Hunting pre-stellar cores with APEX: Corona Australis 151, the densest pre-stellar core or the youngest protostar?

Context. Pre-stellar cores are the birthplaces of Sun-like stars and represent the initial conditions for the assembly of protoplanetary systems. Due to their short lifespans, they are rare. In recent efforts to increase the number of such sources identified in the Solar neighbourhood, we have selected a sample of 40 starless cores from the publicly available core catalogs of the Herschel Gould Belt survey. In this work, we focus on one of the sources that stands out for its high central density: Corona Australis 151. Aims. We use molecular lines that trace dense gas (n>=10^6 cm-3) to confirm the exceptionally high density of this object, to study its physical structure, and to understand its evolutionary stage. Methods. We detected the N2H+ 3-2 and 5-4 transitions, and the N2D+ 3-2, 4-3, and 6-5 lines with the APEX telescope. We use the Herschel continuum data to infer a spherically symmetric model of the core's density and temperature. This is used as input to perform non-local-thermodynamic-equilibrium radiative transfer to fit the observed five lines. Results. Our analysis confirms that this core is characterised by very high densities (a few x 10^7 cm-3 at the centre) and cold temperatures. We infer a high deuteration level of N2D+/N2H+=0.50, indicative of an advanced evolutionary stage. In the large bandwidth covered by the APEX data, we detect several other deuterated species, including CHD2OH, D2CO, and ND3. We also detect multiple sulphurated species that present broader lines with signs of high-velocity wings. Conclusions. The observation of high-velocity wings and the fact that the linewidths of N2H+ and N2D+ become larger with increasing frequency can be interpreted either as an indication of supersonic infall motions developing in the central parts of a very evolved pre-stellar core or as the signature of outflows from a very low luminosity object (VeLLO). *SHORTENED*