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What Percentage of Stars Host Planets?

Estimating the percentage of stars that host planets is not as straightforward as you might think. In a given sample of observed stars, you cannot simply divide the number of planets detected by the number of stars observed. All of the possible observational biases have to be studied in detail and then corrections have to be estimated for the exoplanets that might have been missed due to observational bias. Often, the observational biases must be studied in order to design the survey strategy itself.

Several studies designed to establish the planet incidence rate have been conducted, and the dependence of the incidence of planets on other things such as the relative proportion of heavy elements, or stellar mass, has also been investigated. The studies have been conducted over a range in stellar masses, from about a third of a solar mass to three solar masses. It is found that planet incidence increases from about 2% for the lowest stellar masses, to about 9% for stellar masses greater than about 1.3 times the solar mass. The numbers do depend on the detailed assumptions, however.

Supplementary to the above are estimates for the candidate (not confirmed) exoplanets observed by the Kepler mission. The number of stars observed in the field is about 153,000 and estimates have attempted to correct for geometrical and observational biases of the Kepler candidates sample when the number of exoplanet candidates was about 1200. These were published in Borucki et al. (2011) which found an occurrence rate of about 34%. This rate breaks down as 5.4% less than 1.25 times Earth size; 6.8% between than 1.25 and 2 times Earth size; 19.3% greater than 2 but up to 6 times Earth size; 2.4% greater than 6 but less than 15 times Earth size (i.e., bracketing “Jupiter-size”). Only 0.15% have a size greater than 15 times Earth size. Remember that these numbers are for candidate exoplanets. Also, uncorrected biases may remain and the corrections that are applied are tentative. (Borucki et al. (2011) state, “The readers are cautioned that the sample is affected by many poorly quantified biases.”) Expect updates for the larger number of candidates that is now known since that study (over 2300), and also updates as candidates become demoted or promoted to true exoplanet status. Remember also that the stars and planets in the Kepler field are in one small part of the sky.

The bottom line is that the occurrence rate of planets around stars is currently rather an open question and the current estimates are tentative.

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