Solar Dynamo Mechanism Research Articles

Quasi-biennial oscillation of the Ca ii K plage area

Abstract Solar quasi-biennial oscillations (QBOs) are crucial not only for comprehending the solar dynamo mechanism but also for forecasting space weather. In this present work, composite monthly Ca ii K plage area (PA) data were utilized, derived from cross-calibrated Ca ii K spectra and filtered maps collected at 38 stations from 1892 to 2023 December. The analysis, covering 14–25 solar cycles, employes synchrosqueezed wavelet transforms (SWT) to examine the periodicity of the plage area data. The following prominent results are found: (1) There are many periodic modes with different characteristics in plage area (PA) data, including the $40\:$yr periodic mode, the $22\:$yr magnetic periodic mode, the $11\:$yr Schwabe periodic mode, a medium-term periodic mode, a quasi-sexennial oscillation period mode, and the QBOs periodic modes; (2) the reconstructed solar QBOs exhibit intermittence with signs of stochasticity; (3) the Gnevyshev gap is observed in solar cycles 15–24, and triple peaks are observed in solar cycles 16, 17, and 19. There are two possible mechanisms by which the Gnevyshev gap may occur; one is as a result of the modulation of solar QBOs by the $11\:$yr Schwabe cycle, and the other is as a result of the reversal of the solar magnetic field.

Helioseismic Properties of Dynamo Waves in the Variation of Solar Differential Rotation

Solar differential rotation exhibits a prominent feature: its cyclic variations over the solar cycle, referred to as zonal flows or torsional oscillations, are observed throughout the convection zone. Given the challenge of measuring magnetic fields in subsurface layers, understanding deep torsional oscillations becomes pivotal in deciphering the underlying solar dynamo mechanism. In this study, we address the critical question of identifying specific signatures within helioseismic frequency-splitting data associated with the torsional oscillations. To achieve this, a comprehensive forward modeling approach is employed to simulate the helioseismic data for a dynamo model that, to some extent, reproduces solar-cycle variations of magnetic fields and flows. We provide a comprehensive derivation of the forward modeling process utilizing generalized spherical harmonics, as it involves intricate algebraic computations. All estimated frequency-splitting coefficients from the model display an 11 yr periodicity. Using the simulated splitting coefficients and realistic noise, we show that it is possible to identify the dynamo wave signal present in the solar zonal flow from the tachocline to the solar surface. By analyzing observed data, we find similar dynamo wave patterns in the observational data from the Michelson Doppler Imager, Helioseismic Magnetic Imager, and Global Oscillation Network Group. This validates the earlier detection of dynamo waves and holds potential implications for the solar dynamo theory models.

Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism

ABSTRACT Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.

Novel Approach to Forecasting Photospheric Emergence of Active Regions

One key aspect of understanding the solar dynamo mechanism and the evolution of solar magnetism is to properly describe the emergence of solar active regions. In this Letter, we describe the Lagrangian photospheric flows dynamics during a simulated flux emergence that produces an active region formed by pores. We analyze the lower photospheric flow organization prior, during and following the rise of an active region, uncovering the repelling and attracting photospheric structures that act as sources and sinks for magnetic element transport. Our results show that around 10 hr before the simulated emergence, considerable global changes are taking place on mesogranular scales indicated by an increase of the number of regions acting as a source to the multiple and scattered emergences of small-scale magnetic flux. At the location of active region’s appearance, the converging flows become weaker and there is an arising of a diverging region 8 hr before the emergence time. Our study also indicates that the strong concentration of magnetic field affects the flow dynamics beyond the area of the actual simulated pores, leading to complex and strongly diverging flows in the neighboring regions. Our findings suggest that the Lagrangian analysis is a powerful tool to describe the changes in the photospheric flows due to magnetic flux emergence.

Prediction for the amplitude and second maximum of Solar Cycle 25 and a comparison of the predictions based on strength of polar magnetic field and low-latitude sunspot area

ABSTRACTThe maximum of a solar cycle contains two or more peaks, known as Gnevyshev peaks. Studies of this property of solar cycles may help in better understanding the solar dynamo mechanism. We analysed the 13-month smoothed monthly mean Version-2 international sunspot number (SN) during the period 1874–2017 and found that there exists a good correlation between the amplitude (value of the main and highest peak) and the value of the second maximum (value of the second highest peak) during the maximum of a solar cycle. Using this relationship and the earlier predicted value 86 ± 18 (92 ± 11) of the amplitude of Solar Cycle 25, here we predict a value 73 ± 15 (79 ± 15) for the second maximum of Solar Cycle 25. The ratio of the predicted second maximum to the amplitude is found to be 0.85, almost the same as that of Solar Cycle 24. The least-square cosine fits to the values of the peaks that occurred first and second during the maxima of Solar Cycles 12–24 suggest that in Solar Cycle 25 the second maximum would occur before the main maximum, the same as in Solar Cycle 24. However, these fits suggest ≈106 and ≈119 for the second maximum and the amplitude of Solar Cycle 25, respectively. Earlier, we analysed the combined Greenwich and Debrecen sunspot-group data during 1874–2017 and predicted the amplitude of Solar Cycle 25 from the activity just after the maximum of Solar Cycle 24 in the equatorial latitudes of the Sun’s Southern hemisphere. Here, from the hindsight of the results we found the earlier prediction is reasonably reliable. We analysed the polar-fields data measured in Wilcox Observatory during Solar Cycles 20–24 and obtained a value 125 ± 7 for the amplitude of Solar Cycle 25. This is slightly larger – whereas the value ≈86 (≈92) predicted from the activity in the equatorial latitudes is slightly smaller – than the observed amplitude of Solar Cycle 24. This difference is discussed briefly.

Performance of AICC Statistic as Time Series Modeling and Forecasting of Sunspots

Dynamics of the Sun is quite complex. Sunspot number is an important index to understand the solar dynamo mechanism that governs the solar magnetic cycle. This paper is an attempt to forecast Sunspots number by finding an appropriate time series model. For the purpose, Sunspots datasets from 1749 to 2010 were used. Also, 23 minimum to minimum (m-m) and 24 maximum to minimum (M-m) Sunspots cycles were investigated. The results show that Autoregressive Moving average (ARMA) time series models fit the Sunspots number well. They have corrected predictions of the future trend of the Sunspots number within the sample period of study. The results obtained showed that the probability of the AIC corrected model was found better fitted. The problem of over parameterization exited in the model used, but under parameterization was found to minimal.

Periodicities in Solar Activity, Solar Radiation and Their Links with Terrestrial Environment

Solar magnetic activity is expressed via variations of sunspots and active regions varying on different timescales. The most accepted is an 11-year period supposedly induced by the electromagnetic solar dynamo mechanism. There are also some shorter or longer timescales detected: the biennial cycle (2 - 2.7 years), Gleisberg cycle (80 - 100 years), and Hallstatt’s cycle (2100 - 2300 years). Recently, using Principal Component Analysis (PCA) of the observed solar background magnetic field (SBMF), another period of 330 - 380 years, or Grand Solar Cycle (GSC), was derived from the summary curve of two eigenvectors of SBMF. In this paper, a spectral analysis of the averaged sunspot numbers, solar irradiance, and the summary curve of eigenvectors of SBMF was carried out using Morlet wavelet and Fourier transforms. We detect a 10.7-year cycle from the sunspots and modulus summary curve of eigenvectors as well a 22-year-cycle and the grand solar cycle of 342 - 350-years from the summary curve of eigenvectors. The Gleissberg centennial cycle is only detected on the full set of averaged sunspot numbers for 400 years or by adding a quadruple component to the summary curve of eigenvectors. Another period of 2200 - 2300 years is detected in the Holocene data of solar irradiance measured from the abundance of 14C isotope. This period was also confirmed with the period of about 2000 - 2100 years derived from a baseline of the solar background magnetic field, supposedly, caused by the solar inertial motion (SIM) induced by the gravitation of large planets. The implication of these findings for different deposition of solar radiation into the northern and southern hemispheres of the Earth caused by the combined effects of the solar activity and solar inertial motion on the terrestrial atmosphere is also discussed.

Determination of the solar rotation parameters via orthogonal polynomials

Accurate measurements of the solar differential rotation parameters are necessary for understanding the solar dynamo mechanism. We use the orthogonalization process to estimate these parameters. The advantage of the orthogonalization of the data in the tracer motion statistical analysis is outlined. The differential rotation is represented in terms of various types of polynomials. We compare the quality of a set of models of the solar differential rotation using the Akaike information criterion and choose the best one. Applying the proposed method, we studied the solar differential rotation and its North-South asymmetry using observations of coronal holes. A statistical analysis of observations from the Atmospheric Imaging Assembly (AIA) on Solar Dynamics Observatory (SDO) reveals the differential rotation pattern of coronal holes and its North-South asymmetry.

A 3D kinematic Babcock Leighton solar dynamo model sustained by dynamic magnetic buoyancy and flux transport processes

Context. 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. Aims. 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. Furthermore, we seek to explore the relative roles of flux transport by buoyancy, advection by meridional circulation, and turbulent diffusion in this 3D dynamo model. Methods. We perform kinematic dynamo simulations where the prescribed velocity field is a combination of solar-like differential rotation and meridional circulation, along with a parametrized turbulent diffusivity. We use a novel methodology for modeling magnetic buoyancy through field-strength-dependent 3D helical up-flows that results in the formation of tilted bipolar sunspots. Results. The bipolar spots produced in our simulations participate in the process of poloidal-field generation through the Babcock-Leighton mechanism, resulting in self-sustained and periodic large-scale magnetic field reversal. Our parameter space study varying the amplitude of the meridional flow, the convection zone diffusivity, and parameters governing the efficiency of the magnetic buoyancy mechanism reveal their relative roles in determining properties of the sunspot cycle such as amplitude, period, and dynamical memory relevant to solar cycle prediction. We also derive a new dynamo number for the Babcock-Leighton solar dynamo mechanism which reasonably captures our model dynamics. Conclusions. This study elucidates the relative roles of different flux-transport processes in the Sun’s convection zone in determining the properties and physics of the sunspot cycle and could potentially lead to realistic, data-driven 3D dynamo models for solar-activity predictions and exploration of stellar magnetism and starspot formation in other stars.

SOLAR ACTIVE LONGITUDES FROM KODAIKANAL WHITE-LIGHT DIGITIZED DATA

ABSTRACT The study of solar active longitudes has generated great interest in recent years. In this work we have used a unique, continuous sunspot data series obtained from the Kodaikanal observatory and revisited the problem. An analysis of the data shows a persistent presence of active longitudes during the whole 90 years of data. We compared two well-studied analysis methods and presented their results. The separation between the two most active longitudes is found be roughly 180° for the majority of time. Additionally, we also find a comparatively weaker presence of separations at 90° and 270°. The migration pattern of these active longitudes as revealed by our data is found to be consistent with the solar differential rotation curve. We also study the periodicities in the active longitudes and found two dominant periods of ≈1.3 and ≈2.2 years. These periods, also found in other solar proxies, indicate their relation with the global solar dynamo mechanism.

PHASE RELATIONSHIPS OF SOLAR HEMISPHERIC TOROIDAL AND POLOIDAL CYCLES

ABSTRACT The solar northern and southern hemispheres exhibit differences in their intensities and time profiles of the activity cycles. The time variation of these properties was studied in a previous article covering the data from Cycles 12–23. The hemispheric phase lags exhibited a characteristic variation: the leading role was exchanged between hemispheres every four cycles. The present work extends the investigation of this variation using the data of Staudacher and Schwabe in Cycles 1–4 and 7–10 as well as Spörer’s data in Cycle 11. The previously observed variation cannot be clearly recognized using the data of Staudacher, Schwabe, and Spörer. However, it is more interesting that the phase lags of the reversals of the magnetic fields at the poles follow the same variations as those of the hemispheric cycles in Cycles 12–23, i.e., one of the hemispheres leads in four cyles and the leading role jumps to the opposite hemisphere in the next four cycles. This means that this variation is a long-term property of the entire solar dynamo mechanism, for both the toroidal and poloidal fields, which hints at an unidentified component of the process responsible for the long-term memory.

Dynamical systems for modeling the evolution of the magnetic field of stars and Earth

The cycles of solar magnetic activity are connected with a solar dynamo that operates in the convective zone. Solar dynamo mechanism is based on the combined action of the differential rotation and the alpha-effect. Application of these concepts allows us to get an oscillating solution as a wave of the toroidal field propagating from middle latitudes to the equator. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the solar magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the convection zone of the star. It was shown the possibility of coexistence of quiasi-biennial and 22-year cycle. We obtained the different regimes (oscillations, vacillations, dynamo-bursts) depending on the value of the dynamo-number, the meridional circulation, and thickness of the convection zone. We discuss the features of these regimes and compare them with the observed features of evolution of the solar and geo magnetic fields. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

The features of longitudinal distribution of solar spots during the last 13 solar activity minima

We analyzed the features of the longitudinal distribution of the areas of solar spots during the solar activity minima, from the 11th cycle to the last minimum, based on data provided by the Greenwich Observatory and the Marshall Research Center. We discovered that the solar spots evolved in one or two neighboring bands (in terms of longitude), the Carrington longitude of which smoothly displaced from the east to the west, in the phase of the deep minimum in all of the considered cases. The spots at the high latitudes associated with a “new” cycle evolved on the same longitude bands. All of this led to the noticeable longitudinal asymmetry of magnetic fluxes related to the spots and flocculi. Based on our research, we propose the hypothesis that a nonaxisymmetric component of the total magnetic flux of the Sun is generated, together with the dipole component, by the solar dynamo mechanism, which is a typical feature of the phase of a minimum between the solar activity cycles.

On the non‐conjugacy of nightside aurora and their generator mechanisms

AbstractWe have investigated a data set of 19 h of simultaneous global conjugate auroral imaging from space. The data set consists of 10 sequences with durations from 1 to 5 h during active geomagnetic conditions (average AE ∼ 400 nT). We have identified 15 features (including two presented earlier) of auroral forms that appear mainly in one hemisphere, and we define this as non‐conjugate aurora. Three generator mechanisms has been suggested for producing interhemispheric currents and non‐conjugate aurora: (1) Hemispherical differences in solar wind dynamo efficiency due to interplanetary magnetic field (IMF) Bx and dipole tilt angle leading to asymmetric region 1 currents in the two polar hemispheres, (2) interhemispheric currents induced by the penetration of IMF By into the closed nightside magnetosphere, and (3) hemispheric differences in ionospheric conductivity controlled by the dipole tilt angle inducing interhemispheric currents on closed field‐lines. We want to find out if our observations are consistent with these mechanisms. Our analysis shows that five features were consistent with the IMF By penetration mechanism, seven features consistent with the solar wind dynamo mechanism, three features consistent with the conductivity mechanism, and two features could not be explained by any of the three suggested mechanisms. Because two features were consistent with two different mechanisms, the numbers add up to 17 although the total number of features is 15. The analysis also shows the expected correlation between the magnitude of the longitudinal shift of conjugate points, ΔMLT, and the occurrence of non‐conjugate aurora consistent with the By mechanism.

Long-term solar activity and its implications to the heliosphere, geomagnetic activity, and the Earth’s climate

The Sun’s long-term magnetic variability is the primary driver of space climate. This variability is manifested not only in the longobserved and dramatic change of magnetic fields on the solar surface, but also in the changing solar radiative output across all wavelengths. The Sun’s magnetic variability also modulates the particulate and magnetic fluxes in the heliosphere, which determine the interplanetary conditions and impose significant electromagnetic forces and effects upon planetary atmospheres. All these effects due to the changing solar magnetic fields are also relevant for planetary climates, including the climate of the Earth. The ultimate cause of solar variability, at time scales much shorter than stellar evolutionary time scales, i.e., at decadal to centennial and, maybe, even millennial or longer scales, has its origin in the solar dynamo mechanism. Therefore, in order to better understand the origin of space climate, one must analyze different proxies of solar magnetic variability and develop models of the solar dynamo mechanism that correctly produce the observed properties of the magnetic fields. This Preface summarizes the most important findings of the papers of this Special Issue, most of which were presented in the Space Climate-4 Symposium organized in 2011 in Goa, India.

TURBULENT PUMPING OF MAGNETIC FLUX REDUCES SOLAR CYCLE MEMORY AND THUS IMPACTS PREDICTABILITY OF THE SUN'S ACTIVITY

Prediction of the Sun's magnetic activity is important because of its effect on space environment and climate. However, recent efforts to predict the amplitude of the solar cycle have resulted in diverging forecasts with no consensus. Yeates et al. (2008) have shown that the dynamical memory of the solar dynamo mechanism governs predictability and this memory is different for advection- and diffusion-dominated solar convection zones. By utilizing stochastically forced, kinematic dynamo simulations, we demonstrate that the inclusion of downward turbulent pumping of magnetic flux reduces the memory of both advection- and diffusion-dominated solar dynamos to only one cycle; stronger pumping degrades this memory further. Thus, our results reconcile the diverging dynamo-model-based forecasts for the amplitude of solar cycle 24. We conclude that reliable predictions for the maximum of solar activity can be made only at the preceding minimum--allowing about 5 years of advance planning for space weather. For more accurate predictions, sequential data assimilation would be necessary in forecasting models to account for the Sun's short memory.

Forecasting the solar activity cycle: new insights

AbstractHaving advance knowledge of solar activity is important because the Sun's magnetic output governs space weather and impacts technologies reliant on space. However, the irregular nature of the solar cycle makes solar activity predictions a challenging task. This is best achieved through appropriately constrained solar dynamo simulations and as such the first step towards predictions is to understand the underlying physics of the solar dynamo mechanism. In Babcock-Leighton type dynamo models, the poloidal field is generated near the solar surface whereas the toroidal field is generated in the solar interior. Therefore a finite time is necessary for the coupling of the spatially segregated source layers of the dynamo. This time delay introduces a memory in the dynamo mechanism which allows forecasting of future solar activity. Here we discuss how this forecasting ability of the solar cycle is affected by downward turbulent pumping of magnetic flux. With significant turbulent pumping the memory of the dynamo is severely degraded and thus long term prediction of the solar cycle is not possible; only a short term prediction of the next cycle peak may be possible based on observational data assimilation at the previous cycle minimum.

Experimental Evidence for a Transient Tayler Instability in a Cylindrical Liquid-Metal Column

In the current-driven, kink-type Tayler instability (TI) a sufficiently strong azimuthal magnetic field becomes unstable against nonaxisymmetric perturbations. The TI has been discussed as a possible ingredient of the solar dynamo mechanism and a source of the helical structures in cosmic jets. It is also considered as a size-limiting factor for liquid metal batteries. We report on a liquid metal TI experiment using a cylindrical column of the eutectic alloy GaInSn to which electrical currents of up to 8kA are applied. We present results of external magnetic field measurements that indicate the transient occurrence of the TI in good agreement with numerical predictions. The interference of TI with the competing large-scale convection, resulting from Joule heating, is also discussed.

Phase lags of solar hemispheric cycles

The North-South asymmetry of solar activity is variable in time and strength. We analyse the long-term variation of the phase lags of hemispheric cycles and check a conjectured relationship between these phase lags and the hemispheric cycle strengths. Sunspot data are used from cycles 12-23 in which the separation of northern and southern hemispheres is possible. The centers of mass of the hemispheric cycle profiles were used to study the phase relations and relative strengths of the hemispheric cycles. This approach considers a cycle as a whole and disregards the short-term fluctuations of the cycle time profile. The phase of the hemispheric cycles shows an alternating variation: the northern cycle leads in 4 cycles and follows in 4 cycles. No significant relationship is found between the phase and strength differences of the hemispheric cycles. The period of 4+4 cycles appears to be close to the Gleissberg cycle and may provide a key to its physical background. It may raise a new aspect in the solar dynamo mechanism because it needs a very long memory.

Magnetic Fields in the Solar Convection Zone

AbstractActive regions on the solar surface are generally thought to originate from a strong toroidal magnetic field generated by a deep seated solar dynamo mechanism operating at the base of the solar convection zone. Thus the magnetic fields need to traverse the entire convection zone before they reach the photosphere to form the observed solar active regions. Understanding this process of active region flux emergence is therefore a crucial component for the study of the solar cycle dynamo. This article reviews studies with regard to the formation and rise of active region scale magnetic flux tubes in the solar convection zone and their emergence into the solar atmosphere as active regions.