We report the distribution of planets as a function of planet radius , orbital period , and stellar effective temperature for orbital periods less than 50 days around Solar-type ( GK ) stars .
These results are based on the 1,235 planets ( formally “ planet candidates ” ) from the Kepler mission that include a nearly complete set of detected planets as small as 2 R _ { \earth } .
For each of the 156,000 target stars we assess the detectability of planets as a function of planet radius , R _ { p } , and orbital period , P , using a measure of the detection efficiency for each star .
We also correct for the geometric probability of transit , R _ { \star } / a .
We consider first Kepler target stars within the “ solar subset ” having T _ { eff } = 4100–6100 K , \log { g } = 4.0–4.9 , and Kepler magnitude \mathrm { Kp } < 15 mag , i.e .
bright , main sequence GK stars .
We include only those stars having photometric noise low enough to permit detection of planets down to 2 R _ { \earth } .
We count planets in small domains of R _ { p } and P and divide by the included target stars to calculate planet occurrence in each domain .
The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius ( 2 R _ { \earth } ) and out to the longest orbital period ( 50 days , \sim 0.25 AU ) in our study .
For P < 50 days , the distribution of planet radii is given by a power law , \mathrm { d } f / \mathrm { d } \log R = k _ { R } R ^ { \alpha } with k _ { R } = 2.9 ^ { +0.5 } _ { -0.4 } , \alpha = -1.92 \pm 0.11 , and R = R _ { p } / R _ { \earth } .
This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion formation , but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits .
Planets with orbital periods shorter than 2 days are extremely rare ; for R _ { p } > 2 R _ { \earth } we measure an occurrence of less than 0.001 planets per star .
For all planets with orbital periods less than 50 days , we measure occurrence of 0.130 \pm 0.008 , 0.023 \pm 0.003 , and 0.013 \pm 0.002 planets per star for planets with radii 2–4 , 4–8 , and 8–32 R _ { \earth } , in agreement with Doppler surveys .
We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P _ { 0 } .
For smaller planets , P _ { 0 } has larger values , suggesting that the “ parking distance ” for migrating planets moves outward with decreasing planet size .
We also measured planet occurrence over a broader stellar T _ { eff } range of 3600–7100 K , spanning M0 to F2 dwarfs .
Over this range , the occurrence of 2–4 R _ { \earth } planets in the Kepler field linearly increases with decreasing T _ { eff } , making these small planets seven times more abundant around cool stars ( 3600–4100 K ) than the hottest stars in our sample ( 6600–7100 K ) .