Rapid grain growth in post-AGB disc systems from far-infrared and
  sub-millimetre photometry
  The timescales on which astronomical dust grows remain poorly understood,
with important consequences for our understanding of processes like
circumstellar disk evolution and planet formation.A number of post-asymptotic
giant branch stars are found to host optically thick, dust- and gas-rich
circumstellar discs in Keplerian orbits. These discs exhibit evidence of dust
evolution, similar to protoplanetary discs; however since post-AGB discs have
substantially shorter lifetimes than protoplanetary discs they may provide new
insights on the grain-growth process. We examine a sample of post-AGB stars
with discs to determine the FIR and sub-mm spectral index by homogeneously
fitting a sample of data from \textit{Herschel}, the SMA and the literature. We
find that grain growth to at least hundreds of micrometres is ubiquitous in
these systems, and that the distribution of spectral indices is more similar to
that of protoplanetary discs than debris discs. No correlation is found with
the mid-infrared colours of the discs, implying that grain growth occurs
independently of the disc structure in post-AGB discs. We infer that grain
growth to $\sim$mm sizes must occur on timescales $<<10^{5}$ yr, perhaps by
orders of magnitude, as the lifetimes of these discs are expected to be
$\lesssim10^{5}$~yr and all objects have converged to the same state. This
growth timescale is short compared to the results of models for protoplanetary
discs including fragmentation, and may provide new constraints on the physics
of grain growth.
