contraining clumpy dusty torus models using optimized filter sets
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
Nenk
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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