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Contraining clumpy dusty torus models using optimized filter sets

Contraining clumpy dusty torus models using optimized filter sets. Asensio Ramos C. Ramos Almeida Instituto de Astrofísica de Canarias. Torus Workshop 2012 San Antonio – December 5-7 2012. Clumpy dusty torus model. The central engine is surrounded by a dusty torus

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Contraining clumpy dusty torus models using optimized filter sets

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  1. Contrainingclumpydustytorusmodels usingoptimizedfilter sets • Asensio Ramos • C. Ramos Almeida • Instituto de Astrofísica de Canarias TorusWorkshop 2012 San Antonio – December5-7 2012

  2. Clumpydustytorusmodel • 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 homogeneuslyfilling the torus volume (Nenkova et al. 2002; Höniget al. 2006; Schartmannet al. 2008). • Torus dust grains absorb optical & UV photons from matter accretion  re-emission in the infrared (peaking at mid-IR  5-30μm). Nenkova et al. (2002)

  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 torusemission High-resolutionobservations High-spatial resolution infrared observations (e.g., CanariCam, T-ReCS, Michelle, VISIR)are key to isolate torus emission. 10-m classtelescopes

  4. Question • Observations in 10-m classtelescope are difficulttogetgiventhelargeoversubscription • They are time-consumingformanyobjectsexceptforverybrightones Giventhecurrentknowledgeabouttheobject, theassumptionthattheClumpydustytorusmodeliscorrect and a list of potential new filtersto use Whichistheoptimalfilterto 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. Bayesianadaptiveexploration Currentobservations Photometry/spectroscopy Bayesian inference BayesCLUMPY posterior distributionsforclumpyparameters Prediction PredictSEDs compatible with currentobservations and knowledge of parameters Design of new experiment Provide new observationthat maximizestheconstrainingpower forthemodels

  7. Bayesianparameterinference Marginal posteriors

  8. Bayesianprediction Giventheinformationwecurrentlyhave, wemakepredictionsfor new points Likelihood Posterior Predictivedistribution Probability of getting a new observationgivenour currentknowledge

  9. Bayesianadaptiveexploration (Loredo 2004) Ifwehave a new filter f, theexpectedutilitymeasures the new informationwegain Entropy Recipe Pick up thefilterwherewemaximizethe entropy of thepredictivedistribution

  10. Example – 2D bombdetection Use low-sensitivityinstrument and thenproposesampling with a high-sensitivityinstrumentusingmaximumentropy

  11. SEDs compatible withtheobservations Asensio Ramos & Ramos Almeida (2012)

  12. Expectedutility Expectedutility Wavelength [micron] Asensio Ramos & Ramos Almeida (2012)

  13. Simulatedprocess Currentobservations Bayesian inference Prediction Design of new experiment

  14. Simulatedexperiment We pick up thepointwiththeshortestwavelength

  15. Simulatedexperiment

  16. Simulatedexperiment

  17. Thefuture? Westill do notanswerthequestionwhichisthe‘best’filter toconstraintheClumpy (orwhatever) models We ‘only’ answerthefollowingquestion: Givenourcurrentsampling, theassumption of a modelforthe SED and a list of potentially usable filters, whichoneshouldyouchoose? • Otherinterestingquestions: • Whichisthebestlist of filterstoconstrain a model? • Can we use only data (SEDs) todistinguishwhich of theavailablemodelsispreferred?  Bayesianmodelcomparison • Can wemake a meta-modelforclumpytorus?

  18. Meta-modelforClumpymodels – HierarchicalBayesian Parameterized prior distributions Clumpy models Obs 1 Obs 2 Obs N …… Of course, this ‘model’ isdeterminedfromobservations Myopinionisthatwecannotpretendtohave a theory of everything

  19. Conclusions • TheBayesframeworkallowsus, notonlyto do parameterinferencebutotherthingslikemodelcomparison, modelprediction, experimentdesign, hierarchicalmodels, etc. • Ourapproachisthesimplest, butexperimentdesign can alsoincorporatetheeffect of resolution, howeasyitistogetobservingtime, etc. intotheutilityfunction • Thisoptionisalreadyimplemented in thepublicversion of BayesClumpy • Be Bayesianifyouwanttofitmodelswithdegeneraciestosparselysampled data

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