Research Topics

Dynamics of Astrophysical Discs

mri turbulence

Plot illustrating the complex magnetic field structure in local midplane/vertical sections of a turbulent protoplanetary disc. Figure by Tobias Heinemann. A video version is also available.

Discs are ubiquitous in astrophysics and participate in some of its most important processes. Most, but not all, feed a central mass: by facilitating the transfer of angular momentum, they permit the accretion of material that would otherwise stay in orbit. As a consequence, discs are essential to star, planet and satellite formation. They also regulate the growth of supermassive black holes and thus indirectly influence galactic structure and the intra-cluster medium. Although astrophysical discs can vary by ten orders of magnitude in size and differ hugely in composition, all share the same basic dynamics and many physical phenomena.

Our group is interested in the turbulence that prevails in these discs and the instabilities that sustain them. Turbulence helps the discs accrete, and also influences the process of planet formation in protostellar discs. The magnetorotational instability (MRI) is the main cause of activity in well-ionised discs, such as dwarf novae, X-ray binaries, and active galactic nuclei. In more massive colder discs, such as young protostellar discs, gravitational instability is the leading cause (see movie below). At certain times and locations both instabilities or neither occur, leading to rich and violent dynamics, such as FU Ori or EX Lupi outbursts which occur on timescales of 100-1000 years. On the other hand, the interplay between the MRI and thermal instability leads to cycles of repeated outbursts on much shorter timescales (days and weeks) in dwarf novae that amateur astronomers can observe. Our group uses numerical simulations (and analytical techniques when possible) to better understand these complicated processes.

Other topics that we work on include (but are not limited to), (a) the powerful outflows and jets that are launched from almost all discs at certain times of their evolution, (b) how discs become warped and eccentric and what sustains these non-circular geometries, (c) large-scale waves and oscillations in discs around black holes and neutron stars, and the signatures of general relativity upon them, (d) dust dynamics, vortices and dust-gas instabilities in planet formation, and (e) patterns and structures in Saturn's rings.

Disc-Planet Interactions

planet migration

A young planet embedded in a turbulent protoplanetary disc. Image by Clément Baruteau.

Solid material embedded in a gas disc is subject to radial migration. Small particles (up to a few 100 km in size) are subject to aerodynamic drag, causing them to migrate inward on time scales that can be alarmingly fast (100 yr for m-sized objects).

Earth-like planets are massive enough to excite tidal sound waves in the disc, one inside its orbit and one outside. These are of unequal strength in general, mainly due to the non-linear nature of Keplerian rotation (the rotation profile is asymmetric with respect to the orbit of the planet). This leads to a torque on the planet, that usually corresponds to inward migration called Type I migration. For Superearth planets (and also possibly the cores of giant planets) the time scale for inward migration can be as short as 105 years. This has to be compared to a disc life time of 107 years, implying that essentially there should be no planets at large (1-10 AU) radii! This is a serious problem, and possible solutions include MHD turbulence and non-linear effects on the corotation torque, especially in non-barotropic discs.

Massive planets, comparable to Jupiter, excite non-linear waves in the disc, leading to the formation of an annular gap (see picture). The migration of the planet slows down considerably, and is now called Type II migration. Basically, in this regime the planet just accretes with the gas onto the star, making the migration time scale comparable to the disc life time.

For intermediate masses, comparable to Saturn, rapid Type III migration can occur. This mode of migration is driven by a strong coorbital flow, and can in principle be directed either inward or outward. This is a very challenging problem, numerically, because it relies on the flow in the direct vicinity of the planet which is difficult to treat in a realistic way.

Planet formation in binary systems

binary systems

Differential orbital phasing of 1-10 km planetesimals in a binary system in which the secondary star is half the mass of the primary, and is on an eccentric orbit with e=0.4. Shown are the eccentricities of the planetesimals versus their semi-major axis. Color indicates the size in km. This plot is also available as a mpg-movie.

Making planets is difficult in general, and it is even more difficult in systems that have an additional strong perturber in the form of a companion star. Nevertheless, a planet has been found at 2 AU around a star that has a companion of 0.5 Msun at only 20 AU (orbital distance of Uranus!). Moreover, this massive companion in on a very eccentric orbit. The strong gravitational perturbations due to this second star puts planets-to-be in all sorts of trouble. One fundamental problem arises when you try to grow a population of km-sized planetesimals into larger bodies that will eventually accrete gas to form a giant planet. The perturbations of the secondary star excites the eccentricities of the planetesimals. This leads to very high encounter velocities (up to 1 km/s), which makes collisions between planetesimals very violent and destructive. The presence of a gas disc to damp the eccentricities of the planetesimals does not help. Since the strength of gas drag is size-dependent, planetesimals of different size will still be on very different orbits. This so-called differential orbital phasing leads again to very violent collisions between bodies of unequal size. It is difficult to see how to overcome this problem and proceed with building bigger bodies.

Solar, Stellar and Planetary Magnetism

butterfly diagram Magnetic fields in large astrophysical bodies such as the Sun, Earth and stars are produced by dynamo action due to fluid motions in their interiors or atmospheres. Observations show that the resulting fields are highly complex in space and time. We are interested in developing theoretical models that can explain the observations and also aid the fundamental understanding of the nature of the dynamo process.

The picture shows a mean-field solar dynamo simulation with contours of toroidal magnetic field as a function of latitude and time. Like the large-scale magnetic field with the Sun, the magnetic field in this simulation is dipolar and migrates equatorwards during each cycle.

flux separation Recent observations from various ground-based and space instruments have revealed fascinating details of the highly complex magnetic field structures in the solar photosphere. These are produced by the mutual interaction of magnetic fields and convection. We investigate these structures by a combination of numerical simulation and theoretical modelling.

The picture shows a snapshot of a 3d simulation of compressible magnetoconvection. Left: Magnetic energy density. Right: Temperature distribution. This solution illustrates the phenomenon of flux separation - vigourous convection in a flux-free region in the centre of the box is surrounded by weak (magnetically-dominated) small-scale convection.

Please contact Michael Proctor for more information.

Pattern Formation and Nonlinear Dynamics


Internal gravity waves can be excited in radiative regions of solar-type stars by tidal forcing due to planets in short-period orbits. If these waves are of sufficient amplitude, they can break near the centre and transfer angular momentum from the orbit of the planet to the spin of the star. This results in the star being spun up from the inside out, and possibly in the orbital decay of the planet. This plot is also available as a avi-movie. Figure by Adrian Barker.

Studies of order and disorder in the natural world have a long history. Indeed, a diverse collection of physical, chemical and biological systems naturally organise themselves into states with degrees of symmetry, i.e. patterns. A realisation has emerged over the past forty years that the same classes of qualitative behaviour appear repeatedly, and universal mathematical models have been developed to understand each characteristic situation, see, for example, the review by Cross and Hohenberg, Rev. Mod. Phys. 65 (1993). These mathematical models provide a unifying viewpoint and have, in turn, stimulated further research in the relevant experimental disciplines.

One of the longest-studied examples of a pattern forming instability is the Rayleigh-Benard problem of thermal convection in a planar fluid layer; this system has come to be regarded as archetypal. Pattern formation occurs in many other contexts, including liquid crystals in externally imposed electric fields, nonlinear optics, directional solidification, Faraday waves in vertically vibrated layers of fluids or granular media, chemical reactions (such as the Belousov-Zhabotinsky and CIMA systems) and surface catalysis.

The mathematical methods involved in analysing these problems make use of the symmetric nature of the problem. Mathematically (using equivariant bifurcation theory) it is often possible to build up a classification of possible regular patterns; experimental systems select particular patterns from this classification. Instabilities of regular patterns to modulational, long-wavelength, disturbances are also well understood. Recent attention has focused on instabilities near 'mode interaction' points where an initial spatially homogeneous state is simultaneously unstable to instabilities with different wavelengths.

Reduced models (especially ODEs) for pattern-forming systems are often a rich source of interesting nonlinear dynamical behaviour in their own right. Ongoing research into these theoretic systems is concentrating on the dynamics near heteroclinic cycles and networks.

Please contact Michael Proctor for more information.