Differential rotation of solar magnetic fields

The connection of the differential rotation of solar magnetic fields with the field sign and strength is studied. The synoptic maps of magnetic fields over the last three solar cycles taken at the Kitt Peak Observatory served as input data for the study. The algorithm of magnetic field filtering over 14 chosen strengt intervals and successive 5-degree latitude zones was applied to these data. The Fourier transform of the time series obtained was then used. Analysis of the power spectra led to the conclusion that there are two types of magnetic fields. These differ in strength (0–50 and 50–700 G) and rotation characteristics. The rotation differentiality for strong magnetic field is almost twice as large as that for weak magnetic fields.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Revealing of periodicities in the variations of differential rotation of the Sun

It is presumed that a north-southern asymmetry of a solid-body rotation of large spots, depending on even and odd solar activity cycles (Gigolashvili and Khutsishvili 1 1989, 1990) may possibly be explained by the asymmetry of the appearance of large structures with strong magnetic fields in the corresponding hemispheres. Spectral analysis of the observational data shows the presence of cyclic variations of differential rotation of large- and middle-sized spots. Variations of differential rotation of small spots are either absent or overlapped by noise. It is also supposed that the discovered and most frequently realized component of the spectrum of solar differential rotation variations — a four-years periodicity — may be either a real phenomenon or the result of overlapping of multiple quasi bi-annual variations.     

22-Year periodicity in the solar differential rotation

Using the data on sunspot groups compiled during 1879–1975, we determined variations in the differential rotation coefficientsA andB during the solar cycle. The variation in the equatorial rotation rateA is found to be significant only in the odd numbered cycles, with an amplitude ∼ 0.01 μ rads^-1. There exists a good anticorrelation between the variations of the differential rotation rateB derived from the odd and even numbered cycles, suggesting existence of a ‘22-year’ periodicity inB. The amplitude of the variation ofB is ∼ 0.05 μ rad s^-1.     

Determining the rotation law of the solar convection zone

The condition of minimum total dissipation is used to derive stationary rotation and azimuthal magnetic field distributions in the bulk of the solar convection zone with an upper boundary at which the relative radius is r/R=0.95. General equilibrium con figurations with symmetric and antisymmetric (about the equator) angular-velocity and field components are determined. The calculated rotation law matches the observed one in general parameters, but the decrease in angular velocity at high latitudes in theory is larger than that in observations. Besides, there are additional sharp variations in the rotation and field distributions in the theoretical curves near the generation zone of solar torsional waves. The possible cause of the latter discrepancy is discussed. The change in equilibrium distributions due to the presence of an inverse molecular-weight gradient at the base of the convection zone is also studied. This gradient is known to be produced by accelerated gravitational helium settling in the convection zone.     

Background magnetic fields during last three cycles of solar activity

This paper describes our studies of evolution of the solar magnetic field with different sign and field strength in the range from –100 G to 100 G. The structure and evolution of large‐scale magnetic fields on the Sun during the last 3 cycles of solar activity is investigated using magnetograph data from the Kitt Peak Solar Observatory. This analysis reveals two groups of the large‐scale magnetic fields evolving differently during the cycles. The first group is represented by relatively weak background fields, and is best observed in the range of 3–10 Gauss. The second group is represented by stronger fields of 75–100 Gauss. The spatial and temporal properties of these groups are described and compared with the total magnetic flux. It is shown that the anomalous behaviour of the total flux during the last cycle can be found only in the second group. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral methods for analyzing the rotation of solar structures

The application of spectral analysis methods for studying the rotation of solar structures is considered. The time series characterizing the time variation of the solar He I 1083 nm emission in 5° latitude zones have been used. Three types of spectral analysis have been tested: the Welch method, the multitaper method, and the Schuster periodogram method. The first two methods have been chosen for the analysis of observing time intervals 26 and 3 years in length. The Schuster periodogram method is more suitable for the sliding spectral analysis in a 1-year-long temporal window with a shift by half a year. The chosen methods for analyzing the power spectra allow one to obtain the spectral densities, the powers of significant peaks in them and the corresponding periods, the total powers in the specified intervals of periods and to estimate the significance of the peaks found and the intervals in which the true periods corresponding to the peaks can be located.     

Axial rotation, orbital revolution and solar spin–orbit coupling

The orbital motion of the Sun has been linked with solar variability, but the underlying physics remains unknown. A coupling of the solar axial rotation and the barycentric orbital revolution might account for the relationships found. Some recent published studies addressing the physics of this problem have made use of equations from rotational physics in order to model particle motions. However, our standard equations for rotational velocity do not accurately describe particle motions due to orbital revolution. The Sun's orbital motion is a state of free fall; in consequence, aside from very small tidal motions, the associated particle velocities do not vary as a function of position on or within the body of the Sun. In this note, I describe and illustrate the fundamental difference between particle motions in rotation and revolution, in order to dispel some part of the confusion that has arisen in the past and that which may yet arise in the future. This discussion highlights the principal physical difficulty that must be addressed and overcome by future dynamical spin–orbit coupling hypotheses.     

Rotation of solar structures in the upper chromosphere. II. Time variations in the latitudinal distribution of the rotation of active regions and coronal holes

The time variations in the latitudinal distribution of the rotation of active regions and coronal holes are investigated. The synoptic maps obtained from observations in the He I 1083 nm line at Kitt Peak Observatory over almost three solar cycles are used as observational data. A Fourier analysis of the time series constructed from synoptic maps has yielded the following results. The rotation of active regions differs significantly from the rotation of coronal holes in all parameters: the set of the most significant rotation periods, their latitudinal distribution, and time variations. The rotation of active regions and coronal holes is characterized by variations from cycle to cycle, a time-varying north-south asymmetry. The power spectra for consecutive cycles of solar activity differ significantly for both epochs of high activity and minima. Analysis of the total power of the spectra within four selected intervals of periods from 21 to 33 days has shown that the total power is highest in the intervals of periods 24–27 and 27–30 days. This is valid for both active regions and coronal holes. The correlation between the total powers in the above intervals of periods changes noticeably with time. Long-lived or successively appearing active regions with rotation periods in the range 24–30 days are typical of the time of a sharp decrease in the total equivalent width of active regions. This includes not only the decline time of the 11-year cycles, but also the minima between recurrent activity maxima during one cycle. A predominance of long-lived coronal holes as their total equivalent width decreases is noticeable for coronal holes with rotation periods in the interval 30–33 days. All of the above results suggest that the rotation of solar structures is determined mainly by the subphotospheric sources of specific structures, not by the rotation of the main volumes of solar plasma of the quiet Sun.     

Global magnetic activity in 22-year solar cycles

Properties of even and odd 11-year solar cycles as part of the 22-year magnetic cycle have been studied on the basis of the data on the zonal structure of the large-scale magnetic field, of polar faculae activity cycles, duration of 11-year cycles, high-latitude prominence areas, inclinations of the coronal streamers, velocity of magnetic neutral line migration, and peculiarities of the polar magnetic field reversal. It is shown that the properties of the odd cycle depend on those of the preceding even cycle. The 22-year magnetic cycle, consisting of an even and odd cycle, is a unified dynamic process. The new data obtained show that the poloidal magnetic fieldB(p) of ‘+’ and ‘−’ polarity for the new 22-year magnetic cycle is formed simultaneously, possibly in deep layers of the Sun in the form of a certain magnetic configuration, containing alternating ‘+’ and ‘−’ polarities of the field.     

The 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

A study of possible temporal and latitudinal variations in the properties of the solar tachocline

Temporal variations of the structure and the rotation rate of the solar tachocline region are studied using helioseismic data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) obtained during the period 1995–2000. We do not find any significant temporal variation in the depth of the convection zone, the position of the tachocline or the extent of overshoot below the convection zone. No systematic variation in any other properties of the tachocline, like width, etc., is found either. The possibility of periodic variations in these properties is also investigated. Time-averaged results show that the tachocline is prolate with a variation of about 0.02 R_⊙ in its position. Neither the depth of the convection zone nor the extent of overshoot shows any significant variation with latitude.     

Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a Λ‐effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations (∂Ω/∂r < 0 and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to ν^0.5_core, where ν_core is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The properties of solar active regions responsible for ground level enhancements during solar cycles 22 and 23

This is a study designed to analyze the relationship between ground level enhancements（GLEs）and their associated solar active regions during solar cycles 22and 23.Results show that 90.3%of the GLE events that are investigated are accompanied by X-class flares,and that 77.4%of the GLE events originate from super active regions.It is found that the intensity of a GLE event is strongly associated with the specific position of an active region where the GLE event occurs.As a consequence,the GLE events having a peak increase rate exceeding 50%occur in a longitudinal range from W20 to W100.Moreover,the largest GLE events occur in a heliographic longitude at roughly W60.Additionally,an analysis is made to understand the distributional pattern of the Carrington longitude of the active regions that have generated the GLE events.     

On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4–5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of activity complexes and active longitudes on variations in total solar irradiance

A numerical technique of time-longitude analysis has been developed by studying the fine structure of temporal variations in total solar irradiance (TSI). This analysis produces maps of large-scale thermal inhomogeneities on the Sun and reveals corresponding patterns of radiative excess and deficit relative to the unperturbed solar photosphere. These patterns are organized in two-and four-sector structures and exhibit the effects of both activity complexes and the active longitudes. Large-scale patterns with radiative excess show a facular macrostructure caused by the relaxation of large-scale thermo-magnetic perturbations and/or energy output due to very large-scale solar convection. These thermal patterns are related to long-lived magnetic fields that are characterized by rigid rotation. The patterns with radiative excess tend to concentrate around the active longitudes and are centered at 103° and 277° in the Carrington system when averaged over the time-longitude distribution of thermal inhomogeneities during activity cycles 21–23.     

A large-eddy simulation of turbulent compressible convection: differential rotation in the solar convection zone

We present the results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell.
We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the thermodynamics controls the dynamics through the Taylor–Proudman momentum balance . The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity 'bump'.