Contraining clumpy dusty torus modelsusing optimized filter sets

A. Asensio RamosC. Ramos Almeida

Instituto de Astrofísica de Canarias

Torus Workshop 2012San Antonio – December 5-7 2012

Clumpy dusty torus model

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)• 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).

• 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 emissionHigh-resolution observations

10-m class telescopes

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

Question

• Observations in 10-m class telescope are difficult to getgiven 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 theClumpy dusty torus model is correct and a list of

potential new filters to use

Which is the optimal filter to use?

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

Bayesian adaptive exploration

Current observations

Bayesianinference

Prediction

Design of newexperiment

Photometry/spectroscopy

BayesCLUMPY posteriordistributions for clumpy parameters

Predict SEDs compatible withcurrent observations and knowledgeof parameters

Provide new observation thatmaximizes the constraining powerfor the models

Bayesian parameter inference

Marginal posteriors

Bayesian prediction

Given the information we currently have, we make predictions for new points

Predictive distribution

Probability of getting a new observation given ourcurrent knowledge

Likelihood Posterior

If we have a new filter f, the expected utility measuresthe new information we gain

Bayesian adaptive exploration (Loredo 2004)

Pick up the filter where we maximize the entropy of the predictive distribution

Entropy

Recipe

Example – 2D bomb detection

Use low-sensitivity instrument and then propose samplingwith a high-sensitivity instrument using maximum entropy

SEDs compatible with the observations

Asensio Ramos & Ramos Almeida (2012)

Wavelength [micron]

Exp

ecte

d ut

ility

Expected utility

Asensio Ramos & Ramos Almeida (2012)

Simulated process

Current observations

Bayesianinference

Prediction

Design of newexperiment

Simulated experiment

We pick up the point with the shortest wavelength

Simulated experiment

Simulated experiment

The future?

We still do not answer the question which is the ‘best’ filterto 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?

Meta-model for Clumpy models – Hierarchical Bayesian

Obs 1 Obs 2 Obs N

Clumpymodels

……

Of course, this ‘model’ is determined from observations

Parameterizedprior distributions

My opinion is that we cannot pretend to have a theory of everything

Conclusions

• The Bayes framework allows us, not only to do parameter inferencebut 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 observingtime, 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 tosparsely sampled data