Discovery and Characterization of Two Neptune-mass Planets Orbiting HD 212729 with TESS

We report the discovery of two exoplanets orbiting around HD 212729 (TOI 1052, TIC 317060587), a T_ eff=6146K star with V=9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of 2.87^+0.29_-0.24 R_⊕, a mass of 16.9± 1.7 M_⊕, and an orbital period of 9.14 days. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of 34.3^+4.1_-3.7 M_⊕ and an orbital period of 35.8 days, placing it just interior to the 4:1 mean motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of 0.18^+0.09_-0.07 for planet b and 0.24^+0.09_-0.08 for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is 3.9^+1.7_-1.3 g cm^-3 consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of 1500AU, making this a potential wide binary star system.