Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods

Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to extract this information from the observations. We derive minimum variance estimators for projected density reconstruction and its power spectrum and apply them to simulated data sets, showing that they give a good agreement with the theoretical minimum variance expectations. The same estimator can also be applied to the cluster reconstruction, where it remains a useful reconstruction technique, although it is no longer optimal for every application. The method can be generalized to include nonlinear cluster reconstruction and photometric information on redshifts of background galaxies in the analysis. We also address the question of how to obtain directly the 3-d power spectrum from the weak lensing data. We derive a minimum variance quadratic estimator, which maximizes the likelihood function for the 3-d power spectrum and can be computed either from the measurements directly or from the 2-d power spectrum. The estimator correctly propagates the errors and provides a full correlation matrix of the estimates. It can be generalized to the case where redshift distribution depends on the galaxy photometric properties, which allows one to measure both the 3-d power spectrum and its time evolution.Comment: revised version, 36 pages, AAS LateX, submitted to Ap

Probing the Universe with Weak Lensing

Gravitational lenses can provide crucial information on the geometry of the Universe, on the cosmological scenario of formation of its structures as well as on the history of its components with look-back time. In this review, I focus on the most recent results obtained during the last five years from the analysis of the weak lensing regime. The interest of weak lensing as a probe of dark matter and the for study of the coupling between light and mass on scales of clusters of galaxies, large scale structures and galaxies is discussed first. Then I present the impact of weak lensing for the study of distant galaxies and of the population of lensed sources as function of redshift. Finally, I discuss the potential interest of weak lensing to constrain the cosmological parameters, either from pure geometrical effects observed in peculiar lenses, or from the coupling of weak lensing with the CMB.Comment: To appear Annual Review of Astronomy and Astrophysiscs Vol. 37. Latex and psfig.sty. Version without figure, 54 pages, 73Kb. Complete version including 13 figures (60 pages) available on ftp.iap.fr anonymous account in /pub/from_users/mellier/AnnualReview ; file ARAAmellier.ps.gz 1.6 M

A Comparison of Simple Mass Estimators for Galaxy Clusters

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass m_p \simeq 10^{10} \Msun, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

Oesophageal cancer and amplification of the human cyclin D gene CCND1/PRAD1.

The human CCND1/PRAD1 gene, located in the 11q13 chromosomal region, encodes a cyclin D protein with potential oncogenic capacity and is involved in several human malignancies. The amplification and expression status of CCND1 was investigated in a series of oesophageal tumours. CCND1 is amplified in 54% and overexpressed in 63% of the tumours of the squamous cell type

Quasar Microlensing at High Magnification and the Role of Dark Matter: Enhanced Fluctuations and Suppressed Saddlepoints

Contrary to naive expectation, diluting the stellar component of the lensing galaxy in a highly magnified system with smoothly distributed ``dark'' matter increases rather than decreases the microlensing fluctuations caused by the remaining stars. For a bright pair of images straddling a critical curve, the saddlepoint (of the arrival time surface) is much more strongly affected than the associated minimum. With a mass ratio of smooth matter to microlensing matter of 4:1, a saddlepoint with a macro-magnification of mu = 9.5 will spend half of its time more than a magnitude fainter than predicted. The anomalous flux ratio observed for the close pair of images in MG0414+0534 is a factor of five more likely than computed by Witt, Mao and Schechter if the smooth matter fraction is as high as 93%. The magnification probability histograms for macro-images exhibit distinctly different structure that varies with the smooth matter content, providing a handle on the smooth matter fraction. Enhanced fluctuations can manifest themselves either in the temporal variations of a lightcurve or as flux ratio anomalies in a single epoch snapshot of a multiply imaged system. While the millilensing simulations of Metcalf and Madau also give larger anomalies for saddlepoints than for minima, the effect appears to be less dramatic for extended subhalos than for point masses. Morever, microlensing is distinguishable from millilensing because it will produce noticeable changes in the magnification on a time scale of a decade or less.Comment: As accepted for publication in ApJ. 17 pages. Substantial revisions include a discussion of constant M/L models and the calculation of a "photometric" dark matter fraction for MG0414+053

Dark matter halo properties from galaxy-galaxy lensing

We present results for a galaxy-galaxy lensing study based on imaging data from the Canada-France-Hawaii Telescope Legacy Survey Wide. From a 12 million object multi-colour catalogue for 124 deg^2 of photometric data in the u*g'r'i'z' filters we compute photometric redshifts (with a scatter of \sigma_{\Delta z/(1+z)} = 0.033 and an outlier rate of \eta=2.0 per cent for i'<=22.5) and extract galaxy shapes down to i'=24.0. We select a sample of lenses and sources with 0.05 < z_d <= 1 and 0.05 < z_s <= 2. We fit three different galaxy halo profiles to the lensing signal, a singular isothermal sphere (SIS), a truncated isothermal sphere (BBS) and a universal density profile (NFW). We derive velocity dispersions by fitting an SIS out to 100 h^{-1} kpc to the excess surface mass density \Delta\Sigma and perform maximum likelihood analyses out to a maximum scale of 2 h^{-1} Mpc to obtain halo parameters and scaling relations. We find luminosity scaling relations of \sigma_{red} ~ L^{0.24+-0.03} for the red lens sample, \sigma_{blue} ~ L^{0.23+-0.03} for blue lenses and \sigma ~ L^{0.29+-0.02} for the combined lens sample with zeropoints of \sigma*_{red}=162+-2 km/s, \sigma*_{blue}=115+-3 km/s and \sigma*=135+-2 km/s at a chosen reference luminosity L*_{r'} = 1.6 \times 10^10 h^{-2} L_{r',sun}. The steeper slope for the combined sample is due to the different zeropoints of the blue and red lenses and the fact that blue lenses dominate at low luminosities and red lenses at high luminosities. The mean effective redshifts for the lens samples are =0.28 for red lenses, =0.35 for blue lenses and =0.34 for the combined lens sample.Comment: 62 pages, 55 figures, accepted for publication in MNRAS, abridged abstract, includes corrections from final proof. Our created catalogues (photometry, photometric redshifts and shears) are publicly available at http://www.usm.uni-muenchen.de/people/stella/GGL

Phase diagrams of correlated electrons: systematic corrections to the mean field theory

Perturbative corrections to the mean field theory for particle-hole instabilities of interacting electron systems are computed within a scheme which is equivalent to the recently developed variational approach to the Kohn-Luttinger superconductivity. This enables an unbiased comparison of particle-particle and particle-hole instabilities within the same approximation scheme. A spin-rotation invariant formulation for the particle-hole instabilities in the triplet channel is developed. The method is applied to the phase diagram of the t-t' Hubbard model on the square lattice. At the Van Hove density, antiferromagnetic and d-wave Pomeranchuk phases are found to be stable close to half filling. However, the latter phase is confined to an extremely narrow interval of densities and away from the singular filling, d-wave superconducting instability dominates

Electronic doping of graphene by deposited transition metal atoms

We perform a phenomenological analysis of the problem of the electronic doping of a graphene sheet by deposited transition metal atoms, which aggregate in clusters. The sample is placed in a capacitor device such that the electronic doping of graphene can be varied by the application of a gate voltage and such that transport measurements can be performed via the application of a (much smaller) voltage along the graphene sample, as reported in the work of Pi et al. [Phys. Rev. B 80, 075406 (2009)]. The analysis allows us to explain the thermodynamic properties of the device, such as the level of doping of graphene and the ionisation potential of the metal clusters in terms of the chemical interaction between graphene and the clusters. We are also able, by modelling the metallic clusters as perfect conducting spheres, to determine the scattering potential due to these clusters on the electronic carriers of graphene and hence the contribution of these clusters to the resistivity of the sample. The model presented is able to explain the measurements performed by Pi et al. on Pt-covered graphene samples at the lowest metallic coverages measured and we also present a theoretical argument based on the above model that explains why significant deviations from such a theory are observed at higher levels of coverage.Comment: 16 pages, 10 figure

HST/ACS weak lensing analysis of the galaxy cluster RDCS 1252.9-2927 at z=1.24

We present a weak lensing analysis of one of the most distant massive galaxy cluster known, RDCS 1252.9-2927 at z=1.24, using deep images from the Advanced Camera for Survey (ACS) on board the Hubble Space Telescope (HST). By taking advantage of the depth and of the angular resolution of the ACS images, we detect for the first time at z>1 a clear weak lensing signal in both the i (F775W) and z (F850LP) filters. We measure a 5-\sigma signal in the i band and a 3-\sigma signal in the shallower z band image. The two radial mass profiles are found to be in very good agreement with each other, and provide a measurement of the total mass of the cluster inside a 1Mpc radius of M(<1Mpc) = (8.0 +/- 1.3) x 10^14 M_\odot in the current cosmological concordance model h =0.70, \Omega_m=0.3, \Omega_\Lambda=0.7, assuming a redshift distribution of background galaxies as inferred from the Hubble Deep Fields surveys. A weak lensing signal is detected out to the boundary of our field (3' radius, corresponding to 1.5Mpc at the cluster redshift). We detect a small offset between the centroid of the weak lensing mass map and the brightest cluster galaxy, and we discuss the possible origin of this discrepancy. The cumulative weak lensing radial mass profile is found to be in good agreement with the X-ray mass estimate based on Chandr and XMM-Newton observations, at least out to R_500=0.5Mpc.Comment: 38 pages, ApJ in press. Full resolution images available at http://www.eso.org/~prosati/RDCS1252/Lombardi_etal_accepted.pd

Probing Sub-parsec Structure in the Lyman Alpha Forest with Gravitational Microlensing

We present the results of microlens ray-tracing simulations showing the effect of absorbing material between a source quasar and a lensing galaxy in a gravitational lens system. We find that, in addition to brightness fluctuations due to microlensing, the strength of the absorption line relative to the continuum varies with time, with the properties of the variations depending on the structure of the absorbing material. We conclude that such variations will be measurable via UV spectroscopy of image A of the gravitationally lensed quasar Q2237+0305 if the Lyman Alpha clouds between the quasar and the lensing galaxy possess structure on scales smaller than $\sim 0.1$ pc. The time scale for the variations is on the order of order years to decades, although very short term variability can occur. While the Lyman alpha lines may not be accessible at all wavelengths, this approach is applicable to any absorption system, including metal lines.Comment: 8 pages, 11 figures, to appear in MNRAS (note resolution of some figures reduced due to size limitations