Currently , we have only limited means to probe the presence of planets at large orbital separations .
Foreman-Mackey et al .
searched for long-period transiting planets in the Kepler light curves using an automated pipeline .
Here , we apply their pipeline , with minor modifications , to a larger sample and use updated stellar parameters from Gaia DR2 .
The latter boosts the stellar radii for most of the planet candidates found by FM16 , invalidating a number of them as false positives .
We identify 15 candidates , including two new ones .
All have sizes from 0.3 to 1 ~ { } R _ { J } , and all but two have periods from 2 to 10 yr. We report two main findings based on this sample .
First , the planet occurrence rate for the above size and period ranges is 0.70 ^ { +0.40 } _ { -0.20 } planets per Sun-like star , with the frequency of cold Jupiters agreeing with that from radial-velocity surveys .
Planet occurrence rises with decreasing planet size , roughly describable as dN / d \log R \propto R ^ { \alpha } with \alpha = -1.6 ^ { +1.0 } _ { -0.9 } , i.e. , Neptune-sized planets are some four times more common than Jupiter-sized ones .
Second , five out of our 15 candidates orbit stars with known transiting planets at shorter periods , including one with five inner planets .
We interpret this high incidence rate to mean : ( 1 ) almost all our candidates should be genuine ; ( 2 ) across a large orbital range ( from \sim 0.05 to a few astronomical units ) , mutual inclinations in these systems are at most a few degrees ; and ( 3 ) large outer planets exist almost exclusively in systems with small inner planets .