Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

Studies of solar magnetic fields

Solar Physics - The telescope, spectrograph, and magnetograph at the 150-ft Tower Telescope are described, and a chronology of changes in the instrumentation is given. The average magnetic field...     

Studies of solar magnetic fields

In order to provide a smooth transition to a smaller aperture for the Mount Wilson daily magnetograms, a 2-step change was made, with two daily observations made using two different apertures covering an interval of several months. A comparison of these observations has made possible a check on the zero-level and calibration errors of the Mount Wilson magnetograph in recent years, and it has shown that an interval of low measured total magnetic flux resulted at least in part from an increase in the mixing of magnetic elements of the two polarities on a scale comparable with the aperture size.     

Studies of solar magnetic fields

An estimate of the average magnetic field strength at the poles of the Sun from Mount Wilson measurements is made by comparing low latitude magnetic measurements in the same regions made near the center of the disk and near the limb. There is still some uncertainty because the orientation angle of the field lines in the meridional plane is unknown, but the most likely possibility is that the true average field strengths are about twice the measured values (0–2 G), with an absolute upper limit on the underestimation of the field strengths of about a factor 5. The measurements refer to latitudes below about 80°.     

Studies of solar magnetic fields

Magnetic flux data from the Mount Wilson magnetograph are examined over the interval 1967–1973. The total flux in the north is greater than that in the south by about 7% over this interval, reflecting a higher level of activity in the northern hemisphere. Close to 95% of the total flux is confined to latitudes equatorward of 40°, which means that close to 95% of the flux cancels with flux of opposite polarity before it can migrate poleward of 40°. It is pointed out that a consequence of this flux distribution is that ephemeral regions must make a negligible contribution to the long-term largescale magnetic flux distribution. A broad peak in the total flux may be seen centered about one year after activity maximum in the north below 40°. In the south there is a very sharp increase in flux about the same time. In the north, several poleward migrations of flux may be seen. Two of these may correspond with the two poleward prominence migrations seen by Waldmeier. In both the north and the south there is a poleward migration of negative flux about the time of activity maximum. Poleward flux drift rates are about 20 m s^?1.     

High latitude solar magnetic fields

We use Kitt Peak magnetograms to measure polar magnetic fields. The polar mean absolute field increases at the same time as the polar mean field decreases. That is, the polar mean absolute field varies in phase with solar activity, in contrast to the out of phase variation of the mean polar field. We find that the polar fields have a large bipolar component even at solar minimum, with a magnitude equal to that found at low latitudes outside the active latitude bands.     

A search for the footpoints of solar magnetic fields

Solar Physics - High-resolution measurements of magnetic fields have been made in quiet and active regions in order to determine whether the photospheric fine-structures (‘crinkles’),...     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Open magnetic fields and the solar cycle

Models of open magnetic structures on the Sun are presented for periods near solar minimum (CR 1626–1634) and near solar maximum (CR 1668–1678). Together with previous models of open magnetic structures during the declining phase (CR 1601–1611) these calculations provide clues to the relations between open structures, coronal holes, and active regions at different times of the solar cycle. Near solar minimum the close relation between active regions and open structures does not exist. It is suggested that near solar minimum the systematic emergence of new flux with the proper polarity imbalance to maintain open magnetic structures may occur primarily at very small spatial scales. Near solar maximum the role of active regions in maintaining open structures and coronal holes is strong, with large active regions emerging in the proper location and orientation to maintain open structures longer than typical active region lifetimes. Although the use of He I 10830 Å spectroheliograms as a coronal hole indicator is shown to be subject to significant ambiguity, the agreement between calculated open structures and coronal holes determined from He I 10830 Å spectroheliograms is very good. The rotation properties of calculated open structures near solar maximum strongly suggest two classes of features: one that rotates differentially similar to sunspots and active regions and a separate class that rotates more rigidly, as was the case for single large coronal holes during Skylab.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.     

Seismic tomography of the near solar surface

Surface gravity waves have been used to probe flows in the two megameters beneath the photosphere using the techniques of timedistance helioseismology. The results suggest that supergranule velocities are smaller than at the surface. The outward flow outside a sunspot penumbra (the moat) is observed, as is an inward flow in the region beyond the moat.     

Correlation between magnetic shear and magnetic tension in a solar active region

The difference between the magnetic tension and magnetic shear was calculated for four vector magnetograms of NOAA AR 4474. It was seen that this difference between the two independent angular measures of magnetic stress is less than 18° for more than 50% of the pixels. Magnetic tension is thus found to be fairly well correlated with magnetic shear for AR 4474.     

Fine structure of solar magnetic fields

The problem of inequality of results of longitudinal magnetic fields measured in the magnotosensetive lines FeI 5250 and FeI 5247 is investigated. The observed ratio of longitudinal components of magnetic field H ₁₁(5250)/H ₁₁(5247) is compared to the calculated for different combinations of magnetic field elements. The calculations have been made with standard model photosphere for quiet regions. It was concluded that the underestimated value of magnetic field obtained with the FeI 5250 line is explained by the presence of unresolved elements with kilogauss magnetic fields.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

Fine structure of solar magnetic fields

The deduction of magnetic fields from chromospheric structure is extended to active regions and transverse fields. Fields independently predicted by these rules from a high resolution H filtergram are compared with a high resolution magnetogram. The H method has the advantage over conventional magnetograms that it shows transverse fields and relates the fields to the real Sun. It has the disadvantage that higher spatial resolution is required and that it is difficult and time consuming in very complicated regions.The response of the chromosphere to magnetic fields is most consistent. Vertical field is invariably marked by bright plage, with brightness roughly proportional to the field strength (except for sunspots). All dark fibrils mark transverse fields and are parallel to field lines. All polarity changes are marked by dark fibrils, which may be transverse fibrils perpendicular to the field boundary, or filaments (prominences) which connect more distant points, and in which the field lines run nearly parallel to the boundary. The asymmetry between preceding and following polarity found by Veeder and Zirin (1970) does not exist; it was due to the low resolution of the Mount Wilson magnetograms.The complexity of active region field structure depends on the history of the region; all flux erupts in simple bipolar form, and lines of force remain connected to sibling spots until reconnection takes place. Thus the complex structure only occurs after eruption of several dipoles which reconnect. The phenomenon of inverted polarity turns out to be due to the emergence of satellite bipolar fields, where the p spot merges with the rest of the p field and the f spot appears as an included f field. Flares usually occur when the field lines from f spot reconnect from its sibling to the main spot.     

Videomagnetograph studies of solar magnetic fields

Observations of magnetic field diffusion in weak plage regions have been made using the analog videomagnetograph at the California Institute of Technology. Points of magnetic flux, usually described as vertex points of the magnetic network, were found to have a mean lifetime of three to four days, and to disperse primarily by means of two mechanisms: a random walk with a step time short compared to 24 h, and a sudden transport of magnetic flux over distances of 5000 to 20000 km during a time span of one to three hours. The second mechanism is probably the predominant one. Similar observations have been made using K₃ spectroheliograms.     

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.     

Observations of small-scale solar magnetic fields

Spectrograms, obtained during moments of good seeing with the high spatial resolution afforded by the 80-cm solar image at the Kitt Peak National Observatory, show the following:

1. (1)
   Magnetic fields of several hundred gauss occur in tiny areas easily as small as 500 km in extent in regions of the solar surface sometimes well removed from areas of sunspot activity.     
   
   

On the small-scale structure of solar magnetic fields

The small-scale structure of solar magnetic fields has been studied using simultaneous recordings in the spectral lines Fe i 5250 Å and Fe i 5233 Å, obtained with the Kitt Peak multi-channel magnetograph. We find that more than 90% of the magnetic flux in active regions (excluding the sunspots), observed with a 2.4 by 2.4 aperture, is channelled through narrow filaments. This percentage is even higher in quiet areas. The field lines in a magnetic filament diverge rapidly with height, and part of the flux returns back to the neighbouring photosphere. Therefore the strong fields within a magnetic filament are surrounded by weak fields of the order of a few gauss of the opposite polarity. The field-strength distribution within a filament, including the surrounding opposite-polarity fields, seems to be almost the same for all filaments within a given active or quiet region.The analysis of a scan made during an imp. 2 flare showed that observations during and after the flare would give a fictitious decrease of the magnetic energy in the region by a factor of 2–3 due to line-profile changes during the flare.Visiting Astronomer, Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Surface magnetic fields during the solar activity cycle

We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s^-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.