A Statistical Analysis of SEEDS and Other High-Contrast Exoplanet Surveys: Massive Planets or Low-Mass Brown Dwarfs?

We conduct a statistical analysis of a combined sample of direct imaging data, totalling nearly 250 stars. The stars cover a wide range of ages and spectral types, and include five detections ($\kappa$ And b, two $\sim$60 M${}_{\mathrm{J}}$ brown dwarf companions in the Pleiades, PZ Tel B, and CD$-$35 2722B). For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B. We conduct a uniform, Bayesian analysis of all stellar ages using both membership in a kinematic moving group and activity/rotation age indicators. We then present a new statistical method for computing the likelihood of a substellar distribution function. By performing most of the integrals analytically, we achieve an enormous speedup over brute-force Monte Carlo. 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 $\sim$30–100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at $\sim$5 M${}_{\mathrm{J}\mathrm{u}\mathrm{p}}$, with a single power law distribution. We find that $p(M, a) \propto M^{-0.65\pm0.60} a^{-0.85\pm0.39}$(1$\sigma$ errors) provides an adequate fit to our data, with 1.0–3.1% (68% confidence) of stars hosting 5–70 $M_{\mathrm{J}\mathrm{u}\mathrm{p}}$ 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.