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Mean field models of flux transport dynamo and meridional circulation in the Sun and stars
Solar and Stellar Astrophysics · Submitted 18 Feb 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field.
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The abstract, sentence by sentence
The most widely accepted model of the solar cycle is the flux transport dynamo model. This model evolved out of the traditional $\alpha \Omega$ dynamo model which was first developed at a time when the existence of the Sun's meridional circulation was not known. In these models, the toroidal magnetic field (which gives rise to sunspots) is generated by the stretching of the poloidal field by solar differential rotation. The primary source of the poloidal field in the flux transport models is attributed to the Babcock--Leighton mechanism, in contrast to the mean-field $\alpha$-effect used in earlier models. With the realization that the Sun has a meridional circulation, which is poleward at the surface and is expected to be equatorward at the bottom of the convection zone, its importance for transporting the magnetic fields in the dynamo process was recognized. Much of our understanding about the physics of both the meridional circulation and the flux transport dynamo has come from the mean field theory obtained by averaging the equations of MHD over turbulent fluctuations. The mean field theory of meridional circulation makes clear how it arises out of an interplay between the centrifugal and thermal wind terms. We provide a broad review of mean field theories for solar magnetic fields and flows, the flux transport dynamo modeling paradigm and highlight some of their applications to solar and stellar magnetic cycles. We also discuss how the dynamo-generated magnetic field acts on the meridional circulation of the Sun and how the fluctuations in the meridional circulation, in turn, affect the solar dynamo. We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The most widely accepted model of the solar cycle is the flux transport dynamo model. | background 1.00 | 0.03 | 0.04 | asserted 1.00 |
| s1 | This model evolved out of the traditional $\alpha \Omega$ dynamo model which was first developed at a time when the existence of the Sun's meridional circulation was not known. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s2 | In these models, the toroidal magnetic field (which gives rise to sunspots) is generated by the stretching of the poloidal field by solar differential rotation. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s3 | The primary source of the poloidal field in the flux transport models is attributed to the Babcock--Leighton mechanism, in contrast to the mean-field $\alpha$-effect used in earlier models. | background 1.00 | 0.04 | 0.04 | asserted 0.99 |
| s4 | With the realization that the Sun has a meridional circulation, which is poleward at the surface and is expected to be equatorward at the bottom of the convection zone, its importance for transporting the magnetic fields in the dynamo process was recognized. | background 0.99 | 0.05 | 0.04 | asserted 0.76 |
| s5 | Much of our understanding about the physics of both the meridional circulation and the flux transport dynamo has come from the mean field theory obtained by averaging the equations of MHD over turbulent fluctuations. | background 0.94 | 0.06 | 0.04 | asserted 0.98 |
| s6 | The mean field theory of meridional circulation makes clear how it arises out of an interplay between the centrifugal and thermal wind terms. | background 0.92 | 0.09 | 0.04 | asserted 1.00 |
| s7 | We provide a broad review of mean field theories for solar magnetic fields and flows, the flux transport dynamo modeling paradigm and highlight some of their applications to solar and stellar magnetic cycles. | contribution 1.00 | 0.67 | 0.09 | asserted 0.75 |
| s8 | We also discuss how the dynamo-generated magnetic field acts on the meridional circulation of the Sun and how the fluctuations in the meridional circulation, in turn, affect the solar dynamo. | contribution 1.00 | 0.18 | 0.08 | asserted 0.86 |
| s9 | We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field. | future work 1.00 | 0.27 | 0.50 | hedged possibility 0.73 |
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The paper
Original abstract
The most widely accepted model of the solar cycle is the flux transport dynamo model. This model evolved out of the traditional $\alpha \Omega$ dynamo model which was first developed at a time when the existence of the Sun's meridional circulation was not known. In these models, the toroidal magnetic field (which gives rise to sunspots) is generated by the stretching of the poloidal field by solar differential rotation. The primary source of the poloidal field in the flux transport models is attributed to the Babcock--Leighton mechanism, in contrast to the mean-field $\alpha$-effect used in earlier models. With the realization that the Sun has a meridional circulation, which is poleward at the surface and is expected to be equatorward at the bottom of the convection zone, its importance for transporting the magnetic fields in the dynamo process was recognized. Much of our understanding about the physics of both the meridional circulation and the flux transport dynamo has come from the mean field theory obtained by averaging the equations of MHD over turbulent fluctuations. The mean field theory of meridional circulation makes clear how it arises out of an interplay between the centrifugal and thermal wind terms. We provide a broad review of mean field theories for solar magnetic fields and flows, the flux transport dynamo modeling paradigm and highlight some of their applications to solar and stellar magnetic cycles. We also discuss how the dynamo-generated magnetic field acts on the meridional circulation of the Sun and how the fluctuations in the meridional circulation, in turn, affect the solar dynamo. We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field.
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References
How the literature uses it
5 arXiv papers cite this in 5 sentences
Papers citing it
Cites it as background 5 papers
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The magnetic cycle of the Sun can be explained using the Babcock-Leighton (B-L) Solar Dynamo theory [ref] .
Impact of Anomalous Active Regions on the Large-scale Magnetic Field of the Sun · Introduction · 0.97
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For a thorough description, please refer to [ref] .
Physical Models for Solar Cycle Predictions · Toroidal to Poloidal Field generation · 0.97
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These models including this flow are known as flux-transport dynamo models and are reviewed in another chapter of this book [ref] .
Understanding Active Region Emergence and Origins on the Sun and Other Cool Stars · Crucial role of active regions in global field reversals · 0.99
What it cites · 83 sentences without a confident label
Builds on 2 papers
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Recently, [ref] extended the study of [ref] by incorporating radial turbulent pumping.
Exploring cycle period and parity of stellar magnetic activity with dynamo modeling · Extrapolation to stellar dynamos · 0.99
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Recently, [ref] extended the study of [ref] by incorporating radial turbulent pumping.
A dynamo model of magnetic activity in solar-like stars with different rotational velocities · Extrapolation to stellar dynamos · 0.99
Uses data or values from 2 papers
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The left panel of Fig. [ref] (taken from [ref] ) shows the P$_cyc$-P$_rot$ diagram for the stars with observed cycle period.
Chromospheric activity catalogue of 4454 cool stars. Questioning the active branch of stellar activity cycles · Extrapolation to stellar dynamos · 0.95
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By analyzing polar ice cores ($^14$C data), [ref] arrived at the result that there were about 27 grand minima in the last 11,000 yr.
Grand minima and maxima of solar activity: New observational constraints · The effects of random fluctuations in the · 0.87
Compares with 3 papers
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In this context, an independent study by [ref] claims that a relatively faster meridional flow in the rising phase of the cycle followed by a slower flow in the declining phase (on average throughout the meridional flow loop in the convection zone) can explain the occurrence of unusually deep minima between solar activity cycles; the results of [ref] does not appear to be inconsistent with this finding.
The unusual minimum of sunspot cycle 23 a consequence of Sun's meridional plasma flow variations · Evidence for variations · 0.98
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In this context, an independent study by [ref] claims that a relatively faster meridional flow in the rising phase of the cycle followed by a slower flow in the declining phase (on average throughout the meridional flow loop in the convection zone) can explain the occurrence of unusually deep minima between solar activity cycles; the results of [ref] does not appear to be inconsistent with this finding.
A theoretical model of the variation of the meridional circulation with the solar cycle · Evidence for variations · 0.98
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The results of [ref] are in broad agreement with this.
The origin of grand minima in the sunspot cycle · The effects of random fluctuations in the · 0.93
Cites as support 8 papers
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The Babcock-Leighton poloidal source is well constrained by near surface observations and is now thought to be the dominant driver of cycle to cycle variability over at least centennial time-scales [ref] ; these can be adequately captured in data driven surface flux transport models or dynamo models.
Sunspot group tilt angles and the strength of the solar cycle · The Future: Towards bridging mean-field approaches, flux transport dynamos and full magnetohydrodynamic simulations · 0.98
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The Babcock-Leighton poloidal source is well constrained by near surface observations and is now thought to be the dominant driver of cycle to cycle variability over at least centennial time-scales [ref] ; these can be adequately captured in data driven surface flux transport models or dynamo models.
The crucial role of surface magnetic fields for the solar dynamo · The Future: Towards bridging mean-field approaches, flux transport dynamos and full magnetohydrodynamic simulations · 0.98
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Subsequent research has shown that under certain circumstances the flux transport paradigm can work even in the presence of complex, multi-cellular meridional flow [ref] .
Is a deep one-cell meridional circulation essential for the flux transport Solar Dynamo? · Modelling the solar cycle: the paradigm shift from the $αΩ$ dynamo to the flux transport dynamo · 0.97
Cites as background 16 papers
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Within the next few years, different groups studied different aspects of the model [ref] .
Kinematic solar dynamo models with a deep meridional flow · Modelling the solar cycle: the paradigm shift from the $αΩ$ dynamo to the flux transport dynamo · 0.81
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Within the next few years, different groups studied different aspects of the model [ref] .
Towards A Mean-Field Formulation Of The Babcock-Leighton Type Solar Dynamo. I. Alpha Coefficient Versus Durney's Double Ring Approach · Modelling the solar cycle: the paradigm shift from the $αΩ$ dynamo to the flux transport dynamo · 0.81
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Within the next few years, different groups studied different aspects of the model [ref] .
Parity properties of an advection-dominated solar $\alpha^2\Om$-dynamo · Modelling the solar cycle: the paradigm shift from the $αΩ$ dynamo to the flux transport dynamo · 0.81
Discussion
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