  Magnetic reconnection plays an essential role in the generation and evolution
of astrophysical magnetic fields. The best tested and most robust reconnection
theory is that of Parker and Sweet. According to this theory, the reconnection
rate scales with magnetic diffusivity lambda as lambda^0.5. In the interstellar
medium, the Parker-Sweet reconnection rate is far too slow to be of interest.
Thus, a mechanism for fast reconnection seems to be required. We have studied
the magnetic merging of two oppositely directed flux systems in weakly ionized,
but highly conducting, compressible gas. In such systems, ambipolar diffusion
steepens the magnetic profile, leading to a thin current sheet. If the ion
pressure is small enough, and the recombination of ions is fast enough, the
resulting rate of magnetic merging is fast, and independent of lambda. Slow
recombination or sufficiently large ion pressure leads to slower merging which
scales with lambda as lambda^0.5. We derive a criterion for distinguishing
these two regimes, and discuss applications to the weakly ionized ISM and to
protoplanetary accretion disks.
