Sunspots and large-scale magnetic fields at various heights

Height variation of the magnetic field structure over groups of sunspots for heights ranging from the photosphere to the source surface (R = 2.5 Ro, where Ro is the radius of the Sun) is examined. For all heights, starting from the photospheric level, groups of sunspot are shown as being independent of long-lived boundaries of large-scale structures rotating with a period shorter than the Carrington period. At heights of 1–1.5 Ro, there is a clear relation between sunspot groups and boundaries separating the head and tail sunspots in the groups (the Hale boundaries). The rotation periods of these structures are close to the Carrington period, their lifespan being less than three to five rotations. The maximal intensity of the solar magnetic field drops by two orders when height increases from H = 1 to H = 1.1 Ro. Further decrease in intensity proceeds gradually (dropping by one order from H = 1.1 to 2.5 Ro). The results obtained can be considered as evidence that large-scale magnetic field structures and long-lived boundries between them (the lines dividing polarities of the magnetic field or zero lines) all exist irrespective of sunspot fields being generated by other sources than sunspots. At the photospheric level, active regions fields are superimposed on these structures.     

Determining the spatial configurations of the coronal magnetic fields of solar active regions

The fundamental possibility of reliably removing the π ambiguity from the transverse magnetic field detected in solar vector magnetographic measurements, independent of the location of the vector magnetograms on the solar disk is demonstrated. The corrected magnetograms are then used as boundary conditions for the reconstruction of the three-dimensional magnetic field. The calculated field lines agree well with observed non-potential magnetic loops. The π ambiguity is removed using a modified Metropolis algorithm adapted to a spherical geometry. The spatial configuration of the magnetic field is calculated in a nonlinear force-free approximation using an optimization method. Tests of the new algorithm for resolving the π ambiguity are demonstrated for various model cases and comparisons with results of the NPFC method.     

Extrapolation of the solar magnetic field within the potential-field approximation from full-disk magnetograms

This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. The boundary conditions are specified by a distribution on the sphere of the projection of the magnetic field vector into a given direction, i.e., they exactly correspond to the data of daily magnetograms distributed across the full solar disk. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed with regard to the peculiarities of actual data. Results derived from calculating magnetic fields from real magnetograms are presented. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram.     

Relationship between the coronal holes and high-speed streams of solar wind

The relationship between two classes of coronal holes and high-speed quasi-stationary streams of solar wind at the Earth’s orbit is investigated. “Open” coronal holes, whose area is invariable or increases with the height over the solar surface, are rated in the first class, and “closed” coronal holes with areas decreasing with the height are referred to as second-class holes. The parameters of the coronal holes are determined from IR and EUV images and spectroheliograms. It is shown that most open coronal holes can be associated with high-speed solar-wind streams, while most closed coronal holes exhibit a much lower correlation with such streams.     

Study of the structure of streamer belts and chains in the solar corona

A comparison is made of polarization brightness distributions of the white-light corona based on the data from Mark III (MLSO) with calculated magnetic configurations in the corona (a potential-field approximation) between adjacent coronal holes (or associated open magnetic tubes) with magnetic fields of single polarity. It is shown that in these coronal regions, which were referred to as chains of streamers in earlier papers of these authors, magnetic structures in meridional and azimuthal cross-sections typically have the aspect of helmet streamers. The calculated magnetic field configurations under the helmets of chains of streamers have an even number of systems of arched features closely adjacent to each other (unlike the structure of the streamer belt with a neutral line where their number is odd). The height of the helmet top of chains of streamers remains smaller than that of the source surface but changes along the length of the chain and reaches maximum values at the ends of the chain.     

Structure of the magnetic field at altitudes of 1–1.15 solar radii

An analysis of the characteristics of unipolar structures detected at latitudes from ?40? to +40?, longitudes of 0??360?, and altitudes of 1–1.15 solar radii during the period from May 1996 (the 23rd solar minimum) to October 2000 (the 23rd solar maximum) has been carried out. Synoptic maps of the solar radial magnetic field calculated in a potential approximation are used. The boundaries between unipolar structures with opposite magnetic polarities (“+/?” and “?/+” polarities) form chains extending along meridians at all the considered latitudes and altitudes. Depending on the latitude, the single-peaked distributions of the number of structures found at the lowest altitudes are replaced by double-peaked distributions at higher altitudes. The time variations of the total number of structures are non-monotonic. The growth in the number of unipolar structures begins before the growth in the Wolf number. This indicates that new unipolar structures already appear together with flocculi, preceding the formation of sunspots. It is found that structures with positive field have larger mean sizes that do structures with negative field. The polar field in the northern hemisphere penetrates to middle latitudes of the southern hemisphere. The existence of sets of structures with typical sizes is shown. The sizes of the smallest structures vary little with latitude, but increase slightly with altitude.     

Magnetic field variations in the umbra of single sunspots during their passage across the solar disk

Temporal variations of the maximum (B _max) and average (〈B〉) magnetic inductions, minimum (α _min) and average (〈α〉) inclination angles of the field lines to the radial direction from the center of the Sun, and areas of the sunspot umbra S in the umbra of single sunspots during their passage across the solar disk are investigated. The variation of the properties of single sunspots has been considered at different stages of their existence, i.e., during formation, the “quiet” period, and the disappearance stage. It has been found that, for the majority of the selected single sunspots, there is a positive correlation between B _max and S and between 〈B〉 and S defined at different times during the passage of sunspots across the solar disk. It is shown in this case that the nature of the dependence between the parameters α _min and B _max, α _min and S, as well as between 〈α〉 and 〈B〉, 〈α〉 and S, can vary from sunspot to sunspot, but for many sunspots the inclination angle of the field lines decreases on average with the growth of the sunspot umbra area and the field strength.     

A flare of 23 September 1998: relation between temporal and spatial structures

Behavior of the flare in microwaves and other emissions is analyzed. Our study is based, for the first time, on Siberian Solar Radio Telescope imaging data along with other multi-spectral data. The development of the flare shows in height the magnetic structures that were successively involved. The flare was very complex. It consisted of several distinct phases and exhibited many interesting properties. The relationship between microwave sources and soft X-ray structures shows that the responsibility for the flare involves interaction of large-scale loops, whose orientation is strongly different from the potential one. Closer accordance of the potential magnetic field lines and fine structures observed in UV was achieved in the post-flare stage. The development of the flare looks like a `reversed movie' of the preceding evolution of the photospheric magnetic configuration.     

Temporal variations in the large-scale magnetic field of the solar atmosphere at heights from the photosphere to the source surface

Calculations of the magnetic field in the potential approximation (using Bd technology (Rudenko, 2001)) were used to study the time variations of several parameters of the large-scale magnetic field in the solar atmosphere during the last four cycles. Synoptic maps (SMs) for the radial component Br of the calculated magnetic field were plotted at 10 heights between the solar surface (R = R _⊙) and the source (R = 2.5R _⊙). On these SMs, we marked the 10-degree latitudinal areas. The following (averaged within the zone) characteristics of the magnetic field were determined corresponding to these zones: Sp, Sm; S _+fields , where Sp is the positive value of Br, Sm is the averaged modulus of the negative Br; S _+fields is the percentage of latitudinal zones with positive Br. The analysis of temporal variations in the magnitude of S points to different origins of the large-scale magnetic field in the near-equatorial and polar regions of the solar atmosphere. The analysis of temporal variations of S _+fields showed that there were almost no periods with a mixed polarity at R = 2.5R _⊙ during the 21st and 22nd solar cycles and in an ascending phase of the 23rd cycle. However, beginning from the maximum of the 23rd cycle, a mixed polarity in the equatorial region was observed until the end of the long minimum of activity. We hypothesized that this could be a precursor for a long minimum between the 23rd and 24th solar cycles. It was shown that during the maximum phase of the 24th solar cycle the magnetic field at R = R _⊙ is much less than that during the maximum phase of the 23rd cycle, and in the region from 55° to 75°, this difference reaches an order of magnitude.