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

By A. Cumming, Paul Butler, Geoffrey, Marcy, Steven, Vogt, Jason, Wright, Debra, Fischer. 2008

692 citations recorded by the source corpus.

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 ∝ 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 = CMα Pβ 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 MJ 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/c9d24e78b2bdc2ddfe89144e020846610cdfcefd

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In Astronomy and Astrophysics

1. D. Charbonneau
2. Jon Fortney
3. Timothy Morton
4. M. Perryman
5. J. Johnson
6. J. Winn
7. G. Marcy
8. Andrew W. Howard

Citations in the corpus

• THE OCCURRENCE RATE OF SMALL PLANETS AROUND SMALL STARS (2013, result): “…low occurrence rate of giant planets is consistent with previous estimates of the giant planet occurrence rate around cool stars (Butler et al. 2004; Bonfils et al. 2006; Butler et al. 2006; Endl et al. 2006; Johnson et al. 2007; Cumming et al. 2008; Bonfils et al. 2011; Howard et al. 2012).”
• THE EXOPLANET CENSUS: A GENERAL METHOD APPLIED TO KEPLER (2011, background): “For more discussion of these points see Cumming et al. (2008), who rigorously analyze the FSWP in radial velocity surveys by only including the most detectable planet around any star.”
• About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of Their Intrinsic Architecture (2018, background): “For similar reasons, the statistical studies based on the radial velocity (RV) samples also overestimated the fraction of stars with planets, by using the probability to detect the most detectable planet for the probability to detect at least one planet (Cumming et al. 2008; Mayor et al. 2011).”
• Predictions of the WFIRST Microlensing Survey. I. Bound Planet Detection Rates (2018, background): “WFIRST has a high-detection efficiency for large-mass planets, but these have consistently been shown to be rare (e.g., Cumming et al. 2008; Howard et al. 2010; Cassan et al. 2012; Fressin et al. 2013; Shvartzvald et al. 2016; Suzuki et al. 2016).”
• NEAR-INFRARED METALLICITIES, RADIAL VELOCITIES, AND SPECTRAL TYPES FOR 447 NEARBY M DWARFS (2013, result): “A similar finding was reported for M dwarfs targeted by radial velocity surveys (Johnson et al. 2007; Cumming et al. 2008).”
• THE CALIFORNIA PLANET SURVEY. I. FOUR NEW GIANT EXOPLANETS (2010, background): “Remarkably, the exoplanets exhibit a sharp rise in occurrence beyond 1AU (Johnson et al. 2007b; Cumming et al. 2008), indicating a great population of giant planets resides there.”
• TEN NEW AND UPDATED MULTIPLANET SYSTEMS AND A SURVEY OF EXOPLANETARY SYSTEMS (2008, background): “Selection effects in eccentricity do not significantly affect the delectability of planets for e < 0.7 Cumming et al. (2008).”
• State of the Field: Extreme Precision Radial Velocities (2016, methodology): “Keck data have been used to derive planet occurrence rates (Cumming et al. 2008; Howard et al. 2012) and spectra have been used for characterization of host star metallicity and activity (Fischer & Valenti 2005; Valenti & Fischer 2005; Isaacson & Fischer 2010).”
• The Occurrence and Architecture of Exoplanetary Systems (2014, background): “Cumming et al. (2008) analyzed the results of a Doppler campaign in which nearly 600 FGKM stars were monitored for 8 years.”
• Microlensing Surveys for Exoplanets (2012, methodology): “The Cassan et al. (2012) and Cumming et al. (2008) frequencies have been normalized to the typical planet mass of the Gould et al. (2010) sample of ∼83 M ⊕.”
• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms (2009, neutral): “Cumming et al. (2008) normalised the Keplerian periodogram as zKep(ω) = N − 5 4 χ20 − χ 2(ω) χ2best = N − 5 4 pKep(ω) 1− pKep(ωbest) (29) analogous to Eq.”
• The California-Kepler Survey. I. High-resolution Spectroscopy of 1305 Stars Hosting Kepler Transiting Planets (2017, background): “…surveys mapped out the strong correlation between giant-planet occurrence and stellar metallicity (Valenti & Fischer 2005; Fischer & Valenti 2005) and planet occurrence as a function of planet mass, stellar mass, and orbital distance (Cumming et al. 2008; Howard et al. 2010b; Johnson et al. 2010).”
• FRIENDS OF HOT JUPITERS. I. A RADIAL VELOCITY SEARCH FOR MASSIVE, LONG-PERIOD COMPANIONS TO CLOSE-IN GAS GIANT PLANETS (2013, result): “This is similar to the approach taken by Cumming et al. (2008), although with their wellcharacterized planets, pi was approximated by these authors as a δ function.”
• Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution (2009, background): “While this population is still smaller than one would ideally like, it nevertheless already allows to extract statistically a wealth of information (e.g. Udry & Santos 2007; Cumming et al. 2008) to constrain formation models that exceeds by far what one extrasolar planet can do.”
• The Exoplanet Population Observation Simulator. I. The Inner Edges of Planetary Systems (2018, background): “Giant planets orbit 10%–20% of Sun-like stars (Cumming et al. 2008), most of them beyond 1 au.”
• RETIRED A STARS AND THEIR COMPANIONS. III. COMPARING THE MASS–PERIOD DISTRIBUTIONS OF PLANETS AROUND A-TYPE STARS AND SUN-LIKE STARS (2009, background): “Values of α and β are generally consistent among authors; we take the values from Cumming et al. (2008) as being representative of studies in the literature for Sun-like stars.”