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

TL;DR

This paper demonstrates how to measure and incorporate spectral covariances in high-contrast exoplanet spectroscopy, revealing biases in parameter estimation and emphasizing the importance of realistic priors in Bayesian retrievals.

Contribution

It introduces methods to measure spectral errors and covariances and integrates them into parameter retrievals, improving accuracy in exoplanet atmospheric analysis.

Findings

Ignoring spectral covariance biases parameter estimates.

Scaling chi-squared can lead to incorrect confidence regions.

Realistic priors significantly affect inferred parameters.

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 $\chi^2$ per degree of freedom to unity; the input parameters then fall outside the $95\%$ confidence regions in as many as ${\sim}80\%$ of noise realizations. The biases we observe can approach the typical levels of precision achieved in high-contrast spectroscopy. Accounting for realistic priors in fully Bayesian retrievals can also have a significant impact on the inferred parameters. Plausible priors on effective temperature and surface gravity can vary by an order of magnitude across the confidence regions appropriate for objects with weak age constraints; priors for objects with good age constraints are dominated by modeling uncertainties. 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.