The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets
Open accessAbstract
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 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 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 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 0.3–10 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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In units of Jupiter masses and days, the normalization constant C is 1.4 × 10^-3.
“In units corresponding to measuring planet masses in Jupiter masses and orbital periods in days, the value of the normalization is C = 1.4 × 10 -3 .”
From PLANETARY CONSTRUCTION ZONES IN OCCULTATION: DISCOVERY OF AN EXTRASOLAR RING SYSTEM TRANSITING A YOUNG SUN-LIKE STAR AND FUTURE PROSPECTS FOR DETECTING ECLIPSES BY CIRCUMSECONDARY AND CIRCUMPLANETARY DISKS (2012) · cites this paper as Cumming et al. 2008
Section 4, “Summary and Conclusions” (page not provided), gives the normalization in Jupiter masses and days as C = 1.04 × 10^-3, not 1.4 × 10^-3. (LLM, conf=0.94)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredSuper-Earths are more common than giant planets: ∼40% of stars have at least one super-Earth within a fifty day orbital period, whereas only ∼10% of stars have giant planets at any orbital period.
“Super-Earths are more common than giant planets. ∼ 40% of stars have at least one super-Earth within a fifty day orbital period (Howard et al. 2010), whereas only ∼ 10% of stars have giant planets at any orbital period (e.g., Cumming et al. 2008, Zechmeister et al. 2013).”
From Origins of Hot Jupiters (2018) · cites this paper as Cumming et al. 2008
Cumming et al. report that 10.5% of FGK stars have a planet of 0.3–10 Jupiter masses with an orbital period of 2–2000 days (Summary and Conclusions). That supports the approximate 10% figure, but not its extension to ‘any orbital period’: the same section estimates 17%–19% have a gas giant within 20 AU. The super-Earth figure is attributed to Howard et al., not Cumming et al. (LLM, conf=0.90)
Experimental — accuracy not yet measuredThe fraction of FGK stars with a planet in the mass range 0.3-10 M_J and period range 2-2000 days is 10.5%.
“where the normalization constant C is such that the fraction of FGK stars with a planet in the mass range 0.3-10 M J (where M J is a Jupiter mass) and period range 2-2000 days is 10.5% (Cumming et al. 2008).”
From PLANETARY CONSTRUCTION ZONES IN OCCULTATION: DISCOVERY OF AN EXTRASOLAR RING SYSTEM TRANSITING A YOUNG SUN-LIKE STAR AND FUTURE PROSPECTS FOR DETECTING ECLIPSES BY CIRCUMSECONDARY AND CIRCUMPLANETARY DISKS (2012) · cites this paper as Cumming et al. 2008
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Cites
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The HARPS search for southern extra-solar planets: XXXI. The M-dwarf sample
Bonfils, X., Delfosse, X., Udry, S., Forveille, T., Mayor, M., Perrier, C., Bouchy, F., Gillon, M., Lovis, C., Pepe, F., et al. (2013) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201014704 · Cited by 653 · see citing works
Dawson, R. I., & Johnson, J. A. (2018) · Annual Review of Astronomy and Astrophysics · doi:10.1146/annurev-astro-081817-051853 · Cited by 622 · see citing works
One or more bound planets per Milky Way star from microlensing observations
Cassan, A., Kubas, D., Beaulieu, J.-P., Dominik, M., Horne, K., Greenhill, J., Wambsganss, J., Menzies, J., Williams, A., Jørgensen, U. G., et al. (2012) · Nature · doi:10.1038/nature10684 · Cited by 584 · see citing works
The Birth Environment of the Solar System
Adams, F. C. (2010) · Annual Review of Astronomy and Astrophysics · doi:10.1146/annurev-astro-081309-130830 · Cited by 464 · see citing works
THE FREQUENCY OF HOT JUPITERS ORBITING NEARBY SOLAR-TYPE STARS
Wright, J. T., Marcy, G. W., Howard, A. W., Johnson, J. A., Morton, T. D., & Fischer, D. A. (2012) · The Astrophysical Journal · doi:10.1088/0004-637x/753/2/160 · Cited by 371 · see citing works
Self-citationBatygin, K., Adams, F. C., Brown, M. E., & Becker, J. C. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.01.009 · Cited by 181 · see citing works
“20Jovian-class objects like Jupiter and Saturn, on the other hand, are comparatively rare and are believed to reside within 20 AU in only ∼ 20% of sun-like stars (Cumming et al., 2008).”
BackgroundDebris disks as signposts of terrestrial planet formation
Raymond, S. N., Armitage, P. J., Moro-Martín, A., Booth, M., Wyatt, M. C., Armstrong, J. C., Mandell, A. M., Selsis, F., & West, A. A. (2011) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201116456 · Cited by 194 · see citing works
Mamajek, E. E., Quillen, A. C., Pecaut, M. J., Moolekamp, F., Scott, E. L., Kenworthy, M. A., Cameron, A. C., & Parley, N. R. (2012) · The Astronomical Journal · doi:10.1088/0004-6256/143/3/72 · Cited by 140 · see citing works
“…from Doppler radial velocity surveys is dN = CM−3.1±0.2P 0.26±0.1d logMd logP (12) where the normalization constant C is such that the fraction of FGK stars with a planet in the mass range 0.3 - 10 MJ (where MJ is a Jupiter mass) and period range 2- 2000 days is 10.5% (Cumming et al. 2008).”
BackgroundInfluentialHartman, J. D., Gaudi, B. S., Holman, M. J., McLeod, B. A., Stanek, K. Z., Barranco, J. A., Pinsonneault, M. H., Meibom, S., & Kalirai, J. S. (2009) · The Astrophysical Journal · doi:10.1088/0004-637x/695/1/336 · Cited by 51 · see citing works
- Authors
- Cumming, A., Butler, R. P., Marcy, G. W., Vogt, S. S., Wright, J. T., & Fischer, D. A.
- Affiliations
- McGill University (CA)
- Carnegie Institution for Science (US)
- University of California, Berkeley (US)
- University of California, Santa Cruz (US)
- San Francisco State University (US)
- Corresponding author
- Cumming, Andrew
- ORCID
- Venue
- Publications of the Astronomical Society of the Pacific
- Publisher
- IOP Publishing
- Published
- 2008-05
- Volume
- 120
- Issue
- 867
- Pages
- 531-554
- ISSN
- 0004-6280 (ISSN-L)
- 1538-3873
- OpenAlex
- W2177545076
- Cited by
- 892
- References
- 1
- Citations by year
- 2026: 17 · 2025: 36 · 2024: 34 · 2023: 35 · 2022: 47 · 2021: 52 · 2020: 63 · 2019: 44 · 2018: 67 · 2017: 51 · 2016: 69 · 2015: 49 · 2014: 54 · 2013: 43 · 2012: 59
- FWCI
- 32.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Publications of the Astronomical Society of the Pacific (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Instrumentation › Astronomy and Astrophysical Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- exoplanets, radial velocity, false alarm probability, survey completeness, orbital period distribution, planet occurrence rate, M dwarf planets, gas giant planets, stellar jitter
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