Abstract
High-precision spectrographs can on occasion exhibit temporal variations in their reference velocity or nightly zero point (NZP). One way to monitor the NZP is to measure bright stars, whose intrinsic radial velocity variation is assumed to be much smaller than the instrument precision. The variations of these bright stars, which is primarily assumed to be instrumental, are then smoothed into a reference radial velocity time series (master constant) that is subtracted from the observed targets. While this method is effective in most cases, it does not fully propagate the uncertainty arising from NZP variations. We present a new method for correcting for NZP variations in radial velocity time series. This method uses Gaussian processes based on ancillary information to model these systematic effects. Moreover, it enables us to propagate the uncertainties of this correction into the overall error budget. Another advantage of this approach is that it relies on ancillary data that are collected simultaneously with the spectra and does not solely depend on dedicated observations of constant stars. We applied this method to the SOPHIE spectrograph at the Haute-Provence Observatory using a few instrument housekeeping data, such as the internal pressure and temperature variations. Our results demonstrate that this method effectively models the red noise of constant stars, even with a limited number of housekeeping data, while preserving the signals of exoplanets. Using simulations with mock planets and real data, we found that this method significantly improves the false-alarm probability of detections. It improves the probability by several orders of magnitude. Additionally, by simulating numerous planetary signals, we were able to detect up to 10% more planets with small-amplitude radial velocity signals. We used this new correction to reanalyse the planetary system around HD158259 and to improve the detection of the outermost planets. We propose this technique as a complementary approach to the classical master-constant correction of the instrumental red noise. We also suggest to decrease the observing cadence of the constant stars to optimise the telescope time for scientific targets.