Sub-Jupiter Gas Giants Orbiting Giant Stars Uncovered using a Bayesian Framework

Giant stars have been shown to be rich hunting grounds for those aiming to detect giant planets orbiting beyond ~0.5 AU. Here we present two planetary systems around bright giant stars, found by combining the radial-velocity (RV) measurements from the EXPRESS and PPPS projects, and using a Bayesian framework. HIP18606 is a naked-eye (V=5.8 mags) K0III star and is found to host a planet with an orbital period of ~675 days, a minimum mass (Msini) of 0.8 MJ, and a circular orbit. HIP111909 is a bright (V=7.4 mags) K1III star, and hosts two giant planets on circular orbits with minimum masses of Msini=1.2 MJ and Msini=0.8 MJ, and orbital periods of ~490 d and ~890 d, for planets b and c respectively, strikingly close to the 5:3 orbital period ratio. Analysis of 11 known giant star planetary systems arrive at broadly similar parameters to those published, whilst adding a further two new worlds orbiting these stars. With these new discoveries, we have found a total of 13 planetary systems (including three multiple systems) within the 37 giant stars that comprise the EXPRESS and PPPS common sample. Periodogram analyses of stellar activity indicators present possible peaks at frequencies close to proposed Doppler signals in at least two planetary systems, HIP24275 and HIP90988, calling for more long-term activity studies of giant stars. Even disregarding these possible false-positives, extrapolation leads to a fraction of 25-30% of low-luminosity giant stars hosting planets. We find the mass-function exponentially rises towards the lowest planetary masses, however there exists a ~93% probability that a second population of giant planets with minimum masses between 4-5 MJ, is present, worlds that could have formed by the gravitational collapse of fragmenting proto-planetary disks. Finally, our noise modelling reveals a lack of statistical evidence for the presence of correlated noise...(Abridged)