Thesis (Ph. D.)--Ohio State University, 2002. / Title from first page of PDF file. Document formatted into pages; contains xxix, 171 p. Includes abstract and vita. Advisor: Andrew P. Gould, Dept. of Astronomy. Includes bibliographical references (p. 153-157).

Thesis (Ph. D.)--Ohio State University, 2002. / Title from first page of PDF file. Document formatted into pages; contains xxix, 171 p., also contains graphics. Includes abstract and vita. Advisor: Andrew P. Gould. Includes bibliographical references (p. 153-157).

Strong gravitational lensing produces multiple distorted images of a background source when it is closely aligned with a mass distribution along the line of sight. The lensed images provide constraints on the parameters of a model of the lens, and the images themselves can be inverted providing a model of the source. Both of these aspects of lensing are extremely valuable, as lensing depends on the total matter distribution, both luminous and dark. Furthermore, lensed sources are commonly located at cosmological distances and are magnified by the lensing effect. This provides a chance to image sources that would be unobservable when viewed with conventional optics. The semilinear method expresses the source modeling step as a least-squares problem for a given set of lens model parameters. The blurring effect due to the point spread function of the instrument used to observe the lensed images is also taken into account. In general, regularization is needed to solve the source deconvolution problem. We use Krylov subspace methods to solve for the pixelated sources. These optimization techniques, such as the Conjugate Gradient method, provide natural regularizing effects from simple truncated iteration. Using these routines, we are able to avoid the explicit construction of the lens and blurring matrices and solve the least squares source optimization problem iteratively. We explore several regularization parameter selection methods commonly used in standard image deconvolution problems, which lead to previously derived expressions for the number of source degrees of freedom. The parameters that describe the lens density distribution are found by global optimization methods including genetic algorithms and particle swarm optimizers. In general, global optimizers are useful in non-linear optimization problems such as lens modeling due to their parameter space mapping capabilities. However, these optimization methods require many function evaluations and iterative approaches to the least squares problem are beneficial due to the speed advantage that they offer. We apply our modeling techniques to a subset of gravitational lens systems from the Sloan Lens ACS (SLACS) survey, and are able to reliably recover the parameters of the lens mass distribution with both analytical and regularized pixelated sources.

Strong gravitational lensing produces multiple distorted images of a background source when it is closely aligned with a mass distribution along the line of sight. The lensed images provide constraints on the parameters of a model of the lens, and the images themselves can be inverted providing a model of the source. Both of these aspects of lensing are extremely valuable, as lensing depends on the total matter distribution, both luminous and dark. Furthermore, lensed sources are commonly located at cosmological distances and are magnified by the lensing effect. This provides a chance to image sources that would be unobservable when viewed with conventional optics. The semilinear method expresses the source modeling step as a least-squares problem for a given set of lens model parameters. The blurring effect due to the point spread function of the instrument used to observe the lensed images is also taken into account. In general, regularization is needed to solve the source deconvolution problem. We use Krylov subspace methods to solve for the pixelated sources. These optimization techniques, such as the Conjugate Gradient method, provide natural regularizing effects from simple truncated iteration. Using these routines, we are able to avoid the explicit construction of the lens and blurring matrices and solve the least squares source optimization problem iteratively. We explore several regularization parameter selection methods commonly used in standard image deconvolution problems, which lead to previously derived expressions for the number of source degrees of freedom. The parameters that describe the lens density distribution are found by global optimization methods including genetic algorithms and particle swarm optimizers. In general, global optimizers are useful in non-linear optimization problems such as lens modeling due to their parameter space mapping capabilities. However, these optimization methods require many function evaluations and iterative approaches to the least squares problem are beneficial due to the speed advantage that they offer. We apply our modeling techniques to a subset of gravitational lens systems from the Sloan Lens ACS (SLACS) survey, and are able to reliably recover the parameters of the lens mass distribution with both analytical and regularized pixelated sources.

We study the abundance of substructure in the matter density near galaxies using ALMA Science Verification observations of the strong lensing system SDP. 81. We present a method to measure the abundance of subhalos around galaxies using interferometric observations of gravitational lenses. Using simulated ALMA observations we explore the effects of various systematics, including antenna phase errors and source priors, and show how such errors may be measured or marginalized. We apply our formalism to ALMA observations of SDP. 81. We find evidence for the presence of a M = 10(8.96 +/- 0.12)M(circle dot) subhalo near one of the images, with a significance of 6.9 sigma in a joint fit to data from bands 6 and 7; the effect of the subhalo is also detected in both bands individually. We also derive constraints on the abundance of dark matter (DM) subhalos down to M similar to 2 x 10(7) M-circle dot, pushing down to the mass regime of the smallest detected satellites in the Local Group, where there are significant discrepancies between the observed population of luminous galaxies and predicted DM subhalos. We find hints of additional substructure, warranting further study using the full SDP. 81 data set (including, for example, the spectroscopic imaging of the lensed carbon monoxide emission). We compare the results of this search to the predictions of Lambda CDM halos, and find that given current uncertainties in the host halo properties of SDP. 81, our measurements of substructure are consistent with theoretical expectations. Observations of larger samples of gravitational lenses with ALMA should be able to improve the constraints on the abundance of galactic substructure.

This thesis is concerned with developing new methods for performing weak gravitational lensing with the aim of addressing specific systematic effects in weak lensing surveys. The first of these effects is the multiplicative biases which arise as a result of isotropic smearing. This smearing may be due to atmospheric seeing or an instrumental PSF. Isotropic smearing circularizes a galaxy image and leads to a systematic under-estimate of the modulus of the observed ellipticity. The orientation of the observed galaxy is, however, unaffected. We exploit this property by formulating a weak lensing shear estimator that requires measurements of galaxy position angles only, thereby avoiding the contribution from this systematic. We demonstrate the method on simulations and the CFHTLenS data by reconstructing convergence maps and comparing the results with the standard full ellipticity based approach. We show that the difference between the reconstructed maps for the two approaches is consistent with noise in all of the tests performed. We then apply the technique to the GREAT3 challenge data using three distinct methods to measure the position angles of the galaxies. For all three methods, we find that the position angle-only approach yields shear estimates with a performance comparable with current well established shape based techniques. The second effect addressed arises from the intrinsic alignment of the source galaxies. This alignment mimics a shear signal, and hence biases estimates of the shear. To mitigate this effect, we develop three shear estimators that include polarization information from radio observations as a tracer of a galaxy’s intrinsic orientation. In addition to the shear estimator, we also develop estimators for the intrinsic alignment signal. We test these estimators by successfully reconstructing the shear and intrinsic alignment auto and cross-power spectra across three overlapping redshift bins.

This thesis will present a new cosmic shear analysis pipeline SUNGLASS (Simulated UNiverses for Gravitational Lensing Analysis and Shear Surveys). SUNGLASS is a pipeline that rapidly generates simulated universes for weak lensing and cosmic shear analysis. The pipeline forms suites of cosmological N-body simulations and performs tomographic cosmic shear analysis using a novel line-of-sight integration through the simulations while saving the particle lightcone information. Galaxy shear and convergence catalogues with realistic 3-D galaxy redshift distributions are produced for the purposes of testing weak lensing analysis techniques and generating covariance matrices for data analysis and cosmological parameter estimation. This thesis presents a suite of fast medium-resolution simulations with shear and convergence maps for a generic 100 square degree survey out to a redshift of z = 1.5, with angular power spectra agreeing with the theoretical expectations to better than a few percent accuracy up to ℓ = 103 for all source redshifts up to z = 1.5 and wavenumbers up to ℓ = 2000 for source redshifts z ≥ 1.1. A two-parameter Gaussian likelihood analysis of Ωm and σ8 is also performed on the suite of simulations for a 2-D weak lensing survey, demonstrating that the cosmological parameters are recovered from the simulations and the covariance matrices are stable for data analysis, with negligible bias. An investigation into the accuracy of traditional Fisher matrix calculations is presented. Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this thesis, the loss of information is quantified by comparing näıve Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of the suite of mock weak lensing catalogues derived from the SUNGLASS pipeline, for 2-D and tomographic shear analyses of a Euclid-like survey. In both cases the 68% confidence area of the Ωm − σ8 plane is found to increase by a factor 5. However, the marginal errors increase by just 20 to 40%. A new method is proposed to model the effects of non-linear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. The findings in this thesis show that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Ωm − σ8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, three multi-parameter analyses of (Ωm, σ8, ns), (Ωm, σ8, ns, ΩΛ)and (Ωm, σ8, h, ns, w0, wa) are performed to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The multi-parameter volumes of the 1σ error contours for the six-parameter non-linear Fisher analysis are consistently larger than for the Gaussian case, and the shape of the 68% confidence volume is modified. These results strongly suggest that future Fisher Matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

We perform a measurement of the mass-richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey (SDSS). We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-z biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centring, halo triaxiality and projection effects. We also compare measurements of the lensing signal from two independently produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5570 clusters from 0.1 <= z <= 0.33, the normalization of our power-law mass versus. relation is log(10)[M-200m/ h-M-1(circle dot)] = 14.344 +/- 0.021 (statistical) +/- 0.023 (systematic) at a richness lambda= 40, a 7 per cent calibration uncertainty, with a power-law index of 1.33(- 0.10)(+0.09) (1 sigma). The detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time.

Cosmological constraints from galaxy surveys are as accurate as our understanding of the relative distributions of dark matter and galaxies, known as galaxy bias. Weak gravitational lensing is a powerful probe of galaxy bias, since the distortion in the shapes of distant galaxies, called shear, is directly related to the dark matter distribution, which can be compared to the galaxy field. I look at the galaxy clustering amplitude relative to the dark matter field, quantified by the galaxy bias b, as well as the cross-correlation coefficient r, which tells us how correlated the positions of galaxies are with the dark matter. In this thesis I present several techniques to constrain galaxy bias through weak lensing, using both numerical simulations and observational data. The most commonly used method, using aperture statistics, is shown to be subject to serious systematics in the presence of noisy data and scale- and time dependence in the galaxy bias. A local comparison technique is introduced, where the foreground distribution is used to predict the shear in the background, to which it is compared. The technique is tested with simulations, concluding that it requires high quality data. A model fitting approach is proposed, based on the McDonald (2006) galaxy bias model. The two parameters of this model, a large scale bias, b1, and a parameter, b2, that quantifies the scale dependence of the bias, are insufficient in the presence of stochasticity. Therefore, R is introduced as an additional parameter to take this into account. I present galaxy bias constraints for two spectroscopic galaxy samples: the Baryon Oscillations Spectroscopic Survey (BOSS) and the WiggleZ Dark Energy Survey (WiggleZ), applying the traditional aperture method and the model fitting approach to the Red Sequence Cluster Lensing Survey (RCSLenS). Both techniques strongly suggest that galaxies trace mass, but in a complicated way, with differences in scale- and time dependence between the samples considered. The WiggleZ galaxy bias is found to be around b ~ 1:2, depending on redshift and scale, and has a low cross-correlation coefficient of r ~ 0:5 at small scales. The BOSS samples have higher bias with scale dependence around b ~ 2:0 and show no sign of stochasticity, finding r to be close enough to unity to be explained within a deterministic scenario. The observations are in line with previous galaxy bias measurements from lensing data. The thesis incorporates work on the X-ray Luminosity Function (XLF) of galaxy clusters, measured from the Wide Angle ROSAT Pointed Survey (WARPS). Evolution is quantified with a likelihood analysis and I conclude that it is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1:1, as expected in a low density Universe. I conclude by investigating the impact of my galaxy bias measurements from BOSS and WiggleZ on the growth rate of structure, as extracted from Redshift Space Distortions (RSD). The imperfect correlation between the galaxy and matter field, as quantified by R and b2, leads to an underestimation of the true growth rate under the assumption of a linear bias. Therefore, in order to constrain galaxy bias and gravity simultaneously, future cosmological redshift surveys require high quality lensing data.

With a large, unique spectroscopic survey in the fields of 28 galaxy-scale strong gravitational lenses, we identify groups of galaxies in the 26 adequately sampled fields. Using a group-finding algorithm, we find 210 groups with at least 5 member galaxies; the median number of members is 8. Our sample spans redshifts of 0.04 <= z(grp) <= 0.76 with a median of 0.31, including 174 groups with 0.1 < z(grp) < 0.6 The groups have radial velocity dispersions of 60 <= sigma(grp) <= 1200 km s(-1) with a median of 350 km s(-1). We also discover a supergroup in field B0712+472 at z = 0.29 that consists of three main groups. We recover groups similar to similar to 85% of those previously reported in these fields within our redshift range of sensitivity and find 187 new groups with at least five members. The properties of our group catalog, specifically, (1) the distribution of sgrp, (2) the fraction of all sample galaxies that are group members, and (3) the fraction of groups with significant substructure, are consistent with those for other catalogs. The distribution of group virial masses agrees well with theoretical expectations. Of the lens galaxies, 12 of 26 (46%) (B1422+231, B1600+434, B2114+022, FBQS J0951+2635, HE0435-1223, HST J14113+5211, MG0751+2716, MGJ1654+1346, PG 1115+080, Q ER 0047-2808, RXJ1131-1231, and WFI J2033-4723) are members of groups with at least five galaxies, and one more (B0712+472) belongs to an additional, visually identified group candidate. There are groups not associated with the lens that still are likely to affect the lens model; in six of 25 (24%) fields (excluding the supergroup), there is at least one massive (sigma(grp) >= 500 km s(-1)) group or group candidate projected within 2' of the lens.