Sunspot Area Research Articles

Heliospheric Effect on Solar Activity Parameters during MaximumPhase of Solar Cycle 24 (2012-2015)

Abstract The time series of daily data of solar activity proxies, namely the sunspot number (SSN), sunspot area (SSA), solar radio flux (F10.7), modified coronal index (MCI), solar flare index (FI), and cosmic ray intensity (CRI), were analyzed to understand the solar activity modulations and short-term periodicities therein. Rieger-type, and other short-term periods, including the solar rotational period that covers the maximum activity phase period (maximum phase of solar cycle 24). The wavelet power spectra and Periodogram of SSN, SSA, F10.7, MCI, FI, and CRI exhibited a significant short-term period. The heliospheric effects exist for a particular period (~27 days) and it is related to the solar activity phenomena. The cross-correlation coefficients and time lags between the cosmic ray intensity and solar activity parameters were estimated to be 200, 46, 281, 39, and 47 days for SSN, SSA, F10.7, MCI, and FI respectively during the time series 2012-2015 (maximum phase of solar cycle 24).

Statistical Comparison between Pores and Sunspots during the Time Interval 2010–2023

To reveal the physical properties of pores and sunspots varying with solar cycle, we carried out a statistical comparison among pores, transitional sunspots, and mature sunspots using Solar Dynamics Observatory/Helioseismic and Magnetic Imager from 2010 April to 2023 July. The OTSU method and region-growing algorithm were combined to detect umbrae of 11,876 sunspots covering solar cycles 24 and 25. The relationships between umbral area, continuum intensity (I), line-of-sight (LOS) magnetic field strength (B los), and line-of-sight velocity (V los) of umbrae were investigated in detail. The main conclusions are as follows. (1) The steepness between the total magnetic flux and total area of transitional sunspots appears to be flattened in each phase of the observed solar cycles, and does not have a significant variation over the solar cycle. (2) For three groups of sunspots, the umbral physical parameters’ means and their correlations show only minor variations with the solar cycle, which are in error ranges. (3) As the mean umbral LOS magnetic field strength increases, the correlation of the umbral I–B los increases. The flattening of transitional sunspots in total area–total magnetic flux scatter is related to the evolution of sunspots itself, and may not correspond to the solar cycle. The umbral physical parameters and their correlations do not exhibit a discernible regularity over the solar cycle. Our analysis results contribute to a more comprehensive understanding of the dynamic processes of sunspot magnetic fields and give a new perspective on revealing the physical features of vertical magnetic flux tubes.

Adiabatic spectrum of radio emission of plasma clouds, emitted by the Sun during solar flares, and inhomogeneities of the spectrum of radio emission of clouds

It is known that so-called solar flares systematically occur in the area of sunspots. They are accompanied by radiation in almost all frequency ranges and sometimes by the emission of hot plasma. Observations on the RATAN-600 radio telescope have shown that the radio emission spectrum of plasma clouds heated to values of the order of 106K erupted from the solar flare region turned out to be adiabatic. The high correlation of the inhomogeneities of the radio emission spectra of active formation over a group of sunspots indicates the stable presence of recombination radio lines in the radiation of active formation. However, the radio emission spectra of hot plasma clouds ejected from the region of solar flares occurring in this group of spots do not show any correlation.

Extreme value theory applied to long-term sunspot areas

Extreme value theory applied to long-term sunspot areas

Explore the relationship between sunspot area and sunspot number with a new method

Explore the relationship between sunspot area and sunspot number with a new method

Sunspots Identification Through Mathematical Morphology

The implementation of automated methods for sunspot detection is essential to obtain better objectivity, efficiency, and accuracy in identifying sunspots and analysing their morphological properties. A desired application is the contouring of sunspots. In this work, we construct sunspot contours from Solar Dynamics Observatory (SDO)/ Helioseismic and Magnetic Imager intensity images by means of an automated method based on development and application of mathematical morphology. The method is validated qualitatively – the resulting contours accurately delimit sunspots. Here, it is applied to high-resolution data (SDO intensitygrams) and validated quantitatively by illustrating a good agreement between the measured sunspot areas and the ones provided by two standard reference catalogues. The method appears to be robust for sunspot identification, and our analysis suggests its application to more complex and irregular-shaped solar structures, such as polarity inversion lines inside delta-sunspots.

Determining sunspot area through visible range observations. I. Description of algorithms and their testing

Determining sunspot area through visible range observations. I. Description of algorithms and their testing

What Are the Causes of Super Activity of Solar Active Regions?

Flare productivity varies among solar active regions (ARs). This study analyzed 20 ARs of contrasting sunspot areas and flare productivities to understand the super flare productivity of certain ARs. We used the flare index (FI) as an indicator of flare activity. We examined the pattern of morphological evolution of magnetic features. Further, we derived a set of magnetic feature parameters to quantitatively characterize ARs. Our study found that the correlation coefficient is the highest (r = 0.78) between FI and the length of the strong gradient polarity inversion line (SgPIL), while the coefficient is the lowest (r = 0.14) between FI and the total unsigned magnetic flux. For the selected ARs, this study also found that the super flare productive ARs have SgPILs (R value) longer (greater) than 50 Mm (4.5). These results suggest that flare productivity is mainly controlled by the size of the subregion that comprises close interaction of opposite magnetic polarities and is weakly correlated with the size of the whole ARs. Further, even though magnetic flux emergence is important, this study shows that it alone is insufficient to increase flare productivity. New emergence can drive either the interaction of like or opposite magnetic polarities of nonconjugate pairs (i.e., polarities not from the same bipole). In the former case, the magnetic configuration remains simple, and flare productivity would be low. In the latter case, the convergence of opposite magnetic fluxes of nonconjugate pairs results in a magnetic configuration with long SgPIL and an increase in flare productivity.

Sunspot Observations at the Eimmart Observatory: Revision and Supplement

Digital images of sunspot drawings of the archives of Georg Christoph Eimmart stored at the National Library of Russia, St. Petersburg, are analyzed to obtain sunspot-group numbers and sunspot areas as well as heliographic positions. Overall, more than a hundred drawings were processed. The impact of drawing and reproduction uncertainties and the aims of historical observations are considered. The sunspot positions are compared to those reported by contemporary observers of the Maunder minimum. The restored sunspot-group numbers and latitudes are compared to those extracted by Hoyt and Schatten (Solar Phys. 179, 189, 1998) as well as Hayakawa et al. (Solar Phys. 296, 154, 2021b) and Hayakawa et al. (Astrophys. J. 909, 166, 2021d). The persistence of long-lived sunspots over several solar rotations is discussed.

Activity of the Young Solar Analog HD 109833 and Estimates of the Mass Loss Rate from the Atmospheres of Its Two Planets

We present the results of our analysis of the manifestations of activity in the young solar analog HD 109833 and estimate the mass loss rate from the atmospheres of its two planets. HD 109833 probably belongs to the Lower Centaurus Crux (LCC) association with an age of 27 ± 3 Myr, but it is not inconceivable that the star is only spatially associated with the association and may be older, although in any case its age does not exceed 100–200 Myr. Based on data from the TESS archive for HD 109833, we have determined the stellar rotation period P = 5.08 ± 0.30 days and the photometric variability amplitude (about 0.6% of the mean stellar brightness) and estimated the spot areas on its surface, which exceed the maximum sunspot area and are 15 200–17 700 m.s.h. Based on data from the All-Sky Automated Survey archive, we have revealed a stellar activity cycle with a duration 1950 days (5.3 years). Both planets in the HD 109833 system are characterized as sub-Neptunes with radii of 2.9 and 2.6 R⊕ and periods of 9.2 and 13.9 days. The mass loss rates by the planetary atmospheres have been found using an approximate formula corresponding to the energy-limited atmospheric escape model. To estimate the XUV flux, we have applied analytical dependences relating the flux and the parameter logR'HK and information about the distribution of these quantities for G-type stars, suggesting that there are two pronounced peaks with maxima for values -0,5 and -4,5 dex in low-activity and active stars, respectively. In addition, we have used the relation between the X-ray flux from the star and logFXUV . The value found is comparable to the estimate obtained by applying the parameter logR'HK for active stars and exceeds it by a factor of 4. Both exoplanets HD 109833 b and c being considered by us fall into the region on the (M-R) diagram in which the populations of rocky and volatile-rich exoplanets overlap and do not allow their masses to be estimated unambiguously. Our calculations were performed for two cases—rocky exoplanets and volatile-rich exoplanets. The masses of the exoplanets HD 109833 b and c are, respectively, 34.9 and 24 M⊕ for rocky exoplanets and 9.3 and 7.8 M⊕ for volatile-rich exoplanets. We present the results of our calculations of the atmospheric mass loss rates by the planets HD 109833 b and c while varying the parameters related to the estimates of the planetary masses and the UV flux incident on the planets. The parameter M for HD 109833 b and c varies in the ranges from 9.60 ×107 to 1.38 ×1010 g s-1 and from 4.56 ×107 to 5.28 ×109 g s-1, respectively. The high mass loss rates found can be a consequence of a fairly high XUV flux from the solar-type star (an analog of the young active Sun) and a fairly close location of the planets from the host star.

Statistical Study of the Correlation between Solar Energetic Particles and Properties of Active Regions

The flux of energetic particles originating from the Sun fluctuates during the solar cycles. It depends on the number and properties of active regions (ARs) present in a single day and associated solar activities, such as solar flares and coronal mass ejections. Observational records of the Space Weather Prediction Center NOAA enable the creation of time-indexed databases containing information about ARs and particle flux enhancements, most widely known as solar energetic particle (SEP) events. In this work, we utilize the data available for solar cycles 21–24 and the initial phase of cycle 25 to perform a statistical analysis of the correlation between SEPs and properties of ARs inferred from the McIntosh and Hale classifications. We find that the complexity of the magnetic field, longitudinal location, area, and penumbra type of the largest sunspot of ARs are most correlated with the production of SEPs. It is found that most SEPs (≈60%, or 108 out of 181 considered events) were generated from an AR classified with the “k” McIntosh subclass as the second component, and these ARs are more likely to produce SEPs if they fall in a Hale class containing a δ component. The resulting database containing information about SEP events and ARs is publicly available and can be used for the development of machine learning models to predict the occurrence of SEPs.

Hemispheric Sunspot Numbers from the Astronomical Observatory of the University of Valencia (1940 – 1956)

In this work, we present hemispheric sunspot number counts made in the Astronomical Observatory of the University of Valencia for the period 1940 – 1956. We found these data in a secondary source (the bulletins of the Madrid Astronomical Observatory). We digitized the hemispheric sunspot number and group number recorded by the observers. Unfortunately, the sunspot positions or areas were not published in this secondary source. A machine-readable version of the dataset is available as supplementary material. We compare the Valencia hemispheric series with others from other observatories, such as the Madrid Astronomical Observatory, finding similar hemispheric behaviors. We also computed the asymmetry index from the hemispheric data. We found that the northern hemisphere was predominant in our study period (declining phase of Solar Cycle 17, Solar Cycle 18, and rising phase of Solar Cycle 19), and the southern hemisphere was leading. These results agree with those obtained in previous studies. Therefore, the Valencia hemispheric records are one more piece of information to know the behavior of the northern and southern hemispheres during the 20th century.

RETRACTED: Forecasting Solar Cycle 25 Using an Optimized Long Short-term Memory Mode Based on F10.7 and Sunspot Area Data

In this paper, an optimized long short-term memory model is proposed to deal with the smoothed monthly F 10.7 and nonsmoothed monthly sunspot area (SSA) data, aiming to forecast the peak amplitude of both solar activities and the occurring time for Solar Cycle 25 (SC-25), as well as to obtain the maximum amplitude of sunspot number (SSN) and the reaching time according to the relationships between them. The “reforecast” process in the model uses the latest forecast results obtained from the previous forecast as the input for the next forecasting calculation. The forecasting errors between the forecast and observed peak amplitude of F 10.7 for SC-23 and SC-24 are 2.87% and 1.09%, respectively. The results of this evaluation indicator of SSA for SC-21 to SC-24 were 8.85%, 4.49%, 2.88%, and 4.57%, respectively, and the errors for the occurring time were all within 6 months. The forecast peak amplitude of F 10.7 and SSA for SC-25 is 156.3 and 2562.5 respectively, and the maximum values of SSN are calculated as 147.9 and 213 based on F 10.7 and SSA respectively, which implies that SC-25 will be stronger than SC-24, and that SC-25 will reach its peak at the beginning of 2025.

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

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

Predicting Solar cycle 25 using an optimized long short-term memory model based on sunspot area data

In this paper, an optimized long short-term memory (LSTM) model was proposed to deal with the monthly sunspot area (SSA) data, aiming to predict the peak amplitude of SSA and the occurring time for Solar Cycle 25, and obtain the forecasting maximum value of sunspot number (SSN) and the reaching time to maximum. The “re-prediction” process in LSTM + was employed with the latest prediction results obtained from the previous prediction as the input for the next prediction calculation. The accuracy and reliability of LSTM + were performed by the validation of the predicted peak amplitude and occurring time of Solar Cycles 21 to 24. The prediction error between the predicted and the observed peak amplitude for cycles 21 to 24 were 8.85 %, 4.49 %, 2.88 %, and 4.57 %, respectively, and the error for the occurring time for 4 cycles was all within 6 months. The predicted peak amplitude of SSA for Solar Cycle 25 was obtained as 2562.5 with LSTM+, and the maximum value of SSN was calculated as 213 based on the relation between SSA and SSN, which would be stronger than that of Solar Cycle 24. And according to the prediction result, Solar Cycle 25 would reach the peak around January 2025.

The Decay Process of an α-configuration Sunspot

The decay of sunspot plays a key role in magnetic flux transportation in solar active regions (ARs). To better understand the physical mechanism of the entire decay process of a sunspot, an α-configuration sunspot in AR NOAA 12411 was studied. Based on the continuum intensity images and vector magnetic field data with stray light correction from Solar Dynamics Observatory/Helioseismic and Magnetic Imager, the area, vector magnetic field and magnetic flux in the umbra and penumbra are calculated with time, respectively. Our main results are as follows: (1) The decay curves of the sunspot area in its umbra, penumbra, and whole sunspot take the appearance of Gaussian profiles. The area decay rates of the umbra, penumbra and whole sunspot are −1.56 MSH day−1, −12.61 MSH day−1 and −14.04 MSH day−1, respectively; (2) With the decay of the sunspot, the total magnetic field strength and the vertical component of the penumbra increase, and the magnetic field of the penumbra becomes more vertical. Meanwhile, the total magnetic field strength and vertical magnetic field strength for the umbra decrease, and the inclination angle changes slightly with an average value of about 20°; (3) The magnetic flux decay curves of the sunspot in its umbra, penumbra, and whole sunspot exhibit quadratic patterns, their magnetic flux decay rates of the umbra, penumbra and whole sunspot are −9.84 × 1019 Mx day−1, −1.59 × 1020 Mx day−1 and −2.60 × 1020 Mx day−1, respectively. The observation suggests that the penumbra may be transformed into the umbra, resulting in the increase of the average vertical magnetic field strength and the reduction of the inclination angle in the penumbra during the decay of the sunspot.

Rediscovering the observations of solar prominences from 1906 to 1957 recorded at the Madrid Astronomical Observatory

The Madrid Astronomical Observatory implemented a solar observation program from 1876 to 1986. In addition to sunspots, the observers at this observatory recorded other solar features such as prominences. In this work, we have consulted the documentary sources of the Madrid Astronomical Observatory (the information is not digitally available), digitized the records of the observers on the annual number of prominences, and constructed a homogeneous series of the total and hemispheric annual number of prominences with heights of 25″ and more for the period 1906–1957. To evaluate the quality of the data and assess their potential, we have compared the Madrid prominence series with the number of prominences recorded by the Astronomical Observatory of the University of Coimbra and other time series such as the sunspot number index, solar radio flux at 10.7 cm, and sunspot areas. We have also analyzed the hemispheric prominence numbers and the asymmetry index. We obtained the strongest correlation between Madrid and Coimbra prominence series (r = 0.7), whereas the correlations between the Madrid prominence series and the other solar activity time series are similar (r ≈ 0.6). In addition, we found that the correlation coefficient between the Madrid prominence series and the sunspot number is lower than that from the Coimbra prominence series and the sunspot number. We suggest that these differences are a consequence of the way prominences were counted in the Madrid Astronomical Observatory.

Probability Distribution Functions of Sunspot Magnetic Flux

We investigated the probability distributions of sunspot area and magnetic flux by using data from the Royal Greenwich Observatory and USAF/NOAA. We constructed a sample of 2995 regions with maximum-development areas ≥500 MSH (millionths of solar hemisphere), covering 146.7 yr (1874–2020). The data were fitted by a power-law distribution and four two-parameter distributions (tapered-power-law, gamma, lognormal, and Weibull distributions). The power-law model was unfavorable compared to the four models in terms of AIC, and was not acceptable according to the classical Kolmogorov–Smirnov test. The lognormal and Weibull distributions were excluded because their behavior extended to smaller regions (S ≪ 500 MSH) do not connect to previously published results. Therefore, our choices were tapered-power-law and gamma distributions. The power-law portion of the tapered-power-law and gamma distributions was found to have a power exponent of 1.35–1.9. Due to the exponential falloff of these distributions, the expected frequencies of large sunspots are low. The largest sunspot group observed had an area of 6132 MSH, and the frequency of sunspots larger than 104 MSH was estimated to be every 3–8 × 104 yr. We also estimated the distributions of the Sun-as-a-star total sunspot areas. The largest total area covered by sunspots on record was 1.67% of the visible disk, and can be up to 2.7% by artificially increasing the lifetimes of large sunspots in an area evolution model. These values are still smaller than those found on active Sun-like stars.

Inferring Quadrupolar Dynamo Mode from Sunspot Statistics

Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation analysis and wavelet analysis of so-defined PFs reveal quadrupolar oscillations with a period of about 16 yr and amplitude of about 0.17 relative to the amplitude of the dominant 22-yr dipolar mode.

Scrutinising the relationship between plage areas and sunspot areas and numbers

Context. Studies and reconstructions of past solar activity require data on all magnetic regions on the surface of the Sun (i.e. on dark sunspots as well as bright faculae–plage and network). Such data are also important for understanding the magnetic activity and variability of the Sun and Sun-like stars. The longest available direct faculae–plage datasets are white-light facular and Ca II K observations going back to 1874 and 1892, respectively. Prior to that time the only direct data available are for sunspots. Aims. We reassess the relationship between plage areas and sunspot records (areas and numbers) since 1892, to allow reconstructions of facular–plage areas which can be employed for studies going further back in time to the period when solely sunspot observations are available. Methods. We use the plage areas derived from 38 consistently processed Ca II K archives as well as the plage area composite based on these archives. The considered archives include both the well-known observatories (e.g. Coimbra, Kodaikanal, Meudon, Mt Wilson), and the less explored observatories (e.g. Kharkiv, Mees, and Upice). These data allow us to study the relationship between plage area and sunspot records (areas and number) over a period of 12 solar cycles and for different bandpasses. Results. We find the relationship between plage and sunspot areas to be well represented by a power-law function; the relationship between the plage areas and the sunspot number is also best fit with a power-law function. We further find that the relationships depend on the bandwidth and the solar cycle strength. The reconstructions with a power-law relationship are in good agreement with the original plage area series, whereas employment of a cycle-strength-dependent relationship improves the reconstructions only marginally. We also estimate the error in the plage areas reconstructed from the sunspot areas or numbers. Performing the same analysis on other previously published plage area series, usually derived from a single archive with diverse processing techniques, returns different results when using different time series. This highlights the importance of applying a consistent processing to the various archives and demonstrates the uncertainties introduced by using previously published series for studies of past solar activity, including irradiance reconstructions. Conclusions. Our results have implications for past solar activity and irradiance reconstructions and for stellar activity studies, which sometimes assume a linear dependence between plage and sunspot areas.