Constraining clumpy dusty torus models using optimized filter sets

TL;DR

This paper presents a Bayesian adaptive exploration method to identify optimal photometric filters for constraining clumpy dusty torus models in active galactic nuclei, maximizing information gain from limited data.

Contribution

It introduces a novel application of Bayesian adaptive exploration to select the most informative filters for studying dusty tori, improving parameter constraints efficiently.

Findings

Optimal filters are between 10 and 200 micrometers.

Sub-millimeter data from ALMA can also enhance constraints.

Method accounts for spatial resolution in utility evaluation.

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.