E. Yu. Nagovitsyna

The Gnevyshev-Ohl rule for physical parameters of the solar magnetic field: The 400-year interval

We consider a number of questions pertaining to the famous Gnevyshev-Ohl rule. We discuss various formulations of the rule and show that it is not violated in its exact formulation in the last pair of 11-year cycles 22 and 23. The rule has been found to hold not only for statistical indices of solar activity but also in the context of physical parameters of the solar magnetic field: the sunspot magnetic flux and the open magnetic flux. We have established that the hypothesis by Usoskin et al. (2001) about the “loss“ of one cycle at the end of the 18th century allows the Gnevyshev-Ohl rule, which regulates the behavior of physical parameters of the solar magnetic field, to be made universal, without any exceptions, at least in the last 400 years. Thus, in fact, we can talk about the Gnevyshev-Ohl law of the long-term dynamics of the solar magnetic field, a law that holds at both normal and extreme levels of solar activity.

Spatial variations in parameters of quasi-hourly sunspot fragment oscillations and a singular penumbra oscillator

We obtained three-dimensional interpolated portraits for the radial and torsional oscillations of fragments of 12 sunspots in the form of deviations of their polar coordinates from drift as functions of the time and distance from the sunspot center. We performed a wavelet analysis of the two orthogonal components and determined the dominant oscillation modes; the period varies between 40 and 100 min for different sunspots. We revealed two types of dominant modes, one is associated with the sunspot and the other is associated with its surrounding pores: the central-mode frequency depends on the maximum field strength of the sunspot and decreases from its center toward the boundary, while the peripheral-mode frequency depends on the heliographic latitude and decreases toward the sunspot boundary from the far periphery. We revealed radial variations in frequency and amplitude with a spatial period of 0.8 sunspot radius. The types of dominant modes and the radial variations in oscillation parameters are linked with the subphotospheric structure of an active region—with two types of spiral waves and concentric magnetic-field waves. We estimated the mean pore oscillation energy to be ∼1030 erg and found a singular oscillator with a mean energy of ∼1031 erg in the penumbra at a distance of 0.8 sunspot radius. We argue that the singular penumbra oscillator is the source of solar flares.

The Maunder minimum: North-south asymmetry in sunspot formation, mean sunspot latitudes, and the butterfly diagram

An approach to reconstructing solar activity in the past is used to study its time evolution. It is already possible to reconstruct not only the general level of solar activity on long timescales, but also particular aspects of its development: sunspot dominance in either hemisphere, the drift and latitude spread of the sunspot-formation zone, and features in the spatial distribution of the activity at specific epochs, such as the Maunder minimum.

Series of classical solar activity indices: Kislovodsk data

We present data on the series of solar activity indices, Wolf sunspot numbers W and total sunspot areas S, obtained at the Kislovodsk high-altitude station of the Pulkovo Observatory. The problem of properly extending the 133-year-long Zürich series of W and the 102-year-long Greenwich series of S, which were discontinued in 1980 and 1976, respectively, is emphasized. We stress that the Kislovodsk data have retained mutual homogeneity with the classical series until now and that they are preferred for extension. The question under consideration is of fundamental importance in studying the solar activity variations on long time scales and related processes in the Sun-Earth system.

Long-period oscillation processes in sunspot groups (ground-based and exoatmospheric observations)

The SOHO (MDI) exoatmospheric observations have proved the existence of long-period oscillations in active solar regions, which are manifested in a number of spatial and temporal modes; this had been established earlier by ground-based observations.

Oscillations of flux tube bundles and the structure of sunspot magnetic fields

Observational aspects of the previously found quasi-hourly oscillations of magnetic fragments in sunspot polar coordinates are investigated. The orientation of the oscillations is shown to be azimuthally anisotropic, with their amplitude reaching a maximum in penumbra at a distance of ∼0.8 sunspot radius (the maximum amplitude is estimated to be 3700 km). Based on the detected deviations of the oscillations from the radial direction, we numerically simulate the horizontal configuration of field lines in the region of the major spots in bipolar groups.

The area and absolute magnetic flux of sunspots over the past 400 years

A new series of yearly-mean relative sunspot numbers SN2 that has been extrapolated into the past (to 1610) is presented. The Kislovodsk series with the scale factor b = 1.0094 ± 0.0059 represents a reasonable continuation of the mean-monthly and mean-yearly total sunspot areas of the Greenwich series after 1976. The second maximum of the 24th solar-activity cycle was not anomalously low, and was no lower than 6 of the past 13 cycles. A series A2 of values for the total sunspot area in 1610–2015 has been constructed, and is complementary to new versions of the series of the relative number of sunspots SN2 and the number of sunspot groups GN2. When needed, this series can be reduced to yield a quantity having a clear physical meaning—the spot absolute magnetic flux ΦΣ(t)[Mx] = 2.16 × 1019A(t) [mvh]. The maximum sunspot area during the Maunder minimum is much higher in the new series compared to the previous version. This at least partially supports the validity of arguments that cast doubt on the anomalously low ampltude of the solar cycles during the Maunder minimum that has been assumed by many researchers earlier.

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.

Magnetic field variations and spatial configurations of long-period sunspot oscillations according to the SOHO data

The phenomenon of long-period sunspot oscillations with periods from several tens to a thousand minutes is studied using data on the magnetic field strength and sunspot coordinates obtained based on the SOHO MDI data. It has been indicated that oscillations of the sunspot magnetic field strength are related to relative and absolute horizontal oscillation modes, as a result of which certain limitations are imposed on the interpretation of the phenomenon.

Long-term oscillations in solar active regions based on magnetic fields and radio emission

A comparative analysis of sunspot oscillations and related radio sources in the active regions AR 8949, AR 8951, and AR 8953 is carried out using SOHO MDI data and simultaneous observations with the Nobeyama Radioheliograph, with a one-minute time resolution on scales of tens to hundreds of minutes. The radio sources in the selected active regions are ∼40 000–60 000 km away from the corresponding spots, with the periods of long-term oscillations of the radio sources being ∼12% longer.