Magnetic fields in Astrophysics

D.J. Price
Institute of Astronomy, Madingley Rd, Cambridge, CB3 0HA, UK
Thesis submitted for the degree of Doctor of Philosophy
August 2004 (final version Oct 2004) [Errata]


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Summary

In this thesis we develop approaches to studying two of the most longstanding theoretical problems in astrophysics, namely the nature and origin of astrophysical jets and the role of magnetic fields in star formation. The results are, however, more widely applicable to a range of problems in which magnetic fields are important.

For the former problem we employ a very simplified physical model of the jet acceleration process. We use time-dependent, spherically symmetric wind models in Newtonian and relativistic gravitational fields to ask whether the energy input rates required to produce the jet velocities observed in Young Stellar Objects (of about 2 $\times$ the escape velocity from the central object) can also produce Active Galactic Nuclei jet velocities (Lorentz factors of $\gamma \sim$ 10). Such a scaling would be expected if there is a common production mechanism for such jets. We demonstrate that such a scaling does exist, provided that the energy input process takes place sufficiently deep in the gravitational potential well, enabling physical use to be made of the speed of light as a limiting velocity, and provided that the energy released in the accretion process is imparted to a small fraction of the available accreting material.

For the latter problem we focus on developing accurate numerical methods for solving the equations of magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The implementation of a `Smoothed Particle Magnetohydrodynamics' algorithm has previously been accompanied by numerous technical difficulties all of which are addressed at some level in this thesis in order to develop a robust and accurate method which can be applied to a wide range of problems of current theoretical interest. In the process we have undertaken a thorough review of the SPH method itself, from which several new results are derived. Amongst the technical issues addressed in the development of the SPMHD algorithm are the treatment of terms proportional to the divergence of the magnetic field in the MHD equations, the self-consistent formulation of the discrete equations from a variational principle, numerical stability of the algorithm and the self-consistent treatment of terms relating to the use of a spatially varying smoothing length. Considerable attention is paid to the ability of the algorithm to capture shocks for which artificial dissipation terms are formulated. Several methods are also examined for maintaining the divergence-free constraint in an SPMHD context. Perhaps most importantly the algorithm is benchmarked against a wide range of standard problems used to test recent high resolution shock-capturing grid-based MHD codes.

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 The entire thesis is available as: price_PhD.ps.gz (2.5Mb) or price_PhD.pdf (21.4Mb) or by chapter as below (as gzipped postscript or pdf). Postscript figures may be obtained by email request. All files are formatted for double sided printing. See also price_PhD_errata.pdf (25kb).

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