TESS and HARPS reveal two sub-Neptunes around TOI 1062

The Transiting Exoplanet Survey Satellite (\textit{TESS}) mission was designed to perform an all-sky search of planets around bright and nearby stars. Here we report the discovery of two sub-Neptunes orbiting around the TOI 1062 (TIC 299799658), a V=10.25 G9V star observed in the TESS Sectors 1, 13, 27 & 28. We use precise radial velocity observations from HARPS to confirm and characterize these two planets. TOI 1062b has a radius of 2.265^{+0.095}_{-0.091} Re, a mass of 11.8 +\- 1.4 Me, and an orbital period of 4.115050 +/- 0.000007 days. The second planet is not transiting, has a minimum mass of 7.4 +/- 1.6 Me and is near the 2:1 mean motion resonance with the innermost planet with an orbital period of 8.13^{+0.02}_{-0.01} days. We performed a dynamical analysis to explore the proximity of the system to this resonance, and to attempt at further constraining the orbital parameters. The transiting planet has a mean density of 5.58^{+1.00}_{-0.89} g cm^-3 and an analysis of its internal structure reveals that it is expected to have a small volatile envelope accounting for 0.35% of the mass at maximum. The star's brightness and the proximity of the inner planet to the "radius gap" make it an interesting candidate for transmission spectroscopy, which could further constrain the composition and internal structure of TOI 1062b.