Constraining clumpy dusty torus models using optimized filter sets

Abstract

Recent success in explaining several properties of the dusty torus around the central engine of active galactic nuclei has been gathered with the assumption of clumpiness. The properties of such clumpy dusty tori can be inferred by analyzing spectral energy distributions (SEDs), sometimes with scarce sampling given that large aperture telescopes and long integration times are needed to get good spatial resolution and signal. We aim at using the information already present in the data and the assumption of clumpy dusty torus, in particular, the CLUMPY models of Nenkova et al., to evaluate the optimum next observation such that we maximize the constraining power of the new observed photometric point. To this end, we use the existing and barely applied idea of Bayesian adaptive exploration, a mixture of Bayesian inference, prediction and decision theories. The result is that the new photometric filter to use is the one that maximizes the expected utility, which we approximate with the entropy of the predictive distribution. In other words, we have to sample where there is larger variability in the SEDs compatible with the data with what we know of the model parameters. We show that Bayesian adaptive exploration can be used to suggest new observations, and ultimately optimal filter sets, to better constrain the parameters of the clumpy dusty torus models. In general, we find that the region between 10 and 200 um produces the largest increase in the expected utility, although sub-mm data from ALMA also prove to be useful. It is important to note that here we are not considering the angular resolution of the data, which is key when constraining torus parameters. Therefore, the expected utilities derived from this methodology must be weighted with the spatial resolution of the data.