Long-period oscillations of active region patterns: least-squares   mapping on second-order curves
  Active regions (ARs) are the main sources of variety in solar dynamic events. Automated detection and identification tools need to be developed for solar features for a deeper understanding of the solar cycle. Of particular interest here are the dynamical properties of the ARs, regardless of their internal structure and sunspot distribution. We studied the oscillatory dynamics of two ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern recognition. We developed a novel method of automated AR border detection and compared it to an existing method for the proof-of-concept. The first method uses least-squares fitting on the smallest ellipse enclosing the AR, while the second method applies regression on the convex hull.} After processing the data, we found that the axes and the inclination angle of the ellipse and the convex hull oscillate in time. These oscillations are interpreted as the second harmonic of the standing long-period kink oscillations (with the node at the apex) of the magnetic flux tube connecting the two main sunspots of the ARs. In both ARs we have estimated the distribution of the phase speed magnitude along the magnetic tubes (along the two main spots) by interpreting the obtained oscillation of the inclination angle as the standing second harmonic kink mode. After comparing the obtained results for fast and slow kink modes, we conclude that both of these modes are good candidates to explain the observed oscillations of the AR inclination angles, as in the high plasma $\beta$ regime the phase speeds of these modes are comparable and on the order of the Alfv\'{e}n speed. Based on the properties of the observed oscillations, we detected the appropriate depth of the sunspot patterns, which coincides with estimations made by helioseismic methods. The latter analysis can be used as a basis for developing a magneto-seismological tool for ARs. 
G. Dumbadze, B.M. Shergelashvili, V. Kukhianidze, G. Ramishvili, T.V.   Zaqarashvili, M. Khodachenko, E. Gurgenashvili, S. P...
astro-ph.SR astro-ph.EP astro-ph.IM physics.data-an physics.flu-dyn