Sunspots in the context of Umbra, penumbra and antumbra

In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements.

Solar phenomena are natural phenomena which occur within the atmosphere of the Sun. They take many forms, including solar wind, radio wave flux, solar flares, coronal mass ejections, coronal heating and sunspots.

These phenomena are believed to be generated by a helical dynamo, located near the center of the Sun's mass, which generates strong magnetic fields, as well as a chaotic dynamo, located near the surface, which generates smaller magnetic field fluctuations. All solar fluctuations together are referred to as solar variation, producing space weather within the Sun's gravitational field.

The umbra, penumbra and antumbra are three distinct parts of a shadow, created by any light source after impinging on an opaque object of lesser size. In cases of equal or smaller impinging objects, only an umbra and penumbra are generated. Assuming no diffraction, for a collimated beam (such as a point source) of light, only the umbra is cast.

These phenomena are generally observed within solar systems, as the size of the stars within the system are larger than the orbiting satellites, hence these terms are most often used for the shadows cast by celestial bodies, though they are sometimes used to describe levels of darkness, such as in sunspots.

George Ellery Hale (June 29, 1868 – February 21, 1938) was an American astrophysicist, best known for his discovery of magnetic fields in sunspots, and as the leader or key figure in the planning or construction of several world-leading telescopes; namely, the 40-inch refracting telescope at Yerkes Observatory, 60-inch Hale reflecting telescope at Mount Wilson Observatory, 100-inch Hooker reflecting telescope at Mount Wilson, and the 200-inch Hale reflecting telescope at Palomar Observatory. He played a key role in the foundation of the International Union for Cooperation in Solar Research and the National Research Council, and in developing the California Institute of Technology into a leading research university.