We use the microlensing variability observed for 11 gravitationally lensed quasars to show that the accretion disk size at a rest-frame wavelength of 2500 Å is related to the black hole mass by log(R 2500 /cm) = (15.78 ± 0.12) + (0.80 ± 0.17) log(M BH /10 9 M ). This scaling is consistent with the expectation from thin-disk theory (R ∝ M 2/3 BH ), but when interpreted in terms of the standard thin-disk model (T ∝ R −3/4 ), it implies that black holes radiate with very low efficiency, log(η) = −1.77 ± 0.29 + log(L/L E ), where η = L/(Ṁc 2 ). Only by making the maximum reasonable shifts in the average inclination, Eddington factors, and black hole masses can we raise the efficiency estimate to be marginally consistent with typical efficiency estimates (η ≈ 10%). With one exception, these sizes are larger by a factor of ∼4 than the size needed to produce the observed 0.8 μm quasar flux by thermal radiation from a thin disk with the same T ∝ R −3/4 temperature profile. While scattering a significant fraction of the disk emission on large scales or including a large fraction of contaminating line emission can reduce the size discrepancy, resolving it also appears to require that accretion disks have flatter temperature/surface brightness profiles.

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 Hubble Space Telescope images and 2 years of optical photometry of the quadruple quasar HE 0435-1223. The time delays between the intrinsic quasar variations are ∆t AD = −14.37 +0.75 −0.85 , ∆t AB = −8.00 +0.73 −0.82 , and ∆t AC = −2.10 +0.78 −0.71 days. We also observed non-intrinsic variations of ∼0.1 mag yr −1 that we attribute to microlensing. Instead of the traditional approach of assuming a rotation curve for the lens galaxy and then deriving the Hubble constant (H 0 ), we assume H 0 = (72 ± 7) km s −1 Mpc −1 and derive constraints on the rotation curve. On the scale over which the lensed images occur (1. ′′ 2 = 5h −1 kpc ≃ 1.5R e ), the lens galaxy must have a rising rotation curve, and it cannot have a constant mass-to-light ratio. These results add to the evidence that the structures of early-type galaxies are heterogeneous.

We analyzed the microlensing of the X-ray and optical emission of the lensed quasar PG 1115+080. We find that the effective radius of the X-ray emission is 1.3 +1.1 −0.5 dex smaller than that of the optical emission. Viewed as a thin disk observed at inclination angle i, the optical accretion disk has a scale length, defined by the point where the disk temperature matches the rest frame energy of the monitoring band (kT = hc/λ rest with λ rest = 0.3µm), of log[(r s,opt /cm) cos(i)/0.5] = 16.6±0.4 . The X-ray emission region (1.4-21.8 keV in the rest frame) has an effective half-light radius of log[r 1/2,X /cm] = 15.6 +0.6 −0.9 . Given an estimated black hole mass of 1.2 × 10 9 M ⊙ , corresponding to a gravitational radius of log[r g /cm] = 14.3, the X-ray emission is generated near the inner edge of the disk while the optical emission comes from scales slightly larger than those expected for an Eddington-limited thin disk. We find a weak trend supporting models with low stellar mass fractions near the lensed images, in mild contradiction to inferences from the stellar velocity dispersion and the time delays.

Based on the microlensing variability of the two-image gravitational lens HE 1104Y1805 observed between 0.4 and 8 m, we have measured the size and wavelength-dependent structure of the quasar accretion disk. Modeled as a power law in temperature, T / R À , we measure a B-band (0.13 m in the rest frame) half-light radius of R 1/2; B ¼ 6:7 þ6:2 À3:2 ; 10 15 cm (68% confidence level) and a logarithmic slope of ¼ 0:61 þ0:21 À0:17 (68% confidence level) for our standard model with a logarithmic prior on the disk size. Both the scale and the slope are consistent with simple thin disk models where ¼ 3/4 and R 1/2; B ¼ 5:9 ; 10 15 cm for a Shakura-Sunyaev disk radiating at the Eddington limit with 10% efficiency. The observed fluxes favor a slightly shallower slope, ¼ 0:55 þ0:03 À0:02 , and a significantly smaller size for ¼ 3/4.