Large-scale magnetic fields in discs with strong differential rotation

The evolution of a large-scale magnetic field is considered in the non-linear dynamo situation in discs with α-effect due to non-mirrorsymmetric turbulence and with strong differential rotation. The maximal value of the field strength is estimated by using an idealized dependence of the α-coefficient on the field strength. It is assumed that α is a positive constant if the field strength is below, and equal to zero if the field strength is above a certain critical value. On natural assumptions it can be concluded that the maximal value of the field strength exceeds that critical value by about one power of ten.     

Reorientation of global coronal magnetic fields due to differential rotation

Because of the progressive decrease in rotation rate of the solar plasma at increasing latitudes, the photospheric foot-points of large-scale closed magnetic structures in the corona, which are originally widely separated in longitude, may ultimately be brought into proximity. Magnetic mergers and reconnections between magnetic fields of opposite polarity are presumed to occur, producing major structural changes in the corona and in the locations of underlying filaments. Thus we believe that the differential rotation phenomenon is essential to understanding both gradual (evolutionary) and sudden (transient) changes in the corona, and that they can occur without any observable change in the photospheric magnetic flux. A process is suggested for the splitting or bifurcation of a high-latitude magnetic structure, producing two separate components at the same latitude, whose rotation rates are influenced by their respective magnetic linkages to other regions on the Sun.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the relationship between magnetic fields and supergranule velocity fields

We studied the size, correlation lifetime and horizontal velocity amplitude of supergranules in regions with different magnetic activity. We found that the supergranule velocity cells have similar scale, correlation lifetime and horizontal velocity amplitude in the unipolar enhanced magnetic network regions and in the mixed-polarity quiet Sun. However, the correlation lifetime of magnetic structure is much longer in the enhanced network. We investigated the velocity pattern of moving magnetic features (MMF) surrounding a decaying sunspot. The velocity of MMFs is consistent with the outflow surrounding the sunspot as measured by Dopplergrams. The velocity cell surrounding the sunspot has a much larger velocity amplitude and a longer lifetime than regular supergranule cells. We found that ephemeral regions (ER) have a slight tendency to emerge at or near boundaries of supergranules. Almost all the magnetic flux disappears at the supergranule boundaries. In most cases, two poles of cancelling features with opposite magnetic polarities approach along the boundaries of supergranules.     

Imbalance of magnetic fields on the Sun

Differences of magnetic field flows of “+” and “?” polarities, i.e. the imbalance of magnetic fields for 26 years—from January 1, 1977, to September 30, 2003—are investigated,. The synoptic maps of the longitudinal vector of Sun’s magnetic field strength obtained at the Kitt Peak National Observatory (United States) and kindly given to us by Dr. J. Harvey have served as the initial material. The imbalance of magnetic fields’ cyclicity features and the deviations from the dipole structure of Sun’s magnetic field are determined. The contribution of latitude zones and fields of various strength into the general magnetic flux from the Sun is found. The latter characteristic was compared with the Sun’s mean magnetic field (MMF) obtained from the observations of the Sun as a star (Kotov et al., 2002; Kotov, 2008). The obtained results testify that the imbalance is one of physical characteristics of the Sun. The confirmations of this conclusion are the strict regularities of the Sun’s dipole structure changing; the complicated character of the imbalance cyclicity, i.e., the multiplicity of cycles; the solar nature of MMF changing; and the distinction between two classes of magnetic fields in the imbalance characteristics.     

On the relation between the synodic and sidereal rotation period of the Sun

It is pointed out that by taking Kepler's second law into account, the sidereal correction, i.e., the correction to be added to the observed synodic rotation rate of the Sun in order to get the sidereal rate, can be calculated more directly than described in a recent paper by Roa et al. (1995).     

Magnetic field and differential rotation in the radiative zone of the Sun

The problem of the interaction between magnetic fields and differential rotation in the radiative zone of the Sun is investigated. It is demonstrated that effects of magnetic buoyancy can be neglected in the analysis of this interaction. It is shown that hydromagnetic torsional waves propagating from the solar core cannot be responsible for the 22-year solar cycle. A possible geometry of the magnetic field that conforms with stationary differential rotation is considered. A verifying method for hypotheses on the structure of the magnetic field and torsional oscillations in the radiative zone of the Sun is proposed based on helioseismic data.     

Modelling the magnetic field and differential rotation effects for the vicinity of the base of convective zone in the Sun

In this work, some numerical solutions of magnetohydrodynamics equations are investigated in the presence of differential rotation with the use of previously developed algorithm. This algorithm includes the thin shell approximation and a special separation of variables which were used to obtain the radial and latitudinal variations of physical parameters in spherical coordinates. The magnetic field profile is chosen to produce comparable magnetic fluxes found in previous works. The sphericity and density shape parameters relevant to model is determined by using two different known differential rotation profiles. It is found that the shape of variations in physical parameters is strongly dependent to magnetic field profile and there is a considerable change in density with respect to reference model. It is as well shown that the spherical symmetric distributions of physical parameters are broken for the region of study.     

Evidence for non-potential magnetic fields in the quiet Sun

A comparison of BBSO H centerline filtergrams and videomagnetograms was made to investigate the existence of non- potential magnetic fields in the quiet Sun near magnetic network. We use the fibril structure in the H images as a proxy for the horizontal chromospheric magnetic field which we compare with the horizontal field obtained by potential extrapolation of the observed, line-of-sight photospheric field. The quiet-Sun field was found to be consistently and significantly non-potential in each of the three fields of view studied. A transient extreme ultraviolet (EUV) brightening, known as a blinker, occurred during the observations of a region where the field is highly non-potential, suggesting a connection between magnetic reconnection and non-potentiality.     

Convective intensification of magnetic fields in the quiet Sun

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B _e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B _p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealized numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and characterized by a pattern of vigorous, time-dependent, 'granular' motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localized concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B _e and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contains ultraintense magnetic fields that are significantly greater than B _p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultraintense fields develop owing to non-linear interactions between magnetic fields and convection; they cannot be explained in terms of 'convective collapse' within a thin flux tube that remains in overall pressure equilibrium with its surroundings.     

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.     

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.     

Coronal magnetic fields from faraday rotation observations

In the first part of this communication we briefly summarize the results of the first observation of linear polarization in the microwave emission above a solar active region obtained with the Westerbork Synthesis Radio Telescope, taking advantage of the very narrow bandwidths of a multi-channel spectral line receiver. The intensity of the Stokes parameterU, measured at several points close to the line of zero circular polarization, showed a clear sinusoidal trend as a function of ², in accordance to what is expected from Faraday rotation (Alissandrakis and Chiuderi Drago, 1994). Combining the measured period of the Faraday rotation with the observed deplacement of the depolarization line with respect to the photospheric neutral line, the height above the photosphere of the depolarization point and the value of the electron density and the magnetic field at this point are computed. Although the calculations are done in the very simplified assumptions of a bipolar magnetic field and of a density following hydrostatic equilibrium, they represent the first estimate of the coronal magnetic field in an active region, far from sunspots.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

White dwarfs with magnetic field and differential rotation

We compute classical white-dwarf models distorted by magnetic field and differential rotation. In the computations we implement a complex-plane strategy and a multiple-partition technique, which have been developed recently by the first author.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Photospheric magnetic field rotation: Rigid and differential

An autocorrelation of the direction of the large-scale photospheric magnetic field observed during 1959–1967 has yielded evidence that the field structure at some heliographic latitudes can display both differential rotation and rigid rotation properties.     

Polar magnetic fields of the Sun: 1960–1971

Observations of the magnetic fields in the polar regions of the Sun are presented for the period 1960–1971. At the start of this interval the fields at the two poles were consistently of opposite sign and averaged around 1 G. Early in 1961 the field in the south decreased suddenly and the field in the north decreased in strength slowly over the next few years. By the mid-1960's the fields at both poles were quite weak and irregular. Throughout the period of these observations the fields at both poles often showed a remarkable tendency to vary in unison. About the middle of 1971 the north polar field became significantly positive, first at lower latitudes, then above 70 °. An autocorrelation analysis of the polar fields in the north shows a weak rotation peak, indicating significant features in these regions. A comparison of field strengths in the east and west quadrants in the north suggests that even at the extreme polar latitudes the following polarity fields are inclined slightly toward the rotation and the preceding polarity field lines are inclined slightly to trail the rotation.     

Differential rotation and sector structure of solar magnetic fields

The differential rotation and sector structure of solar magnetic fields has been studied using digitized data on photospheric magnetic fields recorded at the Mount Wilson Observatory during the period August 1959–May 1970. The power spectra show considerable power in high-frequency peaks, corresponding to harmonic components with wavelengths less than 1/10 solar rotation. Calculations for a series of shorter time intervals show how the distribution of power over the various harmonic components in the sector pattern varies strongly with the solar cycle. The equatorial rotation rate of solar magnetic fields is about 0.1 km s^-1 faster than that of the photospheric plasma determined from Doppler shifts. It is shown that the Doppler measurements mainly refer to the non-network regions. The differential flow of 0.1 km s^-1 forms streamlines around the magnetic fine structures. The different rotation rates of various solar features can be explained in terms of the rotation rates of magnetic and non-magnetic regions. The rotation rates of the magnetic fields in active and quiet regions agree at the equator. At higher latitudes, however, the background fields deviate less from solid-body rotation, indicating that their source is below the deepest layers to which the sunspot magnetic fields penetrate. This suggests that turbulent diffusion of the field in old active regions may not be the main source for the background magnetic field, but that the source is located close to a rigidly rotating solar core with a synodic rotation period of 26.87 days.     

The relation between the synodic and sidereal rotation period of the Sun

The relation between the synodic and sidereal rotation period of the Sun for an arbitrary date of observation is derived taking into account details of the Earth's motion. The transformation procedure between the synodic (apparent) and sidereal rotation period presented here can be performed without using the annual ephemerides.     

Differential rotation and the structure and energy content of coronal magnetic fields

It is argued that differential rotation of the photospheric magnetic fields will induce currents in the corona. The work done against surface magnetic stresses will increase the energy content of the coronal magnetic field. The electrical conductivities are high and the foot points of field lines move with the differential rotation. The force-free field equations are solved with this constraint to obtain a minimum estimate of the energy increase for a quadrupole field. During a solar rotation the magnetic energy increases by 25%. Local release of this energy in the corona would have a significant effect. The expansion of field lines as a result of the differential rotation should increase the amount of flux and the field strength in the solar wind region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Lifetime,age, and rotation of coronal magnetic fields

The rotation of the solar electron corona is determined for intervals when nearly periodic variations dominated the polarization brightness record during 1964–1976. Coronal rotation rates derived for 765 intervals vary with height, latitude, and interval length. These rotation rates show a decrease of differential rotation with height and support earlier rotation studies which included much less stationary data. Analyses of the selected intervals and autocorrelation of the complete K-coronameter data set give quantitative estimates of the rotational effects of magnetic tracer age and lifetime. The principal effects detected are a relatively fast rotation of very long-lived tracers at high latitude and a relatively fast rotation of very short-lived tracers at low latitudes. The observations indicate that high-to-low latitude magnetic connections extending through the corona speed up rotation at high latitudes and retard it at low latitudes.