Precise radial velocities of giant stars XVI. Planet occurrence rates from the combined analysis of the Lick, EXPRESS, and PPPS giant star surveys

RV surveys of evolved stars allow us to probe a higher stellar mass range compared to main-sequence samples. Differences between the planet populations can be caused by either the differing stellar mass or stellar evolution. To properly disentangle the effects of both, the planet population around giant stars needs to be characterized as accurately as possible. Our goal is to investigate the giant planet occurrence rate around evolved stars and determine its dependence on stellar mass, metallicity, and orbital period. We combine data from the Lick, EXPRESS, and PPPS giant star surveys, yielding a sample of 482 evolved stars and 37 planets. We homogeneously rederived the stellar parameters and accounted for varying observational coverage, precision, and stellar noise properties by computing detection maps via injection and retrieval of synthetic planetary signals. We then computed occurrence rates as a function of period, stellar mass, and metallicity, corrected for incompleteness. Our findings agree with previous studies that found a positive planet-metallicity correlation for evolved stars and identified a peak in the occurrence rate as a function of stellar mass, but our results place it at a slightly smaller mass of 1.68Msun. The period dependence of the occurrence rate seems to follow a broken power-law or log-normal peaking at 700-800 days, roughly corresponding to 1.6AU for a 1Msun star and 2.0AU for a 2Msun star. This peak could be a remnant from halted migration around intermediate-mass stars, caused by stellar evolution, or an artifact from contamination by false positives. The global occurrence rate of giant planetary systems is 10.7% for the entire sample, while the subsets of RGB and HB stars exhibit 14.2% and 6.6%, respectively. However, we demonstrate that the different stellar mass distributions suffice to explain the apparent change of occurrence with evolutionary stage.