Companions of hot Jupiters: Two decades of radial velocity monitoring with CORALIE

Hot Jupiters are thought to form through multiple pathways, some of which can leave observable signatures in the architecture of their planetary systems. Massive outer companions, in particular, can provide important constraints on the dynamical histories of hot Jupiters. We aim to characterize the occurrence rate and orbital properties of additional giant companions in hot Jupiter systems and to investigate whether these companions provide evidence for the role of dynamical interactions in shaping the hot Jupiter population. We performed a homogeneous long-term radial-velocity analysis of 147 WASP hot Jupiter systems observed with the CORALIE spectrograph between 2007 and 2025. We identified or refined 13 outer giant companions and used individual radial-velocity posteriors within a Bayesian occurrence-rate framework to measure the frequency of giant companions over orbital periods of 10--6250 days. The occurrence rate of additional giant companions increases strongly with orbital period, from $<0.01$ and 0.02 at orbital periods of 10--50 and 50--250 days to 0.05 and 0.17 at orbital periods of 250--1250 and 1250--6250 days, respectively, in agreement with the giant-planet occurrence of the general FGK population and with previous estimates of outer companions to hot Jupiters. Hot Jupiters with detected companions have longer orbital periods and higher eccentricities than those without. We also find that companion eccentricity decreases with hot Jupiter period and that the companion-to-hot-Jupiter mass ratio increases with period ratio, both consistent with expectations from high-eccentricity migration (HEM). Our results support HEM as the mechanism shaping hot Jupiters with outer companions. Long-baseline radial velocities combined with future Gaia astrometry will further constrain companion masses, mutual inclinations, and dynamical histories.