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) Degrees of Freedom Information Content Bayes Theorem: y - measurement vector x - state vector Cost Function: F(x) = Kx - forward model K -Jacobian matrix— S e - data error matrix x a - prior state vector S a - prior uncertainty matrix Retrieval Uncertianty Retrieved State Averaging Kernel

Forward Model F(x) Parmentier & Guillot 2011 Analytical TP κ v1,κ v2, α, κ IR,T irr, T int Constant with Altitude Mixing Ratios H 2 O, CH 4, CO, CO 2, H 2, He Reference Forward Model ( -HITEMP Database for H 2 O, CO, CO 2 -HITRAN Database for CH 4 -H 2 -H 2, H 2 -He Opacities (from A. Borysow)

HD189733b Jacobian

HD189733b Retrieval DOF~ 5 Χ 2 =0.86 A priori State Retrieved State Retrieved State (Hi Res)

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 T irr =1220 Kf H2 =0.86 T int =100 Kf He =0.14 κ v1 =4×10 -3 cm 2 g -1 f H2O =5×10 -4 κ v2 =4×10 -3 cm 2 g -1 f CH4 =1×10 -6 α=0.5f CO =3×10 -4 κ IR = 1×10 -2 cm 2 g -1 f CO2 =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 Prior Information y - measurement vector x - true state vector - retrieved state vector x a - prior state vector F(x)=Kx-forward model K -Jacobian matrix— S e - data error matrix S a - prior uncertainty matrix Ŝ-retrieval uncertainty matrix Degrees of Freedom Information Content