Babcock-Leighton Solar Dynamo Model Research Articles

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.

Incorporating Surface Convection into a 3D Babcock–Leighton Solar Dynamo Model

Abstract The convective flows observed on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock–Leighton (BL) process to generate large-scale polar fields from sunspot fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields are modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. We present the first kinematic 3D Flux-Transport/BL model to explicitly incorporate realistic convective flows based on solar observations. Though we describe a means to generalize these flows to 3D, we find that the kinematic small-scale dynamo action they produce disrupts the operation of the cyclic dynamo. The cyclic solution is found by limiting the convective flow to act only on the vertical radial component of the magnetic field. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity of the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and a shorter cycle than in the convective models. Also, the convective models exhibit bands of mixed polarity in the polar regions that have no counterpart in solar observations, and the poleward migration speed of poloidal flux is determined mainly by the meridional flow and the vertical diffusion.

Recovery from Maunder-like Grand Minima in a Babcock–Leighton Solar Dynamo Model

Abstract The Sun occasionally goes through Maunder-like extended grand minima when its magnetic activity drops considerably from the normal activity level for several decades. Many possible theories have been proposed to explain the origin of these minima. However, how the Sun managed to recover from such inactive phases every time is even more enigmatic. The Babcock–Leighton type dynamos, which are successful in explaining many features of the solar cycle remarkably well, are not expected to operate during grand minima due to the lack of a sufficient number of sunspots. In this Letter, we explore the question of how the Sun could recover from grand minima through the Babcock–Leighton dynamo. In our three-dimensional dynamo model, grand minima are produced spontaneously as a result of random variations in the tilt angle of emerging active regions. We find that the Babcock–Leighton process can still operate during grand minima with only a minimal number of sunspots, and that the model can emerge from such phases without the need for an additional generation mechanism for the poloidal field. The essential ingredient in our model is a downward magnetic pumping, which inhibits the diffusion of the magnetic flux across the solar surface.

A Three dimensional Babcock-Leighton Solar Dynamo Model with Non-axisymmetric Convective Flows

AbstractThe observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields is modeled as an effective turbulent diffusion. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity on the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and shorter cycle.

Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock–Leighton Solar Dynamo Model

Abstract We present results from a three-dimensional Babcock–Leighton (BL) dynamo model that is sustained by the emergence and dispersal of bipolar magnetic regions (BMRs). On average, each BMR has a systematic tilt given by Joy’s law. Randomness and nonlinearity in the BMR emergence of our model produce variable magnetic cycles. However, when we allow for a random scatter in the tilt angle to mimic the observed departures from Joy’s law, we find more variability in the magnetic cycles. We find that the observed standard deviation in Joy’s law of produces a variability comparable to the observed solar cycle variability of ∼32%, as quantified by the sunspot number maxima between 1755 and 2008. We also find that tilt angle scatter can promote grand minima and grand maxima. The time spent in grand minima for is somewhat less than that inferred for the Sun from cosmogenic isotopes (about 9% compared to 17%). However, when we double the tilt scatter to , the simulation statistics are comparable to the Sun (∼18% of the time in grand minima and ∼10% in grand maxima). Though the BL mechanism is the only source of poloidal field, we find that our simulations always maintain magnetic cycles even at large fluctuations in the tilt angle. We also demonstrate that tilt quenching is a viable and efficient mechanism for dynamo saturation; a suppression of the tilt by only 1°–2° is sufficient to limit the dynamo growth. Thus, any potential observational signatures of tilt quenching in the Sun may be subtle.

Role of response time of a Babcock-Leighton solar dynamo model in meridional flow-speed reconstruction by EnKF data assimilation

Ensemble Kalman Filter in the framework of Data Assimilation Research Testbed (DART) has been successfully implemented into a 2D kinematic flux-transport dynamo model by Dikpati and colleagues in order to do a parameter estimation, the parameter being the meridional flow-speed as function of time. They performed several ‘Observing System Simulation Experiments’ (OSSEs), and showed that an optimal reconstruction of time-series of meridional flow-speed can be obtained by using 16 ensemble members and only one surface magnetic observation with 30% observational error. Error in reconstruction can be reduced by increasing the ensemble size and number of observations. However, this parameter reconstruction has been found to be sensitive to locations from where observational data are taken. While assimilation of low-latitudes’ surface poloidal magnetic field data can produce good reconstruction, medium-frequency oscillations appear in time-series of reconstructed flow-speed if tachocline toroidal field data are assimilated. These oscillations occur primarily because tachocline toroidal fields change very little during an assimilation interval taken to be 15days, due to changes in meridional flow. A Babcock-Leighton dynamo model’s response time to changes in meridional flow-speed is a few months. We show here that rms error in reconstruction can be significantly reduced if model’s response time is taken into consideration in assimilation of tachocline toroidal field data.

A three-dimensional Babcock–Leighton solar dynamo model: Initial results with axisymmetric flows

The main objective of this paper is to introduce the STABLE (Surface flux Transport And Babcock–LEighton) solar dynamo model. STABLE is a 3D Babcock–Leighton/Flux Transport dynamo model in which the source of poloidal field is the explicit emergence, distortion, and dispersal of bipolar magnetic regions (BMRs). Here we describe the STABLE model in more detail than we have previously and we verify it by reproducing a 2D mean-field benchmark. We also present some representative dynamo simulations, focusing on the special case of kinematic magnetic induction and axisymmetric flow fields. Not all solutions are supercritical; it can be a challenge for the BL mechanism to sustain the dynamo when the turbulent diffusion near the surface is ⩾1012cm2s−1. However, if BMRs are sufficiently large, deep, and numerous, then sustained, cyclic, dynamo solutions can be found that exhibit solar-like features. Furthermore, we find that the shearing of radial magnetic flux by the surface differential rotation can account for most of the net toroidal flux generation in each hemisphere, as has been recently argued for the Sun by Cameron and Schüssler (2015).

A mean-field Babcock-Leighton solar dynamo model with long-term variability

Dynamo models relying on the Babcock-Leighton mechanism are successful in reproducing most of the solar magnetic field dynamical characteristics. However, considering that such models operate only above a lower magnetic field threshold, they do not provide an appropriate magnetic field regeneration process characterizing a self-sustainable dynamo. In this work we consider the existence of an additional α-effect to the Babcock-Leighton scenario in a mean-field axisymmetric kinematic numerical model. Both poloidal field regeneration mechanisms are treated with two different strength-limiting factors. Apart from the solar antisymmetric parity behavior, the main solar features are reproduced: cyclic polarity reversals, mid-latitudinal equatorward migration of strong toroidal field, poleward migration of polar surface radial fields, and the quadrature phase shift between both. Long-term variability of the solutions exhibits lenghty periods of minimum activity followed by posterior recovery, akin to the observed Maunder Minimum. Based on the analysis of the residual activity during periods of minimum activity, we suggest that these are caused by a predominance of the α-effect over the Babcock-Leighton mechanism in regenerating the poloidal field.

Turbulent magnetic pumping in a Babcock-Leighton solar dynamo model

The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. In this work, we have explored the effects of the turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. The results reveal the importance of the pumping mechanism for solving current limitations in mean field dynamo modeling such as the storage of the magnetic flux and the latitudinal distribution of the sunspots. In the case that a meridional flow is assumed to be present only in the upper part of the convective zone, it is the full turbulent pumping that regulates both the period of the solar cycle and the latitudinal distribution of the sunspots activity.