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Since 2011, the SOPHIE spectrograph has been used to search for Neptunes andsuper-Earths in the Northern Hemisphere. As part of this observational program,290 radial velocity measurements of the 6.4 V magnitude star HD 158259 wereobtained. Additionally, TESS photometric measurements of this target areavailable. We present an analysis of the SOPHIE data and compare our resultswith the output of the TESS pipeline. The radial velocity data, ancillaryspectroscopic indices, and ground-based photometric measurements were analyzedwith classical and $\ell_1$ periodograms. The stellar activity was modeled as acorrelated Gaussian noise and its impact on the planet detection was measuredwith a new technique. The SOPHIE data support the detection of five planets,each with $m \sin i \approx 6 M_\oplus$, orbiting HD 158259 in 3.4, 5.2, 7.9,12, and 17.4 days. Though a planetary origin is strongly favored, the 17.4 dsignal is classified as a planet candidate due to a slightly lower statisticalsignificance and to its proximity to the expected stellar rotation period. Thedata also present low frequency variations, most likely originating from amagnetic cycle and instrument systematics. Furthermore, the TESS pipelinereports a significant signal at 2.17 days corresponding to a planet of radius$\approx 1.2 R_\oplus$. A compatible signal is seen in the radial velocities,which confirms the detection of an additional planet and yields a $\approx 2M_\oplus$ mass estimate. We find a system of five planets and a strongcandidate near a 3:2 mean motion resonance chain orbiting HD 158259. Theplanets are found to be outside of the two and three body resonances.

The SOPHIE search for northern extrasolar planets. XVI. HD 158259: A compact planetary system in a near-3:2 mean motion resonance chain