Constraints on the circumstellar dust around KIC 8462852

We present millimetre (SMA) and sub-millimetre (SCUBA-2) continuum observations of the peculiar star KIC 8462852 which displayed several deep and aperiodic dips in brightness during the Kepler mission. Our observations are approximately confusion-limited at 850 $\mu$m and are the deepest millimetre and sub-millimetre photometry of the star that has yet been carried out. No significant emission is detected towards KIC 8462852. We determine upper limits for dust between a few 10$^{-6}$ M$_{\oplus}$ and 10$^{-3}$ M$_{\oplus}$ for regions identified as the most likely to host occluding dust clumps and a total overall dust budget of $<$7.7 M$_{\oplus}$ within a radius of 200 AU. Such low limits for the inner system make the catastrophic planetary disruption hypothesis unlikely. Integrating over the Kepler lightcurve we determine that at least 10$^{-9}$ M$_{\oplus}$ of dust is required to cause the observed Q16 dip. This is consistent with the currently most favoured cometary breakup hypothesis, but nevertheless implies the complete breakup of $\sim$ 30 Comet 1/P Halley type objects. Finally, in the wide SCUBA-2 field-of-view we identify another candidate debris disc system that is potentially the largest yet discovered.