Distribution of sunspot umbral areas - 1917-1982

Abstract

Over 24,000 measurements of individual sunspot umbral areas taken from the Mount Wilson white-light plate collection covering the period 1917-1982 are used to determine the relative size distribution of sunspot umbras. In the range 1.5-141 millionths of a solar hemisphere, the sunspot umbral areas are found to be distributed lognormally. Moreover, the same distribution is obtained for all phases of the solar cycle (maximum, minimum, ascending, descending), as well as for various individual cycles, between 1917 and 1982. Both the mean and the geometric logarithmic standard deviation of this distribution appear to be intrinsically constant over the entire data set; only the number of spots exhibits the familiar solar cycle variations. If the observed lognormal umbral size distribution is not a particular attribute of the sunspot umbras but is instead of a more fundamental property of emerging magnetic flux, then the data would predict a maximum in the size spectrum of photospheric magnetic structures for flux tubes with radii in the range 500-800 km. The absence of solar cycle variations in the relative distribution of umbral areas and especially the lognormal character of this distribution may both argue for the fragmentation of magnetic elements in the solar envelope.