The millennium Arecibo 21 centimeter absorption-line survey. IV. Statistics of magnetic field, column density, and turbulence

We discuss observations of the magnetic field, column density, and turbulence in the cold neutral medium (CNM). The observed quantities are only indirectly related to the intrinsic astronomical ones. We relate the observed and intrinsic quantities by relating their univariate and bivariate probability distribution functions (pdf's). We find that observations of the line-of-sight component of a magnetic field do not constrain the pdf of the total field B(tot) very well but do constrain the median value of B(tot). In the CNM, we find a well-defined median magnetic field 6.0 +/- 1.8 mu G. The CNM magnetic field dominates thermal motions. Turbulence and magnetism are in approximate equipartition. We find that the probability distribution of column density N(perpendicular to)(H I) in the sheets closely follows N(perpendicular to)(H I)(-1) over a range of 2 orders of magnitude, 0.026 less than or similar to N(perpendicular to)(H I) less than or similar to 2.6 x 10(20) cm(-2). The bivariate distributions are not well enough determined to constrain structural models of CNM sheets.