Frequency of Solar-like Systems and of Ice and Gas Giants Beyond the Snow Line from High-magnification Microlensing Events in 2005-2008

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 \endgraf\vbox{\begin{center}$\displaystyle{d^2 N{_{\rm pl}}\over d\log q\, d\log s} = (0.36\pm 0.15)\;{\rm dex}^{-2}$\end{center}}\noindentat the mean mass ratio q = 5 × 10?4 with no discernible deviation from a flat (?pik's law) distribution in log-projected separation s. The determination is based on a sample of six 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 ~ 0.5 M ?, and detection is sensitive to planets over a range of planet-star-projected separations (s ?1 max R E, s max R E), where R E ~ 3.5 AU(M host/M ?)1/2 is the Einstein radius and s max ~ (q/10?4.3)1/3. This corresponds to deprojected separations roughly three times the "snow line." We show that the observations of these events 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-follow-up high-magnification channel is very efficient: half of all high-mag events were successfully monitored and half of these yielded planet detections. The extremely high sensitivity of high-mag events leads to a policy of monitoring them as intensively as possible, independent of whether they show evidence of planets. This is what allows us to construct an unbiased sample. The planet frequency derived from microlensing is a factor 8 larger than the one derived from Doppler studies at factor ~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 two or more planet detections. This compares to six planets including one two-planet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.