Dynamics and depletion in thermally supercritical starless cores

In previous studies, we identified two classes of starless cores, thermally subcritical and supercritical, distinguished by different dynamical behaviour and internal structure. Here, we study the evolution of the dynamically unstable, thermally supercritical cores by means of a numerical hydrodynamic simulation that includes radiative equilibrium and simple molecular chemistry. From an initial state as an unstable Bonnor-Ebert (BE) sphere, a contracting core evolves towards the configuration of a singular isothermal sphere by inside-out collapse. We follow the gas temperature and abundance of CO during the contraction. The temperature is predominantly determined by radiative equilibrium, but in the rapidly contracting centre of the core compressive heating raises the gas temperature by a few degrees over its value in static equilibrium. The time-scale for the equilibration of CO depends on the gas density and is everywhere shorter than the dynamical time-scale. The result is that the dynamics do not much affect the abundance of CO which is always close to that of a static sphere of the same density profile, and CO cannot be used as a chemical clock in starless cores. We use our non-local thermodynamic equilibrium (non-LTE) radiative transfer code mollie to predict observable CO and N2H+ line spectra, including the non-LTE hyperfine ratios of N2H+, during the contraction. These are compared against observations of the starless core L1544. The comparison indicates that the dust in L1544 has an opacity consistent with ice-covered rather than bare grains, the cosmic ray ionization rate is about 1 x 10-17 s-1 and the density structure of L1544 is approximately that of a BE sphere with a maximum central density of 2 x 107 cm-3, equivalent to an average density of 3 x 106 cm-3 within a radius of 500 au. The observed CO linewidths and intensities are reproduced if the CO desorption rate is about 30 times higher than the rate expected from cosmic ray strikes alone, indicating that other desorption processes are also active.