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

TL;DR

This study analyzes 8 years of Keck radial velocity data to determine the detectability, distribution, and occurrence rates of extrasolar planets around solar-type stars, revealing a significant increase in planet frequency at longer orbital periods.

Contribution

It provides a systematic analysis of detection thresholds and derives the planet mass-period distribution, including occurrence rates and differences between star types, based on extensive observational data.

Findings

All planets with periods <2000 days and amplitudes >20 m/s have been announced.

Approximately 10.5% of solar-type stars host planets between 0.3-10 Jupiter masses and 2-2000 days.

M dwarfs are 3 to 10 times less likely to host Jupiter-mass planets than solar-type stars.

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 <2000 days, velocity amplitudes >20 m/s, and eccentricities <0.6 have been announced, and summarize the candidates at lower amplitudes and longer orbital periods. For the remaining stars, we calculate upper limits on the velocity amplitude of a companion, typically 10 m/s, and use the non-detections to derive completeness corrections at low amplitudes and long orbital periods. We give the fraction of stars with a planet as a function of planet mass and orbital period, and extrapolate to long period orbits and low planet masses. A power law fit for planet masses >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.