The Sub-mm Variability of IRC+10216 and $o$ Ceti

We present the sub-mm variability of two of the most well studied AGB stars, IRC+10216 and $o$ Ceti. The data are obtained at $450~\micron$ and $850~\micron$ as part of pointing calibration observations for the James Clerk Maxwell Telescope's SCUBA-2 instrument over a span of 7 years. The periods are derived using non-parametric methods, \texttt{Gatspy Supersmoother} and \texttt{P4J} in order not to assume an underlying shape to the periodicity. These were compared to two Lomb-Scargle parametric methods. We find that for both sources and wavelengths the periods derived from all methods are consistent within $1\sigma$. The $850~\micron$ phase folded light curves of IRC+10216 show a time lag of $\sim 540$ days compared to its optical counterpart. We explore the origins of the sub-mm variability and the phase lag using radiative transfer models. Combining the modelling with findings in the literature, we find that the sub-mm emission and phase lag can be partially attributed to the dust formation/destruction cycle. A second, unknown mechanism must be invoked; we defer an investigation of the origin and nature of this mechanism to a future work.