Estimating electric current densities in solar active regions

Electric currents in solar active regions are thought to provide the energy released via magnetic reconnection in solar flares. Vertical electric current densities $J_z$ at the photosphere may be estimated from vector magnetogram data, subject to substantial uncertainties. The values provide boundary conditions for nonlinear force- free modelling of active region magnetic fields. A method is presented for estimating values of $J_z$ taking into account uncertainties in vector magnetogram field values, and minimizing $J_z^2$ across the active region. The method is demonstrated using the boundary values of the field for a force-free twisted bipole, with the addition of noise at randomly chosen locations.