The concept of a hybrid star, a stellar object that has some sort of atypical internal structure, particularly in regards to its energy budget, has been around for over a century. Arguably the pre-Gamow explanations offered for the source of luminosity for all stars correspond to a form of hybrid star models, from Kelvin's thermal explanation, to Landau's suggestion that the sun harboured a neutron degenerate core. This dissertation focuses on the study of exotic stellar objects, both a class of hybrid stars with a neutron core known as Thorne-Żytkow Objects (TŻOs), and highly magnetized, super-Chandrasekhar mass white dwarfs. A Thorne-Żytkow Object may form as a result of a Common Envelope Evolution (CEE) event between a giant or supergiant star with a neutron star companion. It consists of a large, diffuse giant envelope surrounding a neutron degenerate core. We investigate the structure and evolution of these objects here. Focusing on the central degenerate component of these objects themselves leads to the study of exotic compact objects in their own right, in this case, white dwarfs that harbour intense magnetic fields, which provide sufficient magnetic pressure support for them at masses above the Chandrasekhar mass, making them possible progenitors of overly luminous Type Ia supernovae.

In Chapter 1, I provide a brief introduction to the venerable field of stellar evolution to provide the necessary context for the following Chapters of this work. In Chapter 2, I present an introduction to the physics, structure and evolution of Thorne-Żytkow Objects, the canonical models thereof as they exist in the literature and the challenges and some of the approaches taken to overcome them. I also discuss the formation and death of TŻOs. In Chapter 3, I provide a similar introduction to the study of highly magnetized compact objects, white dwarfs (B-WDs) and neutron stars (B-NS / magnetars) as well as the relevant microphysics that we must consider to study these objects. In particular I discuss the mechanisms by which thermal neutrinos can be produced in such objects. This is essential to understanding their cooling.

In Chapter 4 I introduce and explain the numerical techniques and codes used throughout this dissertation, specifically the STARS and MESA Henyey-style one-dimensional stellar evolution codes. I also explain the modifications made to the codes in question to model the exotic objects I study.

In Chapter 5 I present a novel series of solutions for envelopes of TŻOs which, while qualitatively similar to those of the canonical TŻO models that I discussed in Chapter 2, differ in a few key ways. The solutions resemble the canonical supergiant-like solutions, dominated by nuclear burning, even for masses that admit a giant-like solution, dominated by accretion on to the neutron core, in these earlier models. I have investigated the thermodynamic consistency of these models and how robust the qualitative structure of the solutions is to changing accretion rates and other boundary conditions. I found that our use of revised, updated tables of thermal neutrino loss rates compared those used in the canonical work serves to explain the majority of the structural differences between our models. I also present a series of hybrid-AGB models, in which the core exists in a state between that of a neutron star and a white dwarf, and is modelled in full. Anomalous surface chemical abundances in these models indicate a method by which TŻOs could be identified observationally.

In Chapter 6, I investigate the structure and evolution of super-Chandrasekhar mass B-WDs, finding that solutions do exist at masses above the Chandrasekhar mass, given a sufficiently large magnetic field permeating the object. I also present a modified field prescription that addresses an issue regarding non-physical current sheaths in the B-WDs, by means of a saturation radius. This was shown to replicate the previous results and suggests that highly magnetized supermassive white dwarfs could indeed serve as progenitors for overly luminous Type Ia supernovae.

In Chapter 7 I summarize the content of this dissertation, contextualising and expanding upon the results and providing a short review of possible future avenues for related research.