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), as well as the absolute radial velocity (RV) derived from the Gaussian fit of a weighted average CCF$_ tot $ of the CCFs. Our aim was to test the benefits of the application of the shift-finding algorithm developed by Pierre Connes directly to the total CCF$_ tot $, and to compare the resulting RV shifts (DRVs) with the results of the Gaussian fits. In a second step, we investigated how the individual DRV profiles along the velocity grid derived from the shift-finding algorithm can be used as an easy tool for detection of stellar line shape variations. We developed the corresponding algorithm and tested it on 1151 archived spectra of the K2.5 V star HD 40307 obtained with ESO/ESPRESSO during a one-week campaign in 2018. Tests were performed based on the comparison of DRVs with RVs from Gaussian fits. DRV profiles along the velocity grid (DRV(i)) were scrutinized and compared with direct CCF$_ tot $ ratios. The dispersion of residuals from a linear fit to RVs from 406 spectra recorded within a single night, a measure of mean error, was found to be sigma =1.03 and 0.83 ms$^ $ for the Gaussian fit and the new algorithm, respectively, which is a significant 20<!PCT!> improvement in accuracy. The two full one-week series obtained during the campaign were also fitted with a three-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. Such a difference was found to be associated in a large part with an increase of simeq 1.3 m.s$^ $ in the difference between the two types of RV values between the third and fourth nights. Interestingly, the DRV(i) profiles reveal at the same time a significant variation of line shape. The shift-finding algorithm is a fast and easy tool that provides additional diagnostics on the RV measurements in series of exposures. For observations made in the same instrumental configuration, and if line shapes are not varying significantly, it increases the accuracy of velocity variation determinations. On the other hand, departures from constancy of the DRV(i) profiles, as well as varying differences between RVs from this new method and RVs from a Gaussian fit can detect and report in a simple way line shape variations due to stellar activity.