On the Use of Correlations to Determine the Motions and Properties of Mesoscale Magnetic Features in the Solar Photosphere

Herschel B. Snodgrass and Adam A. Smith
2001 Astrophysical Journal  
The use of correlations to determine both intrinsic properties and collective motions of patterns is investigated, and the results are applied to the study of the magnetic features in the solar photosphere. Simulations with artiÐcial data are used as a bridge between theory and practical correlation calculations. It is shown that the correlation amplitude as a function of lag can be used to determine not only pattern displacement, but also feature sizes and lifetimes. It is found that reliable
more » ... esults are obtained only when a normalized correlation function is employed, and then only when the signal-to-noise level is greater than D 1.5. For weak correlations, we show that this ratio must be enhanced by averaging the correlation amplitudes, but when applied to the photospheric magnetic Ðeld patterns, this gives a result di †erent from that obtained by averaging the individual correlation results. We Ðnd this to be the root of the di †erences between the magnetic rotation rates that have been reported and resolve this longstanding puzzle. The correlations indicate the ubiquitous presence of di †erentially rotating magnetic features of two types : small-scale features that have lifetimes of D 1 day, and "" mesoscale ÏÏ features with lifetimes of many solar rotations. The latter are estimated to have diameters on the order of 100 Mm, and their motions relative to the ambient plasma are consistent with a random walk with di †usion constant D m \ 530^100 km2 s~1. Our value for agrees with that required in the model of Sheeley, Nash, & Wang, D m but these features are too large to have their random walks propelled by the supergranular convection. Furthermore, analysis of their relative contributions to the background Ðeld implies they decay at a rate consistent with a smaller di †usion constant km2 s~1. This agrees with the value determined in D s^2 50 high-resolution studies, which suggests that the mesoscale features are aggregates of small-scale features undergoing random walks as well, like those observed in these studies.
doi:10.1086/318220 fatcat:wwso5gyxh5h4pojidl5rdtg6ru