Temporal and Periodic Analysis of Penumbra–Umbra Ratio for the Last Four Solar Cycles

Abstract

We investigate the long-term dynamic behavior of the sunspot penumbra to umbra area ratio by analyzing the Debrecen Photoheliographic Data (DPD) of sunspot groups during the period 1976–2017 (Solar Cycles 21–24). We consider all types of spots and find that the average penumbra–umbra ratio does not exhibit any significant variation with spot latitudes, solar-cycle phases as well as sunspot-cycle strengths. However, the behavior of this ratio is different when we consider the latitudinal distribution of the northern and southern hemispheres separately. Our analysis indicates that for daily total sunspot area the average spot ratio varies from 5.5 to 6.5 and for very large sunspots (> 5000 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mu$\\end{document}Hem; one μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mu$\\end{document}Hem is 10−6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$10^{-6}$\\end{document} the area of visual solar hemisphere) its value rises to about 8.3. In the case of the group-sunspot area, the average spot ratio is ∼6.76. Furthermore, we found that this ratio exhibits a trend for both smaller (area <100 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mu$\\end{document}Hem) and large (area > 100 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mu$\\end{document}Hem) sunspots. Finally, we report the periodic and quasiperiodic variations present in this ratio time series after applying the multitaper method (MTM) and Morlet-wavelet technique. We found that along with the ∼11-year solar-cycle period, the penumbra to umbra area ratio also shows several midterm variations, specifically, Rieger-type and quasibiennial periodicities. We also found that Rieger-type periods occur in all cycles, but the temporal evolution and the modulation of these types of periodicities are different in different solar cycles.