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An Optimal Estimation Spectral Retrieval Approach for Exoplanet Atmospheres

An Optimal Estimation Spectral Retrieval Approach for Exoplanet Atmospheres. M.R. Line 1 , X. Zhang 1 , V. Natraj 2 , G. Vasisht 2 , P. Chen 2 , Y.L. Yung 1 1 California Institute of Technology 2 Jet Propulsion Laboratory, California Institute of Technology EPSC-DPS 2011, Nantes France.

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An Optimal Estimation Spectral Retrieval Approach for Exoplanet Atmospheres

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  1. An Optimal Estimation Spectral Retrieval Approach for Exoplanet Atmospheres M.R. Line1, X. Zhang1, V. Natraj2, G. Vasisht2, P. Chen2, Y.L. Yung1 1California Institute of Technology 2Jet Propulsion Laboratory, California Institute of Technology EPSC-DPS 2011, Nantes France Line et al. in prep

  2. Goals • Find a robust technique for retrieving atmospheric compositions and temperatures from exoplanet spectra • Determine the number of allowable atmospheric parameters that can be retrieved from a given spectral dataset

  3. Method: Optimal Estimation (Rodgers 2000) Bayes Theorem: Cost Function: Retrieval Uncertianty y - measurement vector x - state vector Retrieved State F(x) = Kx - forward model K -Jacobian matrix— Se- data error matrix Averaging Kernel xa- prior state vector Sa- prior uncertainty matrix Degrees of Freedom Information Content

  4. Forward Model F(x) • Parmentier & Guillot 2011 Analytical TP κv1,κv2, α, κIR ,Tirr , Tint • Constant with Altitude Mixing Ratios H2O, CH4, CO, CO2, H2, He • Reference Forward Model (http://www.atm.ox.ac.uk/RFM/) -HITEMP Database for H2O, CO, CO2 -HITRAN Database for CH4 -H2-H2, H2-He Opacities (from A. Borysow)

  5. HD189733b Jacobian

  6. HD189733b Retrieval A priori State Retrieved State Retrieved State (Hi Res) Χ2=0.86 DOF~ 5

  7. Degrees of Freedom and Information Content FINESSE NICMOS

  8. Conclusions • Rodgers’ optimal estimation technique can provide a robust retrieval of exoplanetary atmospheric properties • Quality of the retrieval of each parameter can be determined • Knowledge of the Jacobian, Information content, and degrees of freedom can aid future instrument design

  9. Synthetic Data Test Model Atmosphere Tirr=1220 K fH2=0.86 Tint=100 K fHe=0.14 κv1=4×10-3 cm2g-1 fH2O=5×10-4 κv2=4×10-3 cm2g-1 fCH4=1×10-6 α=0.5 fCO=3×10-4 κIR=1×10-2 cm2g-1 fCO2=1×10-7 “Instrumental” Specs R~40 at 2μm (Δλ=0.05 μm) S/N~10

  10. Synthetic Data Jacobian

  11. Synthetic Data Retrieval Χ2=0.01 DOF= 6

  12. Method: Optimal Estimation(Rodgers 2000) Minimize Cost Function from Bayes: Likelihood that data exists given some model Prior Information y - measurement vector x - true state vector - retrieved state vector xa- prior state vector F(x)=Kx-forward model K -Jacobian matrix— Se- data error matrix Sa- prior uncertainty matrix Ŝ-retrieval uncertainty matrix Degrees of Freedom Information Content

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