Sunspot Area Research Articles

Sunspot areas and tilt angles for solar cycles 7–10

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 as the tilt angles of sunspot groups assuming them to be bipolar. There is, of course, no polarity information in the observations. The annually averaged sunspot areas correlate reasonably with sunspot number. We derived an average tilt angle by attempting to exclude unipolar groups with a minimum separation of the two alleged polarities and an outlier rejection method which follows the evolution of each group and detects the moment it turns unipolar at its decay. As a result, the tilt angles, although displaying considerable scatter, place the leading polarity on average 5.85+-0.25 closer to the equator, in good agreement with tilt angles obtained from 20th-century data sets. Sources of uncertainties in the tilt angle determination are discussed and need to be addressed whenever different data sets are combined. The sunspot area and tilt angle data are provided online.

Sunspot drawings handwritten character recognition method based on deep learning

High accuracy scanned sunspot drawings handwritten characters recognition is an issue of critical importance to analyze sunspots movement and store them in the database. This paper presents a robust deep learning method for scanned sunspot drawings handwritten characters recognition. The convolution neural network (CNN) is one algorithm of deep learning which is truly successful in training of multi-layer network structure. CNN is used to train recognition model of handwritten character images which are extracted from the original sunspot drawings. We demonstrate the advantages of the proposed method on sunspot drawings provided by Chinese Academy Yunnan Observatory and obtain the daily full-disc sunspot numbers and sunspot areas from the sunspot drawings. The experimental results show that the proposed method achieves a high recognition accurate rate.

North-south asymmetry in the magnetic deflection of polar coronal hole jets

Measurements of the magnetic field in the interplanetary medium, of the sunspots area, and of the heliospheric current sheet position, reveal a possible North-South asymmetry in the magnetic field of the Sun. We study the North-South asymmetry as inferred from measurements of the deflection of polar coronal hole jets when they propagate throughout the corona. Since the corona is an environment where the magnetic pressure is greater than the kinetic pressure, we can assume that magnetic field controls the dynamics of plasma. On average, jets during their propagation follow the magnetic field lines, highlighting its local direction. The average jet deflection is studied both in the plane perpendicular to the line of sight, and, for a reduced number of jets, in three dimensional space. The observed jet deflection is studied in terms of an axisymmetric magnetic field model comprising dipole We measured the position angles at 1 rs and at 2 rs of the 79 jets from the catalogue of Nistico et al 2009., based on the STEREO ultraviolet and white-light coronagraph observations during the solar minimum period March 2007-April 2008. We found that the propagation is not radial, in agreement with the deflection due to magnetic field lines. Moreover, the amount of the deflection is different between jets over the north and those from the south pole. Comparison of jet deflections and field line tracing shows that a ratio g2/g1 ~ -0.5 for the quadrupole and a ratio g3/g1 ~ 1.6-2.0 for the esapole can describe the field. The presence of a non-negligible quadrupole moment. We find that the magnetic deflection of jets is larger in the North than in the South of the order of 25-40%, with an asymmetry which is consistent with a southward deflection of the heliospheric current sheet of the order of 10 deg, consistent with that inferred from other, independent, datasets and instruments.

Evolutionary aspects and north-south asymmetry of soft X-ray flare index during solar cycles 21, 22, and 23

Aims. In this paper, we investigate the temporal evolution and north-south (N-S) asymmetry in the occurrence of solar flares during cycle 21, 22, and 23, and compare the results with traditional solar activity indices. Methods. The flare activity is characterized by a soft X-ray (SXR) flare index, which incorporates information about flare occurrences during a selected interval along with the peak intensity of individual events. Results. The SXR flare index correlates well with other conventional parameters of solar activity. Further, it exhibits a significantly higher correlation with sunspot area over sunspot number, which suggests the variations in sunspot area to be more closely linked with the transient energy release in the solar corona. The cumulative plots of the flare index indicate a slight excess of activity in the northern hemisphere during cycle 21, while a southern excess clearly prevails for cycles 22 and 23. The study reveals a significant N-S asymmetry, which exhibits variations with the phases of solar cycle. The reliability and persistency of this asymmetry significantly increases when the data is averaged over longer periods, while an optimal level is achieved when data is binned for 13 Carrington rotations. The time evolution of the flare index further confirms evolution of dual peaks in solar cycles during the solar maxima and violation of Gnevyshev-Ohl rule for the pair of solar cycles 22 and 23. Conclusions. The SXR flare index in the northern and the southern hemispheres of the Sun exhibits significant asymmetry during the evolutionary phases of the solar cycle, which implies that N-S asymmetry of solar flares is manifested in terms of the flare counts as well as the intensity of flare events.

风云三号C星太阳总辐照度观测结果分析

Solar Irradiance Monitor-II (SIM-II) onboard FengYun-3C (FY-3C), the third satellite of the second generation of Chinese meteorological polar orbit series, is a successive instrument from FY-3A/B SIMs with improved capabilities of solar tracking and temperature controlling. SIM-II is aimed to observe incoming solar energy over 0.2-50 mm band at top of atmosphere and convert it to total solar irradiance (TSI) at the average sun-earth distance. The instrument has a measuring requirement of 0.1% absolute accuracy and long-term relative precision of 0.02% during its 4-year design lifetime. The TSI observed by SIM-II is analyzed and validated by comparing with SORCE/TIM and the composite time series from Royal Meteorological Institute of Belgium (RMIB) daily mean products. It shows that there is a good consistency on variation trend in TSI among SIM-II, TIM and RMIB, from March 5, 2014 to September 22, 2014. The quantitative comparison shows SIM-II daily TSI product has an 87×10-6 rms relative error compared with SORCE/TIM data and 140×10-6 rms relative error with RMIB composite data. The sunspot data including sunspot number and area is also analyzed with SIM-II TSI product. The sunspot number is negative correlation with SIM-II TSI daily product at solar activities. The TSI variation at the strongest solar activity during the October 2014 shows a good correlation with the sunspot area data. When sunspot area is increased by 2470, the variation in TSI from SIM-II is about -2.94 and -2.98 W/m2 for TIM, which is very close to each other. It can be concluded that the SIM-II TSI observations can quantitatively reflect the variations of the solar emission during solar activities. These studies show that FY-3C TSI product had achieved the same accuracy as those of SORCE/TIM and RMIB data, and can be used in the researches of solar activities and climate changes.

REGULARITY OF THE NORTH–SOUTH ASYMMETRY OF SOLAR ACTIVITY: REVISITED

Extended time series of Solar Activity Indices (ESAI) extended the Greenwich series of sunspot area from the year 1874 back to 1821. The ESAI's yearly sunspot area in the northern and southern hemispheres from 1821 to 2013 is utilized to investigate characteristics of the north-south hemispherical asymmetry of sunspot activity. Periodical behavior of about 12 solar cycles is also confirmed from the ESAI data set to exist in dominant hemispheres, linear regression lines of yearly asymmetry values, and cumulative counts of yearly sunspot areas in the hemispheres for solar cycles. The period is also inferred to appear in both the cumulative difference in the yearly sunspot areas in the hemispheres over the entire time interval and in its statistical Student's t-test. The hemispherical bias of sunspot activity should be regarded as an impossible stochastic phenomenon over a long time period.

Abnormal rotation rates of sunspots and durations of associated flares

Context. Short-duration and long-duration flares are important in terms of their association with coronal heating and coronal mass ejections, respectively. Sunspot motions in the photosphere have been known to be associated with flare occurrences. Aims. We study the association between the abnormal rotation rates (longitudinal displacement in a given latitude in contrast with the rotation of spots around their umbral centre) of sunspots and flare duration. Methods. We compute the rotation rates of sunspots for different days during their evolution. We consider rotation rates that are in excess of one standard deviation as abnormal rotation rates. Also, the duration of time between the initial and final stages of the flares are computed. Results. Using Kodaikanal Observatory white light picture and GOES soft X-ray flare data, we find that a good association with a high significance exists between abnormal rotation rates of sunspots and flare durations. In contrast, we find that duration of flare is independent of sunspot area. Conclusions. The present study suggests that sub-surface dynamics plays a dominant role in determining the duration and rate of dissipation of energy during flares.

A Comparison Between Global Proxies of the Sun’s Magnetic Activity Cycle: Inferences from Helioseismology

The last solar minimum was, by recent standards, unusually deep and long. We are now close to the maximum of the subsequent solar cycle, which is relatively weak. In this article we make comparisons between different global (unresolved) measures of the Sun's magnetic activity, to investigate how they are responding to this weak-activity epoch. We focus on helioseismic data, which are sensitive to conditions, including the characteristics of the magnetic field, in the solar interior. Also considered are measures of the magnetic field in the photosphere (sunspot number and sunspot area), the chromosphere and corona (10.7cm radio flux and 530.3nm green coronal index), and two measures of the Sun's magnetic activity closer to Earth (the interplanetary magnetic field and the galactic cosmic-ray intensity). Scaled versions of the activity proxies diverge from the helioseismic data around 2000, indicating a change in relationship between the proxies. The degree of divergence varies from proxy to proxy with sunspot area and 10.7cm flux showing only small deviations, while sunspot number, coronal index, and the two interplanetary proxies show much larger departures. In Cycle 24 the deviations in the solar proxies and the helioseismic data decrease, raising the possibility that the deviations observed in Cycle 23 are just symptomatic of a 22-year Hale cycle. However, the deviations in the helioseismic data and the interplanetary proxies increase in Cycle 24. Interestingly the divergence in the solar proxies and the helioseismic data are not reflected in the shorter-term variations (often referred to as quasi-biennial oscillations) observed on top of the dominant 11-year solar cycle. However, despite being highly correlated in Cycle 22, the short-term variations in the interplanetary proxies show very little correlation with the helioseismic data during Cycles 23 and 24.

Evolution and Flare Activity of δ $\delta$ -Sunspots in Cycle 23

The emergence and magnetic evolution of solar active regions (ARs) of beta-gamma-delta type, which are known to be highly flare-productive, were studied with the SOHO/MDI data in Cycle 23. We selected 31 ARs that can be observed from their birth phase, as unbiased samples for our study. From the analysis of the magnetic topology (twist and writhe), we obtained the following results. i) Emerging beta-gamma-delta ARs can be classified into three topological types as "quasi-beta", "writhed" and "top-to-top". ii) Among them, the "writhed" and "top-to-top" types tend to show high flare activity. iii) As the signs of twist and writhe agree with each other in most cases of the "writhed" type (12 cases out of 13), we propose a magnetic model in which the emerging flux regions in a beta-gamma-delta AR are not separated but united as a single structure below the solar surface. iv) Almost all the "writhed"-type ARs have downward knotted structures in the mid portion of the magnetic flux tube. This, we believe, is the essential property of beta-gamma-delta ARs. v) The flare activity of beta-gamma-delta ARs is highly correlated not only with the sunspot area but also with the magnetic complexity. vi) We suggest that there is a possible scaling-law between the flare index and the maximum umbral area.

Hilbert–Huang transform analysis of periodicities in the last two solar activity cycles

We investigated periodicities associated with the last two-and-a-half solar activity cycles with the novel Hilbert–Huang transform (HHT) method. Raw data signals of five different observational proxies: the 10.7 cm radio flux intensity, the helioseismic frequency shift, and the sunspot area signals recorded from the whole solar disc, and separately from the Northern and Southern hemispheres, were expanded into a set of intrinsic modes with the ensemble empirical mode decomposition technique. Instant and mean periods of each empirical mode were obtained with the use of the Hilbert transform applied independently to each separate mode. The periodicities were allocated to three distinct groups: short-term variations (with periods shorter than 0.5 yr), quasi-biennial oscillations (with typical periods from 0.5 yr to 3.9 yr), and longer periodicities, e.g. such as the 11 yr cycle. All periodicities detected in the examined solar cycles 22–24 are consistent with the well-known results found in the earlier solar epochs. We have demonstrated that the HHT method is a good tool for characterizing periodicities in the helioseismic data, which are necessarily relatively limited in terms of their time resolution. Periodicities obtained using the helioseismic data are, nevertheless, consistent with those found in other proxies. Since helioseismic oscillations are sensitive to the solar interior, this indicates that the behaviour of surface and atmospheric magnetic activity reflects that of the Sun's internal magnetic field. All identified intrinsic modes are seen to have clear amplitude modulation highly correlated with the 11 yr cycle. This amplitude modulation is most pronounced in the short-period modes. The short-term periodicities were found to be multiples of the shortest period, of 25 d. This ordering of the short-term periodicities is consistent with the previous findings. Signatures of the north–south asymmetry were detected in the individual hemisphere sunspot area indices. Furthermore, evidence of the last ‘extended’ solar minimum was detected too.

LOOKING FOR GRANULATION AND PERIODICITY IMPRINTS IN THE SUNSPOT TIME SERIES

The sunspot activity is the end result of the cyclic destruction and regeneration of magnetic fields by the dynamo action. We propose a new method to analyze the daily sunspot areas data recorded since 1874. By computing the power spectral density of daily data series using the Mexican hat wavelet, we found a power spectrum with a well-defined shape, characterized by three features. The first term is the 22 yr solar magnetic cycle, estimated in our work to be of 18.43 yr. The second term is related to the daily volatility of sunspots. This term is most likely produced by the turbulent motions linked to the solar granulation. The last term corresponds to a periodic source associated with the solar magnetic activity, for which the maximum of power spectral density occurs at 22.67 days. This value is part of the 22-27 day periodicity region that shows an above-average intensity in the power spectra. The origin of this 22.67 day periodic process is not clearly identified, and there is a possibility that it can be produced by convective flows inside the star. The study clearly shows a north-south asymmetry. The 18.43 yr periodical source is correlated between the two hemispheres, but the 22.67 day one is not correlated. It is shown that towards the large timescales an excess occurs in the northern hemisphere, especially near the previous two periodic sources. To further investigate the 22.67 day periodicity we made a Lomb-Scargle spectral analysis. The study suggests that this periodicity is distinct from others found nearby.

Analysis of the Major Parameters in Solar Active Regions Based on the PCA Method

The occurrence of solar flares and solar proton events has a close relation with the solar active regions. A deep analysis on this relation is helpful to build a concrete model of forecasting solar flares and solar proton events. In this paper the Principal Component Analysis (PCA) method is adopted to analyze the main parameters of the solar active regions with solar proton events happened in 1997∼2010, the selected parameters include the magnetic classification of sunspot, the McIntosh classification of sunspot group, the area of sunspot group, the 10.7cm radio flux, the flare index, the proton flare position, and the soft X-ray flare intensity. The order of principal component scores for 81 solar activities has been obtained (the score represents the strength of each event), which is compared with the peak flux of solar proton event, the annual mean values of sunspot area and 10.7cm radio flux, it is found that the similarity is very high, and this shows that the principal component scores can represent the strength of solar activity to some extent.

Hemispheric asymmetry of sunspot area in solar cycle 23 and rising phase of solar cycle 24: Comparison of three data sets

Analysis of long-term solar data from different observatories is required to compare and confirm the various level of solar activity in depth. In this paper, we study the north–south asymmetry of monthly mean sunspot area distribution during the cycle-23 and rising phase of cycle-24 using the data from Kodaikanal Observatory (KO), Michelson Doppler Imager (MDI) and Solar Optical Observing Network (SOON). Our analysis confirmed the double peak behavior of solar cycle-23 and the dominance of southern hemisphere in all the sunspot area data obtained from three different resources. The analysis also showed that there is a 5–6months time delay in the activity levels of two hemispheres. Furthermore, the wavelet analysis carried on the same data sets showed several known periodicities (e.g., 170–180days, 2.1year) in the north–south difference of sunspot area data. The temporal occurrence of these periods is also the same in all the three data sets. These results could help in understanding the underlying mechanism of north–south asymmetry of solar activity.

MODELING SUNSPOT AND STARSPOT DECAY BY TURBULENT EROSION

Disintegration of sunspots (and starspots) by fluxtube erosion, originally proposed by Simon and Leighton, is considered. A moving boundary problem is formulated for a nonlinear diffusion equation that describes the sunspot magnetic field profile. Explicit expressions for the sunspot decay rate and lifetime by turbulent erosion are derived analytically and verified numerically. A parabolic decay law for the sunspot area is obtained. For moderate sunspot magnetic field strengths, the predicted decay rate agrees with the results obtained by Petrovay and Moreno-Insertis. The new analytical and numerical solutions significantly improve the quantitative description of sunspot and starspot decay by turbulent erosion.

Digitization of sunspot drawings by Spörer made in 1861–1894

AbstractMost of our knowledge about the Sun's activity cycle arises from sunspot observations over the last centuries since telescopes have been used for astronomy. The German astronomer Gustav Spörer observed almost daily the Sun from 1861 until the beginning of 1894 and assembled a 33‐year collection of sunspot data covering a total of 445 solar rotation periods. These sunspot drawings were carefully placed on an equidistant grid of heliographic longitude and latitude for each rotation period, which were then copied to copper plates for a lithographic reproduction of the drawings in astronomical journals. In this article, we describe in detail the process of capturing these data as digital images, correcting for various effects of the aging print materials, and preparing the data for contemporary scientific analysis based on advanced image processing techniques. With the processed data we create a butterfly diagram aggregating sunspot areas, and we present methods to measure the size of sunspots (umbra and penumbra) and to determine tilt angles of active regions. A probability density function of the sunspot area is computed, which conforms to contemporary data after rescaling. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

ON THE VARIATION OF SOLAR RADIUS IN ROTATION CYCLES

The Date Compensated Discrete Fourier Transform and CLEANest algorithm are used to study the temporal variations of the solar radius observed at Rio de Janeiro Observatory from 1998 March 2 to 2009 November 6. The CLEANest spectra show several significant periodicities around 400, 312, 93.5, 86.2, 79.4, 70.9, 53.2, and 26.3 days. Then, combining the data on the daily solar radius measured at Calern Observatory and Rio de Janeiro Observatory and the corresponding daily sunspot areas, we study the short-term periodicity of the solar radius and the role of magnetic field in the variation of the solar radius. The rotation period of the daily solar radius is determined to be statistically significant. Moreover, its temporal evolution is anti-phase with that of sunspot activity, and it is found anti-phase with solar activity. Generally, the stronger solar activity is, the more obvious is the anti-phase relation of radius with solar activity. This indicates that strong magnetic fields have a greater inhibitive effect than weak magnetic fields on the variation of the radius.

Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Abstract. Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north–south sunspot asymmetry, which is to be further explored in future work.

Hemispheric Coupling: Comparing Dynamo Simulations and Observations

Numerical simulations that reproduce solar-like magnetic cycles can be used to generate long-term statistics. The variations in N-S hemispheric cycle synchronicity and amplitude produced in simulations has not been widely compared to observations. The observed limits on asymmetry show that hemispheric sunspot area production is no more than 20% asymmetric for cycles 12-23 and phase lags do not exceed 20% (2 yrs) of the total cycle period. Independent studies have found a long-term trend in phase values as one hemisphere leads the other for ~four cycles. Such persistence in phase is not indicative of a stochastic phenomenon. We compare the findings to results from a numerical simulation of solar convection recently produced with the EULAG-MHD model. This simulation spans 1600 yrs and generated 40 regular, sunspot-like cycles. While the simulated cycle length is too long and the toroidal bands remain at too high of latitudes, some solar-like aspects of hemispheric asymmetry are reproduced. The model reproduces the synchrony of polarity inversions and onset of cycle as the simulated phase lags do not exceed 20% of the cycle period. Simulated amplitude variations between the N and S hemispheres are larger than observed in the Sun. The simulations show one hemisphere persistently leads the other for several successive cycles, placing an upper bound on the efficiency of transequatorial magnetic coupling mechanisms. These include magnetic diffusion, cross-equatorial mixing within elongated convective rolls and transequatorial meridional flow cells. One or more of these processes may lead to magnetic flux cancellation whereby the oppositely directed fields come in close proximity and cancel each other across the magnetic equator late in the solar cycle. We discuss the discrepancies between model and observations and the constraints they pose on possible mechanisms of hemispheric coupling.

Sunspot Catalogue of the Valencia Observatory (1920 – 1928)

A sunspot catalogue was maintained by the Astronomical Observatory of Valencia University (Spain) from 1920 to 1928. Here we present a machine-readable version of this catalogue (OV catalogue or OVc), including a quality-control analysis. Sunspot number (total and hemispheric) and sunspot area series are constructed using this catalogue. The OV catalogue data are compared with other available solar data, demonstrating that the present contribution provides the scientific community with a reliable catalogue of sunspot data.

Sunspot Numbers and Areas from the Madrid Astronomical Observatory (1876 – 1986)

The solar program of the Astronomical Observatory of Madrid started in 1876. For ten solar cycles, observations were made in this institution to determine sunspot numbers and areas. The program was completed in 1986. The resulting data have been published in various Spanish scientific publications. The metadata allowed four periods of this program (with different observers and instruments) to be identified. In the present work, the published data were retrieved and digitized. Their subsequent analysis showed that most of these data can be considered reliable given their very high correlation with international reference indices (International Sunspot Number, Group Sunspot Number, and Sunspot Area). An abrupt change emerged in the spots/groups ratio in 1946 which lasted until 1972.