Constraints on the Occurrence and Distribution of 1-20 MJup Companions to Stars at Separations of 5-5000 au from a Compilation of Direct Imaging Surveys

We present the first statistical analysis of exoplanet direct imaging surveys combining adaptive optics (AO) imaging at small separations with deep seeing-limited observations at large separations allowing us to study the entire orbital separation domain from 5 to 5000 au simultaneously. Our sample of 344 stars includes only confirmed members of nearby young associations and is based on all AO direct-imaging detection limits readily available online, with addition of our own previous seeing-limited surveys. Assuming that the companion distribution in mass and a semimajor axis follows a power-law distribution and adding a dependence on the mass of the host star, such as d(2)n proportional to fM(alpha) a(beta) (M-*/M-circle dot)(gamma)dMda we constrain the parameters to obtain alpha = - 0.18(-0.65)(+0.77), beta = - 1.43(-0.24)(+0.23), and gamma = 0.62(-0.50)(+0.56) at a 68% confidence level, and we obtain f = 0.11(-0.05)(+0.11) for the overall planet occurrence rate for companions with masses between 1 and 20 M-Jup in the range of 5-5000 au. Thus, we find that occurrence of companions is negatively correlated with a semimajor axis and companion mass (marginally) but is positively correlated with the stellar host mass. Our inferred mass distribution is in good agreement with other distributions found previously from direct imaging surveys for planets and brown dwarfs, but is shallower as a function of mass than the distributions inferred by radial velocity surveys of gas giants in the 1-3 au range. This may suggest that planets at these wide and very wide separations represent the low-mass tail of the brown dwarfs and stellar companion distribution rather than an extension of the distribution of the inner planets.