An iterative technique for solving equations of statistical equilibrium

Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an N-level model atom, the technique avoids the N3 scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large N due to the accumulation of round-off errors. As a consequence, the technique allows detailed model atoms with N≳103, such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394-level Fe ii ion and a 1266-level Ni i–iv atom.