We report on submillimetre bolometer observations of the isolated neutron star RX J1856.5–3754 using the LABOCA bolometer array on the Atacama Pathfinder Experiment (APEX) Telescope. No cold dust continuum emission peak at the position of RX J1856.5–3754 was detected. The 3 sigma flux density upper limit of 5 mJy translates into a cold dust mass limit of a few earth masses. We use the new submillimetre limit, together with a previously obtained H-band limit, to constrain the presence of a gaseous, circumpulsar disc. Adopting a simple irradiated-disc model, we obtain a mass accretion limit of dM/dt less than 10^{14} g/s, and a maximum outer disc radius of around 10^{14} cm. By examining the projected proper motion of RX J1856.5–3754, we speculate about a possible encounter of the neutron star with a dense fragment of the CrA molecular cloud a few thousand years ago.

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