UC Davis

Dark matter makes up roughly 85 percent of the mass budget of the Universe. Though we cannot see it, hence the name, the formation and behavior of structures from the largest cosmological scales down to sub-galactic scales betray the existence of dark matter via its gravitational interactions. The widely accepted view of cosmological history, informed by observations of hierarchical structure formation, posits non-relativistic dark matter particles that only interact gravitationally, known as cold dark matter (CDM). However, alternative theories of dark matter may describe small-scale observations as well or better. It is essential to test variations on CDM and differentiate between models that agree on larger scales. We can observe even completely invisible dark matter structures from the way they deflect and magnify light. This phenomenon, gravitational lensing, has been used to infer some of the tightest constraints on alternative dark matter models and grows stronger as telescopes improve and sample sizes increase.

This dissertation is focused on strong gravitational lensing, when multiple images of the light source appear on the sky. Particularly, I demonstrate and evaluate a method called flux-ratio analysis, which uses bright, compact sources like quasars that are lensed into four distinct images. In these systems, the main lens is an elliptical galaxy, the mass distribution of which determines the positions and relative brightnesses of the images. Low-mass dark matter structures, called halos, associated with the main lens or along the line of sight are detectable in the additional magnification or demagnification they introduce to individual images. Discrepancies between observed flux ratios and those predicted by a smooth model of the main lens indicate the presence of perturbing halos. With a sample of many lensed quasars, we can characterize the population statistics of low-mass halos. These statistics are determined by the underlying dark matter model, thus they enable us to infer constraints on it.

In Chapter 1 of this work, I provide general background information on dark matter and cosmology and detail the predictions of CDM. I then discuss the use of gravitational lensing to detect dark matter and review the history of flux-ratio analysis to put my work in the context of the field.

Chapter 2 of this work contains a detailed description of my flux-ratio analysis procedure as well as constraints on warm dark matter (WDM) inferred from a sample of 14 lensed quasars. I provide background on WDM theory and describe the process of simulating low-mass halo populations that align with theoretical predictions. Then I walk through my Bayesian inference procedure and its application to infer the strongest gravitational lensing constraints on WDM to date. Lastly, I explore the context of my analysis in relation to other works that used subsets of this lens sample. I highlight the differences in between our analysis procedures and potential sources of systematic error.

In Chapter 3, I investigate the addition of general third- and fourth-order multipoles to the mass model. I find that multipoles with realistic amplitudes, at least when compared to the isophotes of elliptical galaxies, can perturb flux ratios as significantly as low-mass halos. If their orientation angles are left to vary freely, joint third- and fourth-order multipoles are completely degenerate with CDM halo populations when modeling quadruply-imaged quasars. This work calls into question all previous dark matter constraints from flux-ratio analysis, including those presented in Chapter 2. However, those results are still critical to the field moving forward. Until this degeneracy is mitigated, the method and degree of inclusion of multipoles into an inference procedure will strongly impact the result. Chapter 2 explores one extreme end of this spectrum -- the exclusion of multipoles.

In Chapter 4, I summarize and provide a framework for reevaluating past dark matter constraints from flux-ratio analysis. I explain how comparison between observations of lens galaxy isophotes and mass models from associated lensed arcs can provide more informative priors on multipoles in future lens models. Additionally, I forecast ways that high-resolution simulations can provide complementary prior information both regarding multipoles that may be present in galactic dark matter halos and their connection to the distribution of baryons in the galaxy. Finally, I give an overview of the increase in the sample size of strong lens systems that is expected from JWST and Euclid. Though data from these telescopes holds great potential to help us understand the nature of dark matter, we must first untangle the degeneracy between smooth model complexity and low-mass halos.