1999A&A...350..204N

We present detailed time and depth dependent chemical models of low mass dark molecular cloud cores. The cloud is assumed to be in hydrostatic equilibrium with a density and pressure structure described by a polytropic equation of state with negative polytropic index and boundary conditions at the centre and the edge of the cloud constrained by observations of dense and diffuse clouds. We study cloud models with a diameter of ∼1pc, central core temperature of 10K, core central densities in the range of (2-10)x10⁴cm^–3, surface pressures P/k ranging from ∼1-3x10⁴cm^–3K and turbulent velocities of ≲0.4km/s. The cloud is assumed to be subject to cosmic-ray ionization and exposed to the interstellar UV radiation field. We assumed two different geometries for the UV radiation field; one in which the cloud is subject to an isotropic field and the other in which the cloud is exposed to a radiation field in the direction of the observer from both sides, resembling a simple 2-D chemical time and depth dependent model. For calculating the HII density profile and the fractions of atomic and molecular hydrogen as a function of radius we assume an equilibrium of HII photodissociation and HII formation on grains, taking into account the HII self-shielding and dust extinction. The models incorporate time dependent chemical evolution of abundances and column densities of 175 species containing heavy elements C, O, N, S and Na with a C/O ratio of ∼0.55, assuming a depth dependent sulphur depletion which decreases linearly with increasing density from the edge to the centre of the cloud. Chemical models include the effects of additional photons generated by cosmic rays, CO accretion onto dust grains and desorption of CO mantles by direct cosmic-ray heating. The results show that cosmic-ray-induced internal photons, by increasing mainly the C⁺ abundance, make order-of-magnitude difference in the predicted abundances of species notably those whose maximum abundances are reached during the so-called ``early-times'' of a few x10<sup>5</sup> years. Closer chemical connections between HC<sub>3</sub>N, C<sub>2</sub>S and C<sub>3</sub>H<sub>2</sub> have been found under influence of cosmic-ray-induced photo reactions. CO is the key molecule in controlling the chemistry at later times and its loss onto grains critically affects the abundances of the so-called ``late type'' species; when the CO abundance builds up then the dominant ion H₃⁺ is used up in the production and destruction reactions sequence of CO, CO+(H₃⁺)->HCO⁺+(e)->CO, deactivating the overall remaining chemistry. With the loss of CO from the gas phase, H₃⁺ becomes available to stimulate the chemistry of non-carbon containing species, thus contributing significantly in increasing the predicted column density of NH₃ and N₂H⁺ to match their observed values. With depletion of CO from the gas phase, and subsequent overall change in C:O:N:S abundance ratios, close chemical relations between abundance variations of SO and N₂H⁺ with NH₃ are found. Direct desorption by cosmic-ray heating is found to be efficient in recovering the observed gas-phase CO abundance, and provide conditions under which the chemical equilibrium in the cloud is established at ∼5 million years. The results presented include: the time variation of abundances corresponding to the centre of the cloud, variation of abundances with radius and A_v for selected evolution times along the central line of sight, time variation of the column density of selected observed species along the central line of sight and average column densities integrated over various beam sizes. The calculated average column densities for various beam sizes indicate that the models account for the observed size of the maps of HC₃N (∼0.1pc), NH₃ (∼0.15pc) and C₂S (∼0.25pc). Comparisons are made with observations.