On the value of 'αAR' from vector magnetograph data -: I.: Methods and caveats

This investigation centers upon the quantifying magnetic twist by the parameter alpha, commonly defined as (del x B-h)(z)/B-z = mu(0)J(z)/B-z, and its derivation from vector magnetograph data. This parameter can be evaluated at each spatial point where the vector B is measured, but one may also calculate a single value of alpha to describe the active region as a whole, here called 'alpha(AR)'. We test three methods to calculate such a parameter, examine the influence of data noise on the results, and discuss the limitations associated with assigning such a quantity. The three methods discussed are (1) to parameterize the distribution of alpha(x,y) using moments of its distribution, (2) to determine the slope of the function J(z)(x,y) = alpha(AR)B(z)(x,y) using a least-squares fit and (3) to determine the value of alpha for which the horizontal field from a constant-alpha force-free solution most closely matches the observed horizontal magnetic field. The results are qualitatively encouraging: between methods, the resulting value of the alpha(AR) parameter is often consistent to within the uncertainties, even though the resulting alpha(AR) can differ in magnitude, and in some cases in sign as well. The worst discrepancies occur when a minimal noise threshold is adopted for the data. When the calculations are restricted to detections of 3 sigma or better, there is, in fact, fair quantitative agreement between the three methods. Still, direct comparison of different active regions using disparate methods must be carried out with caution. The discrepancies, agreements, and overall robustness of the different methods are discussed. The effects of instrumental limitations (spatial resolution and a restricted field-of-view) on an active-region alpha(AR), and quantifying the validity of alpha(AR), are addressed in Paper II (Leka, 1999).