We present an improved method for correcting the nightly zero-point (NZP) variations in radial-velocity time series obtained from high-precision spectrographs, focusing on the SOPHIE spectrograph at the Haute-Provence Observatory. These systematics affect the instrumental stability of spectrographs. To address this issue, we propose a novel approach that utilizes Gaussian Processes based on ancillary information from the spectrograph to model these systematic effects. This method is inspired by the one commonly used in photometry to correct the intra-pixel sensitivity of space missions like Spitzer and K2. We applied this method using a few instrument's housekeeping data, such as internal pressure and temperature variations.

Our results demonstrate the effectiveness of this method in accurately modeling the red noise of constant stars while preserving the signals of exoplanets. By conducting simulations with mock planets, we observed a significant improvement in the false-alarm probability of detections by several orders of magnitude. Furthermore, our method detected up to 10% more planets with small amplitude radial velocity signals. This promising correction approach enables detecting planetary signals with even smaller amplitudes.

We applied this correction method to the planetary system HD158259, which already has five known planets discovered by SOPHIE (Hara et al. 2019). We successfully recovered all five signals by employing our new correction method and not relying on the noise model developed in the paper. Furthermore, we confirmed the presence of HD158259g, the system's sixth planet, previously identified as a candidate. Our findings include a lower False-Alarm-Probability signal that remains stable in time.

In this talk, I will present all these new results for detecting and characterizing exoplanets with SOPHIE and the future possible improvements of the method, considering more housekeeping variables.