Theoretical and numerical analyses are presented of the passive coherent phasing of an array of fiber lasers that are
combined in a single laser cavity by an Nx1 coupler. In an initial linear analysis it is found that the brightness gain of the
passive coherent array grows linearly for a small number of fibers, however, for practical parameters, the coherent
brightness gain saturates at ~ 8 - 12 for large arrays. An intensity dependent index (Kerr) nonlinearity is then introduced
and it is shown that the expected maximum improvement is modest, with the coherent brightness gain saturating at 10 - 14, depending on the strength of the nonlinearity. These results are compared with recent experiments.