A decade of monitoring the HIP 41378 planetary system. Masses and orbital periods of six planets and a planet candidate

Multi-planetary systems provide key constraints on planet formation and evolution, as their architecture encodes the dynamical history of planets formed within a common protoplanetary disc. However, the current population remains strongly biased towards compact, short-period systems, and only a limited number of such systems with measured masses and radii are known. HIP 41378 is an exceptional system hosting five transiting planets with orbital periods of up to 1.5 years, including an ultra-low-density planet, HIP 41378 f. The outer transiting planets d and e remained poorly constrained with unknown periods and masses, leaving the system architecture only partially characterised. We present long-term monitoring of this target with high-precision radial-velocity (RV) instruments (HARPS, HARPS-N, HIRES, and ESPRESSO) and space-based photometry spanning 2015-2024. We detected RV signals for all the planets, confirming their orbital periods and constraining their masses. In particular, the RV data strongly favour an orbital period of P_d = 278 days for planet d and refine the orbital period of planet e to P_e = 393_ -5 ^ +3 days. We measured a new mass of M_f = 25 ± 5 _ for HIP 41378 f, confirming its super-puff nature with a bulk density of ̊ho_f = 0.166^ +0.033 -0.036 We also confirm the planetary nature of HIP 41378 g, a non-transiting planet with a 63-day period, and determine its minimum mass. In addition, the RVs reveal a long-period signal, with P = 2602_ -433 ^ +468 days, which we attribute to the candidate planet HIP 41378 h, although a stellar magnetic cycle cannot be excluded. Finally, we investigated the system’s dynamical architecture and resonant structure, assessed its completeness by constraining additional undetected planets, and looked into the implications for the origin and internal structure of the remarkable planet HIP 41378 f.