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Ground-based high-resolution spectrographs are key instruments for severalastrophysical domains. Unfortunately, the observed spectra are contaminated bythe Earth's atmosphere. While different techniques exist to correct fortelluric lines in exoplanet atmospheric studies, in radial velocity (RV)studies, telluric lines with an absorption depth of >2% are generally masked,which poses a problem for faint targets and M dwarfs as most of their RVcontent is present where telluric contamination is important. We propose asimple telluric model to be embedded in the ESPRESSO DRS. The goal is toprovide telluric-free spectra and enable RV measurements, including spectralranges where telluric lines fall. The model is a line-by-line radiativetransfer code that assumes a single atmospheric layer. We use the skyconditions and the physical properties of the lines from HITRAN to create thetelluric spectrum. A subset of selected telluric lines is used to robustly fitthe spectrum through a Levenberg-Marquardt minimization algorithm. When appliedto stellar spectra from A0- to M5-type stars, the residuals of the strongestH2O lines are below 2% for all spectral types, with the exception of M dwarfs,which are within the pseudo-continuum. We then determined the RVs from thetelluric-corrected ESPRESSO spectra of Tau Ceti and Proxima. We createdtelluric-free masks and compared the obtained RVs with the DRS RVs. In the caseof Tau Ceti, we identified that micro-telluric lines introduce systematics upto an amplitude of 58 cm/s and with a period of one year. For Proxima, the gainin spectral content at redder wavelengths is equivalent to a gain of 25% inphoton noise. This leads to better constraints on the semi-amplitude andeccentricity of Proxima d. We showcase that our model can be applied to othermolecules, and thus to other wavelength regions observed by otherspectrographs, such as NIRPS.

Automatic model-based telluric correction for the ESPRESSO data reduction software. Model description and application to radial velocity computation