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We investigate which scalar quantity or quantities can best predict the loss of equilibrium and subsequent eruption of magnetic flux ropes in the solar corona. Our models are initialized with a potential magnetic arcade, which is then evolved by means of two effects on the lower boundary: firstly a gradual shearing of the arcade, modelling differential rotation on the solar surface, and secondly supergranular diffusion. These result in flux cancellation at the polarity inversion line and the formation of a twisted flux rope. We use three model setups: full magnetohydrodynamics (MHD) in cartesian coordinates, and the magnetofrictional model in both cartesian and polar coordinates. The flux ropes are translationally-invariant, allowing for very fast computational times and thus a comprehensive parameter study, comprising hundreds of simulations and thousands of eruptions. Similar flux rope behavior is observed using either magnetofriction or MHD, and there are several scalar criteria that could be used as proxies for eruptivity. The most consistent predictor of eruptions in either model is the squared current in the axial direction of the rope, normalised by the relative helicity, although a variation on the previously proposed 'eruptivity index' is also found to perform well in both the magnetofrictional and MHD simulations., Comment: 20 pages, 11 figures, 1 table. Accepted to the Astrophysical Journal on 13th August 2023

We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the solar cycle. The main focus is on the "classical" model: namely, steady axisymmetric profiles for differential rotation and meridional flow, and uniform supergranular diffusion. Nevertheless, the review concentrates on recent advances, notably in understanding the roles of transport parameters and - in particular - the source term. We also discuss the physical justification for the surface flux transport model, along with efforts to incorporate radial diffusion, and conclude by summarizing the main directions where researchers have moved beyond the classical model., Comment: 35 pages, 11 figures, accepted for publication in Space Science Reviews

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index., Comment: 25 pages, 11 figures. To be published in 'Frontiers in Astronomy and Space Sciences', accepted for publication 8th March 2022

The input of the Solar wind models plays a significant role in accurate solar wind predictions at 1 AU. This work introduces a synthetic magnetogram produced from a dynamo model as an input for Magnetohydrodynamics (MHD) simulations. We perform a quantitative study that compares the Space Weather Modeling Framework (SWMF) results for the observed and the synthetic solar magnetogram input. For each case, we compare the results for Extreme Ultra-Violet (EUV) images and extract the simulation data along the earth trajectory to compare with in-situ observations. We initialize SWMF using the real and synthetic magnetogram for a set of Carrington Rotations (CR)s within the solar cycle 23 and 24. Our results help quantify the ability of dynamo models to be used as input to solar wind models and thus, provide predictions for the solar wind at 1 AU.

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index., Comment: 25 pages, 11 figures. To be published in 'Frontiers in Astronomy and Space Sciences', accepted for publication 8th March 2022

Given a known radial magnetic field distribution on the Sun's photospheric surface, there exist well-established methods for computing a potential magnetic field in the corona above. Such potential fields are routinely used as input to solar wind models, and to initialize magneto-frictional or full magnetohydrodynamic simulations of the coronal and heliospheric magnetic fields. We describe an improved magnetic field model which calculates a magneto-frictional equilibrium with an imposed solar wind profile (which can be Parker's solar wind solution, or any reasonable equivalent). These `outflow fields' appear to approximate the real coronal magnetic field more closely than a potential field, take a similar time to compute, and avoid the need to impose an artificial source surface. Thus they provide a practical alternative to the potential field model for initializing time-evolving simulations or modeling the heliospheric magnetic field. We give an open-source Python implementation in spherical coordinates and apply the model to data from Solar Cycle 24. The outflow tends to increase the open magnetic flux compared to the potential field model, reducing the well known discrepancy with in situ observations., Comment: 16 Pages, 6 Figures. To be published in the Astrophysical Journal (accepted 1/10/21)

Given a known radial magnetic field distribution on the Sun's photospheric surface, there exist well-established methods for computing a potential magnetic field in the corona above. Such potential fields are routinely used as input to solar wind models, and to initialize magneto-frictional or full magnetohydrodynamic simulations of the coronal and heliospheric magnetic fields. We describe an improved magnetic field model which calculates a magneto-frictional equilibrium with an imposed solar wind profile (which can be Parker's solar wind solution, or any reasonable equivalent). These `outflow fields' appear to approximate the real coronal magnetic field more closely than a potential field, take a similar time to compute, and avoid the need to impose an artificial source surface. Thus they provide a practical alternative to the potential field model for initializing time-evolving simulations or modeling the heliospheric magnetic field. We give an open-source Python implementation in spherical coordinates and apply the model to data from Solar Cycle 24. The outflow tends to increase the open magnetic flux compared to the potential field model, reducing the well known discrepancy with in situ observations., Comment: 16 Pages, 6 Figures. To be published in the Astrophysical Journal (accepted 1/10/21)

We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method consists of summing up the ultimate contributions of individual active regions to the solar axial dipole moment \revtwo{at the end of the cycle}. A potential limitation of the approach is its dependence on the underlying surface flux transport (SFT) model details. We demonstrate by both analytical and numerical methods that the factor relating the initial and ultimate dipole moment contributions of an active region displays a Gaussian dependence on latitude with parameters that only depend on details of the SFT model through the parameter $\eta/\Delta_u$ where $\eta$ is supergranular diffusivity and $\Delta_u$ is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2$\times$2D dynamo model we further demonstrate that the inaccuracies associated with the algebraic method are minor and the method may be able to reproduce the dipole moment values in a large majority of cycles., Comment: 15 pages, 5 figs. Accepted for publication in the Journal of Space Weather and Space Climate

Coronal jets and bright points occur prolifically in predominantly unipolar magnetic regions, such as coronal holes, where they appear above minority-polarity intrusions. Intermittent low-level reconnection and explosive, high-energy-release reconnection above these intrusions are thought to generate bright points and jets, respectively. The magnetic field above the intrusions possesses a spine-fan topology with a coronal null point. The movement of magnetic flux by surface convection adds free energy to this field, forming current sheets and inducing reconnection. We conducted three-dimensional magnetohydrodynamic simulations of moving magnetic elements as a model for coronal jets and bright points. A single minority-polarity concentration was subjected to three different experiments: a large-scale surface flow that sheared part of the separatrix surface only, a large-scale surface flow that also sheared part of the polarity inversion line surrounding the minority flux, and the latter flow setup plus a "fly-by" of a majority-polarity concentration past the moving minority-polarity element. We found that different bright-point morphologies, from simple loops to sigmoids, were created. When only the field near the separatrix was sheared, steady interchange reconnection modulated by quasi-periodic, low-intensity bursts of reconnection occurred, suggestive of a bright point with periodically varying intensity. When the field near the PIL was strongly sheared, on the other hand, filament channels repeatedly formed and erupted via the breakout mechanism, explosively increasing the interchange reconnection and generating non-helical jets. The fly-by produced even more energetic and explosive jets. Our results explain several key aspects of coronal-hole bright points and jets, and the relationships between them., Comment: 21 pages, 20 figures, accepted for publication in ApJ

The topology of magnetic fields near the open-closed flux boundary in the Sun's corona is an important influencing factor in the process of interchange reconnection, whereby plasma is exchanged between open and closed flux domains. Maps of the magnetic squashing factor at the radial outer boundary in coronal field models reveal the presence of the so-called `S-web', and suggest that interchange reconnection could potentially deposit closed coronal material into high-latitude regions far from the heliospheric current sheet. Here we demonstrate that certain features of the S-web reveal the underlying topological structure of the magnetic field. Specifically, in order for the arcing bands of highly squashed magnetic flux of the S-web to terminate or intersect away from the helmet streamer apex, there must be a null spine line that maps a finite segment of the photospheric open-closed boundary up to a singular point in the open flux domain. We propose that this association between null spine lines and arc termination points may be used to identify locations in the heliosphere that are preferential for the appearance of solar energetic particles or slow solar wind plasma with certain characteristics.

Coronal jets and bright points occur prolifically in predominantly unipolar magnetic regions, such as coronal holes, where they appear above minority-polarity intrusions. Intermittent low-level reconnection and explosive, high-energy-release reconnection above these intrusions are thought to generate bright points and jets, respectively. The magnetic field above the intrusions possesses a spine-fan topology with a coronal null point. The movement of magnetic flux by surface convection adds free energy to this field, forming current sheets and inducing reconnection. We conducted three-dimensional magnetohydrodynamic simulations of moving magnetic elements as a model for coronal jets and bright points. A single minority-polarity concentration was subjected to three different experiments: a large-scale surface flow that sheared part of the separatrix surface only, a large-scale surface flow that also sheared part of the polarity inversion line surrounding the minority flux, and the latter flow setup plus a "fly-by" of a majority-polarity concentration past the moving minority-polarity element. We found that different bright-point morphologies, from simple loops to sigmoids, were created. When only the field near the separatrix was sheared, steady interchange reconnection modulated by quasi-periodic, low-intensity bursts of reconnection occurred, suggestive of a bright point with periodically varying intensity. When the field near the PIL was strongly sheared, on the other hand, filament channels repeatedly formed and erupted via the breakout mechanism, explosively increasing the interchange reconnection and generating non-helical jets. The fly-by produced even more energetic and explosive jets. Our results explain several key aspects of coronal-hole bright points and jets, and the relationships between them., Comment: 21 pages, 20 figures, accepted for publication in ApJ

The topology of magnetic fields near the open-closed flux boundary in the Sun's corona is an important influencing factor in the process of interchange reconnection, whereby plasma is exchanged between open and closed flux domains. Maps of the magnetic squashing factor at the radial outer boundary in coronal field models reveal the presence of the so-called `S-web', and suggest that interchange reconnection could potentially deposit closed coronal material into high-latitude regions far from the heliospheric current sheet. Here we demonstrate that certain features of the S-web reveal the underlying topological structure of the magnetic field. Specifically, in order for the arcing bands of highly squashed magnetic flux of the S-web to terminate or intersect away from the helmet streamer apex, there must be a null spine line that maps a finite segment of the photospheric open-closed boundary up to a singular point in the open flux domain. We propose that this association between null spine lines and arc termination points may be used to identify locations in the heliosphere that are preferential for the appearance of solar energetic particles or slow solar wind plasma with certain characteristics.

On 21 August 2017 a total solar eclipse swept across the contiguous United States providing excellent opportunities for diagnostics of the Sun's corona. The Sun's coronal structure is notoriously difficult to observe except during solar eclipses; thus theoretical models must be relied upon for inferring the underlying magnetic structure of the Sun's outer atmosphere. These models are necessary for understanding the role of magnetic fields in the heating of the corona to a million degrees and generation of severe space weather. Here we present a methodology for predicting the structure of the coronal field based on long-term surface flux transport simulations whose output is utilized to extrapolate the coronal magnetic field structures. This prescription was applied to the 21 August 2017 solar eclipse. Post-eclipse analysis shows good agreement between model simulated and observed coronal structures and their locations on the limb. We demonstrate that slow changes in the Sun's surface magnetic field distribution driven by long-term flux emergence and evolution govern large-scale coronal structures with a (plausibly cycle-phase dependent) dynamical memory timescale on the order of few solar rotations -- opening up the possibility of large-scale, global corona predictions at least a month in advance., Comment: Revised version of manuscript detailing the methodology, models and data utilized to predict the coronal magnetic field structure of the solar eclipse on 21 August, 2017, now including post-eclipse comparisons between predictions and observations. This version replaces the older version and incorporates a correction in the PFSS rendering of the corona

Predictions of the solar wind at Earth are a central aspect of space weather prediction. The outcome of such a prediction, however, is highly sensitive to the method used for computing the magnetic field in the corona. We analyze the impact of replacing the potential field coronal boundary conditions, as used in operational space weather prediction tools, by non-potential conditions. For this, we compare the predicted solar wind plasma parameters with observations at 1 AU for two six-months intervals, one at solar maximum and one in the descending phase of the current cycle. As a baseline, we compare with the operational Wang-Sheeley-Arge model. We find that for solar maximum, the non-potential coronal model and an adapted solar wind speed formula lead to the best solar wind predictions in a statistical sense. For the descending phase, the potential coronal model performs best. The Wang-Sheeley-Arge model outperforms the others in predicting high speed enhancements and streamer interactions. A better parameter fitting for the adapted wind speed formula is expected to improve the performance of the non-potential model here.

Predictions of the solar wind at Earth are a central aspect of space weather prediction. The outcome of such a prediction, however, is highly sensitive to the method used for computing the magnetic field in the corona. We analyze the impact of replacing the potential field coronal boundary conditions, as used in operational space weather prediction tools, by non-potential conditions. For this, we compare the predicted solar wind plasma parameters with observations at 1 AU for two six-months intervals, one at solar maximum and one in the descending phase of the current cycle. As a baseline, we compare with the operational Wang-Sheeley-Arge model. We find that for solar maximum, the non-potential coronal model and an adapted solar wind speed formula lead to the best solar wind predictions in a statistical sense. For the descending phase, the potential coronal model performs best. The Wang-Sheeley-Arge model outperforms the others in predicting high speed enhancements and streamer interactions. A better parameter fitting for the adapted wind speed formula is expected to improve the performance of the non-potential model here.

On 21 August 2017 a total solar eclipse swept across the contiguous United States providing excellent opportunities for diagnostics of the Sun's corona. The Sun's coronal structure is notoriously difficult to observe except during solar eclipses; thus theoretical models must be relied upon for inferring the underlying magnetic structure of the Sun's outer atmosphere. These models are necessary for understanding the role of magnetic fields in the heating of the corona to a million degrees and generation of severe space weather. Here we present a methodology for predicting the structure of the coronal field based on long-term surface flux transport simulations whose output is utilized to extrapolate the coronal magnetic field structures. This prescription was applied to the 21 August 2017 solar eclipse. Post-eclipse analysis shows good agreement between model simulated and observed coronal structures and their locations on the limb. We demonstrate that slow changes in the Sun's surface magnetic field distribution driven by long-term flux emergence and evolution govern large-scale coronal structures with a (plausibly cycle-phase dependent) dynamical memory timescale on the order of few solar rotations -- opening up the possibility of large-scale, global corona predictions at least a month in advance., Comment: Revised version of manuscript detailing the methodology, models and data utilized to predict the coronal magnetic field structure of the solar eclipse on 21 August, 2017, now including post-eclipse comparisons between predictions and observations. This version replaces the older version and incorporates a correction in the PFSS rendering of the corona

We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity., Comment: 11 pages, 8 figures. Accepted for publication in Physics of Plasmas

We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity., Comment: 11 pages, 8 figures. Accepted for publication in Physics of Plasmas

In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions -- where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above) $10^{21}$Mx ($10^{22}$Mx). We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended into smaller fluxes), making our results compatible with the results of Parnell et al. (2009).

In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions -- where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above) $10^{21}$Mx ($10^{22}$Mx). We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended into smaller fluxes), making our results compatible with the results of Parnell et al. (2009).

We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double helmet streamer. This structure was originally observed by the SWAP instrument aboard the PROBA2 satellite between 5 and 10~May~2013. It consists of a pair of filament channels near the south pole of the sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a side-by-side double helmet streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modelling techniques. We describe the topology and dynamic consequences of such a unified structure., Comment: 19 pages, 4 figures, 2 linked animations, accepted by ApJL

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/SOT magnetograms. Eulerian and Lagrangian coherent structures are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (a-LCS) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of a-LCS provides a measure of the local rate of contraction/expansion of the flow., Comment: Submitted to ApJ

We report on the first observation of a single hybrid magnetic structure that contains both a pseudostreamer and a double helmet streamer. This structure was originally observed by the SWAP instrument aboard the PROBA2 satellite between 5 and 10~May~2013. It consists of a pair of filament channels near the south pole of the sun. On the western edge of the structure, the magnetic morphology above the filaments is that of a side-by-side double helmet streamer, with open field between the two channels. On the eastern edge, the magnetic morphology is that of a coronal pseudostreamer without the central open field. We investigated this structure with multiple observations and modelling techniques. We describe the topology and dynamic consequences of such a unified structure., Comment: 19 pages, 4 figures, 2 linked animations, accepted by ApJL

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/SOT magnetograms. Eulerian and Lagrangian coherent structures are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (a-LCS) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of a-LCS provides a measure of the local rate of contraction/expansion of the flow., Comment: Submitted to ApJ

The emergence of tilted bipolar active regions and the dispersal of their flux, mediated via processes such as diffusion, differential rotation and meridional circulation is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed $\alpha$-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithm for modeling the Babcock-Leighton mechanism based on active region eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations we first show that an axisymmetric formulation -- which is usually invoked in kinematic dynamo models -- can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models., Comment: Published in ApJL

The emergence of tilted bipolar active regions and the dispersal of their flux, mediated via processes such as diffusion, differential rotation and meridional circulation is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed $\alpha$-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithm for modeling the Babcock-Leighton mechanism based on active region eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations we first show that an axisymmetric formulation -- which is usually invoked in kinematic dynamo models -- can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models., Comment: Published in ApJL