Sunspot Umbra Research Articles

Reconstruction of Centennial Series of Solar Activity

The results of the digitalization of the centennial series of solar activity are considered. The data contain information on sunspots since 1918, sunspot umbra since 1917, plages since 1907, and spectral corona since 1939. In particular the digitalization of prominences from the observations in the Ca II K line in 1910–1954 and solar filaments from the observations in the H-alpha line in 1912–2002 acquired at the Kodaikanal Observatory are described. The methods of constructing composite maps of solar activity and presenting the resulting data series on the Internet are described. The long-term variations in solar activity are analyzed.

Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector

Context. The Wilson depression is the difference in geometric height of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Aims. We aim to develop a robust method for deriving the Wilson depression that only requires the information about the magnetic field that is accessible from spectropolarimetry, and that does not rely on assumptions on the geometry of sunspots or on their magnetic field. Methods. Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We have focused on large spatial scales only in order to reduce the number of free parameters. Results. We tested the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we applied the method to Hinode observations of a sunspot. The derived Wilson depression (∼600 km) is consistent with results typically obtained from the Wilson effect. We also find that the Wilson depression obtained from using horizontal force balance gives 110–180 km smaller Wilson depressions than both, what we find and what we deduce directly from the simulations. This suggests that the magnetic pressure and the magnetic curvature force contribute to the Wilson depression by a similar amount.

PROBLEM OF SUPER-STRONG MAGNETIC FIELDS ON THE SUN: BRIEF CHRONOLOGY AND NEW OBSERVATIONAL DATA

In this study we present the old and new observational data concerning the problem of extreme magnetic fields (  5 kG) in the Sun's atmosphere. We emphasize that the upper limit of the intensity of the magnetic field in the solar atmosphere is unknown to date. Severny (1957) heuristically suggested that the magnetic fields in the sunspots could reach 50 kG. As for the observational data, at least three arguments in favor of the magnetic fields of the order of 104 G can be specified: (1) the dependence of the measured magnetic field on the factor geff2 of magnetosensitive lines (Gopasyuk et al., 1973; Lozitsky, 1980), (2) local extremums in splitting of bisectors in the profiles I ± V for lines with different Lande factors (Lozitsky, 1980; 2015) and (3) the reliable splitting of emission peaks in Fe I lines with very low Lande factors, about 0.01, in the spectra of powerful solar flares (Lozitsky, 1993; 1998). Theoretically, superstrong fields should have gigantic magnetic pressure and can exist only with a specific topology of field lines, apparently of a force-free type (Soloviev and Lozitsky, 1986). To further develop this problem, we are analyzing new observational data obtained with the NIRIS spectropolarimeter of the largest GST solar telescope of the Big Bear Solar Observatory (BBSO). Our observations relate to the active region NOAA 12673, which was the most flare-productive in the 24th cycle. Stokes-metric measurements are made in the FeI 15648.5 Е line with a signal-to-noise ratio of about 10-4. In this active region, superstrong magnetic field of 5.57 kG was discovered recently by Wang et al. (2018). An additional study of about 70 different places in this active region suggested that there were two types of places that can be conventionally called typical and peculiar. In typical areas, the magnitude of the magnetic field in general is the greater, the less the intensity in the spectral continuum, and the maximum field here does not exceed 4 kG. All peculiar places correspond to positions with the highest intensity in the spectral continuum, and the magnetic field strength is here in the range of 3.0-5.7 kG. Notice, such strong magnetic fields were firstly discovered outside the sunspot umbra. The orientation of the magnetic field vector in peculiar places is close to the transversal, which is also atypical for typical regions and can reflect strong twisting of field lines.

Fine wave dynamics in umbral flash sources

Context. Umbral flashes (UFs) are most common phenomenon of wave processes in sunspots. Studying the relationship between wave time dynamics and the origin of UFs requires further investigation of their fine spatial and height structure. Aims. We investigated the association between a short time increase in the variations of 3-min extreme ultraviolet (EUV) emission at footpoints of coronal magnetic loops and the UF emergence in sunspot umbra. The spatial structure of magnetic field lines and their inclination determine the cut-off frequency and visibility of sunspot waves. Methods. We applied the pixelized wavelet filtering (PWF) technique to analyse a cube of the images obtained by SDO/AIA at 1600 Å, 304 Å, and 171 Å to study the spatio-temporal oscillation power distribution in individual magnetic loops. Time–distance plots were used to obtain the wave front propagation velocity. Results. For the first time, we obtained the 2D images of the fine wave processes in magnetic structures of different spatial scales related to the UFs in sunspot. We revealed two types of the UFs as background and local. The background UFs associated with random increasing of separate parts of wave fronts. These UFs are seen as weak and diffuse details that ride the wave fronts without stable shapes and localization in space. The local UFs sources mainly localize near to the footpoint of magnetic loops, anchored in an umbra, along which the propagation of 3-min waves was observed. The time dynamics of flash evolution shows an increase in 3-min oscillations before the UFs peak value within one low-frequency wave train. It is shown that the maxima of 3-min oscillation trains coincide with the peak intensity of UFs. During the UFs evolution, a fine wave spatial and temporal dynamics in UFs local sources was observed. Conclusions. The sunspot 3-min wave dynamics showed a relation between the localization of oscillations power peak at the coronal magnetic loop footpoints and the UFs origin. The spatial structure of the UFs sources, their power, and lifetime are determined by the cut-off frequency of the waves for the detected waveguides. We concluded that UFs are a global process of short-time increase of the wave activity.

Распределение солнечных вспышек малой мощности по времени подъема яркости к максимуму

Using data from the international flare patrol for 1972–2010, we have formed an electronic database for more than 123 thousand solar flares. We determined the mean brightness rise time (flash-phase) for flare area classes and importance. We show that the mean flash phase increased with increasing area class. For brightness classes this trend is less pronounced. We have found that flares with explosive phase and flares with one brilliant point have the shortest flash phases; two-ribbon flares and flares with several intensity maxima, the longest ones. We have separated 572 cases when the brightness rise time was more than 60 min; 80 % of such ultra-long flares have a shorter brightness decay time (main phase). We have established that low-power flares in terms of developmental features do not differ from large flares. Low-power solar flares, as well as large flares, can be followed by filament activation or disappearance, and can have an explosive phase and several intensity maxima. Two-ribbon flares, white-light flares, and flares covering sunspot umbra can also have low power.

Distribution of low-power solar flares by brightness rise time

For brightness classes this trend is less pronounced. We have found that flares with explosive phase and flares with one brilliant point have the shortest flash phases; two-ribbon flares and flares with several intensity maxima, the longest ones. We have separated 572 cases when the brightness rise time was more than 60 min; 80 % of such ultra-long flares have a shorter brightness decay time (main phase). We have established that low-power flares in terms of developmental features do not differ from large flares. Low-power solar flares, as well as large flares, can be followed by filament activation or disappearance, and can have an explosive phase and several intensity maxima. Two-ribbon flares, white-light flares, and flares covering sunspot umbra can also have low power.

Automatic Detection of Sunspots on Full-disk Solar Images Using the Simulated Annealing Genetic Method

Sunspots with strong magnetic fields are the most important manifestations of solar activity, appearing as dark features in the photosphere observed in continuum images. We proposed an artificial intelligence technology called the simulated annealing genetic (SAG) method, which combined the genetic algorithm and simulated annealing algorithm to self-adaptively derive dual thresholds for detecting the umbra and penumbra of sunspots simultaneously. Full-disk continuum intensity images obtained from Solar Dynamics Observatory/Helioseismic Magnetic Imager (HMI) at a cadence of four hours from 2010 May to 2016 December were used. The detection results showed that the dual thresholds derived by the SAG method have outstanding performance in segmenting the umbra and penumbra from the photosphere with a satisfactory robustness efficiently. The boundaries of the umbra and penumbra were finely delineated, even for sunspots at the extreme solar limb. The total sunspot areas, umbral areas, and penumbral areas match very well with the data reported from HMI Debrecen Data (HMIDD), with the correlation coefficients reaching 0.99, 0.99, and 0.95, respectively. The mean ratios of umbra to sunspot areas per year ranged from 0.159 to 0.233. The ratios decreased with an increase in solar activity, which implies that the ratio was related to the solar activity level.

Absolute velocity measurements in sunspot umbrae

Context. In sunspot umbrae, convection is largely suppressed by the strong magnetic field. Previous measurements reported on negligible convective flows in umbral cores. Based on this, numerous studies have taken the umbra as zero reference to calculate Doppler velocities of the ambient active region.Aims. We aim to clarify the amount of convective motion in the darkest part of umbrae, by directly measuring Doppler velocities with an unprecedented accuracy and precision.Methods. We performed spectroscopic observations of sunspot umbrae with the Laser Absolute Reference Spectrograph (LARS) at the German Vacuum Tower Telescope. A laser frequency comb enabled the calibration of the high-resolution spectrograph and absolute wavelength positions for 13 observation sequences. A thorough spectral calibration, including the measurement of the reference wavelength, yielded Doppler shifts of the spectral line Ti I5713.9 Å with an uncertainty of around 5 m s−1. A bisector analysis gave the depth-dependent line asymmetry.Results. The measured Doppler shifts are a composition of umbral convection and magneto-acoustic waves. For the analysis of convective shifts, we temporally averaged each sequence to reduce the superimposed wave signal. Compared to convective blueshifts of up to −350 m s−1in the quiet Sun, sunspot umbrae yield strongly reduced convective blueshifts around −30 m s−1. We find that the velocity in a sunspot umbra correlates significantly with the magnetic field strength, but also with the umbral temperature defining the depth of the Ti I5713.9 Å line. The vertical upward motion decreases with increasing field strength. Extrapolating the linear approximation to zero magnetic field reproduces the measured quiet Sun blueshift. In the same manner, we find that the convective blueshift decreases as a function of increasing line depth.Conclusions. Simply taking the sunspot umbra as a zero velocity reference for the calculation of photospheric Dopplergrams can imply a systematic velocity error reaching 100 m s−1, or more. Setting up a relationship between vertical velocities and magnetic field strength provides a remedy for solar spectropolarimetry. We propose a novel approach of substantially increasing the accuracy of the Doppler velocities of a sunspot region by including the magnetic field information to define the umbral reference velocity.

Height variation of the cutoff frequency in a sunspot umbra

Context. In the solar atmosphere, the acoustic cutoff frequency is a local quantity that depends on atmospheric height. It separates low-frequency evanescent waves from high-frequency propagating waves. Aims. We measure the cutoff frequency of slow magnetoacoustic waves at various heights of a sunspot umbra and compare the results with the estimations from several analytical formulae. Methods. We analyzed the oscillations in the umbra of a sunspot belonging to active region NOAA 12662 observed in the 10 830 Å spectral region with the GREGOR Infrared Spectrograph and in the Fe I 5435 Å line with the GREGOR Fabry-Pérot Interferometer. Both instruments are attached to the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. We computed the phase and amplification spectra between the velocity measured from various pairs of lines that sample various heights of the solar atmosphere. The cutoff frequency and its height variation were estimated from the inspection of the spectra. Results. At the deep umbral photosphere the cutoff frequency is around 5 mHz and it increases to 6 mHz at higher photospheric layers. At the chromosphere the cutoff is ~3.1 mHz. A comparison of the observationally determined cutoff with the theoretically predicted values reveals an agreement in the general trend and a reasonable match at the chromosphere, but also significant quantitative differences at the photosphere. Conclusions. Our analyses show strong evidence of the variation of the cutoff frequency with height in a sunspot umbra, which is not fully accounted for by current analytical estimations. This result has implications for our understanding of wave propagation, the seismology of active regions, and the evaluation of heating mechanisms based on compressible waves.

Revised historical solar irradiance forcing

Context. There is no consensus on the amplitude of historical solar forcing. The estimated magnitude of the total solar irradiance (TSI) difference between the Maunder minimum and the present time ranges from 0.1 to 6 W m−2 making the simulation of the past and future climate uncertain. One reason for this disagreement is the applied evolution of the quiet Sun brightness in solar irradiance reconstruction models. This work addresses the role of the quiet Sun model choice and updated solar magnetic activity proxies on the solar forcing reconstruction. Aims. We aim to establish a plausible range for the solar irradiance variability on decadal to millennial timescales. Methods. The spectral solar irradiance (SSI) is calculated as a weighted sum of the contributions from sunspot umbra, sunspot penumbra, faculae, and quiet Sun, which are pre-calculated with the NLTE Spectral SYnthesis code (NESSY). We introduce activity belts of the contributions from sunspots and faculae and a new structure model for the quietest state of the Sun. We assume that the brightness of the quiet Sun varies in time proportionally to the secular (22-yr smoothed) variation of the solar modulation potential. Results. A new reconstruction of the TSI and SSI covering the period 6000 BCE - 2015 CE is presented. The model simulates solar irradiance variability during the satellite era well. The TSI change between the Maunder and recent minima ranges between 3.7 and 4.5 W m−2 depending on the applied solar modulation potential. The implementation of a new quietest Sun model reduces, by approximately a factor of two, the relative solar forcing compared to the largest previous estimation, while the application of an updated solar modulation potential increases the forcing difference between the Maunder minimum and the present by 25–40%.

Waves of Magnetic-field Variations Observed in a Flare-excited Sunquake Event

Abstract We report on the detection of waves of magnetic-field variations that were associated with flare-excited sunquake waves. An X-9.3 flare that occurred on 2017 September 6 excited strong sunquakes, and the sunquake waves were observed sweeping across the flare’s host active region. This rare event gives us an unprecedented opportunity to study responses of magnetic field to passing sunquake waves. A wave of magnetic-field variations was observed in each of the two sunspots that the sunquake waves swept through, and the time–distance relations for the waves observed in magnetic field and Doppler velocity are similar. The phase relations measured between, as well as the oscillatory power distributions calculated from, the Doppler velocity variations and magnetic-field variations associated with the sunquake waves are compared with those obtained from the background waves in the same areas of the sunspot umbra and penumbra separately. The phase relations seem to favor the theory that the waves of magnetic variations are owing to opacity changes associated with the passing sunquake waves. The comparisons of phases and power distributions indicate that the background magnetic variations observed in sunspots are a combination of various wave modes, and fast magnetoacoustic waves only account for a fraction of those magnetic variations.

The Magnetic Response of the Solar Atmosphere to Umbral Flashes

Abstract Chromospheric observations of sunspot umbrae offer an exceptional view of magnetoacoustic shock phenomena and the impact they have on the surrounding magnetically dominated plasma. We employ simultaneous slit-based spectro-polarimetry and spectral imaging observations of the chromospheric He i 10830 Å and Ca ii 8542 Å lines to examine fluctuations in the umbral magnetic field caused by the steepening of magnetoacoustic waves into umbral flashes. Following the application of modern inversion routines, we find evidence to support the scenario that umbral shock events cause expansion of the embedded magnetic field lines due to the increased adiabatic pressure. The large number statistics employed allow us to calculate the adiabatic index, γ = 1.12 ± 0.01, for chromospheric umbral locations. Examination of the vector magnetic field fluctuations perpendicular to the solar normal revealed changes up to ∼200 G at the locations of umbral flashes. Such transversal magnetic field fluctuations have not been described before. Through comparisons with nonlinear force-free field extrapolations, we find that the perturbations of the transverse field components are oriented in the same direction as the quiescent field geometries. This implies that magnetic field enhancements produced by umbral flashes are directed along the motion path of the developing shock, hence producing relatively small changes, up to a maximum of ∼8°, in the inclination and/or azimuthal directions of the magnetic field. Importantly, this work highlights that umbral flashes are able to modify the full vector magnetic field, with the detection of the weaker transverse magnetic field components made possible by high-resolution data combined with modern inversion routines.

Magnetic Transients During the Flares of May 9, 2012, in NOAA 11476 and July 4, 2012, in NOAA 11515

Variations in the longitudinal magnetic field in NOAA 11476 and NOAA 11515 during M-class solar flares are studied. Magnetic field observations were made by the Solar Dynamics Observatory using the Helioseismic and Magnetic Imager (SDO/HMI) with temporal and spatial resolutions of 45 s and 0".5 pixel-1, respectively. During the maximum phase of the M5.7/2B flare of May 9, 2012, in NOAA 11476, and the M5.3/2B flare of July 4, 2012, in NOAA 11515, there were abrupt changes in the magnetic field of the active regions. Transient structures with the opposite sign appeared in high magnetic fields with negative polarity. The transients were located in the umbra of sunspots and lasted several minutes. We study these features of the magnetic field in detail.

Testing and Improving a Set of Morphological Predictors of Flaring Activity

Efficient prediction of solar flares relies on parameters that quantify the eruptive capability of solar active regions. Several such quantitative predictors have been proposed in the literature, inferred mostly from photospheric magnetograms and/or white-light observations. Two of them are the Ising energy and the sum of the total horizontal magnetic field gradient. The former has been developed from line-of-sight magnetograms, while the latter uses sunspot detections and characteristics, based on continuum images. Aiming to include these parameters in an automated prediction scheme, we test their applicability on regular photospheric magnetic field observations provided by the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). We test their efficiency as predictors of flaring activity on a representative sample of active regions and investigate possible modifications of these quantities. The Ising energy appears to be an efficient predictor, and the efficiency is even improved if it is modified to describe interacting magnetic partitions or sunspot umbrae. The sum of the horizontal magnetic field gradient appears to be slightly more promising than the three variations of the Ising energy we implement in this article. The new predictors are also compared with two very promising predictors: the effective connected magnetic field strength and the total unsigned non-neutralized current. Our analysis shows that the efficiency of morphological predictors depends on projection effects in a nontrivial way. All four new predictors are found useful for inclusion in an automated flare forecasting facility, such as the Flare Likelihood and Region Eruption Forecasting (FLARECAST), but their utility, among others, will ultimately be determined by the validation effort underway in the framework of the FLARECAST project.

High-resolution imaging and near-infrared spectroscopy of penumbral decay

Aims. Combining high-resolution spectropolarimetric and imaging data is key to understanding the decay process of sunspots as it allows us to scrutinize the velocity and magnetic fields of sunspots and their surroundings. Methods. Active region NOAA 12597 was observed on 2016 September 24 with the 1.5-meter GREGOR solar telescope using high-spatial-resolution imaging as well as imaging spectroscopy and near-infrared (NIR) spectropolarimetry. Horizontal proper motions were estimated with local correlation tracking, whereas line-of-sight (LOS) velocities were computed with spectral line fitting methods. The magnetic field properties were inferred with the “Stokes Inversions based on Response functions” (SIR) code for the Si I and Ca I NIR lines. Results. At the time of the GREGOR observations, the leading sunspot had two light bridges indicating the onset of its decay. One of the light bridges disappeared, and an elongated, dark umbral core at its edge appeared in a decaying penumbral sector facing the newly emerging flux. The flow and magnetic field properties of this penumbral sector exhibited weak Evershed flow, moat flow, and horizontal magnetic field. The penumbral gap adjacent to the elongated umbral core and the penumbra in that penumbral sector displayed LOS velocities similar to granulation. The separating polarities of a new flux system interacted with the leading and central part of the already established active region. As a consequence, the leading spot rotated 55° clockwise over 12 h. Conclusions. In the high-resolution observations of a decaying sunspot, the penumbral filaments facing the flux emergence site contained a darkened area resembling an umbral core filled with umbral dots. This umbral core had velocity and magnetic field properties similar to the sunspot umbra. This implies that the horizontal magnetic fields in the decaying penumbra became vertical as observed in flare-induced rapid penumbral decay, but on a very different time-scale.

High-frequency Oscillations in the Atmosphere above a Sunspot Umbra

Abstract We use high spatial and temporal resolution observations, simultaneously obtained with the New Vacuum Solar Telescope and Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory, to investigate the high-frequency oscillations above a sunspot umbra. A novel time–frequency analysis method, namely, the synchrosqueezing transform (SST), is employed to represent their power spectra and to reconstruct the high-frequency signals at different solar atmospheric layers. A validation study with synthetic signals demonstrates that SST is capable of resolving weak signals even when their strength is comparable to the high-frequency noise. The power spectra, obtained from both SST and the Fourier transform, of the entire umbral region indicate that there are significant enhancements between 10 and 14 mHz (labeled as 12 mHz) at different atmospheric layers. Analyzing the spectrum of a photospheric region far away from the umbra demonstrates that this 12 mHz component exists only inside the umbra. The animation based on the reconstructed 12 mHz component in AIA 171 Å illustrates that an intermittently propagating wave first emerges near the footpoints of coronal fan structures, and then propagates outward along the structures. A time–distance diagram, coupled with a subsonic wave speed (∼49 km s−1), highlights the fact that these coronal perturbations are best described as upwardly propagating magnetoacoustic slow waves. Thus, we first reveal the high-frequency oscillations with a period around one minute in imaging observations at different height above an umbra, and these oscillations seem to be related to the umbral perturbations in the photosphere.

Alfvén wave dissipation in the solar chromosphere

Magneto-hydrodynamic (MHD) Alfv\'en waves have been a focus of laboratory plasma physics and astrophysics for over half a century. Their unique nature makes them ideal energy transporters, and while the solar atmosphere provides preferential conditions for their existence, direct detection has proved difficult as a result of their evolving and dynamic observational signatures. The viability of Alfv\'en waves as a heating mechanism relies upon the efficient dissipation and thermalization of the wave energy, with direct evidence remaining elusive until now. Here we provide the first observational evidence of Alfv\'en waves heating chromospheric plasma in a sunspot umbra through the formation of shock fronts. The magnetic field configuration of the shock environment, alongside the tangential velocity signatures, distinguish them from conventional umbral flashes. Observed local temperature enhancements of 5% are consistent with the dissipation of mode-converted Alfv\'en waves driven by upwardly propagating magneto-acoustic oscillations, providing an unprecedented insight into the behaviour of Alfv\'en waves in the solar atmosphere and beyond.

The magnetic nature of umbra–penumbra boundary in sunspots

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aim. Here, we aim at studying the magnetic nature of umbra–penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Methods. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra–penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. Results. We statistically prove that the umbra–penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849–1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. Conclusions. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra–penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.

Long-term oscillations of sunspots and a special class of artifacts in SOHO/MDI and SDO/HMI data

A specific type of artifacts, that originate due to displacement of the image of a moving object along the digital (pixel) matrix of receiver are analyzed in detail. The criteria of appearance and the influence of these artifacts on the study of long-term oscillations of sunspots are deduced. The obtained criteria suggest us methods for reduction or even elimination of these artifacts. It is shown that the use of integral parameters can be very effective against the artifact distortions. The simultaneous observations of sunspot magnetic field and ultraviolet intensity of the umbra have given the same periods for the long-term oscillations. In this way the real physical nature of the oscillatory process, which is independent of the artifacts have been confirmed again. A number of examples considered here confirm the dependence between the periods of main mode of the sunspot magnetic field long-term oscillations and its strength. The dependence was derived earlier from both the observations and the theoretical model of the shallow sunspot. The anti-phase behavior of time variations of sunspot umbra area and magnetic field of the sunspot demonstrates that the umbra of sunspot moves in long-term oscillations as a whole: all its points oscillate with the same phase.

Reconstruction of solar activity according to the data of centenary observations

AbstractDigitization of solar activity data over a period of more than 100 years has been performed. The database presents the characteristics of sunspots, sunspot umbras, filaments, plages in CaIIK line and prominences. The series of vector boundaries and photometric properties of the selected objects are created.The characteristics of individual types of solar activity were determined. An interactive atlas of solar activity has been created, on which daily maps of solar activity, characteristics of individual elements and summary indices of solar activity are presented. The indices of solar activity were reconstructed and the analysis was carried out.