The stability and eigen oscillations of sunspots

Abstract

One of the observational facts about sunspots is that magnetic field strength of sunspots varies in narrow interval $\approx$ from 1 to 4–5 kG. Why sunspot equilibrium is stable only under these values? To answer this question, we propose the energetic model of sunspot, which involves the gravitational energy of the system. Formation of a sunspot is followed by redistribution of gas density along the vertical: cooled plasma flows down, inside the “magnetic funnel”, from above the sunspot to the “low boundary of magnetic flux tube”, i.e. to the region where the magnetic field of sunspot decreases abruptly with depth. Theoretical model gives the interval of stable sunspot equilibria exactly between 0.8–1.0 and 4–6 kG, which suites the observations. The “depth of sunspot” turns to be about 2–4 Mm – this fact now is approved by helioseismology. Also, the long-term (T$\,{>}\,$20 min) eigen oscillations of sunspot, as a whole, are studied. These oscillations were measured by different methods, being observed as quasi periodical vertical displacements of the body of sunspot followed by variations of its radius and magnetic field strength.