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Pi Men hosts a transiting planet detected by the TESS space mission and anouter planet in a 5.7-yr orbit discovered by RV surveys. We studied this systemusing new radial velocity (RV) measurements taken with the HARPS spectrographon ESO's 3.6-m telescope as well as archival data. We constrain the stellar RVsemi-amplitude due to the transiting planet, Pi Men c, as K_c = 1.21 +/- 0.12m/s resulting in a planet mass of M_c = 3.63 +/- 0.38 M_Earth. A planet radiusof R_c= 2.145 +/- 0.015 R_Earth yields a bulk density of rho = 2.03 +/- 0.22g/cm^{-3}. The precisely determined density of this planet and the brightnessof the host star make Pi Men c an excellent laboratory for internal structureand atmospheric characterization studies. Our HARPS RV measurements also revealcompelling evidence for a third body, PI Men d, with a minimum mass M sin i =13.38 +/- 1.35 M_Earth orbiting with a period of P_d = 125 d on an eccentricorbit (e = 0.22). A simple dynamical analysis indicates that the orbit of PiMen d is stable on timescales of at least 20 Myrs. Given the mutual inclinationbetween the outer gaseous giant and the inner rocky planet and the presence ofa third body at 125 d, Pi Men is an important planetary system for dynamicaland formation studies.

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-d Orbit