### 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 (κ And b, two60 M 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 For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B.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 of30-100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at5 M J, with a single power-law distribution. We find that p(M, a)M ^{-0.65 ± 0.60} a ^{-0.85 ± 0.39} (1σ 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.

Original language | English (US) |
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Article number | 159 |

Journal | Astrophysical Journal |

Volume | 794 |

Issue number | 2 |

DOIs | |

State | Published - Oct 20 2014 |

Externally published | Yes |

### Keywords

- brown dwarfs
- methods: statistical
- open clusters and associations: general
- planetary systems
- stars: activity
- stars: imaging

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*794*(2), [159]. https://doi.org/10.1088/0004-637X/794/2/159