Sunspot as an isolated magnetic structure: Stability and oscillations

A simple energy model of a sunspot as a compact magnetic feature is described where the main energy contribution is provided by the coolest and most compressed part of the magnetic force tube of the spot at depths ranging from Wilson’s depression level (300–500 km) down to 2–3 thousand km. The equilibrium and stability conditions for such a system are analyzed using the variation principle, and oscillations of the system as a whole about the inferred equilibrium position are studied. The sunspot is shown to be stable in the magnetic field strength interval from 0.8–1 to 4–5 kG. The dependence of the eigenfrequency on magnetic field strength ω(B) is computed for the main oscillatory mode, where only the umbra of the sunspot takes part in oscillations, ω = ω ₁ (B). Lower subharmonics may appear in the case where penumbra too becomes involved in the oscillatory process: ω ₂ = ω ₁/2, ω ₃ = ω ₁/3. Theoretical curves agree well with the observational data obtained in Pulkovo using various independent methods: from temporal variations of sunspot magnetic field and from line-of-sight-velocity measurements. The periods of oscillations found range from 40 to 200 minutes.     

Torsional oscillations of umbra and penumbra of sunspots

Torsional oscillations of seven single spots are studied based on the observations of the longitudinal magnetic field and the field of radial velocities in the photospheric Fe I λ 525.3 nm line. The periods of umbra and penumbra oscillations are 2.2–7.1 and 3.3–7.7 days, respectively. The spots at a greater solar latitude are characterized by a longer period of oscillations and a smaller axial strength of the magnetic field. The periods of umbra and penumbra oscillations increase with an increase in the period and amplitude of the sunspot umbra oscillations. The obtained results can point to a unitary mechanism of torsional oscillations of umbra and penumbra of single spots and a connection of these oscillations with the differential rotation of the Sun.     

Solar cycles during the Maunder minimum

We have obtained new consistent versions of the 400-yr time series of the Wolf sunspot number W, the sunspot group number G, and the total sunspot area S (or the total sunspot magnetic flux Φ). We show that the 11-yr cycle did not cease during the Maunder minimum of solar activity. The characteristics of the extrema of individual 11-yr cycles in 1600–2005 have been determined in terms of the total sunspot area index. We provide arguments for using alternating (“magnetic”) time series of indices in investigating the solar cyclicity.     

Two populations of sunspots and secular variations of their characteristics

We investigate the magnetic fields and total areas of mid- and low-latitude sunspots based on observations at the Greenwich and Kislovodsk (sunspot areas) and Mount Wilson, Crimean, Pulkovo, Ural, IMIS, Ussuriysk, IZMIRAN, and Shemakha (magnetic fields) observatories. We show that the coefficients in the linear form of the dependence of the logarithm of the total sunspot area S on its maximum magnetic field H change with time. Two distinct populations of sunspots are identified using the twodimensional H–log S occurrence histogram: small and large, separated by the boundaries log S = 1.6 (S = 40 MSH) and H = 2050 G. Analysis of the sunspot magnetic flux also reveals the existence of two lognormally distributed populations with the mean boundary between them Φ = 10²¹ Mx. At the same time, the positions of the flux occurrence maxima for the populations change on a secular time scale: by factors of 4.5 and 1.15 for small and large sunspots, respectively. We have confirmed that the sunspots form two physically distinct populations and show that the properties of these populations change noticeably with time. This finding is consistent with the hypothesis about the existence of two magnetic field generation zones on the Sun within the framework of a spatially distributed dynamo.     

Rotation cycles of the sector structure of the solar magnetic field and its activity

We study the rotation of the sector structure of the solar magnetic field by using Stanford magnetographic observations from 1975 until 2000 and magnetic synoptic Hα-maps obtained from 1904 until 2000. The two independent series of observations yielded the same rotation periods of the two-sector (26.86 days) and four-sector (13.64 days) structures. We introduce a new index of the solar rotation, SSPM(t). The spectral power density of the sector structure of the magnetic field is shown to exhibit a 22-year cyclicity. The two-and four-sector structures of the magnetic field rotate faster at the maxima of even 11-year sunspot cycles. This phenomenon may be called the Gnevyshev-Ohl rule for the solar rotation. The 11-year sector-structure activity cycles are shown to lead the 11-year sunspot cycles (Wolf numbers) by 5.5 years. A 55-year component with the slowest rotation in the 18th cycle (1945–1955) was distinguished in the sector-structure rotation.     

On the possibility of investigation of the magnetic field structure in subphotospheric layers of the Sun according to observations of sunspot torsional oscillations

A method of investigation of the magnetic field structure in subphotospheric layers of the Sun has been developed. The method is based on observations of the torisonal oscillations of single sunspots. Characteristics of the torsional oscillations have been obtained from observations of the longitudinal magnetic field and radial velocities of seven single sunspots in the photospheric line Fe I λ5253 Å. The parameters of the torsional oscillations and magnetic tubes in the deep layers have been determined. The radius of the cross section of a magnetic flux tube forming a sunspot is greatest near the Sun’s surface and is approximately equal to the radius of a sunspot umbra. Down to the deeper layers, it decreases quite quickly. The longitudinal electric current appearing in the magnetic tube changes direction. The typical time of the current changes is determined by the period of the torsional oscillations. The intensity of the longitudinal magnetic field in the tube increases with depth. The Alfven wave velocity averaged over the length of a magnetic tube is tens or hundreds of times less than this velocity in a sunspot umbra. It decreases with an increase in the period of oscillations. A decrease in the Alfven wave velocity leads to an increase in the twisting angle of magnetic field lines.     

To the description of long-term variations in the solar magnetic flux: The sunspot area index

We show that the Wolf sunspot numbers W and the group sunspot numbers GSN are physically different indices of solar activity and that it is improper to compare them. Based on the approach of the so-called “primary” indices from the observational series of W(t) and GSN(t), we suggest series of yearly mean sunspot areas beginning in 1610 and monthly mean sunspot areas beginning in 1749.     

Oscillations Above Sunspots

The 3-min oscillations in the sunspot atmosphere are discussed, based on joint observing with the Transition Region and Coronal Explorer – TRACE and the Solar and Heliospheric Observatory – SOHO. We find that the oscillation amplitude above the umbra increases with increasing temperature, reaches a maximum for emission lines formed close to 1–2× 10⁵ K, and decreases for higher temperatures. Oscillations observed with a high signal-to-noise ratio show deviations from pure linear oscillations. The results do not support the sunspot filter theory, based on the idea of a chromospheric resonator. Whereas the filter theory predicts several resonant peaks in the power spectra, equally spaced 1 mHz in frequency, the observed power spectra show one dominating peak, close to 6 mHz. Spectral observations show that the transition region lines contribute less than 13 percent to the TRACE 171 Å channel intensity above the umbra. The 3-min oscillations fill the sunspot umbra in the transition region. In the corona the oscillations are concentrated to smaller regions that appear to coincide with the endpoints of sunspot coronal loops, suggesting that wave propagation along the magnetic field makes it possible for the oscillations to reach the corona.     

New characteristics of the solar cycle and dynamo theory

Based on an analysis of the observational data for solar cycles 12–23 (Royal Greenwich Observatory-USAF/NOAA Sunspot Data), we have studied various parameters of the “Maunder butterflies.” Based on the observational data for cycles 16–23, we have found that BT/Land S depend linearly on each other, where B is the mean magnetic field of the cycle, T is the cycle duration, S is the cycle strength, and L is the mean sunspot latitude in the cycle (the arithmetic mean of the absolute values of the mean latitudes in the north and south). The connection of the observed quantities with the α-ω-dynamo theory is discussed.     

Turbulent effects of sunspot magnetic field reconstruction

We study the effects of two-dimensional turbulence generated in sunspot umbra due to strong magnetic fields and Alfven oscillations excited in sunspots due to relatively weak magnetic fields on the evolution of sunspots. Two phases of sunspot magnetic field decaying are shown to exist. The initial rapid phase of magnetic field dissipation is due to two-dimensional turbulence. The subsequent slow phase of magnetic field decaying is associated with Alfven oscillations. Our results correspond to observed data that provide evidence for two types of sunspot evolution. The effect of macroscopic diamagnetic expulsion of magnetic field from the convective zone or photosphere toward sunspots is essential in supporting the long-term stability and equilibrium of vertical magnetic flux tubes in sunspots.     

Total sunspot area before 1875 (reconstruction)

Empirical functions approximating the dependences of total sunspot area A on relative sunspot number W and group sunspot number GN have been found. In the function A(W), allowance for its dependence on the secular activity cycle has been made; it is shown that this allowance is not needed for the function A(GN). The yearly mean A for 1700–1874 have been reconstructed using these functions and the available W and GN time series. Having supplemented the original data with archival observations, we have been able to reconstruct the monthly mean A _W since 1821. We discuss the causes of the systematic difference between the reconstructions using W and GN.     

Investigation of Umbral Dots with the <Emphasis Type="Italic">New Vacuum Solar Telescope</Emphasis>

Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae. They are convective phenomena existing inside umbrae. UDs are usually divided into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions inside an umbra. Our purpose is to investigate UD properties and analyze their relationships, and further to find whether or not the properties depend on umbral magnetic field strengths. Thus, we selected high-resolution TiO images of four active regions (ARs) taken under the best seeing conditions with the New Vacuum Solar Telescope in the Fuxian Solar Observatory of the Yunnan Astronomical Observatory, China. The four ARs (NOAA 11598, 11801, 12158, and 12178) include six sunspots. A total of 1220 CUDs and 603 PUDs were identified. Meanwhile, the radial component of the vector magnetic field of the sunspots taken with the Helioseismic and Magnetic Imager on-board the Solar Dynamics Observatory was used to analyze relationships between UD properties and umbral magnetic field strengths. We find that diameters and lifetimes of UDs exhibit an increasing trend with the brightness, but velocities do not. Moreover, diameters, intensities, lifetimes and velocities depend on the surrounding magnetic field. A CUD diameter was found larger, the CUD brighter, its lifetime longer, and its motion slower in a weak umbral magnetic field environment than in a strong one.     

The sun,the cosmic vibration,and the nucleus of the galaxy 4151

Numerous U and V magnitude measurements were performed for the nucleus of the Seyfert galaxy NGC 4151 at the Crimean Laboratory of the SAI (Moscow University) in 1994–2005. Adding them to the previous data for 1968–1997 has led to a substantial increase in the confidence level of the light variations in NGC 4151 with a stable period of P _G = 160.0108(7) min and a mean amplitude of 0.007 U mag (in the “active” state of the nucleus). The period of NGC 4151 agrees well with the period of 160.0101(15) min found previously in the oscillations of the Sun. It is treated as the period of a “coherent cosmic oscillation” independent of redshift z or as the period of “free cosmic vibrations” of the hydrogen atom, the main element of the Universe. The period and initial phase of the P _G oscillation have been constant for 38 years of NGC 4151 observations. The new astrophysical phenomenon appears to be closely related to the quantum nonlocality of photons and is of particular interest in physics and cosmology.     

Search for magnetic field oscillations in a sunspot umbra

In order to search for oscillations in velocity and magnetic field strength within a sunspot umbra, a time series of spectra has been obtained through a circular analyzer and the Gregory-Coudé telescope at the Observatorio del Teide, Tenerife. The velocity oscillations clearly show peaks of power at periods between 2 and 7 minutes, with a maximum at 5 minutes. The apparent variations of the magnetic field strength, however, don't exhibit significant oscillations; these fluctuations are rather produced by the influence of parasitic stray light from the surrouding quiet sun which are also visible in the measured time variations of the umbral contrast of continuum intensity.     

Temperature Dependence of Molecular Line Strengths and Fe i 1565 nm Zeeman Splitting in a Sunspot

Spectroscopic observations at 1565 nm were made in the eastern half of the main umbra of NOAA 9885 on 1 April 2002 using the National Solar Observatory McMath-Pierce Telescope at Kitt Peak with a tip-tilt image stabilization system and the California State University Northridge–National Solar Observatory infrared camera. The line depth of the OH blend at 1565.1 nm varies with the observed continuum temperature; the variation fits previous observations except that the continuum temperature is lower by 600 K. The equivalent width of the OH absorption line at 1565.2 nm shows a temperature dependence similar to previously published umbral molecular observations at 640 nm. A simple model of expected OH abundance based upon an ionization analogy to molecular dissociation is produced and agrees well with the temperature variation of the line equivalent width. A CN absorption line at 1564.6 nm shows a very different temperature dependence, likely due to complicated formation and destruction processes. Nonetheless a numerical fit of the temperature variation of the CN equivalent width is presented. Finally a comparison of the Zeeman splitting of the Fei 1564.8 nm line with the sunspot temperature derived from the continuum intensity shows an umbra somewhat cooler for a given magnetic field strength than previous comparisons using this infrared 1564.8 nm line, but consistent with these previous infrared measurements the umbra is hotter for a given magnetic field strength than magnetic and temperature measurements at 630.2 nm would suggest. Differences between the 630.2 nm and 1564.8 nm umbral temperature and magnetic field relations are explained with the different heights of formation of the lines and continua at these wavelengths.     

SMM/UVSP observations of the distribution of transition region oscillations and other properties in a sunspot

Observations of a sunspot in the Civ line at 1548 Å formed in the transition region have been analyzed to obtain the time variations and/or mean values of the velocity, intensity, longitudinal magnetic field, and line width. Oscillations with periods between approximately 110 and 200 s are observed only over the umbra where the transition region magnetic field is highest and the line width is smallest. When periodic intensity variations occur at the same frequency as the velocity oscillations, the peak intensities occur slightly before the maximum upward motions. No periodic variations in the transition region magnetic field have been detected. Scatter diagrams are presented which show possible relationships between the flow velocity, emission line intensity, line width, and transition region magnetic field.     

Chromospheric Sunspot Oscillations in Hα and Ca ii 8542 Å

We study chromospheric oscillations including umbral flashes and running penumbral waves in a sunspot of active region NOAA 11242 using scanning spectroscopy in Hα and Ca?ii 8542 Å with the Fast Imaging Solar Spectrograph (FISS) at the 1.6 meter New Solar Telescope at the Big Bear Solar Observatory. A bisector method is applied to spectral observations to construct chromospheric Doppler-velocity maps. Temporal-sequence analysis of these shows enhanced high-frequency oscillations inside the sunspot umbra in both lines. Their peak frequency gradually decreases outward from the umbra. The oscillation power is found to be associated with magnetic-field strength and inclination, with different relationships in different frequency bands.     

Variations of microwave emission from solar active regions

Based on observational data obtained with the RT-22 Crimean Astrophysical Observatory radio telescope at frequencies of 8.6 and 15.4 GHz, we investigate the quasi-periodic variations of microwave emission from solar active regions with periods T_p<10 min. As follows from our wavelet analysis, the oscillations with periods of 3–5 min and 10–40 s have the largest amplitudes in the dynamic power spectra, while there are virtually no oscillations with T_p<10 s. Our analysis shows that acoustic modes with T_p?1 min strongly dissipate in the lower solar corona due to thermal conduction losses. The oscillations with T_p=10–40 s are associated with Alfvén disturbances. We analyze the influence of acoustic and Alfvén oscillations on the thermal mechanisms of microwave emission in terms of the homogeneous model. We discuss the probable coronal heating sources.     

Investigating Sub-Pixel 45-Second Periodic Wobble in SDO/AIA Data from January to August 2012

Artifacts could mislead interpretations in astrophysical observations. A thorough understanding of an instrument will help in distinguishing physical processes from artifacts. In this article, we investigate an artifact of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory. Time-series data and wavelet spectra revealed periodic intensity perturbations in small regions over the entire image in certain AIA extreme ultraviolet (EUV) passbands at a period of about 45 seconds. These artificial intensity variations are prominently detected in regions with sharp intensity contrast, such as sunspot light bridges. This artifact was caused by a periodic pointing wobble of the two AIA telescopes ATA 2 (193 and 211 Å channels) and ATA 3 (171 Å and UV channels), to a lesser extent, while the other two telescopes were not found to be affected. The peak-to-peak amplitude of the wobble was about 0.2 pixel in ATA 2 and 0.1 pixel in ATA 3. This artifact was intermittent and affected the data of seven months from 18 January to 28 August 2012, as a result of a thermal adjustment to the telescopes. We recommend that standard pointing-correction techniques, such as local correlation tracking, should be applied before any detailed scientific analysis that requires sub-pixel pointing accuracy. Specifically, this artificial 45-second periodicity was falsely interpreted as abnormal sub-minute oscillations in a light bridge of a sunspot (Yuan and Walsh in Astron. Astrophys.594, A101, 2016).     

Complex structure of the magnetic field of the CP star HD32633

The method of “virtual magnetic charges” is used to analyze the structure of the magnetic field of the CP star HD32633. The phase relation of its magnetic field differs strongly from a sine wave. The structure of the star’s field can be described fairly well by two dipoles located in the opposite regions of the star near its rotation equator. Each of these dipoles produces two pairs of magnetic spots of opposite polarity similar to sunspots. The dipoles are located at a distance of Δa=0.6 R from the center, where R is the radius of the star. The field strength at the poles is equal to ±42 and ±19 kG.