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Highly supersonic, magnetized and differentially rotating, accretion flows provide an environment for the propagation of waves and the growth of instabilities unlike those normally encountered on Earth. In this dissertation, I investigate the properties of oscillations and instabilities in accretion discs, developing theoretical and numerical models to explore the physical nature of variability encountered in a variety of astrophysical contexts. Through linear theory and semi-analytical calculations, I first consider the physical properties of magnetically altered inertial waves. 'Trapped inertial waves' provide an attractive explanation of the fast variability observed in the emission from low-mass black hole binary systems, but such oscillations can be affected by magnetic tension provided by large-scale poloidal magnetic fields threading the accretion disc. Through local and global analyses, I constrain the modification of trapped inertial waves by poloidal, toroidal and helical magnetic fields. I then investigate the excitation of oscillations in deformed discs with eccentric, non-circular streamlines. Many processes can lead to the growth of eccentricity in accretion discs, and turbulence deriving from the excitation of inertial waves by a local parametric instability provides one mechanism for curbing this growth. However, eccentric discs also provide an environment for the excitation of additional, inherently global oscillations, and I present a framework facilitating a semi-analytical investigation of these modes. I finally employ numerical simulations to explore the dynamics of accretion disc oscillations in the non-linear regime. I first follow the non-linear saturation of inertial waves driven by parametric resonance in non-relativistic discs, and confirm the growth of a second family of large-scale, low-frequency oscillations. Using a pseudo-Newtonian framework to approximate relativistic effects, I then demonstrate the excitation of trapped inertial waves through non-linear coupling with accretion disc deformations in a black hole accretion disc, providing preliminary evidence that trapped inertial waves can be excited even in the presence of MHD turbulence.

Abstract: AR Sco is the first known white dwarf pulsar and currently there is no definitive model for its emission or evolution. This type of binary system could be a critical step in the formation of magnetic cataclysmic variables, a type of accreting white dwarf/M dwarf binary system. In this thesis, I outline a new method of finding AR Sco twins. Since AR Sco was originally classified as a δ Scuti pulsating variable star, I examine catalogs of these stars from optical surveys. In these catalogs, I find possible candidates that are more blue in color and are dim compared to the rest of the sample since these qualities mimic those of AR Sco. We apply these selection criteria to catalogs from the All-sky Automated Survey for Supernovae, the Zwicky Transient Facility, and Rodriguez et al. 2000. In addition, I analyze Gaia data using a similar method, but this was limited by the relative lack of time-series data. I also try to identify X-ray and radio counterparts to our possible candidates. Modeling the distribution of δ Scutis in the Galaxy, I find that our catalogs are the most complete for high-amplitude variables. Using the high-amplitude subset of our possible candidates, I calculate an upper and lower limit on the number of δ Scutis in the Galaxy that could be misidentified AR Sco twins. In the future, I will ask for follow-up time on Chandra X-ray Observatory, Very Large Array, and Gemini to study possible candidate twins.

In this dissertation we focus on the accretion disks which surround accreting white dwarfs as they are some of the most abundant and well observed accretion disk systems. In many of these systems (e.g. dwarf novae), the accretion disk switches between a low luminosity state (quiescence) and a high luminosity state (outburst). These outbursts enable observers to place numeric constraints on the strength of turbulence (i.e. the α parameter) in these accretion disks. This dissertation focuses on results of local (stratified shearing-box) computer simulations of white dwarf accretion disks, and uses these results to gain a better theoretical understanding of these disks. As expected we find that the magnetorotational instability (MRI) is the predominant source of turbulence in these systems. However, we also find that hydrodynamic convection plays a key role as well. During the high luminosity state the disk becomes convectively unstable and the resulting convection enhances the MRI by seeding it with vertical magnetic field. This provides the first robust theoretical mechanism for enhancing turbulence only in outburst; a result required by observations. This convection also prevents the magnetic dynamo in our simulations from exhibiting the typical behavior of magnetic field reversals propagating vertically throughout the simulation. We also examine how the convection in our simulation changes the prior theoretical understanding of these disks. Specifically, we examine how these disks change luminosity over time by generating synthetic lightcurves using a modified disk instability model. These models can successfully reproduce observed outburst and quiescence durations, as well as outburst amplitudes. However, these lightcurves exhibit reflares in the decay from outburst, which are not generally observed in dwarf novae. Although, we highlight the problematic aspects of the quiescence physics in the disk instability model and MRI simulations that are responsible for this behavior.

High-mass X-ray binaries (HMXBs) consist of a black hole or neutron star accreting material from a high-mass stellar companion. Although these systems are very rare, with only about 100 having been discovered in the Milky Way Galaxy, they provide crucial insights into the evolution of high-mass stars and may have played an important role in the early Universe, heating the gas in the intergalactic medium and facilitating its reionization by the ultraviolet light produced by the first stars and galaxies. The advent of gravitational wave astronomy further motivates a more thorough understanding of HMXB populations, since HMXBs are the likely progenitors of many of the double compact binaries whose mergers will be detected by gravitational wave observatories. This dissertation presents three studies of HMXB populations, addressing open questions about the faint end of the HMXB luminosity function, the metallicity dependence of HMXB evolution, and the nature of compact objects in non-pulsating HMXBs.In order to identify low-luminosity HMXBs and study their properties and Galactic number density, we surveyed a square-degree region in the direction of the Norma spiral arm with the Chandra and NuSTAR X-ray telescopes. We discovered three low-luminosity HMXB candidates, all of which have main-sequence Be/B-type counterparts and X-ray luminosities equal to 0.1-1 solar luminosities. The Chandra and NuSTAR surveys of the Norma region also provided the opportunity to study other low-luminosity X-ray populations in the Galaxy. We found that the majority of sources detected at energies above 2 keV are cataclysmic variables (CVs), which likely dominate the hard X-ray component of the Galactic Ridge X-ray Emission. The CV candidates in the Norma region have plasma temperatures of kT = 10-20 keV, whereas the CVs found in similar surveys of the Galactic Center region have temperatures of kT = 20-50 keV. The lower temperatures of Norma CVs may result from a significant number of them being nonmagnetic CVs, polars, or symbiotic binaries whereas the Galactic Center CVs are likely dominated by intermediate polars. The second part of this dissertation discusses the X-ray emission of star-forming galaxies at redshifts between z=1.4 and z=2.6. Simulated models of HMXB populations predict that luminous HMXBs should be more numerous in low-metallicity environments. Studies of nearby galaxies have found an excess of luminous HMXBs in very metal-poor blue compact dwarf galaxies, and it has been suggested that the observed increase of the X-ray luminosity per star formation rate (SFR) of star-forming galaxies at higher redshifts is a result of the metallicity dependence of HMXBs. In order to test this hypothesis, we divided a sample of high-redshift galaxies from the MOSDEF survey into different metallicity bins, and stacked the X-ray data from deep Chandra extragalactic surveys to measure the average X-ray luminosity of the galaxies in each bin. Our preliminary results confirm the increase of the X-ray luminosity per SFR with redshift but do not find a significant correlation between the X-ray luminosity per SFR and the metallicity of galaxies. The third part of this dissertation investigates the nature of the compact object in a non-pulsating HMXB. X-ray pulsations provide strong evidence that an HMXB hosts a neutron star (NS), but the absence of pulsations does not rule out the possibility that an HMXB hosts a NS. Using XMM-Newton and NuSTAR observations of IGR J18214-1318, we study the timing and spectral properties of this supergiant HMXB in detail. Our analysis rules out the presence of pulsations with periods shorter than an hour and detects an exponential cutoff to the power-law spectrum of the source with e-folding energy lower than 25 keV. This low cutoff energy indicates that the compact object in this HMXB is most likely a NS. This study exemplifies the powerful diagnostics provided by the combination of XMM-Newton and NuSTAR observations for the identification of compact objects in HMXBs.