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.

Understanding the relation between underlying matter distribution and biased tracers such as galaxies or dark matter halos is essential to extract cosmological information from ongoing or future galaxy redshift surveys. At sufficiently large scales such as the Baryon Acoustic Oscillation (BAO) scale, a standard approach for the bias problem on the basis of the perturbation theory (PT) is to assume the 'local bias' model in which the density field of biased tracers is deterministically expanded in terms of matter density field at the same position. The higher-order bias parameters are then determined by combining the power spectrum with higher-order statistics such as the bispectrum.As is pointed out by recent studies, however, nonlinear gravitational evolution naturally induces nonlocal bias terms even if initially starting only with purely local bias. As a matter of fact, previous works showed that the second-order nonlocal bias term, which corresponds to the gravitational tidal field, is important to explain the characteristic scale-dependence of the bispectrum. In this paper we extend the nonlocal bias term up to third order, and investigate whether the PT-based model including nonlocal bias terms can simultaneously explain the power spectrum and the bispectrum of simulated halos in N -body simulations. The bias renormalization procedure ensures that only one additional term is necessary to be introduced to the power spectrum as a next-to-leading order correction, even if third-order nonlocal bias terms are taken into account. We show that the power spectrum, including density and momentum, and the bispectrum between halo and matter in Nbody simulations can be simultaneously well explained by the model including up to third-order nonlocal bias terms at k < ∼ 0.1h/Mpc. Also, the results are in a good agreement with theoretical predictions of a simple coevolution picture, although the agreement is not perfect. These trend can be found for a wide range of halo mass, 0.7 < ∼ M halo [10 13 M⊙/h] < ∼ 20 at various redshifts, 0 ≤ z ≤ 1. These demonstrations clearly show a failure of the local bias model even at such large scales, and we conclude that nonlocal bias terms should be consistently included in order to accurately model statistics of halos.

Searches for extrasolar planets have uncovered an astonishing diversity of planetary systems, yet the frequency of solar system analogs remains unknown. The gravitational microlensing planet search method is potentially sensitive to multiple-planet systems containing analogs of all the solar system planets except Mercury. We report the detection of a multiple-planet system with microlensing. We identify two planets with masses of approximately 0.71 and approximately 0.27 times the mass of Jupiter and orbital separations of approximately 2.3 and approximately 4.6 astronomical units orbiting a primary star of mass approximately 0.50 solar mass at a distance of approximately 1.5 kiloparsecs. This system resembles a scaled version of our solar system in that the mass ratio, separation ratio, and equilibrium temperatures of the planets are similar to those of Jupiter and Saturn. These planets could not have been detected with other techniques; their discovery from only six confirmed microlensing planet detections suggests that solar system analogs may be common.

We present the discovery of a Neptune-mass planet OGLE-2007-BLG-368Lb with a planet-star mass ratio of q = [9.5 ± 2.1] × 10 −5 via gravitational microlensing. The planetary deviation was detected in real-time thanks to the high cadence of the Microlensing Observations in Astrophysics survey, real-time light-curve monitoring and intensive follow-up observations. A Bayesian analysis returns the stellar mass and distance at M l = 0.64 +0.21 −0.26 M and D l = 5.9 +0.9 −1.4 kpc, respectively, so the mass and separation of the planet are M p = 20 +7 −8 M ⊕ and a = 3.3 +1.4 −0.8 AU, respectively. This discovery adds another cold Neptune-mass planet to the planetary sample discovered by microlensing, which now comprises four cold Neptune/super-Earths, five gas giant planets, and another sub-Saturn mass planet whose nature is unclear. The discovery of these 10 cold exoplanets by the microlensing method implies that the mass ratio function of cold exoplanets scales as dN pl /d log q ∝ q −0.7±0.2 with a 95% confidence level upper limit of n < −0.35 (where dN pl /d log q ∝ q n). As microlensing is most sensitive to planets beyond the snow-line, this implies that Neptune-mass planets are at least three times more common than Jupiters in this region at the 95% confidence level.

We study the large-scale anisotropic two-point correlation function using 46,760 luminous red galaxies at redshifts 0.16 -0.47 from the Sloan Digital Sky Survey. We measure the correlation function as a function of separations parallel and perpendicular to the line of sight in order to take account of anisotropy of the large-scale structure in redshift space. We find a slight signal of baryonic features in the anisotropic correlation function, i.e., a "baryon ridge" corresponding to a baryon acoustic peak in the spherically averaged correlation function which has already been reported using the same sample. The baryon ridge has primarily a spherical structure with a known radius in comoving coordinates. It enables us to divide the redshift distortion effects into dynamical and geometrical components and provides further constraints on cosmological parameters, including the dark energy equation-of-state. With an assumption of a flat Λ cosmology, we find the best-fit values of Ω m = 0.218 +0.047 −0.037 and Ω b = 0.047 +0.016 −0.016 (68% CL) when we use the overall shape of the anisotropic correlation function of 40 < s < 200 h −1 Mpc including a scale of baryon acoustic oscillations. When an additional assumption of Ω b h 2 = 0.024 is adopted, we obtain Ω DE = 0.770 +0.051 −0.040 and w = −0.93 +0.45 −0.35 . These constraints are estimated only from our data of the anisotropic correlation function, and they agree quite well with values both from the cosmic microwave background (CMB) anisotropies and from other complementary statistics using the LRG sample. With the CMB prior from the 3 year WMAP results, we give stronger constraints on those parameters.

We investigate the orientation correlation of giant elliptical galaxies by measuring the intrinsic ellipticity correlation function of 83,773 luminous red galaxies (LRGs) at redshifts 0.16 -0.47 from the Sloan Digital Sky Survey. We have accurately determined the correlation up to 30 h −1 Mpc. Luminosity dependence of the ellipticity correlation is also detected although the error bars are large, while no evidence is found for its redshift evolution between z = 0.2 and z = 0.4. Then we use a cosmological N -body simulation to examine misalignment between the central LRGs and their parent dark matter halos. Central and satellite galaxies are assigned to simulated halos by employing a halo occupation distribution model for the LRGs. The ellipticity correlation is predicted to have the same shape as but an amplitude about 4 times higher than our observation if the central LRGs are perfectly aligned with their host halos. This indicates that the central LRG galaxies are preferentially but not perfectly aligned with their host halos. With the assumption that there is a misalignment angle between a central LRG and its host halo which follows a Gaussian distribution with a zero mean and a width σ θ , we obtain a tight constraint on the misalignment parameter, σ θ = 35.4 +4.0 −3.3 deg. This type of intrinsic ellipticity correlation, if not corrected, can lead to contamination at 5% level to the shear power spectrum in weak lensing surveys of limiting magnitude R AB = 24.5 if the source central galaxies follow the same misalignment distribution as the LRGs.

Abstract. We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of µ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of µ and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift space is more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.

Abstract. Numerical simulations show that redshift space distortions (RSD) introduce strong scale dependence in the power spectra of halos, with ten percent deviations relative to linear theory predictions even on relatively large scales (k < 0.1h/M pc) and even in the absence of satellites (which induce Fingers-of-God, FoG, effects). If unmodeled these effects prevent one from extracting cosmological information from RSD surveys. In this paper we use Eulerian perturbation theory (PT) and Eulerian halo biasing model and apply it to the distribution function approach to RSD, in which RSD is decomposed into several correlators of density weighted velocity moments. We model each of these correlators using PT and compare the results to simulations over a wide range of halo masses and redshifts. We find that with an introduction of a physically motivated halo biasing, and using dark matter power spectra from simulations, we can reproduce the simulation results at a percent level on scales up to k ∼ 0.15h/M pc at z = 0, without the need to have free FoG parameters in the model.