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Thirty-five stable single sunspots of sufficiently regular round shapes were studied to determine the vertical magnetic field strength at the sunspot umbra–penumbra (UP) boundary and the degree of inclination of the total field vector at this boundary. A new data tool (SDO/hmi) called Space-weather HMI Active Region Patches (SHARPs) was used. Four different methods have been used to determine the UP boundary, including Otsu's mathematical method (Otsu, 1979). It is shown that there is no single value of the vertical component of the field at the UP boundary that is universal for spots of all sizes and field strengths. The value of 1867 G found earlier by Jurčák, (2011) was not confirmed either by our data or by the data of other authors (Schmassmann, et al., 2018; Loptien et al., 2020). We obtained the UP border, 〈Bver〉, of ~1.6 kg with a fairly large dispersion. It is important to note that the inclination of the total field vector γ remains almost constant at this boundary with very small dispersion (SD ~ 1.5–2.5 deg). This gives grounds to believe that this quantity determines the transition of the spot plasma to the magnetoconvection regime. [ABSTRACT FROM AUTHOR]

The pixel-to-pixel (p2p) artifact, which occurs due to the discrete nature of matrix receivers, sets an independent frequency standard. For this reason, this effect can be used to study the differential rotation of the Sun based on tracers such as solar faculae. The results are in good agreement with ground-based observations of sunspots and radial velocities; however, they are significantly overestimated when compared with the helioseismological data. This may be due to the fact that magnetic tracers (sunspots, faculae) are captured by the supergranulation grid, which, due to the presence of the leptocline in the upper part of the convective zone, rotates faster than the topmost surface layers of the Sun, the angular velocity of which is recorded by helioseismological methods. Knowledge of the leptocline structure makes it possible to use such a model to estimate the depth of the lower, densest boundary of the superconvection cell (approximately 30 Mm). [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

Two main features define a sunspot as an object: a strong magnetic field and a low umbra temperature. The same can be said about a facular knot, in the center of which there is a dark micropore, and the magnetic field is several hundred Gauss (which noticeably exceeds the level of equipartition of about 200–250 G), sometimes reaching 1000 or 1200 G. The temperature decrease in these activity elements is explained by the suppression of circulation (overturning) convection by a strong vertical magnetic field. The first to express this idea was Biermann (1941). Within the framework of this conception, a saturation effect should be expected: when the magnetic field completely suppresses convection, its further growth should not lead to a decrease in temperature. There is still no clear answer to the question of the saturation effect. We will try to answer it in the first part of the work according to the Solar Dynamics Observatory. We show that saturation occurs at B = 2300–2400 G. A further increase in the magnetic field of the spot no longer leads to a decrease in the brightness of its umbra. The relationship of the magnetic field and intensity is also manifested in long-period oscillations of the magnetic field of spots. In this case, the brightness of the spot umbra changes in antiphase with its magnetic field (Efremov et al., 2020) in accordance with the theoretical model of a shallow sun spot (Solov'ev and Kirichek, 2014, 2016). A similar effect was established by us in the second part of this work for facular knots: during slow facular oscillations with periods of more than 1 h, its brightness changes in antiphase with a magnetic field. The obtained results convincingly confirm the Birman hypothesis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper considers a special class of artifacts that appears in the useful signal when the source moves along a discrete matrix of the receiver. A parasitic component forms in the signal due to the displacement of the extreme value of the distributed field of the physical quantity from pixel to pixel (p2p effect). It is shown that a stepwise discretization of Δt < T (p2p) is a necessary but not sufficient condition for the formation of the p2p-artifact. For small field gradients (in particular, with good spatial resolution), the parasitic signal in the time series of the studied variable is either weakened or does not form at all. This assumption has been qualitatively verified by comparative analysis of sunspot data obtained with SOHO/MDI and SDO/HMI. In addition, the Y-p2p effect, which is associated with sunspot displacement along the meridian and influences the process of long-period sunspot oscillations, is considered in detail based on SDO/HMI data. It was found that there is an inverse relationship between changes in the umbral area of a spot and variations of its magnetic field strength. This property of long-period sunspot oscillations as a single magnetic structure indicates the magnetic flux in the sunspot umbra is preserved, and it plays an extremely important role for our understanding of the physical nature of these oscillations. [ABSTRACT FROM AUTHOR]

Abstract: 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A solar faculae having an appearance of quite long-lived magnetic nodes can perform (as well as sunspots, chromospheric filaments, coronal loops) free oscillations, i.e., they can oscillate about the stable equilibrium position as a single whole, changing quasi-periodically magnetic field averaged over the section with periods from 1 to 4 hours. Kolotkov et al. (2017) described the case in which the average magnetic field strength of the facula node considerably decreased during observations of SDO magnetograms (13 hours), and, at the same time, its oscillations acquired a specific character: the fundamental mode of free oscillations of the facula considerably increased in amplitude (by approximately two times), while the period of oscillations increased by three times. At the end of the process, the system dissipated. In this work, we present the exact solution of the equation of small-amplitude oscillations of the system with a time-variable rigidity, describing the oscillation behavior at which the elasticity of the system decreases with time, while the period and amplitude of oscillations grow. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]