title: On the determination of mass density profiles for gravitational lenses from gravitational wave data
Creators: name: Wright, Mick
Publisher: name: University of Glasgow
Year: 2024

description: With the dawning of the age of gravitational wave astronomy, we are rapdily moving from the detection of a single event being extraordinary by itself to this being much more routine. This has opened the doors to a number of investigative avenues of the phenomena that may be probed using these signals or that affect these signals on their path from their source to us here on Earth.

One of these phenomena is gravitational lensing. This occurs when the signal passes by massive objects en-route, and General Relativity predicts that because massive objects warp spacetime this will change the path of the signal. This occurs in a similar fashion to the bending of light by a lens resulting in the name. This phenomenon has been seen in light for over a century, beginning with the first observations by Arthur Eddington in 1919 but has, as of the end of the third observing run of the current ground-based gravitational wave detector network not been observed.

In this thesis, I first aim to present the necessary foundations of gravitational physics and statistical analysis to understand the theory and analysis of gravitational waves and gravitational lensing thereof, before moving on to the work that I have done throughout the course of this degree to investigate what we may learn from future observations of gravitationally lensed gravitational wave signals.

In particular, I will first discuss the development of Gravelamps—a framework that at inception, was designed to investigate gravitational wave signals to determine if there are any signatures of microlensing—gravitational lensing by small compact objects such as stars or black holes and in the case of such a detection, determine the most likely distribution of the mass of the lens which can tell us a great deal about the object that has served to lens the signal. I detail the design, philosophy, and initial testing done to validate the software.

With the framework available, I will then go on to discuss some of the first deployments of the Gravelamps software on real gravitational wave signals. Specifically these were signals identified by the lensing investigations from the LIGO-Virgo-KAGRA Collaboration collaborations to be interesting— though in all cases these signals had been ultimately determined to be non-lensed upon thorough investigation of the possibility, as well as an interesting candidate from the, at time of writing, currently ongoing fourth observing run which also yields no support for the microlensing hypothesis.

I then turn my attention to the strong lensing regime—that where the lensing object is a galaxy or galactic cluster—to investigate how one may determine the mass density profile of the lens here. In this regime, multiple signals are produced that retain the frequency evolution but differ in magnification, time delay, and an overall phase shift. These signals must be analysed together to yield answers, and I demonstrate a means to acquire this information using the model agnostic outputs of strong lensing detection analyses. I show the demonstrations that this method is both valid and stable, and can be deployed at speed, given that it can be done without the need to re-sample an extended parameter space.

Finally, I turn the discussion to the question of gravity. General Relativity is currently the best theory of gravity available to us, but there have been many proposed alternatives that may result in some deviations from the expectations within it. I show an investigation of the possibility that events that Gravelamps determines to be of interest from the perspective of the microlensing hypothesis could instead be the result of deviations from General Relativity. The conclusion of that investigation is that for certain scenarios—some ruled out by current constraints, others still possible—such a false positive can occur.

Ultimately, this work aims to show some of the development of investigations into not just the question of “is a gravitational wave signal lensed” but the question of the lens itself. With the ongoing increases in the sensitivities of the current detector network as well as the on-boarding of other detectors coming in the near future, the detection of gravitational wave lensing is just a matter of time and when it comes we will want to know as much about the lens from that signal as we can and this work aims to assist in ways to acquire that knowledge.