Molecular Evolution in Collapsing Prestellar Cores III: Contraction of A Bonnor-Ebert Sphere

The gravitational collapse of a spherical cloud core is investigated by numerical calculations. The initial conditions of the core lie close to the critical Bonnor-Ebert sphere with a central density of \sim 10^4 cm^{-3} in one model (alpha=1.1), while gravity overwhelms pressure in the other (alpha=4.0), where alpha is the internal gravity-to-pressure ratio. The alpha=1.1 model shows reasonable agreement with the observed velocity field in prestellar cores. Molecular distributions in cores are calculated by solving a chemical reaction network that includes both gas-phase and grain-surface reactions. When the central density of the core reaches 10^5 cm^{-3}, carbon-bearing species are significantly depleted in the central region of the alpha=1.1 model, while the depletion is only marginal in the other model. The two different approaches encompass the observed variations of molecular distributions in different prestellar cores, suggesting that molecular distributions can be probes of contraction or accumulation time scales of cores. The central enhancement of the NH3/N2H+ ratio, which is observed in some prestellar cores, can be reproduced under certain conditions by adopting recently measured branching fractions for N2H+ recombination. Various molecular species, such as CH3OH and CO2, are produced by grain-surface reactions. The ice composition depends sensitively on the assumed temperature. Multi-deuterated species are included in our most recent gas-grain chemical network. The deuterated isotopomers of H3+ are useful as probes of the central regions of evolved cores, in which gas-phase species with heavy elements are strongly depleted. At 10 K, our model can reproduce the observed abundance ratio of ND3/NH3, but underestimates the isotopic ratios of deuterated to normal methanol