On the value of 'αAR' from Vector Magnetograph data

Abstract

This investigation is the second of two centering on the parameter α=(∇×B_h)_z/B_z=μ₀J_z/B_zand its derivation from photospheric vector magnetogram data. While α can be evaluated at every spatial position where the vector B is measured, for many reasons it is useful to determine a single value of α to parameterize the magnetic complexity of an entire active region, here called α_AR(see Leka and Skumanich, 1999). As such, the limitations in today's vector magnetograph data, e.g., finite spatial resolution and limited field of view, may influence any final 'α_AR' value. We apply three methods of calculating 'α_AR' to degraded high-spatial-resolution data and find that in general the discrepancies worsen for decreasing resolution compared to the original. We apply the three methods to sub-regions centered on the constituent sunspots for AR 7815. Two of the sub-regions are shown to have magnetic twist with significant magnitude but opposite sign. We show by mosaicing or otherwise combining separate sunspot observations that a measure of α_ARcan be calculated which is consistent with a single large field-of-view observation. Still, the α_AR≈0 assigned for the entire active region is an average, and does not accurately represent the magnetic morphology of this flux system. To measure the validity of the α_ARparameterization, we demonstrate that, from each method, a relevant quantity can be calculated which describes the 'goodness of fit' of the resulting α_AR. Given the spatial variation of α(x,y) over an active region, it is suggested that such a second parameter be used either to indicate uncertainty in α_ARor as a criterion for data selection, as appropriate.