An Optimal Estimation Spectral Retrieval Approach for Exoplanet Atmospheres

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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
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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

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Method Optimal Estimation (Rodgers 2000)
xa- prior state vector Sa - prior uncertainty
matrix
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Forward Model F(x)

• Parmentier Guillot 2011 Analytical TP
• ?v1,?v2, a, ?IR ,Tirr , Tint
• Constant with Altitude Mixing Ratios
• H2O, CH4, CO, CO2, H2, He
• Reference Forward Model (http//www.atm.ox.ac.uk/R
  FM/)
• -HITEMP Database for H2O, CO, CO2
• -HITRAN Database for CH4
• -H2-H2, H2-He Opacities (from A. Borysow)

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HD189733b Jacobian
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HD189733b Retrieval
A priori State Retrieved State Retrieved State
(Hi Res)
?20.86
DOF 5
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Degrees of Freedom and Information Content
FINESSE
NICMOS
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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

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Synthetic Data Test
Model Atmosphere Tirr1220 K fH20.86 Tint100
K fHe0.14 ?v1410-3 cm2g-1 fH2O510-4 ?v241
0-3 cm2g-1 fCH4110-6 a0.5 fCO310-4 ?IR
110-2 cm2g-1 fCO2110-7
Instrumental Specs R40 at 2µm (??0.05
µm) S/N10
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Synthetic Data Jacobian
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Synthetic Data Retrieval
?20.01
DOF 6
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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 S-retrieval uncertainty matrix
Degrees of Freedom
Information Content