We present C18O observations of the pre-stellar core L1689B, in the (J=3-2) and (J=2-1) rotational transitions, taken at the James Clerk Maxwell Telescope in Hawaii. We use a lambda-iteration radiative transfer code to model the data. We adopt a similar form of radial density profile to that which we have found in all pre-stellar cores, with a `flat inner profile, steepening towards the edge, but we make the gradient of the `flat region a free parameter. We find that the core is close to virial equilibrium, but there is tentative evidence for core contraction. We allow the temperature to vary with a power-law form and find we can consistently fit all of the CO data with an inverse temperature gradient that is warmer at the edge than the centre. However, when we combine the CO data with the previously published millimetre data we fail to find a simultaneous fit to both data-sets without additionally allowing the CO abundance to decrease towards the centre. This effect has been observed qualitatively many times before, as the CO freezes out onto the dust grains at high densities, but we quantify the effect. Hence we show that the combination of mm/submm continuum and spectral line data is a very powerful method of constraining the physical parameters of cores on the verge of forming stars.
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