Direct imaging (DI) campaigns are uniquely suited to probing the outer regions around young stars in pursuit of giant exoplanet and brown dwarf companions, providing key complementary information to radial velocity (RV) and transit searches for demographic studies. However, the critical 5-20 au region, where most giant planets are thought to form, remains poorly explored, as it lies between current RV and DI capabilities. Significant gains in detection performances can be attained at no instrumental cost by means of advanced post-processing techniques. In the context of the COBREX project, we have assembled the largest collection of archival DI observations to date with the aim of undertaking a large and uniform reanalysis. In particular, this paper details the reanalysis of 400 stars from the Gemini Planet Imager Exoplanet Survey (GPIES) operated at GPI@Gemini South. Following the prereduction of raw frames, the GPI data cubes were processed by means of the PACO algorithm. Candidates were identified and vetted based on multi-epoch proper motion analysis (whenever possible) and by means of a suitable color-magnitude diagram. The conversion of detection limits into detectability maps allowed us to estimate the unbiased occurrence frequencies of giant planets and brown dwarfs. We derived deeper detection limits than those reported in the literature, with up to a two-fold gain in minimum detectable mass, compared to previous GPI-based publications. Although no new substellar companion was confirmed, we identified two interesting planet candidates awaiting follow-up observations. We derived an occurrence rate of $1.7_ <!PCT!>$ for $5$ < m < 13$ planets in $10 au < a < 100 au $. This rises to $2.2_ <!PCT!>$ when including substellar objects up to 80 Our results are in line with the literature, but with lower uncertainties, thanks to the enhanced detection sensitivity. We confirm, as hinted at by previous studies, a more frequent occurrence of giant planets around BA hosts compared to FGK stars. Moreover, we tentatively observe a smaller occurrence of brown dwarf companions around BA stars, although larger samples are needed to shed light on this point. While awaiting the wealth of data anticipated from future instrument and facilities, valuable information can still be extracted from existing data. In this regard, a complete reanalysis of SPHERE and GPI data is expected to provide the most precise demographic constraints ever provided by direct imaging.
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