On the value of 'alpha(AR)' from vector magnetograph data - II. Spatial resolution, field of view, and validity

This investigation is the second of two centering on the parameter alpha = (del x B-h)(z)/B-z = mu(0)J(z)/B-z and its derivation from photospheric vec tor magnetogram data. While alpha can be evaluated at every spatial positio n where the vector B is measured, for many reasons it is useful to determin e a single value of alpha to parameterize the magnetic complexity of an ent ire active region, here called alpha(AR) (see Leka and Skumanich, 1999). As such, the limitations in today's vector magnetograph data, e.g., finite sp atial resolution and limited field of view, may influence any final 'alpha( AR)' value. We apply three methods of calculating 'alpha(AR)' to degraded h igh-spatial-resolution data and find that in general the discrepancies wors en for decreasing resolution compared to the original. We apply the three m ethods to sub-regions centered on the constituent sunspots for AR 7815. Two of the sub-regions are shown to have magnetic twist with significant magni tude but opposite sign. We show by mosaicing or otherwise combining separat e sunspot observations that a measure of alpha(AR) can be calculated which is consistent with a single large field-of-view observation. Still, the alp ha(AR) approximate to 0 assigned for the entire active region is an average , and does not accurately represent the magnetic morphology of this flux sy stem. To measure the validity of the alpha(AR) parameterization, we demonst rate that, from each method, a relevant quantity can be calculated which de scribes the 'goodness of fit' of the resulting alpha(AR). Given the spatial variation of alpha(x, y) over an active region, it is suggested that such a second parameter be used either to indicate uncertainty in alpha(AR) or a s a criterion for data selection, as appropriate.