Statistical Studies on the Physical Parameters and Oscillations of Sunspots and Flares

We perform three statistical studies on the physical properties and oscillations in the confined plasma such as a photospheric sunspot and confined coronal loop. From the statistical studies on the sunspot umbra and its oscillation, we find that (1) the total magnetic flux inside the umbra for the three groups increases proportionally with the powers of the umbral area and the power indices in the three groups significantly differ from each other; (2) the three groups have different characteristics in their umbral area, intensity, magnetic field strength, and Doppler velocity as well as their relationships; (3) the mean frequency of the umbral oscillations increases with the umbral mean magnetic field strength and height; (4) the time delay of the core intensity of Fe I absorption line relative to the continuum which are de-convolved with the frequency range higher than 3.5 mHz is mostly positive, implying that the photospheric umbral oscillations are likely upwardly propagating; (5) the umbral mean plasma beta ranges approximately 0.6-1.1 and does not vary significantly from pores to mature sunspots. From the comparative study on the quasi-periodic pulsations (QPPs) in the solar and stellar flares, (6) we find that the power index of the periods scaling the damping times observed in the stellar QPPs is consistent with that observed in the solar QPPs, suggesting that physical mechanisms responsible for the stellar QPPs are likely the magneto-hydrodynamic oscillation of solar coronal loops.