A Radial Velocity Study of the Planetary System of pi Mensae: Improved Planet Parameters for pi Mensae c and a Third Planet on a 125 Day Orbit

pi Men hosts a transiting planet detected by the Transiting Exoplanet Survey Satellite space mission and an outer planet in a 5.7 yr orbit discovered by radial velocity (RV) surveys. We studied this system using new RV measurements taken with the HARPS spectrograph on ESO's 3.6 m telescope, as well as archival data. We constrain the stellar RV semiamplitude due to the transiting planet, pi Men c, as K (c) = 1.21 +/- 0.12 m s(-1), resulting in a planet mass of M (c) = 3.63 +/- 0.38 M (circle plus). A planet radius of R (c) = 2.145 +/- 0.015 R (circle plus) yields a bulk density of rho (c) = 2.03 +/- 0.22 g cm(-3). The precisely determined density of this planet and the brightness of the host star make pi Men c an excellent laboratory for internal structure and atmospheric characterization studies. Our HARPS RV measurements also reveal compelling evidence for a third body, pi Men d, with a minimum mass M (d) sin i (d) = 13.38 +/- 1.35 M (circle plus) orbiting with a period of P (orb,d) = 125 days on an eccentric orbit (e (d) = 0.22). A simple dynamical analysis indicates that the orbit of pi Men d is stable on timescales of at least 20 Myr. Given the mutual inclination between the outer gaseous giant and the inner rocky planet and the presence of a third body at 125 days, pi Men is an important planetary system for dynamical and formation studies.