This paper introduces a new method of inferring the intrinsic exoplanet population from Kepler data , based on the assumption that the frequency of exoplanets can be represented by a smooth function of planet radius and period .
The method is applied to the two most recent data releases from the Kepler project , q1-16 and q1-17 , over the range of periods 0.5 to 512 days , and radii 0.5 to 16 Earth radii .
Both of these releases have known biases , with the first believed to contain excess false positives , and the second excess false negatives , so any analysis of them should be viewed with caution .
We apply the new method of population estimation to these releases , treating them like practice data sets .
With this method , we tentatively find that the average number of planets per star would be about 5.7 \pm 0.8 for F stars , 5.0 \pm 0.2 for G stars , 4.0 \pm 0.3 for K stars , and 6.5 \pm 1.7 for M stars , indicating a decreasing trend with FGK spectral type , but an upward jump for M stars .
A second conclusion is that the number of planets per G star , per natural log unit of period ( days ) and radii ( Earths ) at the period and radius of the Earth around the Sun , is about \Gamma _ { \oplus } ( G ) = 1.1 \pm 0.1 .
A related parameter , \eta _ { \oplus } , which in addition depends on the range of period and radius considered , is found to be \eta _ { \oplus } ( G ) \simeq 1.0 \pm 0.1 .
More definitive conclusions , and validation of these preliminary values , await the final release of Kepler ’ s transiting exoplanet list .