Current singularities in planar magnetic X points of finite compressibility

The formation of current singularities in nonresistive, line-tied magnetic X points is addressed. It is pointed out that, although gas pressure suppresses the current singularity development when strictly antiparallel, one-dimensional magnetic fields implode, the pressure is likely to be less effective in the more realistic case of two-dimensional magnetic fields. Detailed nonlinear relaxation computations at various levels of compressibility confirm that singularity is present even in the incompressible limit, but its strength, as determined by the amplitude and morphology of the current density, is considerably reduced. The singularity strength is quantified by computing the scalings of the peak current density with resolution. The scalings show that localized current structures can be expected only for negligible gas pressures. The numerical results imply that the inclusion of gas pressure effectively stalls fast magnetic reconnection in line-tied X-point geometries