The COBREX archival survey: improved constraints on the occurrence rate of wide-orbit substellar companions. I. A uniform re-analysis of 400 stars from the GPIES survey

Direct imaging (DI) campaigns are uniquely suited to probing the outer regions around young stars and looking for giant exoplanet and brown dwarf companions, hence providing key complementary information to radial velocity (RV) and transit searches for the purpose of demographic studies. However, the critical 5-20 au region, where most giant planets are thought to form, remains poorly explored, lying in-between 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 in order to undertake a large and uniform re-analysis. In particular, this paper details the re-analysis of 400 stars from the GPIES survey operated at GPI@Gemini South. Following the pre-reduction of raw frames, 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 for an estimate of unbiased occurrence frequencies of giant planets and brown dwarfs. Deeper detection limits were derived compared to the literature, with up to a twofold 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 derive an occurrence rate of $1.7_{-0.7}^{+0.9}\%$ for $5$~\mjup$ < m < 13$~\mjup planets in $10~\text{au}< a < 100~\text{au}$, that raises to $2.2_{-0.8}^{+1.0}\%$ when including substellar objects up to 80 \mjup.(abridged)