The SOPHIE search for northern extrasolar planets. XVII. A compact planetary system in a near 3:2 mean motion resonance chain

Aims. Since 2011, the SOPHIE spectrograph has been used to search for Neptunes and Super-Earths in the northern hemisphere. As part of this observation program, 290 radial velocity measurements of HD 158259 were obtained. We present the analysis of this dataset. Methods. The radial velocity data, corrected from instrument systematics, are analysed with classical and `1 periodograms. The stellar activity is modelled by a correlated Gaussian noise, and its impact on the planets detection is measured by a new technique based on cross-validation. Ancillary spectroscopic indices as well as photometric measurements are analysed to discuss the planetary origin of the signals. The stability of the system is assessed with numerical simulations. Results. We report the detection of four planets in a chain of near 3:2 mean motion resonances around HD 158259 at 3.4, 5.2, 7.9 and 12 days, with a possible fifth planet at 17.4 days, also near the 3:2 resonance. Additionally, two low frequency signals are found in the data, and are attributed to a magnetic cycle and instrument systematics. The four planets are found to be outside of the two and three body resonances. Conclusions.