Sources of contamination to weak lensing tomography: redshift-dependent shear measurement bias

The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape measurement bias on the cosmological interpretation of tomographic two-point weak lensing shear statistics.
We use a set of realistic image simulations produced by the Shear Testing Programme (STEP) collaboration to derive shape measurement bias as a function of redshift. We define biased two-point weak lensing statistics and perform a likelihood analysis for two fiducial surveys. We present a derivation of the covariance matrix for tomography in real space and a fitting formula to calibrate it for non-Gaussianity.
We find the biased aperture mass dispersion is reduced by  ∼20 per cent  at redshift ∼1, and has a shallower scaling with redshift. This effect, if ignored in data analyses, biases σ₈ and w ₀ estimates by a few per cent. The power of tomography is significantly reduced when marginalizing over a range of realistic shape measurement biases. For a Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)-Wide-like survey,  [Ω_m, σ₈]  confidence regions are degraded by a factor of 2, whereas for a Kilo-Degree Survey (KIDS)-like survey the factor is 3.5. Our results are strictly valid only for KSB methods, but they demonstrate the need to marginalize over a redshift-dependent shape measurement bias in all future cosmological analyses.     

Imaging the cosmic matter distribution using gravitational lensing of pre-galactic H i

21-cm emission from neutral hydrogen during and before the epoch of cosmic reionization is gravitationally lensed by material at all lower redshifts. Low-frequency radio observations of this emission can be used to reconstruct the projected mass distribution of foreground material, both light and dark. We compare the potential imaging capabilities of such 21-cm lensing with those of future galaxy lensing surveys. We use the Millennium Simulation to simulate large-area maps of the lensing convergence with the noise, resolution and redshift-weighting achievable with a variety of idealized observation programmes. We find that the signal-to-noise ratio of 21-cm lens maps can far exceed that of any map made using galaxy lensing. If the irreducible noise limit can be reached with a sufficiently large radio telescope, the projected convergence map provides a high-fidelity image of the true matter distribution, allowing the dark matter haloes of individual galaxies to be viewed directly, and giving a wealth of statistical and morphological information about the relative distributions of mass and light. For instrumental designs like that planned for the Square Kilometre Array, high-fidelity mass imaging may be possible near the resolution limit of the core array of the telescope.     

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale structures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.     

High-resolution imaging of the cosmic mass distribution from gravitational lensing of pre-galactic H i

Low-frequency radio observations of neutral hydrogen during and before the epoch of cosmic re-ionization will provide ∼1000 quasi-independent source planes, each of precisely known redshift, if a resolution of ∼1 arcmin or better can be attained. These planes can be used to reconstruct the projected mass distribution of foreground material. Structure in these source planes is linear and Gaussian at high redshift  (30 < z < 300)  but is non-linear and non-Gaussian during re-ionization. At both epochs, significant power is expected down to subarcsecond scales. We demonstrate that this structure can, in principle, be used to make mass images with a formal signal-to-noise ratio (S/N) per pixel exceeding 10, even for pixels as small as an arcsecond. With an ideal telescope, both resolution and S/N can exceed those of even the most optimistic idealized mass maps from galaxy lensing by more than an order of magnitude. Individual dark haloes similar in mass to that of the Milky Way could be imaged with high S/N out to   z ∼ 10  . Even with a much less ambitious telescope, a wide-area survey of 21-cm lensing would provide very sensitive constraints on cosmological parameters, in particular on dark energy. These are up to 20 times tighter than the constraints obtainable from comparably sized, very deep surveys of galaxy lensing, although the best constraints come from combining data of the two types. Any radio telescope capable of mapping the 21-cm brightness temperature with good frequency resolution (∼0.05 MHz) over a band of width ≳10 MHz should be able to make mass maps of high quality. The planned Square Kilometre Array may be able to map the mass with moderate S/N down to arcminute scales, depending on the re-ionization history of the universe and the ability to subtract foreground sources.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Galaxy–QSO correlation induced by weak gravitational lensing arising from large-scale structure

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.     

Numerical study of the statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.     

Source–lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source–lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, S ₃, is examined using a non-linear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on S ₃ to be of the order of  5–40  per cent. It depends significantly on the redshift distribution of sources and on the way in which the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.