Master thesis defense by Rasmus Staugaard Thomsen

Title: Microlensing by dark substructure at high optical depth

Abstract: Dark matter is a mysterious form of matter that does not interact electromagnetically making it invisible to most modern observational probes. According to our modern understanding, it plays a crucial role in the expansion of the Universe and the formation of structure. In particular, all galaxies and galaxy clusters are thought to reside within dark matter halos, which provide the dominant contribution to their mass.

While dark matter is recognized to have a significant impact on our Universe, its microscopic properties remain largely unknown. It is however well established that none of the known elementary particles can account for the majority of dark matter. Consequently, the dark matter hypothesis suggests the existence of new, yet-discovered particles. Little is still known about the properties of these hypothetical particles.

One of the few model-independent characteristics of dark matter relates to their primordial velocities. If the particles were ever relativistic in the early Universe, such models are referred to as 'warm dark matter' (WDM). In contrast, dark matter particles that were produced in a non-relativistic state are known as 'cold dark matter' (CDM). This characteristic has significant implications for structure formation as a whole. Specifically, this distinction leads to differing predictions for sub-galactic structures between CDM and WDM models. As the Universe's structure forms hierarchically under gravitational influence --- small collapsed structures merging to form larger ones --- each galaxy or galaxy cluster is anticipated to host numerous dark substructures of varying masses. The distribution of these structures over masses remains a subject of active debate within the cosmological community. Consequently, measuring these properties could provide a way to differentiate between particle physics models of warm and cold dark matter.

In this thesis, I propose novel methods for searching for such structures, namely, utilizing microlensing at high optical depth. Microlensing refers to the bending of light from a distant star or quasar by a compact object, such as a star or a dark matter clump, leading to a temporary magnification of the background source. This phenomenon is particularly effective for detecting compact objects, as it does not rely on the emission of light from the lensing object itself. This makes it an ideal tool for probing dark matter substructures. Particularly, in high-optical depth microlensing, the gravitational interaction of many objects plays a role in the light's deflection. This can possibly lead to fluctuations in the magnification of a source. While numerous studies have investigated high-optical depth microlensing by stars, there has been significantly less research on high-optical depth microlensing by substructure. We therefore try to adapt an existing model for high-optical depth microlensing, referred to as 'The random star-field model' in literature, to microlensing by substructure. Another formalism is also developed utilizing a ratio distribution to devise the probability of scattering.

This new formalism reveals that discreteness effects likely impose an effective upper limit on the masses involved in microlensing. Despite this limit, adapting the 'random-star field model' to dark matter subhalos indicates that their microlensing effects are considerably greater than that of stars. This suggests further research into high-optical depth microlensing by dark substructure might be warranted. Although our models indicate that microlensing is primarily influenced by the largest masses, a conclusion that has also been reached in other inquiries, it is also found that if the subhalos are not distributed uniformly around the line-of-sight, then this may potentially lead to a small dependence on the lower mass bound.