Constructing the coronal magnetic field by correlating parameterized magnetic field lines with observed coronal plasma structures

A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (i) the normal component of the photospheric field remains unchanged, (ii) the field is given in the entire corona over an active region, (iii) the field remains divergence-free, and (iv) electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10(-5.5) g cm s(-2) resulting from an electric current density of 0.079 mu A m(-2). Calculations show that the plasma beta becomes larger than unity at a relatively low height of similar to 0.25 r. supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients to maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.