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<p dir="ltr">In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.In this dissertation, we develop novel methods of performing shear measurements in individual exposures and apply them to images obtained from WIYN-ODI. We generalize forced photometry and call this new method forced measurement. This involves performing a single iteration of a traditional moment-matching algorithm with reasonable initial guess values and correcting for negative pixel values after background subtraction. We find that this allows us to make flux, shape, size, and ellipticity measurements at extremely low S/N < 1. We compare the performance of this method to existing approaches and find our method to be superior. A novel Monte Carlo PSF correction scheme is also introduced that allows us to dramatically increase the source density and hence perform more accurate weak lensing. These methods are then applied to measure shear across 411 ×30 individual exposures of the galaxy cluster Abell 2390. We find that we are successfully able to recover the main mass structures. We also find that we are able to recover the smaller galaxy groups over a very large field. Examining data from a variety of wavelengths and sources such as X-ray, Radio, and spectroscopic methods, we find Abell 2390 is likely to be a case of late-stage merger. The hot gas during the infall phase experienced friction causing loss of angular momentum and hence is almost merged with the main core. The Dark Matter (DM) cores, however, did not experience such friction and continue to be in the merger phase.</p>

We have acquired Hubble Space Telescope (HST) and Very Large Telescope near-infrared spectra and images of supernova (SN) Refsdal after its discovery as an Einstein cross in fall 2014. The HST light curve of SN Refsdal has a shape consistent with the distinctive, slowly rising light curves of SN. 1987A-like SNe, and we find strong evidence for a broad H alpha P-Cygni profile and Na I D absorption in the HST grism spectrum at the redshift (z = 1.49) of the spiral host galaxy. SNe. IIn, largely powered by circumstellar interaction, could provide a good match to the light curve of SN Refsdal, but the spectrum of a SN IIn would not show broad and strong H alpha and Na I D absorption. From the grism spectrum, we measure an H alpha expansion velocity consistent with those of SN. 1987A-like SNe at a similar phase. The luminosity, evolution, and Gaussian profile of the H alpha emission of the WFC3 and X-shooter spectra, separated by similar to 2.5 months in the rest frame, provide additional evidence that supports the SN. 1987A-like classification. In comparison with other examples of SN. 1987A-like SNe, photometry of SN Refsdal favors bluer B - V and V - R colors and one of the largest luminosities for the assumed range of potential magnifications. The evolution of the light curve at late times will provide additional evidence about the potential existence of any substantial circumstellar material. Using MOSFIRE and X-shooter spectra, we estimate a subsolar host-galaxy metallicity (8.3 +/- 0.1 dex and <8.4 dex, respectively) near the explosion site.

A hierarquia de equações de Boltzmann que descreve a temperatura e polarização da radiação cósmica de fundo ´e tratada no espaço das posições. Mostramos neste formalismo que temperatura e polarização podem ser descritas como medias dos termos de fonte ponderados por probabilidades associadas a um problema de voos aleatórios. Decorre da estrutura geral da hierarquia que se pode fazer uma expansão da temperatura e polarização em termos do numero de espalhamentos ocorridos durante a recombinação. Incorporamos o efeito de lentes gravitacionais sobre a radiação cósmica de fundo tirando proveito da estrutura das equações no espaço das posições. Mostraremos que o efeito ´e incorporado através de correções aos coeficientes da decomposição angular dos campos de temperatura e polarização. Para descrever o efeito de lentes gravitacionais fazemos uma revisão sobre resultados formais da teoria e apresentamos uma derivação de equações centrais em espaços-tempo arbitrários. / The Boltzmann hierarchy describing the temperature and polarization of the cosmic microwave background is presented in a position space formalism. We show that temperature and polarization can be described in terms of averages over source terms weighted by probabilities densities that appear in problems of random flights. The temperature and polarization signals can be expanded in terms of the number of scatterings photons suffered during the recombination. The gravitational lensing effects are incorporated over the free-propagation phase of the CMB photons. This effect can be included in the position space formalism as a correction to the expansion coefficients of the temperature and polarization fields. The bases of the theory of gravitational lensing are also presented and a rederivation of the central equations of the theory in arbitrary spacetimes is here developed.

Les relevés à venir comme Euclid, LSST et WFIRST vont nous ouvrir la perspective d’étudier l’univers profond. Pour ces grands relevés, l’astigmatisme cosmique correspond à une sonde indispensable pour étudier la nature de l’énergie noire et la matière noire. Compte tenu de la précision attendue par ces observations, nous devons faire des prédictions basées sur des simulations correspondant à l’état de l’art afin de quantifier avec précision la variance, les biais et les dégénérescences potentielles liés aux baryons. Dans ce contexte, ma thèse se focalise sur la construction d’estimateurs précis basés sur les observables de lentillage. La première partie de ma thèse consiste à caractériser la géométrie des grandes structures par astigmatisme cosmique (Gouin et al. 2017). Une décomposition multipolaire du signal est appliquée afin de quantifier la distribution azimutale de la matière noire, centrée sur les amas. Les propriétés statistiques de ces moments sont estimées à partir d’une simulation cosmologique. Les distorsions harmoniques calculées dans le voisinage des amas tracent la structure filamentaire. Un plus grand nombre de filaments semblent connectés aux amas de forte masse. Dans la dernière partie de ma thèse, je synthétise le signal d’astigmatisme cosmique dans le cône de lumière de la simulation Horizon AGN. Pour ce faire, je propage les rayons de lumière le long du cône dans l’approximation des plans de lentillage multiples. L’effet des baryons est significatif dans la statistique du cisaillement aux échelles angulaires inférieures à l’arc-minute. Le signal de cisaillement galaxie-galaxie est comparée aux observations récentes, et semble être en bon accord. / Upcoming weak lensing surveys such as Euclid, LSST and WFIRST will provide an unprecedented opportunity to investigate the dark Universe. Through these large scale surveys, gravitational lensing is an indispensable cosmological probe to investigate the dark energy and the dark matter. Due to the new level of accuracy in observations, we must perform cosmological predictions in state-of-art simulations, to precisely quantify its variances, biases and potential degeneracies coming from baryonic physics. In this context, my thesis focuses on the construction of accurate weak lensing observables. The first part of my PhD work characterises the geometry of large-scale structure through weak lensing (Gouin et al. 2017). I relied on multipolar decomposition of weak lensing signal to quantify the azimuthal distribution of dark matter centred on galaxy clusters. The statistical properties of these moments are estimated from a large N-body simulation. The harmonic distortions computed in the vicinity of clusters appear to trace the filamentary structure. Larger number of filaments seem to be connected to high-mass clusters.The detection level of this statistical estimator is estimated. In the last part of my thesis, I mock the weak gravitational lensing signal in the light-cone of the Horizon-AGN simulation (Gouin et al. 2019). To do so, I propagate light-rays along the light-cone in the multiple-lens-plane approximation. The impact of baryons is significant in cosmic shear statistics for angular scales below a few arcmins. In addition, the galaxy-galaxy lensing signal is compared to current observational measurements (Leauthaud et al. 2017), and seems in good agreement.

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters. Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem). Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain. Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.

This research was a collaborative effort between the Air Force Research Laboratory (AFRL) and the University of Texas to examine the laser-tissue interaction of thermal lensing induced by continuous-wave, CW, near-infrared, NIR, laser radiation in the eye and its influence on the formation of a retinal lesion from said radiation. CW NIR laser radiation can lead to a thermal lesion induced on the retina given sufficient power and exposure duration as related to three basic parameters; the percent of transmitted energy to, the optical absorption of, and the size of the laser-beam created at the retina. Thermal lensing is a well-known phenomenon arising from the optical absorption, and subsequent temperature rise, along the path of the propagating beam through a medium. Thermal lensing causes the laser-beam profile delivered to the retina to be time dependent. Analysis of a dual-beam, multidimensional, high-frame rate, confocal imaging system in an artificial eye determined the rate of thermal lensing in aqueous media exposed to 1110, 1130, 1150 and 1318-nm wavelengths was related to the power density created along the optical axis and linear absorption coefficient of the medium. An adaptive optics imaging system was used to record the aberrations induced by the thermal lens at the retina in an artificial eye during steady-state. Though the laser-beam profiles changed over the exposure time, the CW NIR retinal damage thresholds between 1110-1319-nm were determined to follow conventional fitting algorithms which neglected thermal lensing. A first-order mathematical model of thermal lensing was developed by conjoining an ABCD beam propagation method, Beer's law of attenuation, and a solution to the heat-equation with respect to radial diffusion. The model predicted that thermal lensing would be strongest for small (< 4-mm) 1/e² laser-beam diameters input at the corneal plane and weakly transmitted wavelengths where less than 5% of the energy is delivered to the retina. The model predicted thermal lensing would cause the retinal damage threshold for wavelengths above 1300-nm to increase with decreasing beam-diameters delivered to the corneal plane, a behavior which was opposite of equivalent conditions simulated without thermal lensing. / text

This research was a collaborative effort between the Air Force Research Laboratory (AFRL) and the University of Texas at Austin to study laser induced thermal lensing. Analysis with a high-frame rate thermal camera system in an optical cuvette determined rates of heating and cooling in water exposed to 1200, 1310 and 1318-nm wavelengths. Thermal modeling software (BTEC) developed at AFRL was used to simulate the beam parameters that were used experimentally. The simulation was also used to compute axial temperature for various power levels, beam diameters, and pulse durations. Laser-induced optical pathlength modulation or phase-shift was computed to study the thermal lensing effect. Power and irradiance damage thresholds were calculated for collimated and focused geometries to study the effect in a focusing eye on retinal damage thresholds. / text

Dans le modèle standard de cosmologie ΛCDM, environ 72% de la densité d'énergie totale de l'Univers se présente sous la forme d'énergie sombre qui causerait la présente accélération de l'Univers. Parmi les sondes cosmologiques couramment utilisées, l'effet de lentille gravitationnel forte dans les amas est une technique prometteuse fournissant des contraintes orthogonales sur les paramètres cosmologiques. Le programme HFF a permis une amélioration significative de l'estimation de la distribution de masse des amas. Cependant, la modélisation de l'effet de lentille forte dans les amas semble ne pas atteindre la résolution angulaire des observations HST. Cette thèse fournit une meilleure compréhension de l'impact des erreurs systématiques dans la modélisation paramétrique de l'effet de lentille forte dans les amas de galaxies et, donc, sur la détermination des paramètres cosmologiques. Premièrement, j'ai analysé deux amas de galaxies simulés, ayant les mêmes caractéristiques que les amas du programme HFF, Ares et Hera. J'ai utilisé plusieurs estimateurs afin d'évaluer la qualité de nos reconstructions obtenues, permettant de quantifier l'impact des erreurs systématiques dues, au choix des profils de densité et configurations et, ensuite, de la disponibilité d'images multiples dans la détermination de paramètres cosmologiques. Deuxièmement, en utilisant deux amas de galaxies, j'ai testé quatre modèles cosmologiques pour lesquels l'équation d'état de l'énergie sombre, w(z), est paramétrisée en fonction du redshift. J'ai réalisé plusieurs modélisations pour quantifier l'impact des erreurs systématiques liées à la position des images multiples sur les paramètres cosmologiques. / In the standard cosmological model ΛCDM, about 70% of the energy density of the Universe is in the form of a dark energy that would cause the current acceleration of the Universe. Among the extensively used cosmological probes, using strong lensing features in galaxy clusters is a promising technique yielding orthogonal constraints on cosmological parameters. The program HFF has led to a significant improvement of cluster mass estimates. However, strong lensing modelling appears to be still unable to match the HST observations angular resolution.This thesis provides a better understanding of how systematic errors impact the retrieval of cosmological parameters in order to use strong lensing clusters as reliable cosmological probes. Firstly, I have analyzed two simulated HFF-like clusters, Ares and Hera, I use several estimators to assess the goodness of our reconstructions by comparing our multiple models, with the input models. This allows to quantify the impact of systematic errors arising from the choice of different density profiles and configurations and, secondly, from the availability of constraints in the parametric modelling of strong lensing clusters and therefore on the retrieval of cosmological parameters. Secondly, I probe four cosmological models in which the equation of state of dark energy, w(z), is parameterized as a function of redshift using strong lensing features in two galaxy clusters. To quantify how the cosmological constraints are biased due to systematic effects in the strong lensing modelling, I carry out several modelling attempts considering different uncertainties for the multiple images positions.