Evidence for grain growth in molecular clouds: a Bayesian examination of the extinction law in Perseus

We investigate the shape of the extinction law in two 1 degrees square fields of the Perseus molecular cloud complex. We combine deep red-optical (r, i and z band) observations obtained using Megacam on the MMT with UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey near-infrared (J, H and K band) data to measure the colours of background stars. We develop a new hierarchical Bayesian statistical model, including measurement error, intrinsic colour variation, spectral type and dust reddening, to simultaneously infer parameters for individual stars and characteristics of the population. We implement an efficient Markov chain Monte Carlo algorithm utilizing generalized Gibbs sampling to compute coherent probabilistic inferences. We find a strong correlation between the extinction (A(V)) and the slope of the extinction law (parametrized by R-V). Because the majority of the extinction towards our stars comes from the Perseus molecular cloud, we interpret this correlation as evidence of grain growth at moderate optical depths. The extinction law changes from the ` diffuse' value of R-V similar to 3 to the 'dense cloud' value of R-V similar to 5 as the column density rises from A(V) = 2 to 10 mag. This relationship is similar for the two regions in our study, despite their different physical conditions, suggesting that dust grain growth is a fairly universal process.