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.