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Changes in the umbra brightness and in the magnetic field over time should occur on long-period sunspot oscillations in accordance with Birman’s idea of inhibition of circulation (overturning) convection by a strong vertical magnetic field in antiphase mode.When the sunspot as a whole shifts upward, its power flux tube expands with a fixed magnetic flux, the magnetic field decreases, and the umbra brightness should increase. Vice versa, when the magnetic flux tube of the sunspot is lowered, it is compressed, the field grows, and the umbra brightness should decrease. Until now, this oscillatory process, which is described by the theoretical model of a shallow sunspot, has remained unexplored. This paper attempts to prove the Birman effect (Biermann, 1941) on the example of long-period oscillations of the sunspot 2010/12/07-13 (NOAA 11 133), for which there are available data from both the Solar and Heliospheric Observatory (SOHO) and Solar Dynamics Observatory (SDO).

A distinctive feature of chromospheric magnetic fields in the facular regions on the Sun is their very fine spatial structure. In accordance with the observations performed in Ca II K and H line (the level of the lower chromosphere, about 0.5–1 Mm over the photosphere), numerous “slender fibrils mapping the magnetic field” were recorded. It is noted that “…the loops are organized in canopy-like arches” (Jafarzadeh et al., 2017). In this paper we perform some modification of the facular model presented by Solov’ev and Kirichek (2019) as a steady magnetic “fountain” with many thin trickles of plasma flows. The radial-azimuthal temperature profiles of the facula are calculated. It is shown that the difference in the vertical and horizontal scales of the system does not improve the correspondence between the model parameters of the faculae and their observed characteristics.

Long-term variations of the magnetic field of solitary solar pores with periods in the range of 4–12 h are detected with the Helioseismic and Magnetic Imager (HMI) of the Solar Dynamics Observatory (SDO). These long-term oscillations of the pores obviously reflect the movements of these structures as whole magnetic formations around their equilibrium position. In this article, long-period oscillations of the solar pore are studied based on the SDO data for the first time. The results are interpreted with the solution obtained earlier for eigen oscillations of the system with time-varying stiffness.

Long-period oscillations in the brightness of the Sun as a star have been analyzed on the basis of measurements of the solar light reflected by planets when they come into the field of view of the Large Angle and Spectrometric Coronagraph (LASCO C3) onboard the Solar and Heliospheric Observatory (SOHO). We took sequences of FITS intensitygrams from the archive of the SOHO/LASCO C3 space observatory for the observational data; they were 1024 × 1024 pixels in size, and they were acquired with the 12-min interval. In 5-day continuous time series of the brightness of Mars and Jupiter, coinciding modes of 8–10 and 36–38 h were found. This coincidence apparently indicates their solar origin. In addition, for Mars, we obtained 25-day series of time variations of the reflected solar radiation, in which a mode with even a lower frequency of 8–10 days was detected.

The properties of the 12-h artifact in the data of the SDO/HMI instrument (Helioseismic and Magnetic Imager) caused by the nonzero radial velocity of the station relative to the Sun are investigated. The study has been carried out with respect to long-period oscillations of the magnetic field of sunspots for different station positions in the Earth’s orbit by the alternative spectral method of singular decomposition of the signal CaterPillarSSA. Features of artifact filtering, both in special positions of the station (at the points of aphelion and perihelion) and at arbitrarily selected orbital points, are considered. It is shown that the 12-h artifact mode can be completely filtered from the time series of the observed variable, not only at these two orbital points (because of the symmetry of the station’s radial velocity with respect to the zero mean here) but also at any others. It is shown that only a 12-h mode is physically justified, while the 24-h harmonic appears only as an artifact in the Fourier decomposition of the amplitude-modulated signal. It is emphasized that the values of the magnetic field measured with SDO/HMI are sensitive only to the station’s radial velocity absolute values with respect to the Sun and do not depend on its direction. It has been noted that the periods of sunspot oscillation as a whole obtained from SDO/HMI data after orbital artifact filtration fit well into the dependence diagram of the period of sunspot oscillations on the value of its magnetic field strength constructed earlier by SOHO/MDIdata.

The fundamental small-scale structures such as granules, faculae, micropores that are observed in the solar photosphere under high resolution are discussed. As a separate constituent of the fine structure, a continuous net of dark intergranular lanes is considered. The results due to image processing of micropores and facular knots obtained on modern adaptive optics telescopes are presented. For intergranular lanes and micropores, a steady-state magnetic diffusion model is proposed, in which the horizontal-vertical plasma flows converging to a intergranular lane (and to the body of a micropore) compensate for the dissipative spreading of the magnetic flux at a given scale. A theoretical estimate of the characteristic scales of these structures in the photosphere is obtained as 20–30 km for the thickness of dark intergranular lanes (and the diameter of the thinnest magnetic tube in the solar photosphere), 200–400 km for the diameter of micropores. A model of a facular knot with the darkening core on the axis, which physically represents a micropore, stabilizing the entire magnetic configuration over a time interval of up to 1 day, is briefly described.

For the first time, the ultra-low oscillation mode of the sunspot magnetic field strength has been detected with a high degree of confidence by ground-based observations of sunspots with the Global Oscillation Network Group (GONG) network of telescopes. Synchronous series of magnetograms derived from the GONG and Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) have been processed. They were obtained on September 27–30, 2010, for the active region NOAA 11109 with a total duration of 80 h. The periods of magnetic field oscillations found by space data coincide with the periods defined with GONG. This confirms the physical reality of the oscillatory process. The power spectrum contains harmonics with periods of 26 h, 8–10 h, and 3–4 h.

The data of ground-based telescopes of the Global Oscillation Network Group (GONG) obtained in the $\mathrm{H}\upalpha$ line provide an opportunity to study the long-period oscillations of chromospheric filaments (quiescent prominences). For the first time, on the basis of time series of 5 days duration that we combined from the observations of three observatories of the GONG network, a new ultra-low mode with a period of between 20 and 30 hours was reliably detected in oscillations of a long-lived dark filament on the solar disk.

The global long term periodic oscillations of the Sun are investigated on the base of three independent sets of data: It is found that in the low-frequency spectrum of global solar oscillations, there are modes with periods of 8–10, 36–38 hours and the main stable prominent mode with a period of ∼9-days.

The geometric parameters and relationships of the horizontal and vertical velocities in a giant convective cylindrical cell were analyzed based on a continuity equation with the given vertical distribution of unperturbed gas density in the convective zone of the Sun. It has been found that the lower edge of such a convective cell must be positioned at a depth of 20 Mm in the secondary helium ionization zone. In addition, under the assumption that the plasma conductivity in the convective zone is caused by small-scale turbulence, a new stationary solution was obtained for the problem of magnetic field diffusion in the pattern of slow conductive plasma flows in scales of a convective cell.

Three independent sets of data: i). series of filtergrams obtained in line CaII K (393.416 nm) with the ground-based telescope Precision Solar Photometric Telescope (PSPT) of Mauna Loa Solar Observatory; ii). series of filtergrams of Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) in {\lambda}160 nm and iii). series of magnetograms of Helioseismic and Magnetic Imager (HMI) of SDO have been processed to reveal reliably the existence of spatial cellular structures on the solar photosphere at scale about of 300 arcsec. This scale is intermediate between supergranules and giant cells (~30,000 and ~300,000 kilometers across, respectively). To identify the different spatial structures the tens of two-dimensional power spectra (2DFFT) have been averaged. For one-dimensional photometric cross sections of frames, the Fourier power spectra (FFT) and wavelet transforms (Morlet 5-th order) have been calculated., Comment: 10 pages, 6 figures. Accepted in Astrophys Space Sci

We processed magnetograms that were obtained with the Michaelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). The results confirm the basic properties of long-period oscillations of sunspots that have previously been established and also reveal new properties. We show that the limiting (lowest) eigenmode of low-frequency oscillations of a sunspot as a whole is the mode with a period of 10 – 12 up to 32 – 35 hours (depending on the sunspot’s magnetic-field strength). This mode is observed consistently throughout an observation period of 5 – 7 days, but its amplitude is subject to quasi-cyclic changes, which are separated by about 1.5 – 2 days. As a result, the lower mode with a period of about 35 – 48 hours appears in the power spectrum of sunspot oscillations. But this lowest mode is apparently not an eigenmode of a sunspot because its period does not depend on the magnetic field of the sunspot. Perhaps the mode reflects the quasi-periodic sunspot perturbations caused by supergranulation cells that surround it. We also analyzed SOHO/MDI artifacts, which may affect the low-frequency power spectra of sunspots.

Long-period oscillations of the magnetic field and the line-of-sight velocity have been detected in sunspots based on the synchronous 90-h time series of magnetograms and dopplergrams obtained with the MDI(SOHO) device. The sunspot eigenmode (12–30 h), the periods of which nonlinearly depend on the magnetic field strength, predominates in the magnetic field oscillation spectrum. The mode, which is probably induced by motions of supergranulation cells (33 h), predominates in the sunspot line-of-sight velocity oscillation spectrum. A strong mode (33 h), which indicates that long-period quasi-oscillations of supergranulation exist, was also detected in the velocity power spectrum for a quiet photosphere, together with the known 5-min mode.

An analysis of oscillatory processes with periods not shorter than several tens of minutes in three isolated sunspots, which were observed during identical periods in the optical and radio bands, is illustrated. SDO/HMI magnetograms at an interval of 45 s and radio maps at a wavelength of 1.76 cm, obtained using a Nobeyama radioheliograph (NoRH), have been used. The time profiles, which were constructed based on the NoRH and SDO/HMI data, indicate that the oscillations of the radioemission correlate with those of the sunspot magnetic field. The wavelet spectra and cross-wavelet transform reveal common oscillation periods of 30–40, 70–100, and 150–200 min. The identical oscillation periods, found using fundamentally different methods from ground-based and space observations, confirm the solar nature of these oscillations, which can be interpreted as oscillations of a sunspot as a whole.

It is shown that long-period (T = 10–20 h) oscillations of the magnetic field in sunspots, combined in bipolar groups, are excited synchronously in the main and tail spots of a group. At the same time, there is no correlation between long-period oscillations of the field of sunspots which are in different active regions, i.e., spaced sunspots oscillate independently. This fact eliminates the question about the apparatus nature of the oscillations of interest (if there is an artifact, oscillations of all sunspots on the visible solar hemisphere would be synchronous!). High-resolution (0.5 angular seconds per pixel) MDI(SOHO) data show a high correlation between long-period oscillations of the magnetic field at isolated points of the sunspot shadow. This points to the fact that the sunspot shadow participates in long-period oscillations as a quite integral physical formation.

As a result of processing long (up to 144 h) series of sunspot magnetograms obtained on the SOHO (Solar and Heliospheric Observatory) spacecraft with the MDI (Michelson Doppler Imager) instrument it is shown that the mode with a period of 800–1300 min is a limiting low-frequency oscillation mode of the magnetic field of a sunspot as a whole. Its period is essentially and nonlinearly depends on the sunspot magnetic field strength. In addition to this mode, higher harmonics are also revealed in the sunspot oscillation spectra in the bands 40–45, 60–80, 135–170, 220–250, and 480–520 min. The oscillation power in these bands monotonically and rapidly decreases with increasing frequency, which is characteristic for overtones arising due to the nonlinear nature of oscillations. The limiting oscillation mode stably exists in sunspots for 1.5–2 days, which coincides with the average lifetime of a supergranular cell. The mode with the period of 35–48 h observed in the power spectrum is not an eigen mode of sunspots, because its period is independent of its magnetic field strength. Probably, it occurs as a quasiperiod of an external exciting force caused by disturbances from supergranular cells surrounding the sunspot.

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s−1. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.

We present the results of processing three 256-min series of observations of quasi-periodic oscillations of the field of line-of-sight velocities in three sunspots. The Doppler shifts were determined simultaneously for six spectral lines formed at different heights in the solar atmosphere. In addition to the well-known high-frequency (periods of 3–5 min) oscillations, a band of low-frequency oscillations with periods of 60–80 min is revealed in the spectra of the sunspot umbra and magnetic elements located in immediate proximity of the sunspot. Unlike the short-period modes, the power of the long-period mode of line-of-sight velocity oscillations in the sunspot decreases sharply with height: these oscillations are distinctly seen in the line formed at a height of 200 km and almost are not seen in the line with the formation height of 500 km. This is indicative of different physical nature of the short-period and long-period oscillations of a sunspot. If the former are caused by slow magnetosonic waves within the field tube of the spot, the latter are representative of global vertical-radial oscillations of a magnetic element (spot, pore) as a whole near the position of a stable equilibrium.

New observational data on long-period oscillations of the line-of-sight velocities detected via the Doppler shifts of spectral lines observed at various heights in and near sunspots are presented. The sunspots and nearby magnetic elements oscillate with periods ranging from 40 to 80 min. The oscillations in the line-of-sight velocities persist over the entire observation session (up to four hours). These results support theoretical models in which this phenomenon represents natural long-period oscillations (vertical-radial displacements) of entire magnetic elements (sunspots, pores, and magnetic knots) about some stable equilibrium positions.

Long (up to 100 hours) time series of SOHO/MDI Doppler data are analyzed. The power spectrum of radial velocity time series in the quiet photosphere is observed to have, along with the known 5-min mode, a stable strong mode with a period of about 32 h, which is close to the supergranulation cell lifetime. The spatial distribution of the amplitudes of these oscillations also coincides with the characteristic size scale of supergranulation (~35 Mm)., Comment: 6 pages, 4 figures

High-quality stratospheric photographs in the continuum were used to investigate spatial scales of the solar granulation field. Two-dimensional intensity power spectra are shown to contain most frequently the modes corresponding to the sizes of granules, protogranules, mesogranules, and supergranules. The place of these four, the most steady formations of the quiet Sun in the global structure of the solar photosphere, is discussed as well as their interconnection and their relation to weak and strong magnetic fields. The protogranulation scale is argued to play an important role in organization of the fine structure of the photosphere and magnetic fields in the quiet and active regions of the Sun.

TV observations of the full disk number of HeI dark points show that it varies nearly in antiphase with the sunspot number. This confirms the result of K.Harvey (1985). The number of HeI dark points ranged from 120 to 500.

We present an investigation of oscillatory processes with periods in the range of several tens of minutes for some single sunspots of a new solar cycle, observed in 2010–2011 at the same time intervals in the optical and radio ranges. We used magnetograms from SDO/HMI with a cadence of 45 s, and radio images at a frequency of 17 GHz obtained with the Nobeyama Radioheliograph (NoRH). Radio images in intensity (Stokes parameter I ) and circular polarization (Stokes parameter V ) were synthesized with a cadence of ten seconds and ten-second averaging. Time profiles obtained with NoRH and SDO/HMI show a correlation between the radio emission of sunspots and a magnetic field. Wavelet spectra and cross-wavelet transforms give similar oscillation periods: 30–40 min, 60–70 min, 100–110 min, and 150–200 min. The same periods found by fundamentally different methods from ground-based and space observations confirm the solar nature of these oscillations. One of the possible interpretations of our results is that detected oscillations reflect eigen oscillations of a sunspot as a whole predicted by the shallow sunspot model.

Aims. The artifacts of SDO/HMI magnetograms that may affect the low-frequency power spectrum of sunspot oscillations are analyzed. Methods. Several examples are given that present false (artificial) harmonics, which are produced by Doppler shifts in the power spectra of long-period oscillations of sunspots. This arises from peculiarities in the orbital movements of SDO. Results. It was found that those artifacts with periods of 12 and 24 h, as revealed even in variations of weak background magnetic fields, are actually present in SDO/HMI magnetograms. However, the quantitative impact of artifacts remains quite weak and does not change the picture of sunspot oscillations dramatically for as long as the magnetic field in the spot is less than about of 2000 Gauss. When the magnetic field strength is greater than 2000 G, the influence of these artifacts increases sharply to become the dominant factor. One can suggest that the amplification of noise components of these artifacts has a highly nonlinear character with the growth of the magnetic field, and the field strength of about 2000 G then takes on meaning of a threshold value.

This paper describes a method developed and used at the Main (Pulkovo) Observatory, Russian Academy of Sciences, for recording Doppler shifts, as well as the broadenings of spectral lines caused by their Zeeman splitting, from digital optical spectrograms of active regions of the sun. It is shown that, in fairly prolonged (more than 4h) continuous observations, long-period variations of the line-of-sight velocities and the magnetic field, with a characteristic period of about 80min, are detected in sunspots and in magnetic elements of the surrounding photosphere. These variations are interpreted as vertical or line-of-sight oscillations of the entire spot (or the magnetic element) as a whole, caused by perturbing action from the surrounding turbulent medium (the photosphere and the convective zone).

The photospheric, chromospheric, and magnetic field structure of large active region No. 18474 of July 1982 are studied. Various morphological features observed are described and their possible role in the evolution of sunspots group discussed. The abundance of different light bridges is a characteristic feature for this group. It is shown that the light bridges in the photosphere coincide with the location and direction of arch filaments or fibril streams in the chromosphere, and appear in the region of a developing rotating magnetic field.