The SPIRou Legacy Survey Rotation period of quiet M dwarfs from circular polarization in near-infrared spectral lines: I. The SPIRou APERO analysis

Context. The rotation period of stars is an important parameter along with mass, radius, effective temperature. It is an essential parameter for any radial velocity monitoring, as stellar activity can mimic the presence of a planet at the stellar rotation period. Several methods exist to measure it, including long sequences of photometric measurements or temporal series of stellar activity indicators. Aims. Here, we use the circular polarization in near-infrared spectral lines for a sample of 43 quiet M dwarfs and compare the measured rotation periods to those obtained with other methods. Methods. From Stokes V spectropolarimetric sequences observed with SPIRou at CFHT and the data processed with the APERO pipeline, we compute the least squares deconvolution profiles using different masks of atomic stellar lines with known Land\'e factor appropriate to the effective temperature of the star. We derive the longitudinal magnetic field to examine its possible variation along the 50 to 200 observations of each star. For determining the stellar rotation period, we apply a Gaussian process regression enabling us to determine the rotation period of stars with evolving longitudinal field. Results. Among the 43 stars of our sample, we were able to measure a rotation period for 27 stars. For 8 stars, the rotation period was previously unknown. We find a good agreement of our rotation periods with periods found in the literature based on photometry and activity indicators and confirm that near-infrared spectropolarimetry is an important tool to measure rotation periods, even for magnetically quiet stars. Furthermore, we compute ages for 20 stars of our sample using gyrochronology.