1. Contraining clumpy dusty torus models using optimized filter sets A.Asensio Ramos C. Ramos Almeida Instituto de Astrofísica de Canarias Torus Workshop 2012 San Antonio – December 5-7 2012

2. Clumpy dusty torus model Nenkova et al. (2002) The central engine is surrounded by a dusty torus If this torus is clumpy, some observational properties are easily reproduced Therefore, we assume that dust is distributed in clumps instead of homogeneusly filling the torus volume (Nenkova et al. 2002; Hönig et al. 2006; Schartmann et al. 2008). Torus dust grains absorb optical & UV photons from matter accretion  re-emission in the infrared (peaking at mid-IR  5-30μm).

3. Mid-IR range is key to constrain the parameters of torus models If we want to isolate the torus emission (as small as 10 pc), interferometry & mid-IR are an option. Large aperture data (e.g. ISO, Spitzer, IRAS) are contaminated with circumnuclear stellar emission. Isolation of torus emission High-resolution observations 10-m class telescopes High-spatial resolution infrared observations (e.g., CanariCam, T-ReCS, Michelle, VISIR) are key to isolate torus emission.

4. Question Observations in 10-m class telescope are difficult to get given the large oversubscription They are time-consuming for many objects except for very bright ones Given the current knowledge about the object, the assumption that the Clumpy dusty torus model is correct and a list of potential new filters to use Which is the optimal filter to use?

5. List of filters HST VLT (near-IR and mid-IR) UKIRT 2.2m ESO IRTF 3.6m ESO Gemini (Michelle, TReCS) GTC (CanariCAM) SOFIA Herschel (PACS, Spire) ALMA

6. Bayesian adaptive exploration Current observations Bayesian inference Prediction Design of new experiment Photometry/spectroscopy BayesCLUMPY  posterior distributions for clumpy parameters Predict SEDs compatible with current observations and knowledge of parameters Provide new observation that maximizes the constraining power for the models

7. Bayesian parameter inference Marginal posteriors

8. Bayesian prediction Given the information we currently have, we make predictions for new points Predictive distribution Probability of getting a new observation given our current knowledge LikelihoodPosterior

9. If we have a new filter f, the expected utility measures the new information we gain Bayesian adaptive exploration (Loredo 2004) Pick up the filter where we maximize the entropy of the predictive distribution Entropy Recipe

10. Example – 2D bomb detection Use low-sensitivity instrument and then propose sampling with a high-sensitivity instrument using maximum entropy

12. SEDs compatible with the observations Asensio Ramos & Ramos Almeida (2012)

13. Wavelength [micron] Expected utility Asensio Ramos & Ramos Almeida (2012)

14. Simulated process Current observations Bayesian inference Prediction Design of new experiment

15. Simulated experiment We pick up the point with the shortest wavelength

16. Simulated experiment

18. The future? We still do not answer the question which is the ‘best’ filter to constrain the Clumpy (or whatever) models We ‘only’ answer the following question: Given our current sampling, the assumption of a model for the SED and a list of potentially usable filters, which one should you choose? Other interesting questions: Which is the best list of filters to constrain a model? Can we use only data (SEDs) to distinguish which of the available models is preferred?  Bayesian model comparison Can we make a meta-model for clumpy torus?

19. Meta-model for Clumpy models – Hierarchical Bayesian Obs 1Obs 2Obs N Clumpy models …… Of course, this ‘model’ is determined from observations Parameterized prior distributions My opinion is that we cannot pretend to have a theory of everything

20. Conclusions The Bayes framework allows us, not only to do parameter inference but other things like model comparison, model prediction, experiment design, hierarchical models, etc. Our approach is the simplest, but experiment design can also incorporate the effect of resolution, how easy it is to get observing time, etc. into the utility function This option is already implemented in the public version of BayesClumpy Be Bayesian if you want to fit models with degeneracies to sparsely sampled data