In this paper we complete the presentation of a new hybrid $2\times2$D flux transport dynamo (FTD) model of the solar cycle based on the Babcock-Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. 2015 to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship between the surface dipole and the BMR-generating internal field, and correlation between dipole strength at cycle maximum and peak amplitude of the next cycle. The saturation of the cycle amplitude takes place through the quenching of the BMR tilt as a function of the internal field. The observed statistical scatter about the mean BMR tilt, built into the model, acts as a source of stochasticity which dominates amplitude fluctuations. The model thus can produce Dalton-like epochs of strongly suppressed cycle amplitude lasting a few cycles and can even shut off entirely following an unfavorable sequence of emergence events.
The contribution of the Babcock-Leighton mechanism to the generation of the Sun's poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper.
In this review, we explain recent progress made in the Babcock-Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are 2D axisymmetric and the mean-field dynamo equations are solved in the meriodional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton mechanism) involved in these models are inherently 3D process and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., Mean-field Babcock-Leighton dynamo models and Surfa…
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 fac…
The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a…
The 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 are 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 m…
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 …
Accurate knowledge of time-variation in meridional flow-speed and profile is crucial for estimating a solar cycle's features, which are ultimately responsible for causing space climate variations. However, no consensus has been reached yet about the Sun's meridional circulation pattern observations and theories. By implementing an Ensemble Kalman Filter (EnKF) data assimilation in a Babcock-Leighton solar dynamo model using Data Assimilation Research Testbed (DART) framework, we find that the best reconstruction of time-variation in meridional flow-speed can be obtained when ten or more observ…
We present the first global, three-dimensional simulations of solar/stellar convection that take into account the influence of magnetic flux emergence by means of the Babcock-Leighton (BL) mechanism. We have shown that the inclusion of a BL poloidal source term in a convection simulation can promote cyclic activity in an otherwise steady dynamo. Some cycle properties are reminiscent of solar observations, such as the equatorward propagation of toroidal flux near the base of the convection zone. However, the cycle period in this young sun (rotating three times faster than the solar rate) is ver…
The Sun is a magnetic star whose cyclic activity is thought to be linked to internal dynamo mechanisms. A combination of numerical modelling with various levels of complexity is an efficient and accurate tool to investigate such intricate dynamical processes. We investigate the role of the magnetic buoyancy process in 2D Babcock-Leighton dynamo models, by modelling more accurately the surface source term for poloidal field. Methods. To do so, we reintroduce in mean-field models the results of full 3D MHD calculations of the non-linear evolution of a rising flux tube in a convective shell. More…
Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes -- that is, the Babcock-Leighton mechanism. We perform kinematic dynamo simulations where the prescribed velocity field is a combination o…
Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a …
Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. Solutions with high-magnetic-diffusivity have too short periods and a wrong migration of their active belts. Only the low-diffusivity regime with advective meridional flows is usually considered. Aims. In the present paper we discuss these assumptions and applied a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes which supposedly form at the tachocline. We study the effect of the del…
At present, Babcock-Leighton flux transport solar dynamo models appear as the most promising model for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun's convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10 % of the Sun) and more complex than previously thought. Taken together these observations raise serious concerns on the validity of…
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…
We present a 3D kinematic solar dynamo model in which poloidal field is generated by the emergence and dispersal of tilted sunspot pairs (more generally Bipolar Magnetic Regions, or BMRs). The axisymmetric component of this model functions similarly to previous 2D Babcock-Leighton (BL) dynamo models that employ a double-ring prescription for poloidal field generation but we generalize this prescription into a 3D flux emergence algorithm that places BMRs on the surface in response to the dynamo-generated toroidal field. In this way, the model can be regarded as a unification of BL dynamo models…
Extreme solar activity fluctuations and the occurrence of solar grand minima and maxima episodes, are well established, observed features of the solar cycle. Nevertheless, such extreme activity fluctuations and the dynamics of the solar cycle during Maunder minima-like episodes remain ill-understood. We explore the origin of such extreme solar activity fluctuations and the role of dual poloidal field sources, namely the Babcock-Leighton mechanism and the mean-field alpha effect in the dynamics of the solar cycle. We mainly concentrate on entry and recovery from grand minima episodes such as th…
The toroidal magnetic field is assumed to be generated in the tachocline in most Babcock-Leighton (BL)-type solar dynamo models, in which the poloidal field is produced by the emergence and subsequent dispersal of sunspot groups. However, magnetic activity of fully convective stars and MHD simulations of global stellar convection have recently raised serious doubts regarding the importance of the tachocline in the generation of the toroidal field. In this study, we aim to develop a new BL-type dynamo model, in which the dynamo operates mainly within the bulk of the convection zone. Our 2D mode…
Constraining the outer boundary condition for the Babcock-Leighton dynamo models
School of Space and Earth Sciences, Beihang University（北京航空航天大学空间与地球科学学院）；Key Laboratory of Space Environment Monitoring and Information Processing of MIIT（工业和信息化部空间环境监测与信息处理重点实验室）；Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学研究中心）；Institute of Space Sciences, Shandong University（山东大学空间科学研究院）
The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series of papers we present one such dynamo model, and document its behavior and properties. This first paper focuses on one of the model's key components, namely surface magnetic flux evolution. Using a genetic algorithm, we obtain best-fit parameters of the transport model by least-squares minimization of the differences between the associated synthetic synoptic …
The 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. 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. Since most Flux-Transport (FT)/BL mode…
In Sun and sun-like stars, it is believed that the cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock--Leighton type kinematic dynamo…
The key elements of the Babcock-Leighton dynamos are the generation of poloidal field through decay and dispersal of tilted bipolar active regions and the generation of toroidal field through the observed differential rotation. These models are traditionally known as flux transport dynamo models as the equatorward propagations of the butterfly wings in these models are produced due to an equatorward flow at the bottom of the convection zone. Here we investigate the role of downward magnetic pumping near the surface using a kinematic Babcock-Leighton model. We find that the pumping causes the p…
We present results from a three-dimensional Babcock--Leighton dynamo model that is sustained by the explicit 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 $σ_δ= 15^\circ$ produces a variability comparable t…
We explore the cause of the solar cycle variabilities using a novel 3D Babcock--Leighton dynamo model. In this model, based on the toroidal flux at the base of the convection zone, bipolar magnetic regions (BMRs) are produced with statistical properties obtained from observed distributions. We find that a little quenching in BMR tilt is sufficient to stabilize the dynamo growth. The randomness and nonlinearity in the BMR emergences make the poloidal field unequal and cause some variability in the solar cycle. However, when observed scatter of BMR tilts around Joy's law with a standard deviatio…
The flux transport dynamo, in which the poloidal magnetic field is generated by the Babcock--Leighton mechanism and the meridional circulation plays a crucial role, has emerged as an attractive model for the solar cycle. Based on theoretical calculations done with this model, we argue that the fluctuations in the Babcock--Leighton mechanism and the fluctuations in the meridional circulation are the most likely causes of the irregularities of the solar cycle. With our increased theoretical understanding of how these irregularities arise, it can be possible to predict a future solar cycle by fee…
Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock-Leighton mechanism is the only source of the poloidal field. Yeates et al. (2008) argue that the discrepancy arises due to different memories of the solar dynamo for advection- and diffusion-dominated solar convection zones. We aim to investigate the differences in solar cycle memory obtained from advection-dominated and diffusion-dominated kinematic solar dynamo models. Specifically, we explore whether the inclusion of Parker's mean-field $α$ effect, in …
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 $α$-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 surf…
We study the influence of various magnetic diffusivity profiles on the evolution of the poloidal and toroidal magnetic fields in a kinematic flux transport dynamo model for the Sun. The diffusivity is a poorly understood ingredient in solar dynamo models. We mathematically construct various theoretical profiles of the depth-dependent diffusivity, based on constraints from mixing length theory and turbulence, and on comparisons of poloidal field evolution on the Sun with that from the flux-transport dynamo model. We then study the effect of each diffusivity profile in the cyclic evolution of th…
Recent results indicate that the Babcock-Leighton mechanism for poloidal field creation plays an important role in the solar cycle. However, modelling this mechanism has not always correctly captured the underlying physics. In particular, it has been demonstrated that using a spatially distributed near-surface alpha-effect to parametrize the Babcock-Leighton mechanism generates results which do not agree with observations. Motivated by this, we are developing a physically more consistent model of the solar cycle in which we model poloidal field creation by the emergence and flux dispersal of d…
An explanation is suggested for the north-south asymmetry of the polar magnetic field reversal in the current cycle of solar activity. The contribution of the Babcock-Leighton mechanism to the poloidal field generation is estimated using sunspot data for the current activity cycle. Estimations are performed separately for the northern and southern hemispheres. The contribution of the northern hemisphere exceeded considerably that of the southern hemisphere during the initial stage of the cycle. This is the probable reason for the earlier reversal of the northern polar field. The estimated cont…
Parameters of a special kind of α-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates evidence the presence of the Babcock-Leighton α-effect on the Sun. Fluctuations of the α-effect are also estimated. The fluctuation amplitude appreciably exceeds the mean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numerical model for the solar dynamo. Computations show irregular changes in the amplitudes of the magn…
The Babcock-Leighton (BL) flux-transport model is a widely-accepted dynamo model of the Sun. 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. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. We also report initial results of cyclic BL dynamo…
The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt-angle proportional to the rotation rate are constructed to probe this idea. Two versions of the model - treating the tilt-angles globally and using Joy's law for its latitude depend…
In 1969 Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock(1961). Here we present a modification and extension of Leighton's model. Using the axisymmetric component of the magnetic field, we consider the radial field component at the solar surface and the radially integrated toroidal magnetic flux in the convection zone, both as functions of latitude. No assumptions are made with regard to the radial location of the toroidal flux. The model includes the effects of turbulent diffusion at the surface and in the convection …
A new formula for predicting solar cycles based on the current theoretical understanding of the solar cycle from flux transport dynamo is presented. Two important processes---fluctuations in the Babcock-Leighton mechanism and variations in the meridional circulation, which are believed to be responsible for irregularities of the solar cycle---are constrained by using observational data. We take the polar field near minima of the cycle as a measure of the randomness in the Babcock-Leighton process, and the decay rate near the minima as a consequence of the change in meridional circulation. We c…
We amend Babcock's original scenario for the global dynamo process that sustains the Sun's 22-year magnetic cycle. The amended scenario fits post-Babcock observed features of the magnetic activity cycle and convection zone, and is based on ideas of Spruit and Roberts (1983) about magnetic flux tubes in the convection zone. A sequence of four schematic cartoons lays out the proposed evolution of the global configuration of the magnetic field above, in, and at the bottom of the convection zone through sunspot Cycle 23 and into Cycle 24. Three key elements of the amended scenario are: (1) as the …
Aims: To understand stellar magnetism and to test the validity of the Babcock-Leighton flux transport mean field dynamo models with stellar activity observations Methods: 2-D mean field dynamo models at various rotation rates are computed with the STELEM code to study the sensitivity of the activity cycle period and butterfly diagram to parameter changes and are compared to observational data. The novelty is that these 2-D mean field dynamo models incorporate scaling laws deduced from 3-D hydrodynamical simulations for the influence of rotation rate on the amplitude and profile of the meridion…
One peculiar feature of the solar cycle which is yet to be understood properly is the frequent occurrence of double peaks (also known as the Gnevyshev peaks). Not only the double peaks but also multiple peaks and spikes are often observed in any phase of the cycle. We propose that these peaks and spikes are generated due to fluctuations in the Babcock-Leighton process (the poloidal field generation from tilted bipolar magnetic regions). When the polar field develops, large negative fluctuations in the Babcock-Leighton process can reduce the net polar field abruptly. As these fluctuations in th…
The solar magnetic activity cycle has an amplitude that varies within a wide but limited range of values. This implies that there are nonlinear mechanisms that prevent runaway solutions. The purpose of this paper is to propose observable nonlinear mechanisms in the framework of the Babcock-Leighton-type dynamo. Sunspot emergences show systematic properties that strong cycles tend to have higher mean latitudes and lower tilt angle coefficients. We use the surface flux transport model to investigate the effect of these systematic properties on the expected final total dipolar moment, i.e. cancel…
Context: The Sun's polar fields and open flux around the time of activity minima have been considered to be strongly correlated with the strength of the subsequent maximum of solar activity. Aims: We aim to investigate the behavior of a Babcock-Leighton dynamo with a source poloidal term that is based on the observed sunspot areas and tilts. In particular, we investigate whether the toroidal fields at the base of convection zone from the model are correlated with the observed solar cycle activity maxima. Methods: We used a flux transport dynamo model that includes convective pumping and a polo…
It is proposed that the observed near-surface inflows towards the active regions and sunspot zones provide a nonlinear feedback mechanism that limits the amplitude of a Babcock-Leighton-type solar dynamo and determines the variation of the cycle strength. This hypothesis is tested with surface flux transport simulations including converging latitudinal flows that depend on the surface distribution of magnetic flux. The inflows modulate the build-up of polar fields (represented by the axial dipole) by reducing the tilt angles of bipolar magnetic regions and by affecting the cross-equator transp…
We explore a reduced Babcock-Leighton (BL) dynamo model based on delay differential equations using numerical bifurcation analysis. This model reveals hysteresis, seen in the recent mean-field dynamo model and the direct numerical simulations of turbulent dynamos. The BL model with 'magnetic noise' as an additional weak-source of the poloidal field recovers the solar cycle every time from grand minima, which BL source alone cannot do. The noise-incorporated model exhibits a bimodal distribution of toroidal field energy confirming two modes of solar activity. It also shows intermittency and rep…
Context. The solar dynamo consists of a process that converts poloidal field to toroidal field followed by a process which creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We use synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories to construct the poloidal field as a function of time and latitude, and Wilcox Solar Observatory and SOHO/MDI full disk images to infer the longitudinally aver…
We propose that the poloidal field at the end of the last sunspot cycle before the Maunder minimum fell to a very low value due to fluctuations in the Babcock--Leighton process. With this assumption, a flux transport dynamo model is able to explain various aspects of the historical records of the Maunder minimum remarkably well on choosing the parameters of the model suitably to give the correct growth time.
We begin with a review of the predictions for cycle~24 before its onset. After summarizing the basics of the flux transport dynamo model, we discuss how this model had been used to make a successful prediction of cycle~24, on the assumption that the irregularities of the solar cycle arise due to the fluctuations in the Babcock--Leighton mechanism. We point out that fluctuations in the meridional circulation can be another cause of irregularities in the cycle.
It is shown that the holographic principle of quantum gravity (in the hologram of the Universe, and therefore in our Galaxy, and of course on the Sun!), in which the conflict between the theory of gravitation and quantum mechanics disappears, gives rise to the Babcock-Leighton holographic mechanism. Unlike the solar dynamo models, it generates a strong toroidal magnetic field by means of the thermomagnetic Ettingshausen-Nernst (EN) effect in the tachocline. Hence, it can be shown that with the help of the thermomagnetic EN effect, a simple estimate of the magnetic pressure of an ideal gas in t…
The nonlocal alpha-effect of Babcock-Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha-effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha-effect. The same model shows catastrophic quenching when the alpha-effect is changed to its local formulation. The nonlocal model shows the preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal-to-polar fields ratio of about a thousa…
The Babcock-Leighton type of dynamo has received recent support in terms of the discovery in the observational records of systematic cycle-to-cycle variations in the tilt angle of sunspot groups. It has been proposed that these variations might be the consequence of the observed inflow into the active region belt. Furthermore simulations have shown that such inflows restrict the creation of net poloidal flux, in effect acting to quench the alpha effect associated with the Coriolis force acting on rising flux tubes. In this paper we expand on these ideas.
Aims: We aim to investigate how converging flows towards active regions affect the surface transport of magnetic flux, as well as their impact on the generation of the Sun's poloidal field. The inflows constitute a potential non-linear mechanism for the saturation of the global dynamo and may contribute to the modulation of the solar cycle in the Babcock-Leighton framework. Methods: We build a surface flux transport code incorporating a parametrized model of the inflows and run simulations spanning several cycles. We carry out a parameter study to assess how the strength and extension of the i…
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property …
