The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets

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Abstract
We analyze 8 years of precise radial velocity measurements from the Keck Planet Search, characterizing the detection threshold, selection effects, and completeness of the survey. We carry out a systematic search for planets by assessing the false alarm probability associated with Keplerian orbit fits to the data. This allows us to understand the detection threshold for each star in terms of the number and time baseline of the observations, and size of measurement errors and stellar jitter. We show that all planets with orbital periods 20 m/s, and eccentricities 0.3 Jupiter masses and periods <2000 days gives a mass-period distribution dN=C M^\alpha P^\beta dlnM dlnP with \alpha=-0.31 \pm 0.2, \beta=0.26\pm 0.1, and the normalization constant C such that 10.5% of solar type stars have a planet with mass in the range 0.3-10 Jupiter masses and orbital period 2-2000 days. The orbital period distribution shows an increase in the planet fraction by a factor of 5 for orbital periods beyond 300 days. Extrapolation gives 17-20% of stars having gas giant planets within 20 AU. Finally, taking into account differences in detectability, we find that M dwarfs are 3 to 10 times less likely to harbor a Jupiter mass planet than solar type stars.Comment: 20 pages, 17 figures, accepted for publication in PAS
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