MASSIVE: A Bayesian analysis of giant planet populations around low-mass stars

Direct imaging has led to the discovery of several giant planet and brown dwarf companions. These imaged companions populate a mass, separation and age domain (mass>1MJup, orbits>5AU, age<1Gyr) quite distinct from the one occupied by exoplanets discovered by the radial velocity or transit methods. This distinction could pinpoint that different formation mechanisms are at play. We aim at investigating correlations between the host star's mass and the presence of wide-orbit giant planets, and at providing new observational constraints on planetary formation models. We observed 58 young and nearby M-type dwarfs in L'-band with the VLT/NaCo instrument and used ADI algorithms to optimize the sensitivity to planetary-mass companions and to derive the best detection limits. We estimate the probability of detecting a planet as a function of its mass and physical separation around each target. We conduct a Bayesian analysis to determine the frequency of substellar companions orbiting low-mass stars, using a homogenous sub-sample of 54 stars. We derive a frequency of $4.4^{+3.2}_{-1.3}\%$ for companions with masses in the range of 2-80MJup}, and $2.3^{+2.9}_{-0.7}$\% for planetary mass companions (2-14MJup), at physical separations of 8 to 400AU for both cases. Comparing our results with a previous survey targeting more massive stars, we find evidence that substellar companions more massive than 1MJup with a low mass ratio Q with respect to their host star (Q<1%), are less frequent around low-mass stars. This may represent an observational evidence that the frequency of imaged wide-orbit substellar companions is correlated with stellar mass, corroborating theoretical expectations. On the opposite, we show statistical evidence that intermediate-mass ratio (1%<Q<5%) companion with masses >2MJup might be independent from the mass of the host star.