Characterizing planetary systems with SPIRou: Detection of a sub-Neptune in a 6-day period orbit around the M dwarf Gl 410

The search for exoplanets around nearby M dwarfs represents a crucial milestone in the census of planetary systems in the vicinity of our Solar System. Since 2018 our team has been conducting a blind search program for planets around nearby M dwarfs with the near-IR spectro-polarimeter and velocimeter SPIRou at the Canada-France-Hawaii Telescope and with the optical velocimeter SOPHIE at the Haute-Provence Observatory in France. The aim of this paper is to present our results on Gl 410, a 0.55 M_⊙ 480±150 Myr old active M dwarf distant 12 pc. We searched for planetary companions using radial velocities (RVs). We used the line-by-line (LBL) technique to measure the RVs with SPIRou and the template matching method with SOPHIE. Three different methods were employed, two based on principal component analysis (PCA), to clean the SPIRou RVs for systematics. We applied Gaussian processes (GP) modeling to correct the SOPHIE RVs for stellar activity. The ell_1 and apodized sine periodogram analysis was used to search for planetary signals in the SPIRou data taking into account activity indicators. We analyzed TESS data and searched for planetary transits. We report the detection of a M,sin$(i)$=8.4±1.3 M_⊕ sub-Neptune planet at a period of 6.020±0.004 days in circular orbit with SPIRou. The same signal, although with lower significance, was also retrieved in the SOPHIE RV data after correction for activity using a GP trained on SPIRou's longitudinal magnetic field (B_ measurements. The TESS data indicate that the planet is not transiting. Within the SPIRou wPCA RVs, we find tentative evidence for two additional planetary signals at 2.99 and 18.7 days. Infrared RVs are a powerful method to detect extrasolar planets around active M dwarfs. Care should be taken, however, to correct or filter systematics generated by residuals of the telluric correction or small structures in the detector plane. The LBL technique combined with PCA offers a promising way to reach this objective. Further monitoring of Gl 410 is necessary.