Solar cycle variation of photospheric and chromospheric magnetic and ultraviolet emission features observed by the Solar Dynamics Observatory

The solar magnetic field exhibits cyclic behaviour over a period of 22 years, continually reprocessing the poloidal, dipolar magnetic field into toroidal, quadrupolar magnetic field and vice versa. The cyclic behaviour of the solar magnetic field has been revealed through long-term measurements of the photospheric magnetic field strength. In addition, the long-term behaviour of phenomena associated with the magnetic field, such as sunspots and coronal loops, can be observed through ultraviolet emission measurements. We use statistical tools to analyse magnetic field strength and ultraviolet emission intensity data from the Solar Dynamics Observatory to determine the variation of photospheric and chromospheric magnetic and ultraviolet emission features over a full solar cycle. The nature of the observed distributions of these features at different times during the solar cycle may contribute towards a better understanding of the magnetic field generation mechanisms. This contribution may be in the form of theoretical interpretation of the physical processes which lead to such distributions or by providing physical constraints to numerical models of the solar dynamo, turbulent convection, and flux emergence. We consider a number of statistical models including a single power law, a truncated Weibull-lognormal, and a smooth double power law, amongst others. We investigate the plausibility and goodness-of-fit of such models for four full cycle datasets; magnetic features observed by the Helioseismic and Magnetic Imager, and emission features observed by the 304\AA, 1600\AA, and 1700\AA\ channels of the Atmospheric Imaging Assembly. We determine that a double power law performs well over the full solar cycle in all four cases and discuss the potential implications of a double power law distribution for solar magnetic field generation. We propose that the double power law is a suitable fit as the flexibility of two separate power law regimes accurately reflects the physical conditions which produce the observed magnetic field and ultraviolet emission features.