Statistical analysis of exoplanet surveys

We use this method to place upper limits on the maximum semimajor axis of the distribution function derived from radial-velocity planets, finding model-dependent values of ~30-100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at ~5 M_J_, with a single power-law distribution. We find that p(M,a){prop.to}M^-0.65+/-0.60^a^-0.85+/-0.39^ (1{sigma} errors) provides an adequate fit to our data, with 1.0%-3.1% (68% confidence) of stars hosting 5-70 M_J_ companions between 10 and 100 AU.

This suggests that many of the directly imaged exoplanets known, including most (if not all) of the low-mass companions in our sample, formed by fragmentation in a cloud or disk, and represent the low-mass tail of the brown dwarfs.