Long-Term Solar Cycle Evolution: Review of Recent Developments

Abstract

The sunspot number series forms the longest directly observed index of solar activity and allows to trace its variations on the time scale of about 400 years since 1610. This time interval covers a wide range from seemingly vanishing sunspots during the Maunder minimum in 1645 - 1700 to the very high activity during the last 50 years. Although the sunspot number series has been studied for more than a century, new interesting features have been found even recently. This paper gives a review of the recent achievements and findings in long-term evolution of solar activity cycles such as determinism and chaos in sunspot cyclicity, cycles during the Maunder minimum, a general behaviour of sunspot activity during a great minimum, the phase catastrophe and the lost cycle in the beginning of the Dalton minimum in 1790s and persistent 22-year cyclicity in sunspot activity. These findings shed new light on the underlying physical processes responsible for sunspot activity and allow a better understanding of such empirical rules as the Gnevyshev-Ohl rule and the Waldmeier relations. In order to study the statistical properties of solar activity one needs some numer- ical characteristics related to the entire Sun (or its significant part) which reflect its main activity features. Such characteristics are called indices of solar activity. Although there are many different indices such as those based on faculae, flares, coronal holes, and electromagnetic radiation in various bands (10.7 cm radio flux, green corona, etc.), the number of sunspots on the solar disk (so called sunspot activity) is the most famous and widely used index of solar activity. It is based on the longest series of continuous solar observations and reflects the varying strength of the hydromagnetic dynamo process which generates the solar magnetic field. Regular sunspot observations were started by Galileo in 1610 soon after the invention of the telescope. Since that time, sunspot observations were more or less regular covering nearly four hundred years by routine observations. Sunspot num- ber series is the most used index of solar activity and probably the most analyzed time series in astrophysics. The most pronounced feature of solar activity is the 11-year cycle, also called the Schwabe cycle. This cycle dominates the sunspot activity during almost the