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\ndata, totalling nearly 250 stars. The stars cover a wide range of ages and\nspectral types, and include five detections ($\\kappa$ And b, two $\\sim$60\nM$_{\\rm J}$ brown dwarf companions in the Pleiades, PZ Tel B, and CD$-$35\n2722B). For some analyses we add a currently unpublished set of SEEDS\nobservations, including the detections GJ 504b and GJ 758B. We conduct a\nuniform, Bayesian analysis of all stellar ages using both membership in a\nkinematic moving group and activity/rotation age indicators. We then present a\nnew statistical method for computing the likelihood of a substellar\ndistribution function. By performing most of the integrals analytically, we\nachieve an enormous speedup over brute-force Monte Carlo. We use this method to\nplace upper limits on the maximum semimajor axis of the distribution function\nderived from radial-velocity planets, finding model-dependent values of\n$\\sim$30--100 AU. Finally, we model the entire substellar sample, from massive\nbrown dwarfs to a theoretically motivated cutoff at $\\sim$5 M$_{\\rm Jup}$, with\na single power law distribution. We find that $p(M, a) \\propto M^{-0.65\\pm0.60}\na^{-0.85\\pm0.39}$ (1$\\sigma$ errors) provides an adequate fit to our data, with\n1.0--3.1\\% (68\\% confidence) of stars hosting 5--70 $M_{\\rm Jup}$ companions\nbetween 10 and 100 AU. This suggests that many of the directly imaged\nexoplanets known, including most (if not all) of the low-mass companions in our\nsample, formed by fragmentation in a cloud or disk, and represent the low-mass\ntail of the brown dwarfs.\n