Ambipolar diffusion in interstellar clouds - Time-dependent solutions in one spatial dimension

It has previously been emphasized that the essential feature of ambipolar diffusion is a redistribution of mass in at least some interior flux tubes of an interstellar cloud, without such a redistribution necessarily being accompanied by a reduction of the magnetic flux (or the magnetic energy) threading a cloud. On the other hand, if a cloud (or a portion of a cloud) is compressed relatively rapidly (e.g., by a strong shock), ambipolar diffusion can result in both a redistribution of mass among flux tubes and a flux leakage from the cloud. The latter case is studied in this paper.

We present analytical and numerical time-dependent solutions for ambipolar diffusion in cold interstellar clouds, idealized as slabs embedded in a hot and tenuous external medium, and threaded by a magnetic field parallel to the slab faces. The neutral particles are assumed to be at rest. Magnetic forces set up a drift velocity of the plasma (ions and electrons) relative to the neutrals which reaches a maximum value within a time τ_* equal to 130-300 times the ion-neutral collision time (within about 6 × l0^-4 to 3 yr for neutral density in the respective range 10⁷ -10³ cm^-3). For this density range, the maximum drift velocity lies in the interval 0.25-15 km s^-1. The corresponding characteristic time τ_B for ambipolar diffusion lies in the range 6.6 × 10⁵ to 6.6 × 10³ yr. Beyond the time τ_*, the driving magnetic force is almost exactly balanced by the retarding collisional force between ions and neutrals, and the asymptotic behavior of the drift velocity (t^-1) is determined by the inertial term in the force equation and by the imposed space uniformity. These results are insensitive to the rate at which microscopic physical processes (such as ionization by high-energy cosmic rays) tend to reestablish ionization equilibrium as plasma and magnetic flux leak out of a cloud (or fragment). The asymptotic decrease of the magnetic field, however, is t^-1 and t^-1/2 if reestablishment of ionization equilibrium is "slow" or "instantaneous," respectively.

The achievable large drift speeds may result in sputtering of grains and return of metals to the gaseous phase.