Distribution Of Sunspots Research Articles

Simplified Model of the Solar Magnetic Field

This paper considers a structure consisting of two rings of magnetic dipoles symmetrical relative to the equatorial plane as a possible model for the source of the solar magnetic field. It shows that the magnetic field generated by this structure corresponds to Joy’s law and Hale’s polarity law. Approximate calculations show that the form and shape of the equatorial field of this structure are close to measured values, and the resulting distribution of sunspots is in agreement with Joy's law to Maunder’s butterfly diagram. Based on this structure, it is possible to explain the appearance of two peaks (Gnevyshev gap) in the distribution of sunspots at the maximum of solar activity. Calculating the polar field based on the principles of magnetic hysteresis shows a good coincidence of the calculated and measured values and makes it possible to predict the behavior of the polar field in the interval to the nearest minimum of solar activity. Analyzing dipole nutation makes it possible to predict the intensity of the upcoming solar activity maxima, while a nutation period of approximately 8 months can be associated with 1.3 yr-period field oscillations. Despite the fact that the emergence and the functioning of the proposed configuration of magnetic dipoles is considered in a simplified manner and only from the point of view of gyromagnetic and thermal forces for speed and clarity, this does not limit the use of the proposed structure as a potential model in other, more global-scale general hydromagnetic theories of solar magnetism.

Toroidal Flux Loss due to Flux Emergence Explains why Solar Cycles Rise Differently but Decay in a Similar Way.

A striking feature of the solar cycle is that at the beginning, sunspots appear around midlatitudes, and over time the latitudes of emergences migrate toward the equator. The maximum level of activity (e.g., sunspot number) varies from cycle to cycle. For strong cycles, the activity begins early and at higher latitudes with wider sunspot distributions than for weak cycles. The activity and the width of sunspot belts increase rapidly and begin to decline when the belts are still at high latitudes. Surprisingly, it has been reported that in the late stages of the cycle the level of activity (sunspot number) as well as the widths and centers of the butterfly wings all have the same statistical properties independent of how strong the cycle was during its rise and maximum phases. We have modeled these features using a Babcock-Leighton type dynamo model and show that the flux loss through magnetic buoyancy is an essential nonlinearity in the solar dynamo. Our Letter shows that the nonlinearity is effective if the flux emergence becomes efficient at the mean-field strength of the order of 10^{4} G in the lower part of the convection zone.

Spatial and Temporal Distribution of Solar Green-Line Corona for Solar Cycles 18 – 24

The homogeneous coronal data set (HCDS) of the green corona (Fe xiv) and the coronal index of solar activity (CI) have been used to study the time–latitudinal distribution in Solar Cycles 18 – 24 and compared with similar distribution of sunspots, the magnetic fields, and the solar 10.7 cm radio flux. The most important results are: i) the distribution of coronal intensities related to the cycle maximum are different for individual cycles, ii) the poleward migration of the HCDS from mid-latitudes in each cycle exists, even in the extremely weak Cycle 24, and the same is valid for the equatorward migration, iii) the overall values of HCDS are slightly stronger for the northern hemisphere than for the southern one, iv) the distribution of the HDCS is in coincidence with the strongest photospheric magnetic fields (B>50 Gauss) and histograms of the sunspot groups, v) the Gnevyshev gap was confirmed with at least 95% confidence in the CI, however with different behavior for odd and even cycles. Principal component analysis (PCA) showed that the first and second components account for 87.7% and 7.3% of the total variation of the CI. Furthermore, the second PCA component of the green corona was quite different for Cycle 21, compared with other cycles.

Features of the Sunspot Distribution over the Solar Disk in 1874–2016

Features of the Sunspot Distribution over the Solar Disk in 1874–2016

On the size distribution of spots within sunspot groups

The size distribution of sunspots provides key information about the generation and emergence processes of the solar magnetic field. Previous studies of size distribution have primarily focused on either the whole group or individual spot areas. In this paper we investigate the organisation of spot areas within sunspot groups. In particular, we analysed the ratio (R) of the area of the biggest spot (Abig_spot) inside a group, to the total area of that group (Agroup). We used sunspot observations from Kislovodsk, Pulkovo, and Debrecen observatories, together covering solar cycles 17–24. We find that at the time when the group area reaches its maximum, the single biggest spot in a group typically occupies about 60% of the group area. For half of all groups, R lies in the range between roughly 50% and 70%. We also find R to change with Agroup, such that R reaches a maximum of about 0.65 for groups with Agroup ≈ 200 μHem and then remains at about 0.6 for larger groups. Our findings imply a scale-invariant emergence pattern, providing an observational constraint on the emergence process. Furthermore, extrapolation of our results to larger sunspot groups may have a bearing on the giant unresolved starspot features found in Doppler images of highly active Sun-like stars. Our results suggest that such giant features are composed of multiple spots, with the largest spot occupying roughly 55–75% of the total group area (i.e., the area of the giant starspots seen in Doppler images).

Bi-lognormal Distribution of Sunspot Group Areas

Abstract We use daily observations from the Royal Greenwich Observatory and Kislovodsk Mountain Astronomical Station of Pulkovo Observatory to study the distribution properties of sunspot areas. To mitigate the poor statistics in the distribution of small areas, we introduce a “precision randomization” approach based on the assumption that all measured areas have a random component within the measurement uncertainty of 1 millionth of the solar hemisphere (M.S.H.). We confirm the presence of two distinct components in the distribution of sunspots previously reported by several authors, and show that the area distribution is described by the sum of two lognormal distributions responsible for small and large groups (sunspots), respectively. We also demonstrate that the area of the main spots in the groups correlates well with the total area of the group, and, thus, the findings derived for the total group areas are equally applicable to the main spots of groups.

Asymmetry of Sunspot Distribution in Solar Cycles 12–24 and the Gnevyshev–Ohl Rule

The nonaxisymmetric component of the sunspot distribution (longitudinal asymmetry) is considered based on the Greenwich–USAF/NOAA data for 1874–2016. Vector summation was used to estimate the value of longitudinal asymmetry. The asymmetry vector modulus characterizes the asymmetry value, whereas the vector phase indicates the active longitude. The longitudinal asymmetry changes with the 11-year cycle of solar activity. It is shown that, in contrast to the solar activity, which obeys the Gnevyshev–Ohl rule (the even cycle is lower than the following odd cycle), only the first pair in the longitudinal asymmetry from each quad of cycles (from cycle 12 to 23) observed the Gnevyshev–Ohl rule, while the following pair conformed to the antirule, i.e., the even cycle was higher than the following odd cycle. This is probably a manifestation of the 44-year periodicity in the nonaxisymmetric component.

The flow of plasma inside the Sun

Solar Physics The activity of the Sun, including the occurrence of sunspots, is driven by magnetic fields that originate from the motion of charged plasma beneath the surface. Helioseismology uses acoustic oscillations to probe the Sun's interior, analogous to seismology's use of earthquakes to investigate Earth's interior. Gizon et al. analyzed helioseismology data from 1996 to 2019, covering two 11-year solar cycles. They measured the latitudinal and radial flow of plasma as a function of depth within the Sun and how it varies with time. The results support magnetic flux-transport dynamo models, which can explain the distribution of sunspots over each solar cycle. Science , this issue p. [1469][1] [1]: /lookup/doi/10.1126/science.aaz7119

Meridional flow in the Sun’s convection zone is a single cell in each hemisphere

The Sun's magnetic field is generated by subsurface motions of the convecting plasma. The latitude at which the magnetic field emerges through the solar surface (as sunspots) drifts toward the equator over the course of the 11-year solar cycle. We use helioseismology to infer the meridional flow (in the latitudinal and radial directions) over two solar cycles covering 1996-2019. Two data sources are used, which agree during their overlap period of 2001-2011. The time-averaged meridional flow is shown to be a single cell in each hemisphere, carrying plasma toward the equator at the base of the convection zone with a speed of ~4 meters per second at 45° latitude. Our results support the flux-transport dynamo model, which explains the drift of sunspot-emergence latitudes through the meridional flow.

Nonaxisymmetric Component of Solar Activity: the Vector of the Longitudinal Asymmetry

The vector representation of sunspots is used to study the nonaxisymmetric features of the solar activity distribution (sunspot data from Greenwich–USAF/NOAA, 1874–2016). Each sunspot is represented by a polar vector with modulus equal to the sunspot area and the phase equal to the sunspot heliolongitude. The vector sum of these individual vectors defines both the magnitude of the longitudinal asymmetry and the dominating longitude of the sunspot distribution. These characteristics are to a large extent free from the influence of a stochastic component and emphasize the nonaxisymmetric component of the solar activity. The longitudinal asymmetry follows the 11-year solar cycle with the amplitude three times lower than the sunspot area maximum. Longitudinal asymmetry is mostly determined by large sunspots: 82% of the longitudinal asymmetry is given by sunspots with area from 100 to 2000 MSH. Longitudinal asymmetries of the northern and southern hemispheres are connected only weakly (correlation coefficient $R = 0.29$ ). The longitudinal distribution displays a maximum at the longitude $\sim 180^{\circ }$ during ascent-maximum and at $\sim 0^{\circ }/360^{\circ }$ during descent-minimum. The active longitude changes with the reversals of polarity of the local (minimum of solar activity) and global magnetic fields (reversal of polar magnetic field).

Thaddäus Derfflinger’s Sunspot Observations during 1802–1824: A Primary Reference to Understand the Dalton Minimum

Abstract As we are heading toward the next solar cycle, presumably with a relatively small amplitude, it is of significant interest to reconstruct and describe the past secular minima on the basis of actual observations at the time. The Dalton Minimum is often considered one of the secular minima captured in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group number vary significantly, and the existing butterfly diagrams have a large data gap during the period. This is partially because most long-term observations at that time have remained unexplored in historical archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two series of Thaddäus Derfflinger’s observational records spanning 1802–1824 (a summary manuscript and logbooks), as well as his Brander’s 5.5 feet azimuthal quadrant preserved in the Kremsmünster Observatory. We have revised the existing Derfflinger’s sunspot group number with Waldmeier classification, and eliminated all the existing “spotless days” to remove contaminations from solar elevation observations. We have reconstructed the butterfly diagram on the basis of his observations and illustrated sunspot distributions in both solar hemispheres. Our article aims to revise the trend of Derfflinger’s sunspot group number and to bridge a data gap of the existing butterfly diagrams around the Dalton Minimum. Our results confirm that the Dalton Minimum is significantly different from the Maunder Minimum, both in terms of cycle amplitudes and sunspot distributions. Therefore, the Dalton Minimum is more likely a secular minimum in the long-term solar activity, while further investigations for the observations at that time are required.

A semi-automated method to reveal the evolution of each sunspot group in a solar cycle

Sunspots are the most important indicator of the magnetic activity on the solar surface during a cycle. Every sunspot group is formed and shaped by the magnetic field of the Sun. Hence, the magnetic field intensity shows itself as the size of a sunspot group area on the surface. This shows that getting the development or evolution of sunspot groups over time means getting the change of magnetic field intensity during same interval. Here, to reveal the evolution of sunspot groups in a cycle, a method called Solar Cycle Analyzer Tool (SCAT) is presented. This method was developed as a part of Computer-Aided Measurements for Sunspots (CAMS) because the same subroutines and subprograms were used for calculations (Cakmak 2014). The developed software tracks sunspot groups every day and gives them the same group number. The confirmation is made by the user to prevent counting re-formations as a continuation of an old group in the same active region. With this method, the evolution of every sunspot group can be listed for each cycle year besides other cycle features like the daily and monthly sunspot relative numbers and distribution frequency of the sunspot group types. Since 2015, SCAT is being used to get data for the annual reports of Istanbul University Observatory.

Shape of the 11-Year Cycle of Solar Activity and the Evolution of Latitude Characteristics of the Sunspot Distribution

The solar activity index and parameters of the spatial distribution of sunspots are known to be related. Using these relationships, we propose interrelated approximations for the sunspot number (SN) and the two key latitude characteristics of their distribution in the cycle: the mean latitude of sunspots and the standard deviation of their latitudes. The two parameters of these approximations are the cycle amplitude SNmax and the drift of its downward branch relative to the cycle beginning t0. These approximations specifically take into account the relationship between amplitudinal and spatial properties of the 11-year solar cycle, as well as the universality of the behavior of the activity and mean latitude of sunspots in the declining phase of the cycle. We demonstrate that the pair of parameters SNmax and t0 allows approximation of both the shape of the cyclic curve and the latitude–time diagram for sunspots of this cycle (“Maunder’s butterfly”).

Prediction of the strength and timing of sunspot cycle 25 reveal decadal-scale space environmental conditions

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 forecast indicates cycle 25 would be similar or slightly stronger than the current cycle and peak around 2024. Sunspot cycle 25 may thus reverse the substantial weakening trend in solar activity which has led to speculation of an imminent Maunder-like grand minimum and cooling global climate. Our simulations demonstrate fluctuation in the tilt angle distribution of sunspots is the dominant mechanism responsible for solar cycle variability.

The Extended Solar Cycle: Muddying the Waters of Solar/Stellar Dynamo Modeling or Providing Crucial Observational Constraints?

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.

Latitudinal Distribution of Sunspot and North-South Asymmetry Revisited

The solar magnetic field plays a central role in the field of solar research, both theoretically and practically. Sunspots are an important observational constraint since they are considered a discernable tracer of emerged magnetic flux tubes, providing the longest running records of solar magnetic activity. In this presentation, we first review the statistical properties of the latitudinal distribution of sunspots and discuss their implications. The phase difference between paired wings of the butterfly diagram has been revealed. Sunspots seem to emerge with the exponential distribution on top of slowly varying trends by periods of ~11 years, which is considered multiplicative rather than additive. We also present a concept for the center-oflatitude (COL) and its use. With this, one may sort out a traditional butterfly diagram and find new features. It is found that the centroid of the COL does not migrate monotonically toward the equator, appearing to form an ‘active latitude’. Furthermore, distributions of the COL as a function of latitude depend on solar activity and the solar North-South asymmetry. We believe that these findings serve as crucial diagnostic tools for any potential model of the solar dynamo. Finally, we find that as the Sun modulates the amount of observed galactic cosmic ray influx, the solar North-South asymmetry seems to contribute to the relationship between the solar variability and terrestrial climate change.

Reconstruction of a Hundred Years Series of Solar Filaments from Daily Observational Data

The preliminary results of solar filaments distinguished in daily H-alpha observations at Kodaikanal (1912–2002) are presented. To mark the boundaries of solar filaments, methods based on automated procedures of marking low-contrast objects on the solar disk, as well as editing of the marked boundaries in a semiautomated manner, were developed. The characteristics of solar filaments were analyzed. Latitudinal diagrams of filaments number in 15–23 activity cycles were constructed. As is shown, one maximum in the filament latitudinal distribution may be clearly distinguished during activity cycles in both hemispheres. This maximum is located slightly higher (θ ~ 25°–30°) than the sunspot distribution maximum (θ ~ 14°–17°). However, there are no other local maxima related to the zonal structure of the large-scale magnetic field (Makarov and Sivaraman, 1989).

Spatial Inhomogeneity in Solar Faculae

AbstractIn this paper, we investigate the inhomogeneous spatial distribution of solar faculae. The focus is on the latitudinal and longitudinal distributions of these highly localised features covering ubiquitously the solar surface. The statistical analysis is based on white light observations of the Solar and Heliospheric Observatory (SOHO) and Solar Dynamics Observatory (SDO) between 1996 and 2014. We found that the fine structure of the latitudinal distribution of faculae displays a quasi-biennial oscillatory pattern. Furthermore, the longitudinal distribution of photospheric solar faculae does not show homogeneous behaviour either. In particular, the non-axisymmetric behaviour of these events show similar properties as that of the active longitude (AL) found in the distribution of sunspots. Our results, preliminary though, may provide a valuable observational constrain for developing the next-generation solar dynamo model.

Starspot activity and superflares on solar-type stars

Abstract We analyze the correlation between starspots and superflares on solar-type stars using observations from the Kepler mission. The analysis shows that the observed fraction of stars with superflares decreases as the rotation period increases and as the amplitude of photometric variability associated with rotation decreases. We found that the fraction of stars with superflares among the stars showing large-amplitude rotational variations, which are thought to be the signature of the large starspots, also decreases as the rotation period increases. The small fraction of superflare stars among the stars with large starspots in the longer-period regime suggests that some of the stars with large starspots show a much lower flare activity than the superflare stars with the same spot area. Assuming simple relations between spot area and lifetime and between spot temperature and photospheric temperature, we compared the size distribution of large starspot groups on slowly rotating solar-type stars with that of sunspot groups. The size distribution of starspots shows the power-law distribution and the size distribution of larger sunspots lies on this power-law line. We also found that frequency–energy distributions for flares originating from spots with different sizes are the same for solar-type stars with superflares and the Sun. These results suggest that the magnetic activity we observe on solar-type stars with superflares and on the Sun is caused by the same physical processes.

Long‐term variations in sunspot magnetic field–area relation

BackgroundSeveral recent studies indicated possible long‐term variations of physical properties of sunspots.Materials and MethodsUsing observations of sunspot magnetic field strengths (H) from the Crimean Astrophysical Observatory and area (S) of sunspots from the Kislovodsk Mountain Astronomical Station of Pulkovo Observatory, we investigate the changes in the relation between H and S over the period of about two solar cycles (1994– 2013). The data were fitted by H = A + B log S, where A = (778 ± 46) and B = (778 ± 25).ResultsWe show that the correlation between H and S varies with the phase of solar cycle, and A coefficient decreases significantly after year 2001, while B coefficient does not change significantly. Furthermore, our data confirm the presence of two distinct populations in the distribution of sunspots (small sunspots with weaker field strength and large sunspots with stronger field). We show that the relative contribution of each component to the distribution of sunspots by their area changes with the phase of solar cycle and on longer‐than‐cycle periods.ConclusionWe interpret these changes as a signature of a long‐term (centennial) variations in the properties of sunspots.