The Transition from Atomic to Molecular Hydrogen in Interstellar Clouds: 21 cm Signature of the Evolution of Cold Atomic Hydrogen in Dense Clouds

We have investigated the timescale for formation of molecular clouds by examining the conversion of H I to H₂ using a time-dependent model with H₂ photodissociation including self-shielding. H₂ formation on dust grains and cosmic-ray destruction are also included in one-dimensional model slab clouds that incorporate time-independent density and temperature distributions. We calculate 21 cm spectral line profiles seen in absorption against a background provided by general Galactic H I emission and compare the model spectra with H I narrow self-absorption (HINSA) profiles absorbed in a number of nearby molecular clouds. The time evolution of the H I and H₂ densities is dramatic, with the atomic hydrogen disappearing in a wave propagating from the central, denser regions, which have a shorter H₂ formation timescales, to the edges, where the density is lower and the timescales for H₂ formation longer. The model 21 cm spectra are characterized by very strong absorption at early times. Emission at early times produced by the warm edges of the cloud is difficult to separate from variations in the background spectrum, when the background temperature is low. The minimum time for cloud evolution based on the model spectra is set by the requirement that most of the H I in the outer portions of the cloud be removed. The characteristic time that has elapsed since cloud compression and initiation of the H I-->H₂ conversion is a few ×10¹⁴ s, or ~=10⁷ yr. This sets a minimum time for the age of these molecular clouds and thus for star formation that may take place within them.