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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 are rare and difficult to study due to their low numbers. Here, we present a statistical analysis of the inclination (tilt) with respect to the equator of Hale versus anti-Hale regions spanning four solar cycles, considering two complementary tilt definitions adopted in previous studies. Our results show that anti-Hale regions belong to a separate population than Hale regions, suggesting a different originating mechanism. However, we find that anti-Hale region tilts present similar systematic tilt properties and similar latitudinal distributions to Hale regions, implying a strong connection between the two. We see this as evidence that they belong to a common toroidal flux system. We speculate that anti-Hale regions originate from poloidal field sheared and strengthened on the spot after the emergence of Hale regions with very strong poloidal contribution. Thus, they are not in contradiction with the idea of largely coherent toroidal flux systems inside the solar interior.

An analysis of the sunspot observations made by Hevelius during 1642-1645 is presented. These records are the only systematic sunspot observations just before the Maunder Minimum. We have studied different phenomena meticulously recorded by Hevelius after translating the original Latin texts. We re-evaluate the observations of sunspot groups by Hevelius during this period and obtain an average value 7% greater than that calculated from his observations given in the current group database. Furthermore, the average of the active day fraction obtained in this work from Hevelius' records previous to the Maunder Minimum is significantly greater than the solar activity level obtained from Hevelius' sunspot observations made during the Maunder Minimum (70% vs. 30%). We also present the butterfly diagram obtained from the sunspot positions recorded by Hevelius for the period 1642-1645. It can be seen that no hemispheric asymmetry exists during this interval, in contrast with the Maunder Minimum. Hevelius noted a ~3-month period that appeared to lack sunspots in early 1645 that gave the first hint of the impending Maunder Minimum. Recent studies claim that the Maunder Minimum was not a grand minimum period speculating that astronomers of that time, due to the Aristotelian ideas, did not record all sunspots that they observed, producing thus an underestimation of the solar activity level. However, we show the good quality of the sunspot records made by Hevelius indicates that his reports of sunspots were true to the observations.

The Sun's axisymmetric flows, differential rotation and meridional flow, govern the dynamics of the solar magnetic cycle and variety of methods are used to measure these flows, each with its own strengths and weaknesses. Flow measurements based on cross-correlating images of the surface magnetic field have been made since the 1970s which require advanced numerical techniques that are capable of detecting movements of less than the pixel size in images of the Sun. We have identified several systematic errors in addition to the center-to-limb effect that influence previous measurements of these flows and propose numerical techniques that can minimize these errors by utilizing measurements of displacements at several time-lags. Our analysis of line-of-sight magnetograms from the {\em Michelson Doppler Imager} (MDI) on the ESA/NASA {\em Solar and Heliospheric Observatory} (SOHO) and {\em Helioseismic and Magnetic Imager} (HMI) on the NASA {\em Solar Dynamics Observatory} (SDO) shows long-term variations in the meridional flow and differential rotation over two sunspot cycles from 1996 to 2020. These improved measurements can serve as vital inputs for solar dynamo and surface flux transport simulations., Comment: 16 pages, 9 figures, 2 tables

In this paper we present a curated dataset from the NASA Solar Dynamics Observatory (SDO) mission in a format suitable for machine learning research. Beginning from level 1 scientific products we have processed various instrumental corrections, downsampled to manageable spatial and temporal resolutions, and synchronized observations spatially and temporally. We illustrate the use of this dataset with two example applications: forecasting future EVE irradiance from present EVE irradiance and translating HMI observations into AIA observations. For each application we provide metrics and baselines for future model comparison. We anticipate this curated dataset will facilitate machine learning research in heliophysics and the physical sciences generally, increasing the scientific return of the SDO mission. This work is a direct result of the 2018 NASA Frontier Development Laboratory Program. Please see the appendix for access to the dataset., Accepted to The Astrophysical Journal Supplement Series; 11 pages, 8 figures

In this paper we address a discrepancy between the surface flux evolution in a 3D kinematic dynamo model and a 2D surface flux transport model that has been closely calibrated to the real Sun. We demonstrate that the difference is due to the connectivity of active regions to the toroidal field at the base of the convection zone, which is not accounted for in the surface-only model. Initially, we consider the decay of a single active region, firstly in a simplified Cartesian 2D model and subsequently the full 3D model. By varying the turbulent diffusivity profile in the convection zone, we find that increasing the diffusivity - so that active regions are more rapidly disconnected from the base of the convection zone - improves the evolution of the surface field. However, if we simulate a full solar cycle, we find that the dynamo is unable to sustain itself under such an enhanced diffusivity. This suggests that in order to accurately model the solar cycle, we must find an alternative way to disconnect emerging active regions, whilst conserving magnetic flux., Comment: 10 pages, 13 figures, accepted for publication in A&A

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. In order 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., 15 pages, 10 figures, accepted for publication in ApJ

In 1844 Schwabe discovered that the number of sunspots increased and decreased over a period of about 11 years, that variation became known as the sunspot cycle. Almost eighty years later, Hale described the nature of the Sun's magnetic field, identifying that it takes about 22 years for the Sun's magnetic polarity to cycle. It was also identified that the latitudinal distribution of sunspots resembles the wings of a butterfly showing migration of sunspots in each hemisphere that abruptly start at mid-latitudes towards the Sun's equator over the next 11 years. These sunspot patterns were shown to be asymmetric across the equator. In intervening years, it was deduced that the Sun (and sun-like stars) possess magnetic activity cycles that are assumed to be the physical manifestation of a dynamo process that results from complex circulatory transport processes in the star's interior. Understanding the Sun's magnetism, its origin and its variation, has become a fundamental scientific objective \-- the distribution of magnetism, and its interaction with convective processes, drives various plasma processes in the outer atmosphere. In the past few decades, a range of diagnostic techniques have been employed to systematically study finer scale magnetized objects, and associated phenomena. The patterns discerned became known as the ``Extended Solar Cycle'' (ESC). The patterns of the ESC appeared to extend the wings of the activity butterfly back in time, nearly a decade before the formation of the sunspot pattern, and to much higher solar latitudes. In this short review, we describe their observational patterns of the ESC and discuss possible connections to the solar dynamo as we depart on a multi-national collaboration to investigate the origins of solar magnetism through a blend of archived and contemporary data analysis with the goal of improving solar dynamo understanding and modeling., Comment: 11 Pages; 03 Figures

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., Comment: 15 pages, 18 figures, to be published in A&A

The Sun has a polar magnetic field which oscillates with the 11 year sunspot cycle. This polar magnetic field is an important component of the dynamo process which is operating in the solar convection zone and produces the sunspot cycle. We have systematic direct measurements of the Sun's polar magnetic field only from about mid 1970s. There are, however, indirect proxies which give us information about this field at earlier times. The Ca K spectroheliograms taken in Kodaikanal Solar Observatory during 1904 - 2007 have now been digitized with the 4k x 4k CCD and have higher resolution (0.86 arcsec) than the other available historical datasets. From these Ca-K spectroheliograms, we have developed a completely new proxy (Polar Network Index, PNI) for the Sun's polar magnetic field. We calculate the PNI from the digitized images using an automated algorithm and calibrate our measured PNI against the polar field as measured by the Wilcox Solar Observatory for the period of 1976 - 1990. This calibration allows us to estimate polar fields for the earlier period up to 1904. The dynamo calculations done with this proxy as input data reproduce the Sun's magnetic behavior for the past century reasonably well., Comment: 19 pages, 5 figures Accepted for publication in APJL

The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and Earth?s upper atmosphere (commonly referred to as space weather and climate). In recent years there has been an effort to develop accurate solar cycle predictions, leading to nearly a hundred widely spread predictions for the amplitude of solar cycle 24. Here we show that cycle predictions can be made more accurate if performed separately for each hemisphere, taking advantage of information about both the dipolar and quadrupolar moments of the solar magnetic field during minimum. Fil: Muñoz-Jaramillo, Andrés. Harvard-Smithsonian Center For Astrophysics; Estados Unidos de América; Fil: Balmaceda, Laura Antonia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico - CONICET - San Juan. Instituto de Ciencias Astronómicas de la Tierra y del Espacio; Argentina; Fil: Deluca, Edward. Harvard-Smithsonian Center For Astrophysics; Estados Unidos de América

Although the Sun's polar magnetic fields are thought to provide important clues for understanding the 11-year sunspot cycle, including the observed variations of its amplitude and period, the current database of high-quality polar-field measurements spans relatively few sunspot cycles. In this paper we address this deficiency by consolidating Mount Wilson Observatory polar faculae data from four data reduction campaigns, validating it through a comparison with facular data counted automatically from MDI intensitygrams, and calibrating it against polar field measurements taken by the Wilcox Solar Observatory and average polar field and total polar flux calculated using MDI line-of-sight magnetograms. Our results show that the consolidated polar facular measurements are in excellent agreement with both polar field and polar flux estimates, making them an ideal proxy to study the evolution of the polar magnetic field. Additionally, we combine this database with sunspot area measurements to study the role of the polar magnetic flux in the evolution of the heliospheric magnetic field (HMF). We find that there is a strong correlation between HMF and polar flux at solar minimum and that, taken together, polar flux and sunspot area are better at explaining the evolution of the HMF during the last century than sunspot area alone., 14 pages, 17 figures

We propose a phenomenological technique for modelling the emergence of active regions within a three-dimensional, kinematic dynamo framework. By imposing localised velocity perturbations, we create emergent flux-tubes out of toroidal magnetic field at the base of the convection zone, leading to the eruption of active regions at the solar surface. The velocity perturbations are calibrated to reproduce observed active region properties (including the size and flux of active regions, and the distribution of tilt angle with latitude), resulting in a more consistent treatment of flux-tube emergence in kinematic dynamo models than artificial flux deposition. We demonstrate how this technique can be used to assimilate observations and drive a kinematic 3D model, and use it to study the characteristics of active region emergence and decay as a source of poloidal field. We find that the poloidal components are strongest not at the solar surface, but in the middle convection zone, in contrast with the common assumption that the poloidal source is located near the solar surface. We also find that, while most of the energy is contained in the lower convection zone, there is a good correlation between the evolution of the surface and interior magnetic fields., Comment: 14 pages, 16 figures, to appear in MNRAS

The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric-average of the dynamically quenched diffusivity. Here, we provide an analytic fit to the dynamically quenched diffusivity profile, which can be used in kinematic dynamo simulations. Having successfully reconciled the mixing-length theory estimated diffusivity profile with kinematic dynamo models, we argue that they remain a viable tool for understanding the solar magnetic cycle., Submitted to ApJL

We are currently experiencing solar cycle 24, the latest roughly 11-year cycle of solar magnetic activity since the scientific recording of sunspot activity began in 1755. The Sun is currently extremely active, but the recent, deep activity minimum that occurred during cycle 23 was characterized by an unexpectedly large number of sunspot-less days (unprecedented in almost a century), very low radiative energy output (irradiance), and high cosmic ray flux. Nandy et al. use kinematic dynamo simulations to explain the possible origin of this unusual solar minimum. They find that rapid solar plasma flows during the first half of a cycle, followed by slower flows in the second half, reproduce the characteristics of the minimum of sunspot cycle 23. Direct observations over the past four centuries show that the number of sunspots observed on the Sun's surface varies periodically. After sunspot cycle 23, the Sun went into a prolonged minimum characterized by a very weak polar magnetic field and an unusually large number of days without sunspots. This study reports kinematic dynamo simulations which demonstrate that a fast meridional flow in the early half of a cycle, followed by a slower flow in the latter half, reproduces both characteristics of the minimum of sunspot cycle 23. Direct observations over the past four centuries1 show that the number of sunspots observed on the Sun’s surface varies periodically, going through successive maxima and minima. Following sunspot cycle 23, the Sun went into a prolonged minimum characterized by a very weak polar magnetic field2,3 and an unusually large number of days without sunspots4. Sunspots are strongly magnetized regions5 generated by a dynamo mechanism6 that recreates the solar polar field mediated through plasma flows7. Here we report results from kinematic dynamo simulations which demonstrate that a fast meridional flow in the first half of a cycle, followed by a slower flow in the second half, reproduces both characteristics of the minimum of sunspot cycle 23. Our model predicts that, in general, very deep minima are associated with weak polar fields. Sunspots govern the solar radiative energy8,9 and radio flux, and, in conjunction with the polar field, modulate the solar wind, the heliospheric open flux and, consequently, the cosmic ray flux at Earth3,10,11.

An essential ingredient in kinematic dynamo models is the velocity field within the solar convection zone. In particular, the differential rotation is now well constrained by helioseismic observations. Helioseismology also gives us information about the depth-dependence of the meridional circulation in the near-surface layers. The typical velocity inputs used in solar dynamo models, however, continue to be an analytic fit to the observed differential rotation and a theoretically constructed meridional flow profile that matches only the peak flow speed at the surface. Here we take the first steps towards realistic helioseismic data assimilation, by presenting methodologies for constructing differential rotation and meridional circulation profiles that more closely conform to the observational constraints currently available. We also present simulations driven by the assimilated rotation and four plausible profiles for the internal meridional circulation -- all of which match the helioseismically inferred near-surface depth-dependence, but whose magnitudes are made to vary. We discuss how the results compare with those that are driven by purely analytic fits. Our results indicate that the latitudinal shear of the rotation in the bulk of the solar convection zone plays a more important role, than either the tachocline or surface radial shear, in the induction of toroidal field. We also find that it is the speed of the equatorward counter-flow in the meridional flow at the base of the convection zone, and not how far into the radiative interior it penetrates, that primarily determines the dynamo cycle period. Given that improved helioseismic constraints are expected to be available in the future, our analysis lays the basis for assimilating these data within dynamo models.

In this work we introduce a new way of binning sunspot group data with the purpose of better understanding the impact of the solar cycle on sunspot properties and how this defined the characteristics of the extended minimum of cycle 23. Our approach assumes that the statistical properties of sunspots are completely determined by the strength of the underlying large-scale field and have no additional time dependencies. We use the amplitude of the cycle at any given moment (something we refer to as activity level) as a proxy for the strength of this deep-seated magnetic field. We find that the sunspot size distribution is composed of two populations: one population of groups and active regions and a second population of pores and ephemeral regions. When fits are performed at periods of different activity level, only the statistical properties of the former population, the active regions, are found to vary. Finally, we study the relative contribution of each component (small-scale versus large-scale) to solar magnetism. We find that when hemispheres are treated separately, almost every one of the past 12 solar minima reaches a point where the main contribution to magnetism comes from the small-scale component. However, due to asymmetries in cycle phase, this state is very rarely reached by both hemispheres at the same time. From this we infer that even though each hemisphere did reach the magnetic baseline, from a heliospheric point of view the minimum of cycle 23 was not as deep as it could have been.

The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and the Earth's upper atmosphere (commonly referred to as space weather). These changes have a direct impact on the lifetime of space-based assets and can create hazards to astronauts in space. In recent years there has been an effort to develop accurate solar cycle predictions (with aims at predicting the long-term evolution of space weather), leading to nearly a hundred widely spread predictions for the amplitude of solar cycle 24. A major contributor to the disagreement is the lack of direct long-term databases covering different components of the solar magnetic field (toroidal vs.\ poloidal). Here we use sunspot area and polar faculae measurements spanning a full century (as our toroidal and poloidal field proxies), to study solar cycle propagation, memory, and prediction. Our results substantiate predictions based on the polar magnetic fields, whereas we find sunspot area to be uncorrelated to cycle amplitude unless multiplied by area-weighted average tilt. This suggests that the joint assimilation of tilt and sunspot area is a better choice (with aims to cycle prediction) than sunspot area alone, and adds to the evidence in favor of active region emergence and decay as the main mechanism of poloidal field generation (i.e. the Babcock-Leighton mechanism). Finally, by looking at the correlation between our poloidal and toroidal proxies across multiple cycles, we find solar cycle memory to be limited to only one cycle., Comment: 7 pages, 5 figures