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Understanding the formation and evolution of giant planets ($\ge$1 $M_{Jup}$)at wide orbital separation ($\ge$5 AU) is one of the goals of direct imaging.Over the past 15 years, many surveys have placed strong constraints on theoccurrence rate of wide-orbit giants, mostly based on non-detections, but veryfew have tried to make a direct link with planet formation theories. In thepresent work, we combine the results of our previously published VLT/NaCo largeprogram with the results of 12 past imaging surveys to constitute a statisticalsample of 199 FGK stars within 100 pc, including 3 stars with sub-stellarcompanions. Using Monte Carlo simulations and assuming linear flatdistributions for the mass and semi-major axis of planets, we estimate thesub-stellar companion frequency to be within 0.75-5.7% at the 68% confidencelevel (CL) within 20-300 AU and 0.5-75 $M_{Jup}$, which is compatible withpreviously published results. We also compare our results with the predictionsof state-of-the-art population synthesis models based on the gravitationalinstability (GI) formation scenario by Forgan & Rice (2013), with and withoutscattering. We estimate that in both the scattered and non-scatteredpopulations, we would be able to detect more than 30% of companions in the 1-75$M_{Jup}$ range (95% CL). With the 3 sub-stellar detections in our sample, weestimate the fraction of stars that host a planetary system formed by GI to bewithin 1.0-8.6% (95% CL). We also conclude that even though GI is not common,it predicts a mass distribution of wide-orbit massive companions that is muchcloser to what is observed than what the core accretion scenario predicts.Finally, we associate the present paper with the release of the Direct ImagingVirtual Archive (DIVA, http://cesam.lam.fr/diva/), a public database that aimsat gathering the results of past, present, and future direct imaging surveys.

astronomy and astrophysics

The VLT/NaCo large program to probe the occurrence of exoplanets and  brown dwarfs at wide orbits. IV. Gravitational instability rarely forms wide,  giant planets