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 d log q d log s = (0.36 ± 0.15) dex −2 at the mean mass ratio q = 5 × 10 −4 with no discernible deviation from a flat (Öpik's law) distribution in logprojected 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 twoplanet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.

We present the first example of binary microlensing for which the parameter measurements can be verified (or contradicted) by future Doppler observations. This test is made possible by a confluence of two relatively unusual circumstances. First, the binary lens is bright enough (I = 15.6) to permit Doppler measurements. Second, we measure not only the usual seven binary-lens parameters, but also the "microlens parallax" (which yields the binary mass) and two components of the instantaneous orbital velocity. Thus, we measure, effectively, six "Kepler+1" parameters (two instantaneous positions, two instantaneous velocities, the binary total mass, and the mass ratio). Since Doppler observations of the brighter binary component determine five Kepler parameters (period, velocity amplitude, eccentricity, phase, and position of periapsis), while the same spectroscopy yields the mass of the primary, the combined Doppler + microlensing observations would be overconstrained by 6 + (5 + 1) − (7 + 1) = 4 degrees of freedom. This makes possible an extremely strong test of the microlensing solution. We also introduce a uniform microlensing notation for single and binary lenses, define conventions, summarize all known microlensing degeneracies, and extend a set of parameters to describe full Keplerian motion of the binary lenses.

We systematically surveyed period variations of superhumps in SU UMa-type dwarf novae based on newly obtained data and past publications. In many systems, the evolution of the superhump period is found to be composed of three distinct stages: an early evolutionary stage with a longer superhump period, a middle stage with systematically varying periods, and a final stage with a shorter, stable superhump period. During the middle stage, many systems with superhump periods of less than 0.08 d show positive period derivatives. We present observational characteristics of these stages and give greatly improved statistics. Contrary to an earlier claim, we found no clear evidence for a variation of period derivatives among different superoutbursts of the same object. We present an interpretation that the lengthening of the superhump period is a result of the outward propagation of an eccentricity wave, which is limited by the radius near the tidal truncation. We interpret that late-stage superhumps are rejuvenated excitation of a 3:1 resonance when superhumps in the outer disk are effectively quenched. The general behavior of the period variation, particularly in systems with short orbital periods, appears to follow a scenario proposed in Kato, Maehara, and Monard (2008, PASJ, 60, L23). We also present an observational summary of WZ Sge-type dwarf novae. Many of them have shown long-enduring superhumps during a post-superoutburst stage having longer periods than those during the main superoutburst. The period derivatives in WZ Sge-type dwarf novae are found to be strongly correlated with the fractional superhump excess, or consequently with the mass ratio. WZ Sge-type dwarf novae with a long-lasting rebrightening or with multiple rebrightenings tend to have smaller period derivatives, and are excellent candidates for those systems around or after the period minimum of evolution of cataclysmic variables.

Aims. We report the discovery of a planet with a high planet-to-star mass ratio in the microlensing event MOA-2009-BLG-387, which exhibited pronounced deviations over a 12-day interval, one of the longest for any planetary event. The host is an M dwarf, with a mass in the range 0.07 M < M host < 0.49 M at 90% confidence. The planet-star mass ratio q = 0.0132 ± 0.003 has been measured extremely well, so at the best-estimated host mass, the planet mass is m p = 2.6 Jupiter masses for the median host mass, M = 0.19 M . Methods. The host mass is determined from two "higher order" microlensing parameters. One of these, the angular Einstein radius θ E = 0.31 ± 0.03 mas has been accurately measured, but the other (the microlens parallax π E , which is due to the Earth's orbital motion) is highly degenerate with the orbital motion of the planet. We statistically resolve the degeneracy between Earth and planet orbital effects by imposing priors from a Galactic model that specifies the positions and velocities of lenses and sources and a Kepler model of orbits. Results. The 90% confidence intervals for the distance, semi-major axis, and period of the planet are 3.5 kpc < D L < 7.9 kpc, 1.1 AU < a < 2.7 AU, and 3.8 yr < P < 7.6 yr, respectively.

We report the detection of the cool, Jovian-mass planet MOA-2007-BLG-400Lb. The planet was detected in a high-magnification microlensing event (with peak magnification A max = 628) in which the primary lens transited the source, resulting in a dramatic smoothing of the peak of the event. The angular extent of the region of perturbation due to the planet is significantly smaller than the angular size of the source, and as a result the planetary signature is also smoothed out by the finite source size. Thus the deviation from a single-lens fit is broad and relatively weak (∼ few percent). Nevertheless, we demonstrate that the planetary nature of the deviation can be unambiguously ascertained from the gross features of the residuals, and detailed analysis yields a fairly precise planet/star mass ratio of q = 2.6 ± 0.4 × 10 −3 , in accord with the large significance (∆χ 2 = 1070) of the detection. The planet/star projected separation is subject to a strong close/wide degeneracy, leading to two indistinguishable solutions that differ in separation by a factor of ∼ 8.5. Upper limits on flux from the lens constrain its mass to be M < 0.75 M ⊙ (assuming it is a main-sequence star). A Bayesian analysis that includes all available observational constraints indicates a primary in the Galactic bulge with a mass of ∼ 0.2 − 0.5M ⊙ and thus a planet mass of ∼ 0.5 − 1.3M Jup . The separation and equilibrium temperature are ∼ 0.6 −1.1 AU (∼ 5.3 −9.7 AU) and ∼ 103 K (∼ 34 K) for the close (wide) solution. If the primary is a mainsequence star, follow-up observations would enable the detection of its light and so a measurement of its mass and distance.