Elementary sunspot energy model

Astronomy and Astrophysics – Astronomy

Scientific paper

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Gravitational Fields, Periodic Variations, Solar Magnetic Field, Sunspots, Magnetic Flux, Photosphere, Stellar Models

Scientific paper

An effort is made to explain the fact that the strength of the magnetic fields observed in spots varies in a quite narrow range (1000 to 4000 Oe). In addition, since a sunspot is a quite isolated and stationary formation, an effort is made to ascertain whether the spot as a whole has characteristic oscillations, and if so, what might be the period. The study is based on an analysis of the total energetics of the spot, but with emphasis on change in the gravitational energy of the plasma as a function of the depth of immersion of the spot into the photosphere. These problems are examined using a simple model of a sunspot in the form of a vertical magnetic cylinder plunged into the photosphere. Calculations reveal that the main contribution to spot energy is from change in the magnetic and gravitational energy of the system. The model made it possible to find the stable equilibrium state of a sunspot for a given magnetic flux. The equilibrium value of magnetic field strength in a spot was determined as a function of its depth (lower boundary) and some characteristics of the medium surrounding the spot. Finally, the effective depth of the spot was estimated. The period of the small free oscillations of the spot is T approx. = 5m.

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