In a recent JCMT submillimeter study, Ward-Thompson et al. (
1994MNRAS.268..276W) obtained the first dust continuum maps of five low-mass dense cores among the sample of starless ammonia cores from Myers and colleagues. Here, we present the results of new 1.3mm continuum mapping observations for one of these cores, L 1689B, taken with the IRAM 30-m telescope equipped with the 7-channel and 19-channel MPIfR bolometer arrays. The new 1.3mm data, which were obtained in the `on-the-fly' scanning mode, have better angular resolution and sensitivity than the earlier 800 µm data, reaching an rms noise level of ∼3mJy/13"beam. Our IRAM map resolves L 1689B as an east-west elongated core of deconvolved size 0.045pcx0.067pc (FWHM), central column density N
H2
∼1.5x10
22cm
–2, and mass M
FWHM∼0.6M
☉, in good agreement with our previous JCMT estimates. We confirm that the radial column density profile N(θ) of L 1689B is not consistent with a single power law with angular radius θ but flattens out near its centre. Comparison with synthetic model profiles simulating our `on-the-fly' observations indicates that N(θ
maj) ∝θ
maj–0.2 for θ
maj≤25" and N(θ
maj) ∝θ
maj–1 for 25"<θ
maj≤90", where θ
maj is measured along the major axis of the core. The observed mean profile is not consistent with a simple Gaussian source, being flatter than a Gaussian in its outer region. However, the profile measured along the minor axis of L 1689B is significantly steeper and apparently consistent with a Gaussian `edge' in the north-south direction. The mass, radius, and density of the relatively flat central region are estimated to be ∼0.3M
☉, ∼4000AU, and ∼2x10
5cm
–3, respectively. The mass of L 1689B and its large (>30) density contrast with the surrounding molecular cloud indicate that it is not a transient structure but a self-gravitating pre-stellar core. The flat inner profile and other measured characteristics of L 1689B are roughly consistent with theoretical predictions for a magnetically-supported, flattened core either on the verge of collapse or in an early phase of dynamical contraction. In this case, the mean magnetic field in the central region should be ≲80µG, which is high but not inconsistent with existing observational constraints. Alternatively, the observed core structure may also be explained by equilibrium models of primarily thermally supported, self-gravitating spheroids interacting with an external UV radiation field. The present study supports the conclusions of our previous JCMT survey and suggests that, in contrast with protostellar envelopes, most pre-stellar cores have flat inner density gradients which approach ρ(r) ∝r
–2 only beyond a few thousand AU. This implies that, in some cases at least, the initial conditions for protostellar collapse depart significantly from a singular isothermal sphere.