Dependence of gas-phase abundances in the interstellar medium on column density

Sight lines through high- and intermediate-velocity clouds allow measurements of ionic gas-phase abundances A at very low values of H I column density N(H I). Present observations cover over 4 orders of magnitude in N(H I). Remarkably, for several ions we find that the A versus N(H I) relation is the same at high and low column densities and that the abundances have a relatively low dispersion (factors of 2-3) at any particular N(H I). Halo gas tends to have slightly higher values of A than disk gas at the same N(H I), suggesting that part of the dispersion may be attributed to the environment. We note that the dispersion is largest for Na I; using Na I as a predictor of N(H I) can lead to large errors. Important implications of the low dispersions regarding the physical nature of the interstellar medium are (I) because of clumping, over sufficiently long path lengths N(H I) is a reasonable measure of the local density of most of the H atoms along the sight line; (2) the destruction of grains does not mainly take place in catastrophic events such as strong shocks but is a continuous function of the mean density; (3) the cycling of the ions becoming attached to grains and being detached must be rapid, and the two rates must be roughly equal under a wide variety of conditions; and (4) in gas that has a low average density the attachment should occur within denser concentrations.