Surface Flux Transport Model Research Articles

How Many Active Regions Are Necessary to Predict the Solar Dipole Moment?

Abstract We test recent claims that the polar field at the end of Cycle 23 was weakened by a small number of large, abnormally oriented regions, and investigate what this means for solar cycle prediction. We isolate the contribution of individual regions from magnetograms for Cycles 21, 22, and 23 using a 2D surface flux transport model, and find that although the top ∼10% of contributors tend to define sudden large variations in the axial dipole moment, the cumulative contribution of many weaker regions cannot be ignored. To recreate the axial dipole moment to a reasonable degree, many more regions are required in Cycle 23 than in Cycles 21 and 22 when ordered by contribution. We suggest that the negative contribution of the most significant regions of Cycle 23 could indeed be a cause of the weak polar field at the following cycle minimum and the low-amplitude Cycle 24. We also examine the relationship between a region’s axial dipole moment contribution and its emergence latitude, flux, and initial axial dipole moment. We find that once the initial dipole moment of a given region has been measured, we can predict the long-term dipole moment contribution using emergence latitude alone.

Information Theoretic Approach to Discovering Causalities in the Solar Cycle

Abstract The causal parameters and response lag times of the solar cycle dynamics are investigated with transfer entropy, which can determine the amount of information transfer from one variable to another. The causal dependency of the solar cycle parameters is bidirectional. The transfer of information from the solar polar field to the sunspot number (SSN) peaks at lag time (τ) ∼ 30–40 months, but thereafter it remains at a persistently low level for at least 400 months (∼3 solar cycles) for the period 1906–2014. The latter may lend support to the idea that the polar fields from the last three or more solar cycles can affect the production of the SSN of the subsequent cycle. There is also a similarly long-term information transfer from the SSN to the polar field. Both the meridional flow speed and flux emergence (proxied by the SSN) transfer information to the polar field, but one transfers more information than the other, depending on the lag times. The meridional flow speed transfers more information than the SSN to the polar field at τ ∼ 28–30 months and at τ ∼ 90–110 months, which may be consistent with some flux transfer dynamo models and some surface flux transport models. However, the flux emergence transfers more information than the meridional flow to the polar field at τ ∼ 60–80 months, which may be consistent with a recently developed surface flux transport model. The transfer of information from the meridional flow to the SSN peaks at τ ∼ 110–120 months (∼1 solar cycle).

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.

A prediction of the solar cycle 25

AbstractHere we report our recent prediction of the solar cycle 25 based on a newly developed scheme, which is used to investigate the predictability of the solar cycle over one cycle. The scheme is a combination of the empirical properties of solar cycles and a surface flux transport model to get the possible axial dipole moment evolution at a few years before cycle minimum, by which to get the subsequent cycle strength based on the correlation between the axial dipole moment at cycle minimum and the subsequent cycle strength. We apply this scheme to predict the large-scale field evolution since 2018 onwards. The results show that the northern polar field will keep on increasing, while the southern polar field almost keeps flat by the end of cycle 24. This leads to the cycle 25 strength of 125 ± 32, which is about 10% stronger than cycle 24 according to the mean value.

The Sun’s polar magnetic field: datasets, proxies and theoretical issues

AbstractThe polar magnetic field of the Sun is a manifestation of certain aspects of the dynamo process and is a good precursor for predicting a sunspot cycle before its onset. Although actual synoptic measurements of this field exist only from the mid-1970s, it has now been possible to determine its evolution from the beginning of the twentieth century with the help of various proxies. The recently developed 3D kinematic dynamo model can study the build-up of the Sun’s polar magnetic field more realistically than the earlier surface flux transport model.

The Large-scale Coronal Structure of the 2017 August 21 Great American Eclipse: An Assessment of Solar Surface Flux Transport Model Enabled Predictions and Observations

Abstract On 2017 August 21, 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 the generation of severe space weather. Here we present a methodology for predicting the structure of the coronal field based on model forward runs of a solar surface flux transport model, whose predicted surface field is utilized to extrapolate future coronal magnetic field structures. This prescription was applied to the 2017 August 21 solar eclipse. A 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 its evolution governs large-scale coronal structures with a (plausibly cycle-phase dependent) dynamical memory timescale on the order of a few solar rotations, opening up the possibility for large-scale, global corona predictions at least a month in advance.

Improvement of solar-cycle prediction: Plateau of solar axial dipole moment

Aims. We report the small temporal variation of the axial dipole moment near the solar minimum and its application to the solar cycle prediction by the surface flux transport (SFT) model. Methods. We measure the axial dipole moment using the photospheric synoptic magnetogram observed by the Wilcox Solar Observatory (WSO), the ESA/NASA Solar and Heliospheric Observatory Michelson Doppler Imager (MDI), and the NASA Solar Dynamics Observatory Helioseismic and Magnetic Imager (HMI). We also use the surface flux transport model for the interpretation and prediction of the observed axial dipole moment. Results. We find that the observed axial dipole moment becomes approximately constant during the period of several years before each cycle minimum, which we call the axial dipole moment plateau. The cross-equatorial magnetic flux transport is found to be small during the period, although the significant number of sunspots are still emerging. The results indicates that the newly emerged magnetic flux does not contributes to the build up of the axial dipole moment near the end of each cycle. This is confirmed by showing that the time variation of the observed axial dipole moment agrees well with that predicted by the SFT model without introducing new emergence of magnetic flux. These results allows us to predict the axial dipole moment in Cycle 24/25 minimum using the SFT model without introducing new flux emergence. The predicted axial dipole moment of Cycle 24/25 minimum is 60--80 percent of Cycle 23/24 minimum, which suggests the amplitude of Cycle 25 even weaker than the current Cycle 24. Conclusions. The plateau of the solar axial dipole moment is an important feature for the longer prediction of the solar cycle based on the SFT model.

Parameter optimization for surface flux transport models

Accurate prediction of solar activity calls for precise calibration of solar cycle models. Consequently we aim to find optimal parameters for models which describe the physical processes on the solar surface, which in turn act as proxies for what occurs in the interior and provide source terms for coronal models. We use a genetic algorithm to optimize surface flux transport models using National Solar Observatory (NSO) magnetogram data for Solar Cycle 23. This is applied to both a 1D model that inserts new magnetic flux in the form of idealized bipolar magnetic regions, and also to a 2D model that assimilates specific shapes of real active regions. The genetic algorithm searches for parameter sets (meridional flow speed and profile, supergranular diffusivity, initial magnetic field, and radial decay time) that produce the best fit between observed and simulated butterfly diagrams, weighted by a latitude-dependent error structure which reflects uncertainty in observations. Due to the easily adaptable nature of the 2D model, the optimization process is repeated for Cycles 21, 22, and 24 in order to analyse cycle-to-cycle variation of the optimal solution. We find that the ranges and optimal solutions for the various regimes are in reasonable agreement with results from the literature, both theoretical and observational. The optimal meridional flow profiles for each regime are almost entirely within observational bounds determined by magnetic feature tracking, with the 2D model being able to accommodate the mean observed profile more successfully. Differences between models appear to be important in deciding values for the diffusive and decay terms. In like fashion, differences in the behaviours of different solar cycles lead to contrasts in parameters defining the meridional flow and initial field strength.

Reconstructing solar magnetic fields from historical observations

Aims. We aim to use the surface flux transport model to simulate the long-term evolution of the photospheric magnetic field from historical observations. In this work we study the accuracy of the model and its sensitivity to uncertainties in its main parameters and the input data.Methods. We tested the model by running simulations with different values of meridional circulation and supergranular diffusion parameters, and studied how the flux distribution inside active regions and the initial magnetic field affected the simulation. We compared the results to assess how sensitive the simulation is to uncertainties in meridional circulation speed, supergranular diffusion, and input data. We also compared the simulated magnetic field with observations.Results. We find that there is generally good agreement between simulations and observations. Although the model is not capable of replicating fine details of the magnetic field, the long-term evolution of the polar field is very similar in simulations and observations. Simulations typically yield a smoother evolution of polar fields than observations, which often include artificial variations due to observational limitations. We also find that the simulated field is fairly insensitive to uncertainties in model parameters or the input data. Due to the decay term included in the model the effects of the uncertainties are somewhat minor or temporary, lasting typically one solar cycle.

Predicting solar surface large-scale magnetic field of Cycle 24

The Sun's surface field, especially the polar field, sets the boundary condition for the coronal and heliospheric magnetic fields, but also provides us insight into the dynamo process. The evolution of the polar fields results from the emergence and subsequent evolution of magnetic flux through the solar surface. In this paper we use a Monte Carlo approach to investigate the evolution of the fields during the decay phase of cycle 24. Our simulations include the emergence of flux through the solar surface with statistical properties derived from previous cycles. The well-calibrated surface flux transport model is used to follow the evolution of the large-scale field. We find the polar field can be well reproduced one year in advance using the observed synoptic magnetograms as the initial condition. The temporary variation of the polar field measured by Wilcox Solar Observatory (WSO), e.g., the strong decrease of the south polar field during 2016–2017 which is not shown by SDO/HMI and NSO/SOLIS data usually is not well reproduced. We suggest observational effects, such as the effect of the large gradient of the magnetic field around the southern polar cap and the low resolution of WSO might be responsible. The northern hemisphere polar field is predicted to increase during 2017. The southern polar field is predicted to be stable during 2017–2018. At the end of 2017, the magnetic field in two poles is predicted to be similar (although of opposite polarities). The expected value for the dipole moment around 2020 is 1.76 ± 0.68 G and 2.11±0.69 G based on the initial conditions from SDO/HMI and NSO/SOLIS synoptic magnetograms, respectively. It is comparable to that observed one at the end of Cycle 23 (about 1.6G based on SOHO/MDI).

A THEORETICAL STUDY OF THE BUILD-UP OF THE SUN’S POLAR MAGNETIC FIELD BY USING A 3D KINEMATIC DYNAMO MODEL

ABSTRACT We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres. We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale’s polarity law, would have on the polar field. We find that there would be some effect—especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle—though the effect is not very dramatic.

A NEW TECHNIQUE FOR THE PHOTOSPHERIC DRIVING OF NON-POTENTIAL SOLAR CORONAL MAGNETIC FIELD SIMULATIONS

ABSTRACT In this paper, we develop a new technique for driving global non-potential simulations of the Sun’s coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an “inductive” electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface flux-transport model. The match for these cases is further improved by including the non-inductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal non-potential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available.

Reconstruction of spectral solar irradiance since 1700 from simulated magnetograms

We present a reconstruction of the spectral solar irradiance since 1700 using the SATIRE-T2 (Spectral And Total Irradiance REconstructions for the Telescope era version 2) model. This model uses as input magnetograms simulated with a surface flux transport model fed with semi-synthetic records of emerging sunspot groups. We used statistical relationships between the properties of sunspot group emergence, such as the latitude, area, and tilt angle, and the sunspot cycle strength and phase to produce semi-synthetic sunspot group records starting in the year 1700. The semisynthetic records are fed into a surface flux transport model to obtain daily simulated magnetograms that map the distribution of the magnetic flux in active regions (sunspots and faculae) and their decay products on the solar surface. The magnetic flux emerging in ephemeral regions is accounted for separately based on the concept of extended cycles whose length and amplitude are linked to those of the sunspot cycles through the sunspot number. The magnetic flux in each surface component (sunspots, faculae and network, and ephemeral regions) was used to compute the spectral and total solar irradiance between the years 1700 and 2009. This reconstruction is aimed at timescales of months or longer although the model returns daily values. We found that SATIRE-T2, besides reproducing other relevant observations such as the total magnetic flux, reconstructs the total solar irradiance (TSI) on timescales of months or longer in good agreement with the PMOD composite of observations, as well as with the reconstruction starting in 1878 based on the RGO-SOON data. The model predicts an increase in the TSI of 1.2[+0.2, -0.3] Wm-2 between 1700 and the present. The spectral irradiance reconstruction is in good agreement with the UARS/SUSIM measurements as well as the Lyman-alpha composite.

Surface flux transport simulations: Effect of inflows toward active regions and random velocities on the evolution of the Sun’s large-scale magnetic field

Aims: We aim to determine the effect of converging flows on the evolution of a bipolar magnetic region (BMR), and to investigate the role of these inflows in the generation of poloidal flux. We also discuss whether the flux dispersal due to turbulent flows can be described as a diffusion process. Methods: We developed a simple surface flux transport model based on point-like magnetic concentrations. We tracked the tilt angle, the magnetic flux and the axial dipole moment of a BMR in simulations with and without inflows and compared the results. To test the diffusion approximation, simulations of random walk dispersal of magnetic features were compared against the predictions of the diffusion treatment. Results: We confirm the validity of the diffusion approximation to describe flux dispersal on large scales. We find that the inflows enhance flux cancellation, but at the same time affect the latitudinal separation of the polarities of the bipolar region. In most cases the latitudinal separation is limited by the inflows, resulting in a reduction of the axial dipole moment of the BMR. However, when the initial tilt angle of the BMR is small, the inflows produce an increase in latitudinal separation that leads to an increase in the axial dipole moment in spite of the enhanced flux destruction. This can give rise to a tilt of the BMR even when the BMR was originally aligned parallel to the equator.

MAGNETIC FLUX TRANSPORT AND THE LONG-TERM EVOLUTION OF SOLAR ACTIVE REGIONS

With multiple vantage points around the Sun, STEREO and SDO imaging observations provide a unique opportunity to view the solar surface continuously. We use He II 304 A data from these observatories to isolate and track ten active regions and study their long-term evolution. We find that active regions typically follow a standard pattern of emergence over several days followed by a slower decay that is proportional in time to the peak intensity in the region. Since STEREO does not make direct observations of the magnetic field, we employ a flux-luminosity relationship to infer the total unsigned magnetic flux evolution. To investigate this magnetic flux decay over several rotations we use a surface flux transport model, the Advective Flux Transport (AFT) model, that simulates convective flows using a time-varying velocity field and find that the model provides realistic predictions when information about the active region's magnetic field strength and distribution at peak flux is available. Finally, we illustrate how 304 \AA\ images can be used as a proxy for magnetic flux measurements when magnetic field data is not accessible.

Source of a Prominent Poleward Surge During Solar Cycle 24

As an observational case study, we consider the origin of a prominent poleward surge of leading polarity, visible in the magnetic butterfly diagram during Solar Cycle 24. A new technique is developed for assimilating individual regions of strong magnetic flux into a surface flux transport model. By isolating the contribution of each of these regions, the model shows the surge to originate primarily in a single high-latitude activity group consisting of a bipolar active region present in Carrington Rotations 2104-05 (November 2010-January 2011) and a multipolar active region in Rotations 2107-08 (February-April 2011). This group had a strong axial dipole moment opposed to Joy's law. On the other hand, the modelling suggests that the transient influence of this group on the butterfly diagram will not be matched by a large long-term contribution to the polar field, because of its location at high latitude. This is in accordance with previous flux transport models.

Modelling total solar irradiance since 1878 from simulated magnetograms

We present a new model of total solar irradiance (TSI) based on magnetograms simulated with a surface flux transport model (SFTM) and the SATIRE (Spectral And Total Irradiance REconstructions) model. Our model provides daily maps of the distribution of the photospheric field and the TSI starting from 1878. We first calculate the magnetic flux on the solar surface emerging in active and ephemeral regions. The evolution of the magnetic flux in active regions is computed using a surface flux transport model fed with the observed record of sunspot group areas and positions. The magnetic flux in ephemeral regions is treated separately using the concept of overlapping cycles. To model the ephemeral region cycles, we assume that their length and amplitude are related to that of the sunspot cycles. We then use a version of the SATIRE model to compute the TSI. The area coverage and the distribution of different magnetic features as a function of time, which are required by SATIRE, are extracted from the simulated magnetograms and the modelled ephemeral region magnetic flux. Previously computed intensity spectra of the various types of magnetic features are employed. Our model reproduces the PMOD composite of TSI measurements starting from 1978 at daily and rotational timescales more accurately than the previous version of the SATIRE model computing TSI over this period of time. The simulated magnetograms provide a more realistic representation of the evolution of the magnetic field on the photosphere and also allow us to make use of information on the spatial distribution of the magnetic fields before the times when observed magnetograms were available. We find that the secular increase in TSI since 1878 is fairly stable to modifications of the treatment of the ephemeral region magnetic flux.

Magnetic Flux Transport at the Solar Surface

After emerging to the solar surface, the Sun’s magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the boundary condition for the coronal and heliospheric magnetic fields. Another is that the surface evolution gives us insight into the dynamo process. In particular, it plays an essential role in the Babcock-Leighton model of the solar dynamo. Describing this evolution is the aim of the surface flux transport model. The model starts from the emergence of magnetic bipoles. Thereafter, the model is based on the induction equation and the fact that after emergence the magnetic field is observed to evolve as if it were purely radial. The induction equation then describes how the surface flows—differential rotation, meridional circulation, granular, supergranular flows, and active region inflows—determine the evolution of the field (now taken to be purely radial). In this paper, we review the modeling of the various processes that determine the evolution of the surface field. We restrict our attention to their role in the surface flux transport model. We also discuss the success of the model and some of the results that have been obtained using this model.

EFFECTS OF MERIDIONAL FLOW VARIATIONS ON SOLAR CYCLES 23 AND 24

The faster meridional flow that preceded the solar cycle 23/24 minimum is thought to have led to weaker polar field strengths, producing the extended solar minimum and the unusually weak cycle 24. To determine the impact of meridional flow variations on the sunspot cycle, we have simulated the Sun's surface magnetic field evolution with our newly developed surface flux transport model. We investigate three different cases: a constant average meridional flow, the observed time-varying meridional flow, and a time-varying meridional flow in which the observed variations from the average have been doubled. Comparison of these simulations shows that the variations in the meridional flow over cycle 23 have a significant impact (~20%) on the polar fields. However, the variations produced polar fields that were stronger than they would have been otherwise. We propose that the primary cause of the extended cycle 23/24 minimum and weak cycle 24 was the weakness of cycle 23 itself - with fewer sunspots, there was insufficient flux to build a big cycle. We also find that any polar counter-cells in the meridional flow (equatorward flow at high latitudes) produce flux concentrations at mid-to-high latitudes that are not consistent with observations.

A THREE-DIMENSIONAL BABCOCK-LEIGHTON SOLAR DYNAMO MODEL

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 (2D in radius/latitude) and surface flux transport models (2D in latitude/longitude) into a more self-consistent framework that captures the full 3D structure of the evolving magnetic field. The model reproduces some basic features of the solar cycle including an 11-yr periodicity, equatorward migration of toroidal flux in the deep convection zone, and poleward propagation of poloidal flux at the surface. The poleward-propagating surface flux originates as trailing flux in BMRs, migrates poleward in multiple non-axisymmetric streams (made axisymmetric by differential rotation and turbulent diffusion), and eventually reverses the polar field, thus sustaining the dynamo. In this letter we briefly describe the model, initial results, and future plans.