Gravity and Non-gravity Modes in the VIRMOS-DESCART Weak Lensing Survey

We analyze the weak lensing data of the VIRMOS imaging survey using projections (called E and B-modes) of the two independents observed correlation functions. The E-mode contains all the lensing signal, while noise and systematics contribute equally to the E and B modes provided that intrinsic alignment is negligible. The mode separation allows a measurement of the signal with a \sqrt{2} smaller error bars, and a separate channel to test for systematic errors. We apply various transformations, including a spherical harmonic space power spectrum C^E_l and C^B_l, which provides a direct measurement of the projected dark matter distribution for 500<l<10^4.Comment: accepted version, minor changes, 18 pages including 6 figure

Sheer shear: weak lensing with one mode

3D data compression techniques can be used to determine the natural basis of radial eigenmodes that encode the maximum amount of information in a tomographic large-scale structure survey. We explore the potential of the Karhunen-Lo\`eve decomposition in reducing the dimensionality of the data vector for cosmic shear measurements, and apply it to the final data from the \cfh survey. We find that practically all of the cosmological information can be encoded in one single radial eigenmode, from which we are able to reproduce compatible constraints with those found in the fiducial tomographic analysis (done with 7 redshift bins) with a factor of ~30 fewer datapoints. This simplifies the problem of computing the two-point function covariance matrix from mock catalogues by the same factor, or by a factor of ~800 for an analytical covariance. The resulting set of radial eigenfunctions is close to ell-independent, and therefore they can be used as redshift-dependent galaxy weights. This simplifies the application of the Karhunen-Lo\`eve decomposition to real-space and Fourier-space data, and allows one to explore the effective radial window function of the principal eigenmodes as well as the associated shear maps in order to identify potential systematics. We also apply the method to extended parameter spaces and verify that additional information may be gained by including a second mode to break parameter degeneracies. The data and analysis code are publicly available at https://github.com/emiliobellini/kl_sample.Comment: 15 pages, 16 figures. Accepted version on OJ

Photometric redshifts: estimating their contamination and distribution using clustering information

We present a new technique to estimate the level of contamination between photometric redshift bins. If the true angular cross-correlation between redshift bins can be safely assumed to be zero, any measured cross-correlation is a result of contamination between the bins. We present the theory for an arbitrary number of redshift bins, and discuss in detail the case of two and three bins which can be easily solved analytically. We use mock catalogues constructed from the Millennium Simulation to test the method, showing that artificial contamination can be successfully recovered with our method. We find that degeneracies in the parameter space prohibit us from determining a unique solution for the contamination, though constraints are made which can be improved with larger data sets. We then apply the method to an observational galaxy survey: the deep component of the Canada-France-Hawaii Telescope Legacy Survey. We estimate the level of contamination between photometric redshift bins and demonstrate our ability to reconstruct both the true redshift distribution and the true average redshift of galaxies in each photometric bin.Comment: 14 pages, 12 figures, accepted for publication in MNRAS V2: Section 4.4 added. Significant additions to analysis in section 5.

Statistics of Dark Matter Halos from Gravitational Lensing

We present a new approach to measure the mass function of dark matter halos and to discriminate models with differing values of Omega through weak gravitational lensing. We measure the distribution of peaks from simulated lensing surveys and show that the lensing signal due to dark matter halos can be detected for a wide range of peak heights. Even when the signal-to-noise is well below the limit for detection of individual halos, projected halo statistics can be constrained for halo masses spanning galactic to cluster halos. The use of peak statistics relies on an analytical model of the noise due to the intrinsic ellipticities of source galaxies. The noise model has been shown to accurately describe simulated data for a variety of input ellipticity distributions. We show that the measured peak distribution has distinct signatures of gravitational lensing, and its non-Gaussian shape can be used to distinguish models with different values of Omega. The use of peak statistics is complementary to the measurement of field statistics, such as the ellipticity correlation function, and possibly not susceptible to the same systematic errors.Comment: 5 pages, 4 figures, matches version accepted for ApJ