Long-Term Changes of Polar Activity of the Sun

We discuss long-time changes of polar activity of the Sun using the new observational data sets in the optical range during 1872–2001. A study of the secular and cycle variations of the magnetic activity at the high-latitude regions is the main goal that includes polar magnetic field reversals during 1872–2001 and secular changes of the duration of polar activity cycles. The secular increase of the area of polar zones during the minimum activity in the last 120 years and as consequence a decrease of coronal temperature of the Sun in the high-latitude zones during the last 50 years. Correlation between the polar cycles of Caii-K bright points with the Wolf sunspot numbers cycles, W(t), and the 22-year polar magnetic cycles of Caii-K bright points at the high latitudes during 1905–1995 is discussed.     

Generalized polytropes: Stellar structure with a boltzmann factor

In order to study the structure of a chemically homogeneous star in equilibrium, a density profile of the form T ^N exp(–µm(–)/kT) is suggested. As for polytropes, qualitative aspects of the resulting stellar model can be discussed analytically. In particular it is shown that one reobtains forN=3 Eddington's standard model, whereas forN<3 nearly polytropic models result. WhenN>3, the effective polytropic index does vary appreciably over the star. Numerical results indicate that the proposed density profile is quite reasonable in view of the simplicity of the model. From a comparison of the degree of precision of a polytropic approximation with that of the newly proposed model it follows that the new approximation is definitely better than the polytropic one. It is suggested that the model may be useful to study the structure of stellar clouds, clusters and (spherical) galaxies.Now at Department of Applied Mathematics, Queen Mary College, University of London, England.     

Increase of the Magnetic Flux From Polar Zones of the sun in the Last 120 Years

Lockwood, Stamper, and Wild (1999) argued that the average strength of the magnetic field of the Sun has doubled in the last 100 years. They used an analysis of the geomagnetic index aa. We calculated the area of polar zones of the Sun, A _pz, occupied by unipolar magnetic field on H synoptic magnetic charts, following Makarov (1994), from 1878 to 2000. We found a gradual decrease of the annual minimum latitude of the high-latitude zone boundaries, _2m, of the global magnetic field of the Sun at the minimum of activity from 53° in 1878 down to 38° in 1996, yielding an average decrease of 1.2° per cycle. Consequently the area of polar zones A _pz of the Sun, occupied by unipolar magnetic field at the minimum activity, has risen by a factor of 2 during 1878–1996. This means that the behavior of the index aa and consequently the magnetic flux from the Sun may be explained by an increase of the area of polar caps with roughly the same value of the magnetic field in this period. The area of the unipolar magnetic field at the poles (A _pz) may be used as a new index of magnetic activity of the Sun. We compared A _pz with the aa, the Wolf number W and A^* -index (Makarov and Tlatov, 2000). Correlations based on `11-year' averages are discussed. A temperature difference of about 1° between the Maunder Minimum and the present time was deduced. We have found that the highest latitude of the polar zone boundaries of the large-scale magnetic field during very low solar activity reaches about 60°, cf., the Maunder Minimum. It is supposed that the _2m-latitude coincides with the latitude where _r=0, with (r,) being the angular frequency of the solar rotation. The causes of the waxing and waning of the Sun's activity in conditions like Maunder Minimum are discussed.     

A class of semi-analytical solutions for a rotating toroidal plasma

In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P _s andf ² are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.     

Pulsation,rotation and sunspot cycle

A suggestion is made that the periods for solar pulsation, solar rotation, and sunspot cycle may be closely related one to another.     

Stellar structure with a Boltzmann factor: An extension to chemically heterogeneous H−He-stars

We present an attempt for an extension of the modified Boltzmann model, which was introduced by Callebautet al. (1982) as an improvement of the polytropic models, to the case of chemically-heterogeneous stars in equilibrium, containing H and He, by proposing a density profile of the formp=C ₁ T ^N exp (–_H m(–_*)/kT) +C ₂ T ^N exp (–_He m(–_*)/kT. Analytical properties are derived and numerical as well as analytical arguments are presented for the conclusion that this hypothesis for a density profile imposes an almost constant chemical profile to the model as a whole, thereby making it in this form unsuited for the study of heterogeneous stars. A comparison is made with the former Boltzmann model in the homogeneous limit.     

Temperature of Polar Corona of the Sun According to Kislovodsk Observations During 1957–2002

We continued a study of the long-term variations of temperature in the solar corona at all latitudes (Makarov, Tlatov, and Callebaut, 2002a). The series of the green (Fe xiv 530.3 nm; KI₅₃₀₃) and red (Fe x 637.4 nm; KI₆₃₇₄) coronal intensities for 1957–2002 has been obtained using the coronal observations at the Kislovodsk Solar Station. The mean monthly coronal intensities have been calculated at all latitudes (0–90^˚) and in the high latitude (45–90^˚) zones. It was found that the value of KI₆₃₇₄/KI₅₃₀₃increased about 2.0 times at the high latitudes during the last 45 years. This corresponds to a decrease of the average temperature by 0.1 ×10⁶K of the polar corona. We suppose that a polar decrease of coronal temperature is connected with an increase of the area of polar zones A _PZoccupied by unipolar magnetic fields (Makarov et al., 2002) and, probably, with an increase of the area of polar coronal holes. The maximum ratio KI₆₃₇₄/KI₅₃₀₃is observed during the minimum sunspot activity.     

LONG-TERM VARIATIONS OF THE TORSIONAL OSCILLATIONS OF THE SUN

We investigated long-term variations of the differential rotation of the solar large-scale magnetic field on 1024 H charts in the latitude zones from +45° to -45° in the period 1915–1990. We used the expansion in terms of Walsh functions. It turns out that the rotation of the Sun becomes more rigid than average during the cycle maximum and the rotation is more differential during minimum. From 1915 to 1990, 7 bands of faster- and 7 bands of slower-than-average rotation are revealed showing an 11-year period. These bands drift towards the equator: 45° in 2.5 to 8 years. The time span of the bands varies from 4 to 6.8 years and is in anti-phase with long-term solar activity. The latitude span of the bands of torsional oscillations varies from 0.5 R to 1.3 R and shows a long-term variation of about 55 years. The poloidal component of velocity, V varies from 2 ms ^-1 to 6 ms ^-1. The maximum rate of the equatorial drift occurs in the period between 1935 and 1955 and it develops prior to the highest maximum activity. At the modern epoch from 1965 to 1985, V does not exceed 3 ms ^-1, but now it has a tendency to increase. The bands of slower-than-average rotation correspond to the evolution of the magnetic activity towards the equator in the butterfly diagram.     

Latitude-time distribution of 3 types of magnetic field activity in the global solar cycle

Large-scale solar activity is considered as a manifestation of 3 types of magnetic field activity which is demonstrated in the 22-year cycle (a) of small-scale flux emergence (polar faculae at latitudes > 40°), (b) of somewhat larger scale flux emergence (sunspots at latitudes < 40°), and (c) of the global magnetic neutral lines at all latitudes. The migration (poleward or equatorward) of the place of birth and/or of the phenomena themselves of these three types of manifestation of magnetic field is discussed. The poleward migration of the global field is explained in a phenomenological way.     

Prediction of peaks in wolf numbers in cycle 24 according to actual numbers of polar faculae

Previous investigations by Makarov et al. have shown a relation between the peaks in the number of polar faculae and the peaks in the Wolf number. In cycles 20 and 22 the delay between peaks in polar faculae and Wolf number was 6.1 ± 0.1 year, north and south taken separately, as their peaks do not coincide. For the odd cycle 21, this shift was 5.6 years average. Polar faculae always precede the sunspots. The relevance of this for the dynamo mechanism is obvious. In cycle 23 the delay was 7.7 year (north) and 7.8 year (south). The approach of a deep minimum is probably responsible for this increased delay; thus for cycle 24 the delay between peaks of polar faculae and sunspots is expected to be at least 7.8 years and probably longer. The present polar faculae show 6 peaks above the smoothed average (north) and similarly 3 peaks south. The first peak for the sunspots will be at the earliest during the very end of 2007. As soon as one peak in the spots occurs the delay for cycle 24 can be estimated and the other peaks predicted.