Diploma projects

Suggestions for diploma and PhD projects

In case you are interested in doing one of the diploma projects (Ex-jobb) below, contact:

Ulf Torkelsson
Department of Physics
Göteborg University
Office: O7108B
Phone: +46 31 772 3136
E-mail: torkel@physics.gu.se

Diploma projects

Simulations of magnetic field generation in galaxies

The origin of the large scale magnetic fields in spiral galaxies is controversial. At the core of the issue is the efficiency of a galactic dynamo. The question is whether the galactic dynamo is able to generate a large scale field from a small scale magnetic field in the time available since the formation of the galaxy. A galactic dynamo requires turbulence in the interstellar medium to generate the magnetic field. In most models this turbulence is produced by individual supernova explosions or by superbubbles that are generated when several supernovae explode in the same part of the interstellar medium in a short time span. The goal of this project is to develop a simple phenomenological model of this process, implement it in a computer code, and study the time evolution of the galactic magnetic field. Parts of the computer exists already, but it has not been tested and debugged. The project can be carried out by one or two students. In the latter case it is expected that models will be refined to a higher degree of realism during the course of the work.

Spin evolution of DQ Her-stars

DQ Her-stars are a type of interacting binaries in which a white dwarf is accreting material from its companion. The accreted material forms an accretion disc around the white dwarf, however the accretion disc is unable to extend all the way down to the surface of the white dwarf, because the magnetic field of the white dwarf is strong enough to truncate the disc above the surface of the white dwarf. In some of these systems one has observed secular changes in the spin rate of the white dwarf. These changes are due to the interaction of the white dwarf with material in the accretion disc, and can be used to test models of magnetospheric accretion. This project consists of a critical survey of the literature on the observations of spin variations in DQ Her-systems, and an evaluation of how well these variations are described by the theoretical models such as the classical Ghosh & Lamb model:

Accretion discs as current sheets in stellar magnetospheres

An accretion disc can be thought of as a thin current sheet in a stellar magnetosphere. The accretion through the disc is driven by magnetic stresses, or equivalently currents, in the disc, which means that the current distribution can be calculated from the accretion flow. Another current is generated through magnetic induction since the accretion disc is rotating inside the stellar magnetosphere. The currents must close outside the accretion disc, and they will also in their turn generate a magnetic field outside of the accretion disc. This results in a complicated three-dimensional electrodynamic problem, whose solution will depend on the electrical conductivity of the plasma in the stellar magnetosphere. For some simple but informative cases the problem can be addressed by a combination of analytical and numerical techniques. An important physical result from these calculations will be that it it possible to calculate the rate at which the star and the accretion disc exchanges angular momentum through the Lorentz force resulting from the coupling between the stellar magnetic field and the currents in the accretion disc (see U. Torkelsson, 1998, MNRAS, 298, L55 - L59), which is interesting for the understanding of spin evolution of both neutron stars and T Tauri-stars. It is also possible to extend this work to the case of magnetospheres generated by accretion discs around black holes. Thus there is the possibility for two students two work on two closely related problems here.

The formation of accretion discs in elliptic binaries

If the two stars in an interacting binary is on circular orbits, then one of the stars is constantly filling its Roche lobe, and matter is streaming over to the compact object through the L1-point. Supposed that the compact object is sufficiently small the stream of overflowing matter will form an accretion disc around the compact object. If the stars are on elliptical orbits the Roche lobes are not well-defined, and mass transfer can become episodic. The extent of the accretion disc may also be affected by the elliptical orbits. Very little theoretical research has been done on this problem, though several systems of this kind are known. In some of these systems, most notably the Be/X-ray transients, outbursts are observed at the time of periastron passage. These outbursts are attributed to that a temporary accretion disc forms at the time of periastron, and then gradually decays. It is probably very difficult to apply an analytical approach to this problem, so the project consists of learning to use an SPH (smooth particle hydrodynamics) computer code and setting up numerical simulations of an elliptic binary in which one of the stars is losing mass through Roche-lobe overflow at the time of periastron passage. The project is suitable for one or two students. With two students more time will be spent on developing a realistic model of a Be-star in a Be/X-ray transient.

Spin evolution of disc-accreting neutron stars

A neutron star in a close binary can accrete matter and angular momentum from its companion. In general the effect on the neutron star should be that it is spinning up, but in practice the neutron star has a substantial magnetic field, which is coupling it to the surrounding plasma, and through which it can also exchange angular momentum with the plasma. Ghosh & Lamb (1979) studied this coupling in the case of a thin accretion disc surrounding the neutron star. Their model suggests that the neutron star will evolve towards an equilibrium in which as much angular momentum is transferred by the neutron star's magnetic field to the outer part of the disc as is transferred from the innermost part of the disc to the neutron star. This model has been challenged by observations over the last decade of disc-accreting X-ray pulsars that oscillate between spin up and spin down phases. Furthermore using the Ghosh & Lamb model it is difficult to explain the appearance of millisecond pulsars. One possible solution to these problems is that the magnetic torque between the neutron star and the accretion disc can be enhanced by a current that is generated by an MHD dynamo in the accretion disc (see Torkelsson 1998). The aim of this project is to calculate the effect of this mechanism on the secular evolution of a neutron star.

PhD projects

Turbulence in accretion discs

An accretion flow is driven by the outwards transport of angular momentum through an accretion disc. Since the molecular viscosity is too small by several orders of magnitude to drive an accretion disc it has been widely assumed since the 1970s that the disc becomes turbulent, and that the turbulence enhances the angular momentum transport. However the Keplerian flow in an accretion disc is stable according to Rayleigh's criterion, and it was only in the 1990s that Balbus & Hawley (1991) realised that the flow becomes unstable in the presence of a weak magnetic field. Several numerical simulations in the mid 1990s (Hawley et al. 1995, Matsumoto & Tajima 1995, Brandenburg et al. 1995) showed that this instability develops into turbulence, and that the turbulence results in an anomalous outwards transport of angular momentm. This is now the most promising mechanism for the angular momentum transport in accretion discs, but several problems remain. The strength of the anomalous viscosity is usually measured by the so-called Shakura-Sunyaev parameter, alpha. The numerical simulations do in general yield a value of 0.01 for alpha. It is virtually impossible to measure alpha for a steady accretion disc, and most of the information we have on alpha comes from observations and modelling of dwarf nova outbursts. These suggest that alpha assumes a value of 0.1 during the outbursts, which is thus higher than the values that are typically generated in the numerical simulations of the turbulence. The goal of this project is to solve this and related puzzles on turbulent transport in accretion discs. One line of attack here is to go for more realistic numerical simulations that study the turbulence as it appears in more realistic models of the accretion disc. That way one can get a better estimate of the turbulent transport, and one might discover other kinds of turbulence in the disc, for instance convection. Another approach is to develop more detailed models of turbulent accretion disks, and for instance develop a more general description of the turbulent transport, than the Shakura-Sunyaev prescription. Such a model can then be calibrated by numerical simulations.

Accretion flows in magnetic cataclysmic variables

DQ Hers and, in particular, AM Hers, are groups of cataclysmic variables in which the magnetic field of the white dwarf is powerful enough to significantly influence the accretion flow from the companion. In the case of an AM Her the magnetic field is so strong that an accretion disc is never formed, and rather the accretion stream from the secondary is captured in the magnetosphere of the white dwarf before it can form an accretion disc. Such systems are amazing laboratories for plasma physics, and since they are binaries it is possible to gain quite a bit of information on the geometry and the processes that go on in these systems. They are also promising from a numerical point of view since the white dwarf is big in contrast to other compact objects, and the distance between the two stars is rather small. It should therefore be possible to study most of the flow in detail in large-scale numerical simulations.

Published by torkel@physics.gu.se