Beyond Part III

Young Researchers in Mathematics 2009

16-18 April 2009

Centre for Mathematical Sciences, Cambridge

Astrophysics Session

Talks will be in MR14 (combined with Fluid Dynamics on Friday morning).



The Origin of debris disc stirring - Alex Mustill

Many main-sequence stars are surrounded by dusty debris discs similar to the Sun's Kuiper belt. These discs are typically detected through their infrared emission. The lifetime of the dust is much less than typical stellar ages, implying a reservoir of larger planetesimals whose collisions generate the dust. An outstanding problem is how to stir the disc, i.e., how to excite relative velocities to cause collisions between planetesimals to be erosive rather than accretional. An unperturbed disc will eventually stir itself as the planetesimals in it grow large enough to perturb their neighbours themselves. We propose a model whereby the disc is stirred by secular perturbations from a planet interior to the disc. A key question is whether this will occur before or after the disc stirs itself. If the planet stirs the disc quickly enough, further growth of planetesimals in the disc may be inhibited. We identify several systems such as Epsilon Eridani and Fomalhaut in which the disc has likely been stirred by the planet. By comparing the time for self-stirring with the star's age, we also identify some disc hosting stars currently without known planets which are likely candidates for hosting planets.

Magnetized Accretion Disks around Spinning Black Holes - Robert Penna

We present results from global 3D GRMHD simulations of accretion disks around black holes, for a range of disk thicknesses and black hole spin parameters. We compare the angular momentum profiles of the disks to the predictions of the standard thin disk theory of Novikov and Thorne (1973). Applications to the continuum-fitting method for measuring the spin of black holes in Galactic X-Ray binaries are discussed.

The Wonderful World of RRATs - Evan Keane

In 2006 a new class of neutron stars were discovered in searches for transient radio bursts in the Parkes Multi-beam Pulsar Survey (PMPS). This new population - dubbed "Rotating Radio Transients" (RRATs) emit very occasional bright pulses of radio emission. Such sources are difficult to find and population estimates predict that they are even more abundant than the well studied radio pulsars - neutron stars which pulse regularly. As well as being of intrinsic interest due to their unusual emission properties the existence of RRATs has large implications for the Galactic population of neutron stars. I will discuss the current status of my research into RRATs including the implications for the Galactic production of neutron stars, some results from ongoing observations with the Lovell telescope at Jodrell Bank, the successful re-processing of the PMPS with improved techniques which has resulted in the discovery of more RRATs as well as simultaneous optical-radio observations and an experimental simultaneous 6-telescope multi-frequency observation.

The Anelastic Approximation: Magnetic Buoyancy and Convection - Nikolai Berkoff

The anelastic approximation (AA) filters out fast moving waves, chiefly sound waves and fast magneto-acoustic waves. This filtering allows numerical schemes to take much larger time-steps. To make the AA we assume the Mach number of the flow must be small. A further assumption that the basic state is isentropic is used in some anelastic equations. This extra assumption allows the thermodynamic variables to be written in terms only of the entropy which creates a large computational saving.
My work is concerned with the uses of the AA and a isentropic AA. Some isentropic anelastic codes have been used in the sun for simulations from the tachocline to the corona. I will investigate when the two forms of the AA are valid, in particular for the magnetic buoyancy and convective instabilities.

The solar tachocline: why is it there and what is it for? - Steve Tobias (keynote speaker)

In this talk I shall discuss the dynamics of the solar tachocline. This region at the base of the solar convection zone is believed to play a key role in the generation of the solar activity cycle and the attendant magnetic phenomena in the Sun. I shall review the observations and describe some of the key issues for maintenance of the tachocline.

The Weather on Jupiter - Rich Wood

Narrow fast flowing currents of fluid, known as jetstreams, circumnavigate the atmosphere of both the Earth and the gas giants. Despite lacking a solid surface, the clouds visible on a gas giant are confined to a thin "weather layer" that is dynamically similar to the atmosphere on Earth. However, on Earth the mechanisms that generate and maintain the jetstreams depend on the solid surface and the large pole-to-equator temperature gradient. Without either a solid surface or a large temperature gradient, gas giants require different mechanisms to explain their jetstream structure.

As the weather layer contains a small fraction of the mass of a gas giant, it is arguably a self consistent model to only consider the dynamics within the weather layer, prescribing the effect of the layers beneath. Such models have successfully reproduced the jetstream structure observed on gas giants. Despite their success, such models have previously lacked a physically motivated method of representing the effect of the layers below. To address this, a physically motivated model that makes use of fundamental theory shall be described. Next, the challenges of numerically simulating such a model will be briefly discussed. Finally the results of numerical simulations will be summarised, demonstrating robust jetstream formation and maintenance.

The Solar Interior (accessible talk) - Toby Wood

We will discuss several of the physical processes at work within the Sun, including heat transport, heavy element settling and the role of magnetic fields. The importance of rotation, shear and stratification will also be described. This talk will (hopefully) not require any prior knowledge of MHD or solar theory.

Babcock-Leighton Type Dynamos - Peter Mann

Babcock-Leighton type dynamos have recently had much success in reproducing many large-scale features of the solar magnetic field. These models are essentially of alpha-omega type, however use a surface poloidal field regeneration mechanism. They also rely on large-scale meridional circulation to connect the two magnetic generation regions. I will review this class of dynamo and discuss some problems, issues and recent results obtained using this as a model for the solar dynamo.

Effects of Fluctuations in αΩ Dynamo Models - Katy Richardson

The generation of large-scale magnetic field on the Sun is believed to be governed by a dynamo process. The α-effect of mean-field dynamo theory acts as a regeneration term, closing the dynamo cycle by turning toroidal field into poloidal field. This work investigates the interaction of a fluctuating α-effect with large-scale shear in a simple 1-d dynamo wave model. We find that there can be a mechanism for magnetic field generation, even when the mean α is zero, provided the spatiotemporal spectrum of the fluctuations has an appropriate form. We adapt the model to form a simple model of the solar cycle and investigate the stability and parity of the system.

Powering the solar dynamo via the magnetic buoyancy instability - Tina Davies

The generation of the sun's magnetic field has been a much-investigated topic in recent years. It is thought that the sun's large-scale magnetic field must be a product of small-scale, turbulent motions within the sun's convection zone. However this has caused problems, particularly in the limit of high magnetic Reynolds number. The important quantity for the generation of large-scale field is the electromagnetic force (emf). This talk is about the possibility of producing emf via the magnetic buoyancy instability -- a convective-type instability which is thought to be responsible for the emergence of sunspots. I will give examples of the emfs generated by unstable flows and what they could mean for the sun's magnetic field.