A new treatment of telluric and stellar features for medium resolution spectroscopy and molecular mapping. Application to the abundance determination on Beta Pic b

Molecular mapping is a supervised method exploiting the spectral diversity of integral field spectrographs to detect and characterize resolved exoplanets blurred into the stellar halo. We present an evolution of the method to remove the stellar halo and the nuisance of telluric features in the datacubes and access a continuum-subtracted spectra of the planets at R$\sim$4000. We derive planet atmosphere properties from a direct analysis of the planet telluric-corrected absorption spectrum. We applied our methods to the SINFONI observation of the planet $\beta$ Pictoris b. We recover the CO and H$_2$O detections in the atmosphere of $\beta$ Pic b using molecular mapping. We further determine some basic properties of its atmosphere, with $T_\text{eq}=1748^{+3}_{-4}$ K, a sub-solar [Fe/H]=$-0.235^{+0.015}_{-0.013}$ dex, and a solar C/O=$0.551 \pm 0.002$ in contrast with values measured for the same exoplanet with other infrared instruments. We confirm a low projected equatorial velocity of 25$^{+5}_{-6}$ km s$^{-1}$. We are also able to measure, for the first time with a medium-resolution spectrograph, the radial velocity of $\beta$ Pic b relative to the central star at MJD=56910.38 with a km/s precision of $-11.3 \pm 1.1$ km s$^{-1}$, compatible with ephemerides based on the current knowledge of the $\beta$ Pic system.