Precise radial velocities of giant stars, XVI.

We homogeneously rederived the stellar parameters of all targets and accounted for varying observational coverage, precision and stellar noise properties by computing a detection probability map for each star via injection and retrieval of synthetic planetary signals. We then computed giant planet 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 giant planet occurrence rate as a function of stellar mass, but our results place it at a slightly smaller mass of (1.68+/-0.59)M_{sun}_.

The period dependence of the giant planet occurrence rate seems to follow a broken power-law or log-normal distribution peaking at (718+/-226)days or (797+/-455)days, respectively, which roughly corresponds to 1.6AU for a 1M_{sun}_ star and 2.0 AU for a 2M_{sun}_ 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 completeness-corrected global occurrence rate of giant planetary systems around evolved stars is 10.7_-1.6_^+2.2^% for the entire sample, while the evolutionary subsets of RGB and HB stars exhibit 14.2_-2.7_^+4.1^% and 6.6_-1.3_^+2.1^%, respectively. However, both subsets have different stellar mass distributions and we demonstrate that the stellar mass dependence of the occurrence rate suffices to explain the apparent change of occurrence with the evolutionary stage.