The Measurement, Treatment, and Impact of Spectral Covariance and Bayesian Priors in Integral-Field Spectroscopy of Exoplanets

The Measurement, Treatment, and Impact of Spectral Covariance and Bayesian Priors in Integral-Field Spectroscopy of Exoplanets

Authors:

Greco et al

Abstract:

The recovery of an exoplanet's atmospheric parameters from its spectrum requires accurate knowledge of the spectral errors and covariances. Unfortunately, the complex image processing used in high-contrast integral-field spectrograph (IFS) observations generally produces spectral covariances that are poorly understood and often ignored. In this work, we show how to measure the spectral errors and covariances and include them self-consistently in parameter retrievals. By combining model exoplanet spectra with a realistic noise model generated from GPI early science data, we show that ignoring spectral covariance in high-contrast IFS data can both bias inferred parameters and lead to unreliable confidence regions on those parameters. This problem is made worse by the common practice of scaling the χ2 per degree of freedom to unity; the input parameters then fall outside the 95% confidence regions in as many as ∼80% of noise realizations. Accounting for realistic priors in fully Bayesian parameter retrievals can also have a significant impact on the inferred parameters. As an example, we show that plausible priors on effective temperature and surface gravity can vary by as much as an order of magnitude across the 95% confidence regions appropriate for objects with weak age constraints like GJ 504b and κ And b. Our methods are directly applicable to existing high-contrast IFSs including GPI and SPHERE, as well as upcoming instruments like CHARIS and, ultimately, WFIRST-AFTA.