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INTRODUCTION 

The solar activity consists of solar events outside of the realm of those characterizing a quiet Sun. These events have the visual form of sunspots and eruptions, during the time of which plasma is ejected from the interior of the Sun, affecting the immediate environment of Sun. As they are directly influencing the environmental conditions on Earth, their study and understanding is of primary importance for mankind. In 1908 Hale succeeded in correlating the sunspots with the existence of a magnetic field (Hale, 1908). Starting from around 1950, it has been realized that if the magnetic field is to play indeed a major role in the ejections of solar matter, it has to be, at least in part, a force-free field. In this case a solar ejection can be explained as a “rope of magnetic flux”, with twisting of magnetic lines due to initial conditions at the surface of the Sun, as in Figure 2 from the work of Gold and Hoyle (Gold, Hoyle, 1959):

The importance of this model of a solar prominence is that it shows that the matter acts somehow on magnetic field, causing an evolution of its lines. The description of this phenomenon, and generally the problem of dynamics of the magnetic field lines, turned out to be a special problem, not completely solved even to date (for a fairly recent review see (Longcope, 2005)). In particular, the hydrodynamics of the solar matter is thought to become important, but then the conditions of the magnetic flux tube under the surface of the Sun are to be guessed. As our phenomenological experience with hot plasma is quite limited, one can figure out that the theoretical description of solar activity is still an open problem, and will remain probably open for a long time. This is why we think that a rational suggestion for alternative solutions is welcome. For the present work we will appeal to the theory of Newtonian forces in order to get such a suggestion.

THE MODEL

Start with the observation that the sunspot formation seems to be a phenomenon varying at a cosmic time scale, as shown in Figure 1 from the work of Eddy, Gilman and Trotter (Eddy et al, 1976) which we reproduce here:

One can read on this figure that there are also some other periodicities of the sunspot phenomenon, as is the case indeed. There are possible longer quiet Sun periods, like that from A. D. 1645 to A.D. 1715 (the Maunder minimum), when the solar activity reduced practically to zero. Anyway, a basic periodicity of the solar activity of around a decade (more exactly, 11 years), regardless of the amplitude of the number of sunspots seems to be in order, and places the phenomenon among the periods of revolution of the planets of solar system.

The order of magnitude of these periods, as well as the order of magnitude of maxima of the number of sunspots, seems to indicate external cosmic sources of this solar activity, acting upon the matter of Sun according to the Newtonian theory of central forces. However, this explanation cannot be understood if we limit the central forces only to those with magnitude depending exclusively on the distance between bodies. Rather, we have to give these forces the freedom assumed by their very first definition from Principia, whereby their magnitude can very well depend on their direction. There are thus situations among the observed celestial motions, where the source of central force is outside the elliptical orbit.

According to this model, an external source of force (galactic center, the matter along the galactic arm, some external stellar formation or even the planets) determines a part of the matter of Sun to move in an organized mode inside the Sun, and that motion has the space shape of an ellipse, due to the centrality of the force. If this source of force is in motion, then the ellipse itself evolves, to the point where part of it is gets into corona, and further goes into a parabolic and then hyperbolic shape. The mass is thus ejected or perhaps cumulated by Sun, as the case may be. This classical natural philosophy seems to be also indicated by the curve-fit for the geometrical shapes for some recent coronal ejection events of limited height (Byrne et al., 2009). This work even suggests a certain kinematics of the magnetic field lines monitored by the parameters of ellipses that fit visible lines of the ejection. As a matter of fact, this is the whole idea of evolution of the lines, only this evolution should be dictated by the external source of force which generated the motion inside the Sun in the first place.

SOLAR SYSTEM AS A WHOLE

The Newtonian central force gives a physical explanation of the old idea of Copernicus that the solar system is the sheer image of cosmic harmony. This harmony requires a certain interaction of the parts of a whole - in this case the solar system - and this Newtonian theory of Sun perturbations allows us to assign the periodicities of sunspot phenomenon to a part of the planets. The idea is not at all new (Schwentek, Elling, 1984; Grandpierre, 1996; Charvátová, 2000 ). What we really want to show is that it has a physical explanation of the same nature with the physical explanation of Kepler laws, from which it all began in modern science.

According to this image of the solar system the external giant planets regulate the different periodicities in the solar activity. Thus, Jupiter can be taken as a regulator of the 11 years period, because its revolution is done in about 12 years; Saturn can be taken as determining the Hale cycle (some 22 years), because its period of revolution is about 29 years, and Uranus can be correlated with the Gleissberg cycle (87 years) because its revolution around the Sun takes some 84 years. Neptun could also be related to Suess-de Vries cycle (210 years - 164 years). In view of the great indecision of the periodicities of the solar activity (for a review see for instance the page of Timo Niroma), one can say that it may be safer to ascribe the periods of solar activity to Jovian planets, according to the Newtonian theory of central forces.

Thus, whatever the mechanism of birth of these interior solar structural accidents may be, their ensemble can be described as a superposition of “harmonics” of different periods. These periods are regulated by the external planets of the solar system. Probably different planets “modulate” somehow the process of multiplication of internal solar accidents, by acting upon the mechanism of interaction between the different magnetic lines inside a flux tube. In this process of modulation, the classical Hannay angle of the flux of line is the essential variable to be used by the theory.

CONCLUSIONS

Having accepted this role of outer planets in the solar economy, one starts wonder about the role of interior planets. Perhaps there are periodicities to be assigned to their periodical motion. But perhaps these periodicities are not as important as the role of these planets in giving birth to at least a category of internal Sun perturbations, close to the surface of Sun. Only at a certain stage from the life of these perturbations enter outer planets the stage by starting the ”modulation” the process of multiplication.

REFERENCES

Byrne, J. P. et al (2009): The Kinematics of Coronal Mass Ejections Using Multiscale Methods, Astronomy and Astrophysics, Vol. 495, pp.325-334; arXiv:astro-ph/0901.3392v1

Charvátová, I. (2000): Can Origin of the 2400-year Cycle of Solar Activity be caused by Solar Inertial Motion?, Annales Geophysicae, Vol. 18, pp. 399 – 405

Eddy, J. A., Gilman, P. A., Trotter, D. E. (1976): Solar Rotation During the Maunder Minimum, Solar Physics, Vol. 46, pp. 3 – 14 

Gold, T., Hoyle, F (1959): On the Origin of Solar Flares, Monthly Notices of the Royal Astronomical Society, Vol. 120, pp. 89–105

Grandpierre, A. (1996): On the Origin of Solar Cycle Periodicity, Astrophysics and Space Science, Vol. 243, pp. 393 – 400

Hale, G. E. (1908): Solar Vortices, The Astrophysical Journal, Vol. 28, pp. 100 – 116

Longcope, D. W. (2005): Topological Methods for the Analysis of Solar Magnetic Fields, Living Reviews in Solar Physics, 2 (2005) 7; http://www.livingreviews.org/lrsp-2005-7

Schwentek, H., Elling, W. (1984): A Possible Relationship Between Spectral Bands in Sunspot Number and the Space-Time Organization of Our Planetary System, Solar Physics, Vol. 93, pp. 403 – 413