Radial velocities: direct application of Pierre Connes' shift finding algorithm to Cross-Correlation Functions

Abstract: Pipelines of state-of-the-art spectrographs dedicated to planet detection provide, for each exposure, series of Cross-Correlation Functions (CCFs) built with a Binary Mask (BM), and the absolute radial velocity (RV) derived from Gaussian fit of a weighted average CCF${tot}$ of the CCFs. Here we tested the benefits of the application of the shift finding algorithm developed by Pierre Connes directly to the total CCF${tot}$, comparing the resulting RV shifts (DRVs) with the results of the Gaussian fits. In a second step, we investigated how the individual DRV profiles along the velocity grid can be used as an easy tool for detection of stellar line shape variations. We tested this new algorithm on 1151 archived spectra of the K2.5 V star HD 40307 obtained with ESO/ESPRESSO during a one-week campaign in 2018. Tests were performed based on the comparison of DRVs with RVs from Gaussian fits. DRV profiles along the velocity grid (DRV(i)) were scrutinized and compared with direct CCF$_{tot}$ ratios. The dispersion of residuals from a linear fit to RVs from 406 spectra recorded within one night, was found to be $\sigma$=1.03 and 0.83 ms$^{-1}$ for the Gaussian fit and the new algorithm respectively, a significant 20\% improvement in accuracy. The two full one-week series obtained during the campaign were also fitted with a 3-planet system Keplerian model. The residual divergence between data and best-fit model is significantly smaller for the new algorithm than for the Gaussian fit. This new algorithm is an easy tool allowing to obtain additional diagnostics on the RV measurements in series of exposures. It increases the accuracy of velocity variation determinations. Also, departures from constancy of the DRVi profiles, as well as varying differences between RVs from this new method and RVs from a Gaussian fit provide diagnostics of line shape variations due to stellar activity.