While the progenitors of Type Ia supernovae (SNe Ia) have long been thought to be thermonuclear explosions of white dwarf stars, what triggers the explosion are still a topic of debate. This thesis considers constraints on single-degenerate progenitors of SNe Ia based on the presence of a Roche-lobe filling companion. The ejecta strips material from the companion, that maybe detectable via Hα emission during the nebular phase. Using the full structure from simulations produces line widths are larger than those produced in simple models. The structure formed by the ejecta-companion interaction produce a broken reverse shock that may be visible in X-rays via the Fe K&alpha; line at the age of Tycho's supernova remnant (SNR). If the similar structures in Tycho’s SNR are produced this way then the companion star must have been massive, with M ~ 2 M_&odot;. Detections of circumstellar material within the supernova provides another way to indirectly probe the companion star. Mass loss through winds or novae are expected to shape the circumsteller medium for single-degenerate progenitors and the velocities, v ~ 100 km s^-1 appear to be consistent with recurrent nova shells, a model that is tested by analysing simulations of RS Ophiuchi. Models of RS Ophiuchi can explain the absorption lines seen around the 2006 outburst if the mass loss is 10⁻⁶ M_&odot; yr<sup>-1,/sup>. The circumsteller medium is shown to produce in the velocity and relative strengths of the features seen in SN 2006X. However, whether density in the shells is high enough to produce the required recombination timescale and to overcome ionization by &gamma;-rays for shells at 5 × 10¹⁶ cm remains uncertain.

Black hole jets and accretion discs are the most extreme objects in modern astrophysics whilst dark energy is undoubtedly the most mysterious. This thesis focuses on understanding these three topics. The majority of this thesis is dedicated to investigating the structure and properties of black hole jets by modelling their emission. I develop an inhomogeneous jet model with a magnetically dominated parabolic accelerating base, transitioning to a slowly decelerating conical jet, with a geometry set by radio observations of M87. This model is able to reproduce the simultaneous multiwavelength spectra of all 38 Fermi blazars with redshifts in unprecendented detail across all wavelengths. I constrain the synchrotron bright region of the jet to occur outside the BLR and dusty torus for FSRQs using the optically thick to thin synchrotron break. At these large distances their inverse-Compton emission originates from scattering CMB photons. I find an approximately linear relation between the jet power and the transition region radius where the jet first comes into equipartition, transitions from parabolic to conical and stops accelerating. The decreasing magnetic field strength and increasing bulk Lorentz factor with jet power are the physical reasons behind the blazar sequence. I calculate the conditions for instability in a thin accretion disc with an α parameter which depends on the magnetic Prandtl number, as suggested by MHD simulations. The global behaviour of the instability induces cyclic flaring in the inner regions of the disc, for parameters appropriate for X-ray binary systems, thereby offering a potential solution to a long standing problem. Finally, I calculate the effect of an interacting quintessence model of dark energy on cosmological observables. I find that a scalar-tensor type interaction in the dark sector results in an observable increase in the matter power spectrum and integrated Sachs-Wolfe effect at horizon scales.

One of the key goals of Milky Way science is measuring the distribution of dark matter in the Galaxy. Through the study of Galactic dynamics, inferences can be made about the structure of the Galaxy, and hence the dark matter distribution. To this end, we present a study of methods useful for modelling and understanding dynamical systems in the Galaxy. A natural choice of coordinate system when studying dynamical systems is the canonical system of angle-action coordinates. We present methods for estimating the angle-actions in both axisymmetric and triaxial potentials. These fall into two categories: non-convergent and convergent. The non-convergent methods are fast approaches, mostly based on approximations to Stäckel potentials. We investigate the accuracy of these methods for realistic Galactic potentials. The slower convergent methods operate by constructing generating functions to take us from simple analytically-tractable potentials to our target potential. Tidal streams should prove useful for constraining the large-scale dark matter distribution in the Galaxy. Armed with our new angle-action tools, we investigate the properties of known streams in a realistic Galactic potential. We present a simple algorithm for constraining the Galactic potential using a tidal stream, which exploits the expected structure of a stream in the angle-frequency space of the true potential. We expand this approach into a fully probabilistic scheme that allows for handling of large errors, missing data and outliers. We close by discussing another tool useful for modelling the dynamics of the Galaxy: extended distribution functions for the Galactic disc. We present a simple extension of an action-based distribution function from Binney (2010) that includes metallicity information, and compare the model predictions with current data. These models are essential for incorporating the selection effects of any survey, and reveal the important chemo-dynamic correlations that expose the history and evolution of the Galaxy.