Black hole-neutron star (BH-NS) mergers are promising candidates for the progenitors of short-duration gamma-ray bursts (GRBs). With the right initial conditions, the neutron star becomes tidally disrupted, eventually forming a dense, accreting disk around the black hole. The thermal energy of this black hole-disk system can be extracted via neutrino processes, while the spin energy of the black hole can be extracted via magnetic processes. Either (or even a combination of these) processes could feasibly power a relativistic jet with energy ≥~ 10 49 erg and duration ≤~ 2 s, hence producing a short-duration GRB. In this thesis, we investigate BH-NS mergers with three-dimensional, pseudo-Newtonian simulations. We use the simulation code Charybdis, which uses a dimensionally-split, reconstruct-solve-average scheme (i.e. using Riemann solvers) to solve the Euler equations of hydrodynamics. Although the code is based on a Newtonian framework, it includes pseudo- Newtonian approximations of local gravitational wave effects and the innermost stable circular orbit of the BH, which are both general relativistic phenomena. The code also includes the effects of global neutrino emission, shear viscosity and self-gravity. This thesis comprises two main projects. The first project is a parameter study of the equation of state, which encapsulates the relationship between the pressure of a fluid and its other thermodynamic properties. Although the EOS is well understood at low densities, it is yet to be constrained at supranuclear densities, and so must be treated as a parameter in numerical studies of BH-NS mergers. We present simulations using three existing EOSs, in order to investigate their effect on the merger dynamics. We find that the EOS strongly influences the fate of the NS, the properties of the accretion disk, and the neutrino emission. In the second project, we begin upgrading Charybdis to include magnetic field effects, in order to investigate the magnetic processes described above. We implement existing reconstruction and Riemann solver algorithms for the equations of magnetohydrodynamics, and present 1D tests to compare them. When modelling magnetic fields in more than one dimension, we must also deal with the divergence-free condition, ∇. B = 0. We develop a new constrained transport algorithm to ensure our code maintains this condition, and present 2D tests to confirm its accuracy. This algorithm has many advantages over existing ones, including easier implementation, greater computational efficiency and better parallelisation. Finally, we present preliminary tests that use these algorithms in simulations of BH-NS mergers.

The circumnuclear disc (CND) orbiting the Galaxy's central black hole is a reservoir of material that can ultimately provide energy through accretion, or form stars in the presence of the black hole, as evidenced by the stellar cluster that is presently located at the CND's centre. In this paper, we report the results of a computational study of the dynamics of the CND. The results lead us to question two paradigms that are prevalent in previous research on the Galactic Centre. The first is that the disc's inner cavity is maintained by the interaction of the central stellar cluster's strong winds with the disc's inner rim, and secondly, that the presence of unstable clumps in the disc implies that the CND is a transient feature. Our simulations show that, in the absence of a magnetic field, the interaction of the wind with the inner disc rim actually leads to a filling of the inner cavity within a few orbital time-scales, contrary to previous expectations. However, including the effects of magnetic fields stabilizes the inner disc rim against rapid inward migration. Furthermore, this interaction causes instabilities that continuously create clumps that are individually unstable against tidal shearing. Thus the occurrence of such unstable clumps does not necessarily mean that the disc is itself a transient phenomenon. The next steps in this investigation are to explore the effect of the magnetorotational instability on the disc evolution and to test whether the results presented here persist for longer time-scales than those considered here.

The solar corona is a highly complex and active plasma environment, containing many exotic phenomena such as solar flares, coronal mass ejections, prominences, coronal loops, and bright points. The fundamental element giving coherence to all this apparent diversity is the strong coronal magnetic field, the dominant force shaping the plasma there. In this thesis, I model the 3D magnetic fields of various coronal features using the techniques of magnetic charge topology (MCT) in a potential field. Often the real coronal field has departures from its potential state, but these are so small that the potential field method is accurate enough to pick out the essential information about the structure and evolution of the magnetic field. First I perform a topological analysis of the magnetic breakout model for an eruptive solar flare. Breakout is represented by a topological bifurcation that allows initially enclosed flux from the newly emerging region in my MCT model of a delta sunspot to reconnect out to large distances. I produce bifurcation diagrams showing how this behaviour can be caused by changing the strength or position of the emerging flux source, or the force-free parameter α. I also apply MCT techniques to observational data of a coronal bright point, and compare the results to 3D numerical MHD simulations of the effects of rotating the sources that underlie the bright point. The separatrix surfaces that surround each rotating source are found to correspond to locations of high parallel electric field in the simulations, which is a signature of magnetic reconnection. The large-scale topological structure of the magnetic field is robust to changes in the method of deriving point magnetic sources from the magnetogram. Next, I use a Green’s function expression for the magnetic field to relax the standard topological assumption of a flat photosphere and extend the concept of MCT into a spherical geometry, enabling it to be applied to the entire global coronal magnetic field. I perform a comprehensive study of quadrupolar topologies in this new geometry, producing several detailed bifurcation diagrams. These results are compared to the equivalent study for a flat photosphere. A new topological state is found on the sphere which has no flat photosphere analogue; it is named the dual intersecting state because of its twin separators joining a pair of magnetic null points. The new spherical techniques are then applied to develop a simple six-source topological model of global magnetic field reversal during the solar cycle. The evolution of the large-scale global magnetic field is modelled through one complete eleven-year cycle, beginning at solar minimum. Several distinct topological stages are exhibited: active region flux connecting across the equator to produce transequatorial loops; the dominance of first the leading and then the following polarities of the active regions; the magnetic isolation of the poles; the reversal of the polar field; the new polar field connecting back to the active regions; the polar flux regaining its dominance; and the disappearance of the transequatorial loops.

This dissertation is a study of the physical conditions in star-forming regions, and combines observational data and theoretical calculations. We studied the physical conditions of Orions Veil, which is an absorbing screen that lies along the line of sight to the Orion H II region. We computed photoionization models of the Veil. We combined calculations with UV, radio, and optical spectra that resolve the Veil into two velocity components. We derive many physical parameters for each component seen in 21 cm absorption. We find the magnetic field energy dominates turbulent and thermal energies in one component while the other component is close to equipartition between turbulent and magnetic energies. We observe H2 absorption for highly excited levels. We find that the low ratio of H2/H0 in the Veil is due to the high UV flux incident upon the Veil. We detect blueshifted S+2 and P+2 ions which must arise from ionized gas between the neutral portions of the Veil and the Trapezium and shields the Veil from ionizing radiation. We determine the ionized and neutral layers of the Veil will collide in less than 85,000 years. The second part of this dissertation involved self-consistently calculating the thermal and chemical structure of an H II region and photodissociation region (PDR) that are in pressure equilibrium. This differs from previous work, which used separate calculations for each gas phase. Our calculations span a wide range of initial conditions. We describe improvements made to the spectral synthesis code Cloudy which made these calculations possible. These include the addition of a molecular network with ~1000 reactions involving 68 molecules and improved treatment of the grain physics. Archival data are used to derive important physical characteristics of observed H II regions and PDRs. These include stellar temperatures, electron densities, ionization parameters, UV flux, and PDR density. The contribution of the H II region to PDR emission line diagnostics is also calculated. Finally, these calculations are used to derive emission line ratios than can tell us the equation of state in star-forming regions.

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A fossil magnetic field embedded in the radiative core of the Sun has been thought possible for some time now. However, such a fossil magnetic field has, a priori, not been considered a visible phenomenon due to the effects of turbulence in the solar convection zone. Since a well developed theory (referred to herein as magnetohydrodynamic dynamo theory) exists for describing the regeneration of magnetic fields in astrophysical objects like the Sun, it is possible to quantitatively evaluate the interaction of a fossil magnetic field with the magnetohydrodynamic dynamo operating in the solar convection zone. In this work, after a brief description of the basic dynamo equations, a spherical model calculation of the solar dynamo is introduced. First, we calculate the interaction of a fossil magnetic field with a dynamo in which the regeneration mechanisms of cyclonic convection and large-scale, nonuniform rotation are confined to spherical shells. It is argued that the amount of amplification or suppression of a fossil magnetic field will be smallest for a uniform distribution of cyclonic convection and nonuniform rotation, as expected in the Sun. Secondly, we calculate the interaction of a fossil magnetic field with a dynamo having a uniform distribution of cyclonic convection and large-scale, nonuniform rotation. We find that the dipole or quadrupole moments of a fossil magnetic field are suppressed by factors of -0.35 and -0.37, respectively. The dynamo modified fossil field, superimposed on the theoretically calculated magnetic fields of the solar magnetic cycle, are compared with the actual sunspot cycle and solar magnetic fields as observed by others, indicating that a fossil magnetic field may be responsible for asymmetries in the sunspot cycle and an observed solar magnetic quadrupole moment. Further observations and reduction of the data are required before the presence of a fossil magnetic field can be established. A discussion is given of the implications for the Sun if a fossil magnetic field is observed and identified. It is considered most likely that a fossil magnetic field would be a remnant of the possible Hayashi phase of a fully convective, protosun. Other possibilities also exist.

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