dynamo. At the surface, the non-axisymmetric magnetic fields, which are generated because of the activity of the BMRs, show a tendency for the bihelical spectrum with positive sign for the low ℓ modes during the maximum of the magnetic activity cycle.

Buildup of the Magnetic Flux Ropes in Homologous Solar Eruptions

Abstract Homologous coronal mass ejections (CMEs) are an interesting phenomenon, and it is possible to investigate the formation of CMEs by comparing multi-CMEs under a homologous physical condition. AR 11283 had been present on the solar surface for several days when a bipole emerged on 2011 September 4. Its positive polarity collided with the preexisting negative polarity belonging to a different bipole, producing recurrent solar activities along the polarity inversion line (PIL) between the colliding polarities, namely the so-called collisional PIL (cPIL). Our results show that a large amount of energy and helicity were built up in the form of magnetic flux ropes (MFRs), with recurrent release and accumulation processes. These MFRs were built up along the cPIL. A flux deficit method is adopted and shows that magnetic cancellation happens along the cPIL due to the collisional shearing scenario proposed by Chintzoglou et al. The total amount of canceled flux was ∼0.7 × 1021 Mx with an uncertainty of ∼13.2% within the confidence region of the 30° Sun-center distance. The canceled flux amounts to 24% of the total unsigned flux of the bipolar magnetic region. The results show that the magnetic fields beside the cPIL are very sheared, and the average shear angle is above 70° after the collision. The fast expansion of the twist kernels of the MFRs and the continuous eruptive activities are both driven by the collisional shearing process. These results are important for better understanding the buildup process of the MFRs associated with homologous solar eruptions.