  Hi-resolution spectroscopy (R > 25,000) has recently emerged as one of the
leading methods to detect atomic and molecular species in the atmospheres of
exoplanets. However, it has so far been lacking in a robust method to extract
quantitative constraints on temperature structure and molecular/atomic
abundances. In this work we present a novel Bayesian atmospheric retrieval
framework applicable to high resolution cross-correlation spectroscopy (HRCCS)
that relies upon the cross-correlation between data and models to extract the
planetary spectral signal. We successfully test the framework on simulated data
and show that it can correctly determine Bayesian credibility intervals on
atmospheric temperatures and abundances allowing for a quantitative exploration
of the inherent degeneracies. Furthermore, our new framework permits us to
trivially combine and explore the synergies between HRCCS and low-resolution
spectroscopy (LRS) to provide maximal leverage on the information contained
within each. This framework also allows us to quantitatively assess the impact
of molecular line opacities at high resolution. We apply the framework to VLT
CRIRES K-band spectra of HD 209458 b and HD 189733 b and retrieve abundant
carbon monoxide but sub-solar abundances for water, largely invariant under
different model assumptions. This confirms previous analysis of these datasets,
but is possibly at odds with detections of water at different wavelengths and
spectral resolutions. The framework presented here is the first step towards a
true synergy between space observatories and ground-based hi-resolution
observations.
