The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets
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 first carry out a systematic search for planets, by assessing the falsealarm 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 the underlying “noise” from measurement errors, intrinsic stellar jitter, or additional lowmass planets. We show that all planets with orbital periods P < 2000 days, velocity amplitudes K > 20 m s^{1}, and eccentricities e ≲ 0.6 have been announced, and we 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. For orbital periods less than the duration of the observations, these are typically 10 m s^{1} and increase ∝ P^{2} for longer periods. We then use the nondetections to derive completeness corrections at low amplitudes and long orbital periods and discuss the resulting distribution of minimum mass and orbital period. We give the fraction of stars with a planet as a function of minimum mass and orbital period and extrapolate to longperiod orbits and low planet masses. A powerlaw fit for planet masses >0.3 M_{J} and periods < 2000 days gives a massperiod distribution dN = CM^{α} P^{β} d ln Md ln P with α = 0.31 ± 0.2, β = 0.26 ± 0.1, and the normalization constant C such that 10.5% of solar type stars have a planet with mass in the range 0.310 M_{J} and orbital period 22000 days. The orbital period distribution shows an increase in the planet fraction by a factor of ≈5 for orbital periods ≳300 days. Extrapolation gives 17%20% of stars having gas giant planets within 20 AU. Finally, we constrain the occurrence rate of planets orbiting M dwarfs compared to FGK dwarfs, taking into account differences in detectability.
 Publication:

Publications of the Astronomical Society of the Pacific
 Pub Date:
 May 2008
 DOI:
 10.1086/588487
 arXiv:
 arXiv:0803.3357
 Bibcode:
 2008PASP..120..531C
 Keywords:

 Astrophysics
 EPrint:
 20 pages, 17 figures, accepted for publication in PASP