Relative abundance constraints from high-resolution optical transmission spectroscopy of WASP-121b, and a fast model-filtering technique for accelerating retrievals

High-resolution Doppler-resolved spectroscopy has presented new opportunities for studying the atmospheres of exoplanets. While the 'classical' cross-correlation approach has proven to be efficient at finding atmospheric species, it is unable to perform direct atmospheric retrievals. Recent work has shown that retrievals are possible using a direct likelihood evaluation or likelihood 'mappings'. The unique aspect of high-resolution retrievals is that the data-processing methods required to remove the stellar and telluric lines also distort the underlying exoplanet's signal and therefore the forward model must be pre-processed to match this filtering. This was the key remaining limitation in our previously published framework. This paper directly addresses this by introducing a simple and fast model-filtering technique that can replicate the processing performed by algorithms such as SysRem and PCA. This enables retrievals to be performed without having to perform expensive injection and pre-processing steps for every model. We show that we can reliably constrain quantitative measures of the atmosphere from transmission spectra including the temperature-pressure profile, relative abundances, planetary velocities and rotational broadening parameters. Finally, we demonstrate our framework using UVES transmission spectroscopy of WASP-121b. We constrain the temperature-pressure profile and relative abundances of Fe, Cr, and V to be $\log_{10}(\chi_{\rm Fe}/\chi_{\rm Cr})$=1.66$\pm$0.28, $\log_{10}(\chi_{\rm Fe}/\chi_{\rm V})$=3.78$\pm$0.29 and $\log_{10}(\chi_{\rm Fe}/\chi_{\rm Mg})$=-1.26$\pm$0.60. The relative abundances are consistent with solar values, with the exception of Fe/Mg, where the large Mg abundance is probably explained by the escaping atmosphere of WASP-121b that is not accounted for in our atmospheric model.