The sector structure of the active longitudes in solar cycles

The longitudinal distributions of the polar faculae, bright K Ca⁺ points, and sunspot areas have been investigated in three-year intervals at the minima and maxima of the last five solar cycles in the rotation system which corresponds to the background magnetic field:T = 27.23 days (Mikhailutsa, 1994b). It has been shown that there were three specific features of the polar faculae and bright K Ca⁺ point longitudinal distributions: (1) The longitudes of maxima and minima of the distributions were approximately the same in the last five solar cycles. (2) There were predominantly two opposite longitudinal maxima and two opposite longitudinal minima in the distributions of each hemisphere. (3) The distributions of the northern and southern hemispheres were in opposite phase. The extremes of the sunspot area longitudinal distributions were preferentially between the longitudes of the polar facular extremes. The period of the sector structure rotation was defined more precisely:T = 27.227 ± 0.003 days. The results found can serve as an indication that there is a global foursector structure seated in the solar interior which plays a visible role in the polar facular and sunspot distributions.     

Measurement of Kodaikanal white-light images – IV. Axial Tilt Angles of Sunspot Groups

The Kodaikanal sunspot data set, covering the interval 1906–1987, is used in conjunction with the similar Mount Wilson sunspot data set, covering the interval 1917–1985, to examine characteristics of sunspot group axial tilt angles. Good agreement is demonstrated between various results derived from the two independent data sets. In particular, the tendency for sunspot groups near the average tilt angle to be larger than those far from the average tilt angle is confirmed. Similarly the faster residual rotation rate for groups near the average tilt angle is also confirmed. Other confirmations are made for the relationships between latitude drift of sunspot groups and tilt angle, polarity separations, and axial expansion. Evidence is presented that tilt angles averaged over these long time intervals differ between the north and south hemispheres by about 1.4 deg. It is suggested that residual tilt angles show a slight systematic variation with phase in the activity cycle.     

Simulation of Sunspot Activity During Active Sun and Great Minima Using Regular,Random and Relic Fields

Developing the idea of Ruzmaikin (1997, 1998), we have constructed a model of sunspot production using three components of solar magnetic field: the 22-year dynamo field, a weak constant relic field, and a random field. This model can reproduce the main features of sunspot activity throughout the 400-year period of direct solar observations, including two different sunspot activity modes, the present, normal sunspot activity and the Maunder minimum. The two sunspot activity modes could be modeled by only changing the level of the dynamo field while keeping the other two components constant. We discuss the role of the three components and how their relative importance changes between normal activity and great minimum times. We found that the relic field must be about 3–10% of the dynamo field in normal activity times. Also, we find that the dynamo field during the Maunder minimum was small but non-zero, being suppressed typically by an order of magnitude with respect to its value during normal activity times.     

A helicity proxy from horizontal solar flow patterns

Motivated by new observations of solar surface flow patterns of mesogranulation, theoretical computations of the horizontal divergence-vorticity correlation are presented. Because of its close relation to the helicity in rotating turbulence such observations and discussions are of particular importance for the conventional dynamo theory. For the northern hemisphere we find a small, but always negative, divergence-vorticity correlation. Both an analytical Second Order Correlation Approximation for slow rotation as well as a numerical simulation (originally done for accretion disks) for fast rotation yield very similar results.     

Deceleration of the rotational velocities of sunspot groups during their evolution

Using the Greenwich Photoheliographic Results for the years 1874–1976 the daily rotational velocities for 955 recurrent and 13169 non-recurrent sunspot groups from the first day of their appearance and during their evolution have been determined. The rotational velocities were divided in six latitude strips with a width of five degrees and grouped according to the age of the groups. It was established that the rotational velocities of recurrent and non-recurrent sunspot groups decrease with time in all studied latitude strips. At their birth the recurrent spot groups rotate faster by about 0.15° day⁻¹ than the non-recurrent ones and settle, within the errors of measurements, to an about 0.5° day⁻¹ slower velocity value during the second disc passage. A comparison of our results with helioseismology measurements indicates that in the frame of the anchoring hypothesis, the recurrent sunspot groups at their birth could be coupled to the fast rotating layer at about r=0.93 R _⊙.     

Two types of differential rotation of the solar corona

The differential rotation of the solar corona has been analyzed using as the input data the brightness of the coronal green line Fe xiv 530.3 nm for more than five activity cycles. It is found that the character of rotation of the solar corona changes during the activity cycle. Approximately at the middle of the descending branch the differential rotation is weakly pronounced, while the greatest differential gradient is observed at the ascending branch and, occasionally, at the maximum of the cycle. An explanation of this difference has been suggested. The total rotation rate of the corona can be represented as a superposition of two rotation modes (components) – the fast and slow ones. The synodic period of the fast mode near the equator is about 27 days, increasing slightly with latitude. The synodic period of the slow mode exceeds 30 days. The changing relative fraction of these two modes results in variation of the latitude dependence of the observed rotation rate during the activity cycle. The characteristics of two principal types of differential rotation of the solar corona have been determined. The first type consists of the fast mode alone and is established approximately at the middle of the descending branch of the cycle. The second type is the sum of both modes with the fast mode dominating at low latitudes and the slow mode at high latitudes. The results obtained can be used for in-depth study of interaction of the velocity field and dynamo mechanism in the Sun and stars.     

The Influence of the Evolution of Sunspot Groups on the Determination of the Solar Velocity Field

Meridional motions and differential rotation of stable recurrent sunspot groups from the Greenwich data set are investigated. Simple and complex, as well as younger and older sunspot groups are treated separately. There is no difference in behavior of the meridional motions for the simple and complex sunspot groups, while complex groups rotate faster than the simple ones. If we attribute the differences of rotational velocities to the errors in position determination, it can be concluded that the rotational velocities determined by using sunspot groups as tracers are slightly overestimated. Both the meridional motions and differential rotation show the same dependence on the age, when simple and complex recurrent sunspot groups are considered. Alexander von Humboldt Research Fellow.     

Solar rotation measurements at Mount Wilson

Possible sources of systematic error in solar Doppler rotational velocities are examined. Scattered light is shown to affect the Mount Wilson solar rotation results, but this effect is not enough to bring the spectroscopic results in coincidence with the sunspot rotation. Interference fringes at the spectrograph focus at Mount Wilson have in two intervals affected the rotation results. It has been possible to correlate this error with temperature and thus correct for it. A misalignment between the entrance and exit slits is a possible source of error, but for the Mount Wilson slit configuration the amplitude of this effect is negligibly small. Rapid scanning of the solar image also produces no measurable effect.     

Active longitudes of the sun: The rotation period and statistical significance

Using data from the Greenwich catalog, we determined the nonuniformity of the longitudinal distribution of sunspot groups as a function of the rotation period taken for the longitude determination. We estimated the statistical significance of the active longitudes found. A fairly high significance was achieved only for sunspot groups of the Northern Hemisphere and odd activity cycles and only for a synodic rotation period close to 28 days. In this case, one interval of active longitudes was found. The active longitudes are assumed to be associated with the fossil magnetic field frozen in the uniformly rotating radiative zone of the Sun.     

On the determination of heliographic positions and rotation velocities of sunspots

In an earlier paper of this series it was shown how the Wilson depression influences the determination of sunspot rotation velocities. Using this finding and the fact that stable recurrent sunspots show a very constant rotation velocity it is possible to determine the effect of wrong solar image radii on the determination of sunspot rotation velocities and correct them.Mitteilungen aus dem Kiepenheuer-Institut Nr. 238.     

On the α-effect for slow and fast rotation

This paper deals with the influence of global rotation on a special inomogeneous field of incompressible turbulence. All its deviations from homogeneity and isotropy may be described only by a constant gradient of turbulence intensity. Using a FOURIER representation we are able to determine the α-effect for any given rotational rates and material constants. In the case of slow rotation our expressions show a strong similarity with those of other authors. Increasing angular velocities do not – as is to be assumed at first sight – suppress the production of mean electromotive force caused by turbulence. They rather lead to a two-dimensionality of this e.m.f. with respect to the axis of rotation. It seems, therefore, that very fast rotation can not completely delete the dynamo instability.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

Simulating the generation of the solar toroidal magnetic field by differential rotation

Within the kinematic dynamo theory, we construct a mathematical model for the evolution of the solar toroidal magnetic field, excited by the differential rotation of the convective zone in the presence of a poloidal field of a relic origin. We use a velocity profile obtained by decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculate the latitudinal profiles of the increasing-with-time toroidal field at different depths in the solar convection zone. It is found that, in the region of differential rotation, the excited toroidal field shows substantial fluctuations in magnitude with depth. Based on the simulations results, we propose an explanation for the “incorrect polarity” of magnetic bipolar sunspot groups in solar cycles.     

High-Resolution Studies of the Solar Polar Magnetic Fields

We present high-resolution studies of the solar polar magnetic fields near sunspot maximum in 1989 and towards sunspot minimum in 1995. We show that, in 1989, the polar latitudes were covered by several unipolar regions of both polarities. In 1995, however, after the polar field reversal was complete, each pole exhibited only one dominant polarity region.Each unipolar region contains magnetic knots of both polarities but the number count of the knots of the dominant polarity exceeds that of the opposite polarity by a ratio of order 4:1, and it is rare to find opposite polarity pairs, i.e., magnetic bipoles.These knots have lifetimes greater than 7 hours but less than 24 hours. We interpret the longitudinal displacement of the knots over a 7-hour period as a measure of the local rotation rate. This rotation rate is found to be generally consistent with Snodgrass' (1983) magnetic rotation law.In an attempt to obtain some insight into the operation of the solar dynamo, sketches of postulated subsurface field configurations corresponding to the observed surface fields at these two epochs of the solar cycle are presented.     

Tilt-angle variations of active regions

An examination of the tilt angles of multi-spot sunspot groups and plages shows that on average they tend to rotate toward the average tilt angle in each hemisphere. This average tilt angle is about twice as large for plages as it is for sunspot groups. The larger the deviation from the average tilt angle, the larger, on average, is the rotation of the magnetic axis in the direction of the average tilt angle. The rate of rotation of the magnetic axis is about twice as fast for sunspot groups as it is for plages. Growing plages and spot groups rotate their axes significantly faster than do decaying plages and spot groups. There is a latitude dependence of this effect that follows Joy's law. The fact that these tilt angles move toward the average tilt angle and not toward 0 deg (the east-west orientation), combined with other results presented here, suggest that a commonly accepted view of the origin of active region magnetic flux at the solar surface may have to be re-examined.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

A statistical study of the spiral spots on the solar disc

After adding the data observed in the years from 1979 to 1982 to those obtained earlier (Ding et al., 1981), we re-examine the previous results and conclude:

1. The longitudinal distribution of spiral spots on the solar disc is generally the same as that of sunspot groups with areas of S _p ≥ 400, but their active longitudes seem to be more concentrated.
2. The distribution of spiral patterns in the southern and northern hemispheres shows that the differential rotation may be a fundamental solar dynamo for the formation of the spiral spots.
3. The statistical directions of the emerging twisted magnetic vectors in the active regions in the southern and northern hemispheres are synchronously inverse with a period of about two years. This period seems to be detected in other solar observations.

     

Systematically Asymmetric Heliospheric Magnetic Field: Evidence for a Quadrupole Mode and Non-Axisymmetry with Polarity Flip-Flops

Recent studies of the heliospheric magnetic field (HMF) have detected interesting, systematic hemispherical and longitudinal asymmetries which have a profound significance for the understanding of solar magnetic fields. The in situ HMF measurements since the 1960s show that the heliospheric current sheet (HCS) is systematically shifted (coned) southward during solar minimum times, leading to the concept of a bashful ballerina. While temporary shifts can be considerably larger, the average HCS shift (coning) angle is a few degrees, less than the 7.2^∘ tilt of the solar rotation axis. Recent solar observations during the last two solar cycles verify these results and show that the magnetic areas in the northern solar hemisphere are larger and their intensity weaker than in the south during long intervals in the late declining to minimum phase. The multipole expansion reveals a strong quadrupole term which is oppositely directed to the dipole term. These results imply that the Sun has a symmetric quadrupole S0 dynamo mode that oscillates in phase with the dominant dipole A0 mode. Moreover, the heliospheric magnetic field has a strong tendency to produce solar tilts that are roughly opposite in longitudinal phase. This implies is a systematic longitudinal asymmetry and leads to a “flip-flop” type behaviour in the dominant HMF sector whose period is about 3.2 years. This agrees very well with the similar flip-flop period found recently in sunspots, as well as with the observed ratio of three between the activity cycle period and the flip-flop period of sun-like stars. Accordingly, these results require that the solar dynamo includes three modes, A0, S0 and a non-axisymmetric mode. Obviously, these results have a great impact on solar modelling.     

Non‐holonomic filamentary dynamos as generalized Arnold's maps in Riemannian space

A filamentary non‐holonomic dynamo solution of self‐induction magnetic field equation is found by considering highly conducting filaments. It is shown that planar filaments cannot support dynamo action since the flow along the filament vanishes for torsion‐free filaments. This is a generalization of the Zeldovich theorem for linear magnetic dynamo filaments. The flow of filament is proportionally to the product between Frenet torsion and curvature. This shows that filamentary dynamos must possess Frenet torsion. A well‐known example of this result is the α ‐dynamo in solar physics. Magnetic helicity and magnetic energy for this filamentary dynamo are computed. Magnetic helicity vanishes by construction and the magnetic field decays with torsion energy in helicoidal dynamos. The approach considered here is useful for the investigation of anisotropic turbulent cascades. As a particular simple example it is shown that under certain constraints the solution can be reduced to the Arnold cat dynamo map solution where the non‐holonomic directional mixed derivative, would play the role of the Lyapunov exponent which appears on stretching the magnetic field in Riemannian space. The solution seems to describe marginal slow dynamos when the velocities involved in the dynamo flows are constants. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.     

Velocity Characteristics of Rotating Sunspots

A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J. 646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h⁻¹. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.