### 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 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 the underlying "noise" from measurement errors, intrinsic stellar jitter, or additional low-mass planets. We show that all planets with orbital periods P < 2000 days, velocity amplitudes K > 20 ms^{-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 ms^{-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 long-period orbits and low planet masses. A power-law fit for planet masses > 0.3 M_{J} and periods < 2000 days gives a mass-period distribution dN = CM ^{α}P^{β}d ln Mdln 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 0.3-10 M _{J} 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 ≳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.

Original language | English (US) |
---|---|

Pages (from-to) | 531-534 |

Number of pages | 4 |

Journal | Publications of the Astronomical Society of the Pacific |

Volume | 120 |

Issue number | 867 |

DOIs | |

State | Published - May 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Publications of the Astronomical Society of the Pacific*,

*120*(867), 531-534. https://doi.org/10.1086/588487

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*Publications of the Astronomical Society of the Pacific*, vol. 120, no. 867, pp. 531-534. https://doi.org/10.1086/588487

**The keck planet search : Detectability and the minimum mass and orbital period distribution of extrasolar planets.** / Cumming, Andrew; Butler, R. Paul; Marcy, Geoffrey W.; Vogt, Steven S.; Wright, Jason; Fischer, Debra A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The keck planet search

T2 - Detectability and the minimum mass and orbital period distribution of extrasolar planets

AU - Cumming, Andrew

AU - Butler, R. Paul

AU - Marcy, Geoffrey W.

AU - Vogt, Steven S.

AU - Wright, Jason

AU - Fischer, Debra A.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - 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 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 the underlying "noise" from measurement errors, intrinsic stellar jitter, or additional low-mass planets. We show that all planets with orbital periods P < 2000 days, velocity amplitudes K > 20 ms-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 ms-1 and increase ∝ P2 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 long-period orbits and low planet masses. A power-law fit for planet masses > 0.3 MJ and periods < 2000 days gives a mass-period distribution dN = CM αPβd ln Mdln 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 0.3-10 M J 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 ≳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.

AB - 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 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 the underlying "noise" from measurement errors, intrinsic stellar jitter, or additional low-mass planets. We show that all planets with orbital periods P < 2000 days, velocity amplitudes K > 20 ms-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 ms-1 and increase ∝ P2 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 long-period orbits and low planet masses. A power-law fit for planet masses > 0.3 MJ and periods < 2000 days gives a mass-period distribution dN = CM αPβd ln Mdln 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 0.3-10 M J 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 ≳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.

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U2 - 10.1086/588487

DO - 10.1086/588487

M3 - Article

VL - 120

SP - 531

EP - 534

JO - Publications of the Astronomical Society of the Pacific

JF - Publications of the Astronomical Society of the Pacific

SN - 0004-6280

IS - 867

ER -