A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt which can explain deviations from the Joy's law for the sunspot bipolar regions at high latitudes. The obtained theoretical results and performed numerical simulations based on the nonlinear mean-field dynamo theory which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15 - 24.
Sunspot groups and bipolar magnetic regions (BMRs) serve as an observational diagnostic of the solar cycle. We use Debrecen Photohelographic Data (DPD) from 1974-2014 that determined sunspot tilt angles from daily white light observations, and data provided by Li & Ulrich that determined sunspot magnetic tilt angle using Mount Wilson magnetograms from 1974-2012. The magnetograms allowed for BMR tilt angles that were anti-Hale in configuration, so tilt values ranged from 0 to 360° rather than the more common $\pm$ 90°. We explore the visual representation of magnetic tilt angles on a traditiona…
Extending the knowledge about the properties of solar cycles into the past is essential for understanding the solar dynamo. This paper aims at estimating areas of sunspots observed by Schwabe in 1825-1867 and at calculating the tilt angles of sunspot groups. The sunspot sizes in Schwabe's drawings are not to scale and need to be converted into physical sunspot areas. We employed a statistical approach assuming that the area distribution of sunspots was the same in the 19th century as it was in the 20th century. Umbral areas for about 130,000 sunspots observed by Schwabe were obtained, as well …
The tilt angle of a sunspot group is a critical quantity in the surface transport of magnetic flux and the solar dynamo. To contribute long-term databases of the tilt angle, we developed an IDL routine, which allows the user to interactively select and measure sunspot positions and areas on the solar disc. We measured the tilt angles of sunspot groups for solar cycles 19-24 (1954.6-2017.8), using the sunspot drawing database of Kandilli Observatory. The method is similar to that used in the discontinued Mt. Wilson and Kodaikanal databases, with the exception that sunspot groups were identified…
Sunspot positions from various historical sets of solar drawings are analysed with respect to the tilt angles of bipolar sunspot groups. Data by Scheiner, Hevelius, Staudacher, Zucconi, Schwabe, and Spoerer deliver a series of average tilt angles spanning a period of 270 years, additional to previously found values for 20th-century data obtained by other authors. We find that the average tilt angles before the Maunder minimum were not significantly different from the modern values. However, the average tilt angles of a period 50 years after the Maunder minimum, namely for cycles 0 and 1, were …
The relationship between bipolar magnetic regions (BMRs) and their sunspots is an important property of the solar magnetic field, but it is not well constrained. One consequence is that it is a challenge for surface flux transport models (SFTMs) based on sunspot observations to determine the details of BMR emergence, which they require as input, from such data. We aimed to establish the relationship between the amount of magnetic flux in newly emerged BMRs and the area of the enclosed sunspots. Earlier attempts to constrain BMR magnetic flux were hindered by the fact that there is no proper da…
Tilt angles of close to 30,600 sunspots are determined using Mount Wilson daily averaged magnetograms taken from 1974 to 2012, and MDI/SoHO magnetograms taken from 1996 to 2010. Within a cycle, more than 90% of sunspots have a normal polarity alignment along the east-west direction following Hale's law. The median tilts increase with increasing latitude (Joy's law) at a rate of ~0.5 degree per degree of latitude. Tilt angles of spots appear largely invariant with respect to time at a given latitude, but they decrease by ~0.9degree per year on average, a trend which largely reflects Joy's law f…
We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information about polarity and strength of magnetic field in sunspots. We identify clusters of sunspots of same polarity, and used these clusters to form ``bipole pairs''. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous stud…
We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycle-to-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux, and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.
We investigate bipolar sunspot regions and how tilt angle and footpoint separation vary during emergence and decay. The Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory collects data at a higher cadence than historical records and allows for a detailed analysis of regions over their lifetimes. We sample the umbral tilt angle, footpoint separation, and umbral area of 235 bipolar sunspot regions in Helioseismic and Magnetic Imager - Debrecen Data (HMIDD) with an hourly cadence. We use the time when the umbral area peaks as time zero to distinguish between the emergence and…
Fine Structure and Formation Mechanism of a Sunspot Bipolar Light Bridge in NOAA AR 13663
Peking University（北京大学）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）；Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Leibniz Institute for Astrophysics Potsdam（波茨坦阿基米德莱布尼茨研究所）
研究通过高分辨率观测揭示了NOAA AR 13663日珥双极光桥的精细结构，发现其由半影细丝状结构构成，源于相反极性日珥的汇聚与剪切运动，最终形成BLB。
We obtain the latitude-time distribution of the averaged tilt angle of solar bipoles. For large bipoles, which are mainly bipolar sunspot groups, the spatially averaged tilt angle is positive in the Northern solar hemisphere and negative in the Southern, with modest variations during course of the solar cycle. We consider the averaged tilt angle to be a tracer for a crucial element of the solar dynamo, i.e. the regeneration rate of poloidal large-scale magnetic field from toroidal. The value of the tilt obtained crudely corresponds to a regeneration factor corresponding to about 10% of r.m.s. …
The average tilt angle of sunspot groups emerging throughout the solar cycle determines the net magnetic flux crossing the equator, which is correlated with the strength of the subsequent cycle. I suggest that a deep-seated, non-local process can account for the observed cycle-dependent changes in the average tilt angle. Motivated by helioseismic observations indicating cycle-scale variations in the sound speed near the base of the convection zone, I determined the effect of a thermally perturbed overshoot region on the stability of flux tubes and on the tilt angles of emerging flux loops. I f…
The study of active region tilt angles and their variations in different time scales plays an important role in revealing the subsurface dynamics of magnetic flux ropes and in understanding the dynamo mechanism. In order to reveal the exact characteristics of tilt angles, precise long-term tilt angle data bases are needed. However, there are only a few different data sets at present, which are difficult to be compared and cross-calibrate because of their substantial deviations. In this paper, we describe new tilt angle data bases derived from the Debrecen Photoheliographic Data ($DPD$) (1974--…
The tilt angles of sunspot groups represent the poloidal field source in Babcock-Leighton-type models of the solar dynamo and are crucial for the build-up and reversals of the polar fields in Surface Flux Transport (SFT) simulations. The evolution of the polar field is a consequence of Hale's polarity rules, together with the tilt angle distribution which has a systematic component (Joy's law) and a random component (tilt-angle scatter). We determine the scatter using the observed tilt angle data and study the effects of this scatter on the evolution of the solar surface field using SFT simula…
We present a systematic study of sunspot physical parameters using full disk magnetograms from MDI/SoHO and HMI/SDO. Our aim is to use uniform datasets and analysis procedures to characterize the sunspots, paying particular attention to the differences and similarities between "Hale" and "anti-Hale" spots. Included are measurements of the magnetic tilt angles, areas, fluxes and polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each measured, on average, at $\sim$66 epochs centered on meridian-crossing. The sunspots are classified as either "Hale" or "anti-Hale", depending o…
We present a physical mechanism of formation of tilt angles of sunspots due to the process of formation of active regions below the solar photosphere. The contribution of Coriolis force factors on large-scale flows of super-granular convection in turbulent media has been investigated in details. On the basis of earlier works by Kleeorin et al. (2016) and Safiullin et al. (2018) we give physical estimates of orders of magnitude of the effect and estimate the tilt angles near the solar equator, in the "Royal" zone of solar activity. The above model is based on the balance of the small-scale and …
Digital images of the observations printed in the books "Rosa Ursina sive solis" and "Prodromus pro sole mobili" by Christoph Scheiner as well as the drawings from Scheiner's letters to Marcus Welser are analysed in order to obtain information on positions and sizes of sunspots that appeared before the Maunder minimum. In most cases, the given orientation of the ecliptic is used to set up the heliographic coordinate system for the drawings. Positions and sizes are measured manually on the screen. Very early drawings have no indication of their orientation. A rotational matching using common sp…
The tilt angle of sunspot groups is crucial in the BL type dynamo. Some studies have shown that the tilt coefficient is anti-correlated with the cycle strength. If the anti-correlation exists, it will be shown to act as an effective nonlinearity of the BL-type dynamo to modulate the solar cycle. However, some studies have shown that the anti-correlation has no statistical significance. We aim to investigate the causes behind the controversial results of tilt angle studies and to establish whether the tilt coefficient is indeed anti-correlated with the cycle strength. We first analyzed the tilt…
We investigate various properties associated with the tilt of isolated magnetic bipoles in magnetograms taken at the solar surface. We show that bipoles can be divided into two groups which have tilts of opposite signs, and reveal similar properties with respect to bipole area, flux and bipolar moment. Detailed comparison of these physical quantities shows that the dividing point between the two types of bipoles corresponds to a bipole area of about 300 millionths of the solar hemisphere (MHS). The time-latitude distribution of small bipoles differs substantially from that for large bipoles. S…
The magnetic polarities of bipolar active regions (ARs) exhibit elongations in line-of-sight magnetograms during their emergence. These elongations are referred to as magnetic tongues and attributed to the presence of twist in the emerging magnetic flux-ropes (FRs) that form ARs. The presence of magnetic tongues affects the measurement of any AR characteristic that depends on its magnetic flux distribution. The AR tilt-angle is one of them. We aim to develop a method to isolate and remove the flux associated with the tongues to determine the AR tilt-angle with as much precision as possible. As…
Recent spectro-polarimetric observations of a sunspot showed the formation of bipolar magnetic patches in the mid penumbra and their propagation toward the outer penumbral boundary. The observations were interpreted as being caused by sea-serpent magnetic fields near the solar surface (Sainz Dalda & Bellot Rubio 2008). In this Letter, we develop a 3D radiative MHD numerical model to explain the sea-serpent structure and the wave-like behavior of the penumbral magnetic field lines. The simulations reproduce the observed behavior, suggesting that the sea-serpent phenomenon is a consequence of ma…
The axes of solar active regions are inclined relative to the east--west direction, with the tilt angle tending to increase with latitude ("Joy's law"). Observational determinations of Joy's law have been based either on white-light images of sunspot groups or on magnetograms, where the latter have the advantage of measuring directly the physically relevant quantity (the photospheric field), but the disadvantage of having been recorded routinely only since the mid-1960s. White-light studies employing the historical Mount Wilson (MW) database have yielded tilt angles that are smaller and that i…
We propose that the flux-rope $Ω$ loop that emerges to become any bipolar magnetic region (BMR) is made by a convection cell of the $Ω$-loop's size from initially-horizontal magnetic field ingested through the cell's bottom. This idea is based on (1) observed characteristics of BMRs of all spans ($\sim$ 1000 km to $\sim$ 200,000 km), (2) a well-known simulation of the production of a BMR by a supergranule-size convection cell from horizontal field placed at cell bottom, and (3) a well-known convection-zone simulation. From the observations and simulations, we (1) infer that the strength of the…
It is known that the tilt angles of active regions increase with their latitude (Joy's law). It has never been checked before, however, whether the average tilt angles change from one cycle to another. Flux transport models show the importance of tilt angles for the reversal and build up of magnetic flux at the poles which is, in turn, correlated with the strength of the next cycle. Here we analyse time series of tilt angle measurements and look for a possible relationship of the tilt angles with other solar cycle parameters, in order to glean information on the solar dynamo and to estimate th…
We present a realistic numerical model of sunspot and active region formation based on the emergence of flux bundles generated in a solar convective dynamo. To this end we use the magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation to drive realistic radiative-magnetohydrodynamic simulations of the upper most layers of the convection zone. The main results are: (1) The emerging flux bundles rise with the mean speed of convective upflows, and fragment into small-scale magnetic elements that further rise to the photosphere, where bip…
One important ingredient of flux transport dynamo models is the rise of the toroidal magnetic field through the convection zone due to magnetic buoyancy to produce bipolar sunspots and then the generation of the poloidal magnetic field from these bipolar sunspots due to the Babcock-Leighton mechanism. Over the years, two methods of treating magnetic buoyancy, a local method and a non-local method have been used widely by different groups in constructing 2D kinematic models of the flux transport dynamo. We review both these methods and conclude that neither of them is fully satisfactory, presum…
Traditionally, the strongest magnetic fields on the Sun have been measured in sunspot umbrae. More recently, however, much stronger fields have been measured at the ends of penumbral filaments carrying the Evershed and counter-Evershed flows. Superstrong fields have also been reported within a light bridge separating two umbrae of opposite polarities. We aim to accurately determine the strengths of the strongest fields in a light bridge using an advanced inversion technique and to investigate their detailed structure. We analyze observations from the spectropolarimeter on board the Hinode spac…
We present a three-dimensional numerical model for the generation and evolution of the magnetic field in the solar convection zone, in which sunspots are produced and contribute to the cyclic reversal of the large-scale magnetic field. We then assess the impact of this dynamo-generated field on the structure of the solar corona and solar wind. This model solves the induction equation in which the velocity field is prescribed. This velocity field is a combination of a solar-like differential rotation and meridional circulation. We develop an algorithm that enables the magnetic flux produced in …
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…
There is no list of bipolar active regions (ARs) with reverse polarity (anti-Hale regions), although statistical investigations of such ARs (bearing the imprint of deep subphotospheric processes) are important for understanding solar-cycle mechanisms. We studied 8606 ARs from 1 January 1989 to 31 December 2018 to detect anti-Hale regions and to compile a catalog. The Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory (SDO) data, as well as the Debrecen Photoheliographic Data, the Mount Wilson Observatory catalog and drawings, and the USAF/NOAA Solar Region Summary wer…
We use the historic record of sunspot groups compiled by the Royal Greenwich Observatory together with the sunspot number to derive the statistical properties of sunspot group emergence in dependence of cycle phase and strength. In particular we discuss the latitude, longitude, area and tilt angle of sunspot groups as functions of the cycle strength and of time during the solar cycle. Using these empirical characteristics the time-latitude diagram of sunspot group emergence (butterfly diagram) is reconstructed from 1700 onward on the basis of the Wolf and group sunspot numbers. This reconstruc…
Comparison Between Cycle-to-Cycle Variations in the Coefficient of Joy's Law and Covariance of Rotation Residuals and Meridional Motions of Sunspot Groups
Solar active region (AR) 12673 produced 4 X-class, 27 M-class, and numerous lower class flares during its passage across the visible solar disk in September 2017. Our study is to answer the questions why this AR was so flare-productive and how the X9.3 flare, the largest one of the last decade, took place. We find that there was a sunspot in the initial several days, and then two bipolar regions emerged nearby it successively. Due to the standing of the pre-existing sunspot, the movement of the bipoles was blocked, while the pre-existing sunspot maintained its quasi-circular shaped umbra only …
The high spatial, temporal and spectral resolution achieved by Hinode instruments give much better understanding of the behavior of some elusive solar features, such as pores and naked sunspots. Their fast evolution and, in some cases, their small sizes have made their study difficult. The moving magnetic features, despite being more dynamic structures, have been studied during the last 40 years. They have been always associated with sunspots, especially with the penumbra. However, a recent observation of a naked sunspot (one with no penumbra) has shown MMF activity. The authors of this report…
Besides their causal connection with long and short-term magnetic variability, solar bipolar magnetic regions are our chief source of insight into the location, size, and properties of large-scale toroidal magnetic structures in the solar interior. The great majority of these regions (~95%) follow a systematic east-west polarity orientation (Hale's law) that reverses in opposite hemispheres and across even and odd cycles. These regions also present a systematic north-south polarity orientation (Joy's law) that helps build the poloidal field that seeds the new cycle. Exceptions to Hale's law ar…
Some preliminary processing results are presented for a dataset obtained with the Solar Optical Telescope on the Hinode satellite. The idea of the project is to record, nearly simultaneously, the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a photospheric level. Our ultimate aim is to elaborate observational criteria to distinguish between the manifestations of two mechanisms of sunspot-group formation --- the rising of an Omega-shaped flux tube of a strong magnetic field and the in situ amplification and structuring of magnetic field by convection (…
The sunspot cycle is the magnetic cycle of the Sun produced by the dynamo process. A central idea of the solar dynamo is that the toroidal and the poloidal magnetic fields of the Sun sustain each other. We discuss the relevant observational data both for sunspots (which are manifestations of the toroidal field) and for the poloidal field of the Sun. We point out how the differential rotation of the Sun stretches out the poloidal field to produce the toroidal field primarily at the bottom of the convection zone, from where parts of this toroidal field may rise due to magnetic buoyancy to produc…
The morphological asymmetry of leading and following sunspots is a well-known characteristic of the solar surface. In the context of large-scale evolution of the surface magnetic field, the asymmetry has been assumed to have only a negligible effect. Using the surface flux transport model, we show that the morphological asymmetry of leading and following sunspots has a significant impact on the evolution of the large-scale magnetic field on the solar surface. By evaluating the effect of the morphological asymmetry of each bipolar magnetic region (BMR), we observe that the introduction of the a…
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…
Much of our knowledge about the solar dynamo is based on sunspot observations. It is thus desirable to extend the set of positional and morphological data of sunspots into the past. Gustav Spörer observed in Germany from Anklam (1861-1873) and Potsdam (1874-1894). He left detailed prints of sunspot groups, which we digitized and processed to mitigate artifacts left in the print by the passage of time. After careful geometrical correction, the sunspot data are now available as synoptic charts for almost 450 solar rotation periods. Individual sunspot positions can thus be precisely determined an…
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 (SFT) models have to be revised.…
$δ$-sunspots, with highly complex magnetic structures, are very productive in energetic eruptive events, such as X-class flares and homologous eruptions. We here study the formation of such complex magnetic structures by numerical simulations of magnetic flux emergence from the convection zone into the corona in an active-region-scale domain. In our simulation, two pairs of bipolar sunspots form on the surface, originating from two buoyant segments of a single subsurface twisted flux rope, following the approach of Toriumi et al. (2014). Expansion and rotation of the emerging fields in the two…
The magnetic flux that is generated by dynamo inside the Sun emerges in the form of bipolar magnetic regions. We have analyzed the whole set of solar magnetograms obtained with the SOHO/MDI instrument in 1995-2011, and automatically identified 160,079 bipolar magnetic regions that span a range of scale sizes across nearly four orders of magnitude. Their properties have been statistically analyzed, in particular with respect to the polarity orientations of the bipolar regions, including their tilt angle distributions. The latitude variation of the average tilt angles (with respect to the E-W di…
Heliographic coordinates are used to identify the positions of solar features, especially the sunspot groups on the Sun's surface. Tracking the positions of sunspot groups provides information about solar rotation and the movement behavior of sunspot groups over Solar Cycles. Two heliographic coordinates are defined: Carrington and Stonyhurst. The calculations used here depend on three solar parameters, position angle P, latitude angle Bo and the starting longitude Lo. These values are calculated by using Astronomical Almanac for the observation time. In this study, a computer program called C…
In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by …
We investigate the effect of the surface bipolar magnetic regions (BMR) on the large-scale dynamo distributed in the bulk of the convection zone. The study employs the nonlinear 3D mean-field dynamo model. We model the emergence of the BMR on the surface through the nonaxisymmetric magnetic buoyancy effect, which acts on the large-scale toroidal magnetic field in the upper half of the convection zone. The nonaxisymmetric magnetic field which results from this mechanism is shallow. On the surface, the effect of the BMR on the magnetic field generation is dominant. {However, because of the shall…
This contribution to "Solar Magnetic Variability and Climate" reviews small-scale magnetic features on the solar surface, in particular the strong-field but tiny magnetic concentrations that constitute network and plage and represent most magnetism outside sunspots and filaments. Where these are mostly of the same polarity, as in active-region plage, their occurrence varies with the activity variations measured by the sunspot number, but when they appear bipolar-mixed on small scales they can also result from granular-scale dynamo action that does not vary with the cycle.
The spatial and temporal distributions of solar filaments were analyzed using data from the Meudon Observatory for the period 1919-2003 and the Kislovodsk Mountain Astronomical Station for the period 1979-2014. We scanned $H_α$ solar synoptic charts on which the filaments were isolated and digitized. The data on each filament comprise its location, length, area, and other geometrical characteristics. The temporal distributions of the number and total length of the filaments have been obtained. We also found latitudinal migration of filament locations with the solar cycle, and analyzed the long…
The Sun's activity cycle governs the radiation, particle and magnetic flux in the heliosphere creating hazardous space weather. Decadal-scale variations define space climate and force the Earth's atmosphere. However, predicting the solar cycle is challenging. Current understanding indicates a short window for prediction best achieved at previous cycle minima. Utilizing magnetic field evolution models for the Sun's surface and interior we perform the first century-scale, data-driven simulations of solar activity and present a scheme for extending the prediction window to a decade. Our ensemble …
Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are th…
