An Optimal Estimation Spectral Retrieval Approach for Exoplanet

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 Line et al. in prep

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

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

Forward Model F(x) • Parmentier & Guillot 2011 Analytical TP κv 1, κv 2, α, κIR , Tirr , Tint • Constant with Altitude Mixing Ratios H 2 O, CH 4, CO 2, He • Reference Forward Model (http: //www. atm. ox. ac. uk/RFM/) -HITEMP Database for H 2 O, CO 2 -HITRAN Database for CH 4 -H 2, H 2 -He Opacities (from A. Borysow)

HD 189733 b Jacobian

HD 189733 b Retrieval A priori State Retrieved State (Hi Res) Χ 2=0. 86 DOF~ 5

Degrees of Freedom and Information Content FINESSE NICMOS

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

Synthetic Data Test Model Atmosphere Tirr=1220 K f. H 2=0. 86 Tint=100 K f. He=0. 14 κv 1=4× 10 -3 cm 2 g-1 f. H 2 O=5× 10 -4 κv 2=4× 10 -3 cm 2 g-1 f. CH 4=1× 10 -6 α=0. 5 f. CO=3× 10 -4 κIR= 1× 10 -2 cm 2 g-1 f. CO 2=1× 10 -7 “Instrumental” Specs R~40 at 2μm (Δλ=0. 05 μm) S/N~10

Synthetic Data Jacobian

Synthetic Data Retrieval Χ 2=0. 01 DOF= 6

Method: Optimal Estimation (Rodgers 2000) Minimize Cost Function from Bayes: Likelihood that data exists given some model 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 Prior Information Degrees of Freedom Information Content