We present the first measurement of the planet frequency beyond the “ snow line ” , for the planet-to-star mass-ratio interval -4.5 < \log q < -2 , corresponding to the range of ice giants to gas giants .
We find

{ d ^ { 2 } N _ { pl } \over d \log q d \log s } = ( 0.36 \pm 0.15 ) { dex } ^ { -2 } at mean mass ratio q = 5 \times 10 ^ { -4 } with no discernible deviation from a flat ( Öpik ’ s Law ) distribution in log projected separation s .
The determination is based on a sample of 6 planets detected from intensive follow-up observations of high-magnification ( A > 200 ) microlensing events during 2005-2008 .
The sampled host stars have a typical mass M _ { host } \sim 0.5 M _ { \odot } , and detection is sensitive to planets over a range of planet-star projected separations ( s _ { max } ^ { -1 } R _ { E } ,s _ { max } R _ { E } ) , where R _ { E } \sim 3.5 { AU } ( M _ { host } / M _ { \odot } ) ^ { 1 / 2 } is the Einstein radius and s _ { max } \sim ( q / 10 ^ { -4.3 } ) ^ { 2 / 3 } .
This corresponds to deprojected separations roughly 3 times the “ snow line ” .
Despite the frenetic nature of these observations , we show that they have the properties of a “ controlled experiment ” , which is what permits measurement of absolute planet frequency .
High-magnification events are rare , but the survey-plus-followup high-magnification channel is very efficient : half of all high-mag events were successfully monitored and half of these yielded planet detections .
The planet frequency derived from microlensing is a factor 7 larger than the one derived from Doppler studies at factor \sim 25 smaller star-planet separations [ i.e. , periods 2 – 2000 days ] .
However , this difference is basically consistent with the gradient derived from Doppler studies ( when extrapolated well beyond the separations from which it is measured ) .
This suggests a universal separation distribution across 2 dex in planet-star separation , 2 dex in mass ratio , and 0.3 dex in host mass .
Finally , if all planetary systems were “ analogs ” of the Solar System , our sample would have yielded 18.2 planets ( 11.4 “ Jupiters ” , 6.4 “ Saturns ” , 0.3 “ Uranuses ” , 0.2 “ Neptunes ” ) including 6.1 systems with 2 or more planet detections .
This compares to 6 planets including one two-planet system in the actual sample , implying a first estimate of 1 / 6 for the frequency of solar-like systems .