A New Shear Estimator for Weak Lensing Observations

We present a new shear estimator for weak lensing observations which properly accounts for the effects of a realistic point spread function (PSF). Images of faint galaxies are subject to gravitational shearing followed by smearing with the instrumental and/or atmospheric PSF. We construct a `finite resolution shear operator' which when applied to an observed image has the same effect as a gravitational shear applied prior to smearing. This operator allows one to calibrate essentially any shear estimator. We then specialize to the case of weighted second moment shear estimators. We compute the shear polarizability which gives the response of an individual galaxy's polarization to a gravitational shear. We then compute the response of the population of galaxies, and thereby construct an optimal weighting scheme for combining shear estimates from galaxies of various shapes, luminosities and sizes. We define a figure of merit --- an inverse shear variance per unit solid angle --- which characterizes the quality of image data for shear measurement. The new method is tested with simulated image data. We discuss the correction for anisotropy of the PSF and propose a new technique involving measuring shapes from images which have been convolved with a re-circularizing PSF. We draw attention to a hitherto ignored noise related bias and show how this can be analyzed and corrected for. The analysis here draws heavily on the properties of real PSF's and we include as an appendix a brief review, highlighting those aspects which are relevant for weak lensing.Comment: 39 pages, 9 figure

A microlensing measurement of dark matter fractions in three lensing galaxies

Direct measurements of dark matter distributions in galaxies are currently only possible through the use of gravitational lensing observations. Combinations of lens modelling and stellar velocity dispersion measurements provide the best constraints on dark matter distributions in individual galaxies, however they can be quite complex. In this paper, we use observations and simulations of gravitational microlensing to measure the smooth (dark) matter mass fraction at the position of lensed images in three lens galaxies: MG 0414+0534, SDSS J0924+0219 and Q2237+0305. The first two systems consist of early-type lens galaxies, and both display a flux ratio anomaly in their close image pair. Anomalies such as these suggest a high smooth matter percentage is likely, and indeed we prefer ~50 per cent smooth matter in MG 0414+0534, and ~80 per cent in SDSS J0924+0219 at the projected locations of the lensed images. Q2237+0305 differs somewhat in that its lensed images lie in the central kiloparsec of the barred spiral lens galaxy, where we expect stars to dominate the mass distribution. In this system, we find a smooth matter percentage that is consistent with zero.Comment: 7 pages, 4 figures. Accepted for publication in Ap

New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts

The abundance of primordial black holes is currently significantly constrained in a wide range of masses. The weakest limits are established for the small mass objects, where the small intensity of the associated physical phenomenon provides a challenge for current experiments. We used gamma- ray bursts with known redshifts detected by the Fermi Gamma-ray Burst Monitor (GBM) to search for the femtolensing effects caused by compact objects. The lack of femtolensing detection in the GBM data provides new evidence that primordial black holes in the mass range 5 \times 10^{17} - 10^{20} g do not constitute a major fraction of dark matter.Comment: 7 pages, 6 figures, submitted to Physical Review

Spectroscopic Redshifts for Seven Lens Galaxies

We report VLT observations of 11 lensed quasars, designed to measure the redshifts of their lens galaxies. We successfully determined the redshifts for seven systems, five of which were previously unknown. The securely measured redshifts for the lensing galaxies are: HE0047-1756 z=0.408; PMNJ0134-0931 z=0.766; HE0230-2130 z=0.522; HE0435-1223 z=0.455; SDSS0924+021 z=0.393; LBQS1009-025 z=0.871; and WFIJ2033-472 z=0.658. For four additional systems (BRI0952-0115, Q1017-207, Q1355-2257 and PMNJ1632-003) we estimate tentative redshifts based on some features in their spectra.Comment: 8 pages, ApJ, submitte

The mass profile of early-type galaxies in overdense environments: the case of the double source plane gravitational lens SL2SJ02176-0513

SL2SJ02176-0513 is a remarkable lens for the presence of two multiply-imaged systems at different redshifts lensed by a foreground massive galaxy at $z_{\rm lens}=0.656$: a bright cusp arc at $z_{\rm arc}=1.847$ and an additional double-image system at an estimated redshift of $z_{\rm dbl}\sim2.9$ based on photometry and lensing geometry. The system is located about 400 kpc away from the center of a massive group of galaxies. Mass estimates for the group are available from X-ray observations and satellite kinematics. Multicolor photometry provides an estimate of the stellar mass of the main lens galaxy. The lensing galaxy is modeled with two components (stars and dark matter), and we include the perturbing effect of the group environment, and all available constraints. We find that classic lensing degeneracies, e.g. between external convergence and mass density slope, are significantly reduced with respect to standard systems and infer tight constraints on the mass density profile: (i) the dark matter content of the main lens galaxy is in line with that of typical galaxies $f_{\rm dm}(<R_{\rm e})=0.41^{+0.09}_{-0.06}$; (ii) the required mass associated with the dark matter halo of the nearby group is consistent with X-ray and weak-lensing estimates ($\sigma_{\rm grp}=550^{+130}_{-240}$); (iii) accounting for the group contribution in the form of an external convergence, the slope of the mass density profile of the main lens galaxy alone is found to be $\alpha=-1.03^{+0.22}_{-0.16}$, consistent with the isothermal ($\alpha=-1$) slope. We demonstrate that multiple source plane systems together with good ancillary dataset can be used to disentangle local and environmental effects.Comment: 10 pages, 6 figures, submitted to A&

The CFHTLS Strong Lensing Legacy Survey: I. Survey overview and T0002 release sample

AIMS: We present data from the CFHTLS Strong Lensing Legacy Survey (SL2S). Due to the unsurpassed combined depth, area and image quality of the Canada-France-Hawaii Legacy Survey it is becoming possible to uncover a large, statistically well-defined sample of strong gravitational lenses which spans the dark halo mass spectrum predicted by the concordance model from galaxy to cluster haloes. METHODS: We describe the development of several automated procedures to find strong lenses of various mass regimes in CFHTLS images. RESULTS: The preliminary sample of about 40 strong lensing candidates discovered in the CFHTLS T0002 release, covering an effective field of view of 28 deg$^2$ is presented. These strong lensing systems were discovered using an automated search and consist mainly of gravitational arc systems with splitting angles between 2 and 15 arcsec. This sample shows for the first time that it is possible to uncover a large population of strong lenses from galaxy groups with typical halo masses of about $10^{13}h^{-1}M_\odot$. We discuss the future evolution of the SL2S project and its main scientific aims for the next 3 years, in particular our observational strategy to extract the hundreds of gravitational rings also present in these fields.Comment: 11 pages, 5 figures, A&A in pres

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

The geometry of the quadruply imaged quasar PG 1115+080; implications for Ho

Time delay measurements have recently been reported for the lensed quasar PG 1115+080. These measurements can be used to derive Ho, but only if we can constrain the lensing potential. We have applied a recently developed deconvolution technique to analyse sub-arcsecond I band images of PG 1115+080, obtained at the Nordic Optical Telescope (NOT) and the Canada France Hawaii Telescope (CFHT). The high performance of the deconvolution code allows us to derive precise positions and magnitudes for the four lensed images of the quasar, as well as for the lensing galaxy. The new measurement of the galaxy position improves its precision by a factor of 3 and thus strengthens the constraints on the lensing potential. With the new data, a range of models incorporating some of the plausible systematic uncertainties yields Ho = 53 (+10/-7) km/s/mpc.Comment: 4 pages, LaTex file + postscript figures, Accepted for publication in AA Letter

The Importance of Einstein Rings

We develop a theory of Einstein rings and demonstrate it using the infrared Einstein ring images of the quasar host galaxies observed in PG1115+080, B1608+656 and B1938+666. The shape of an Einstein ring accurately and independently determines the shape of the lens potential and the shape of the lensed host galaxy. We find that the host galaxies of PG1115+080, B1608+656 and B1938+666 have axis ratios of 0.58+/-0.02, 0.69+/-0.02 and 0.62+/-0.15 including the uncertainties in the lens models. The Einstein rings break the degeneracies in the mass distributions or Hubble constants inferred from observations of gravitational lenses. In particular, the Einstein ring in PG1115+080 rules out the centrally concentrated mass distributions that lead to a high Hubble constant (H_0>60 km/s Mpc) given the measured time delays. Deep, detailed observations of Einstein rings will be revolutionary for constraining mass models and determining the Hubble constant from time delay measurements.Comment: 21 pages, 8 figures, submitted to the Ap