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

Abstract

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 ($\hat{I}º$ 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 For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B.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{Jup}}$, with a single power law distribution. We find that $p(M,a)\propto M^{-0.65\pm 0.60}{a}^{-0.85\pm 0.39}$ (1$\ddot{I}ƒ$ errors) provides an adequate fit to our data, with 1.0--3.1\% (68\% confidence) of stars hosting 5--70 $M_{\mathrm{Jup}}$ 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.

ApJ in press, replaced with accepted version. Methodology clarified, conclusions mostly unchanged