The interior of the Sun is the only astrophysical fluid flow for which all the relevant dynamical variables are known with precision. In particular, helioseismology has revealed the details of the Sun's interior rotation. We seek a dynamical explanation for the origin of the internal angular velocity function of the Sun. The problem is a rich challenge on its own, but it also bears on frontline issues across theoretical astrophysics: dynamo theory, transport of angular momentum and entropy, and turbulence. Moreover, it combines numerical simulation, mathematical analysis, physical theory, and direct observation in a highly interactive combination, perhaps uniquely so in astrophysics.
The Sun's outer layers are convectively unstable and highly turbulent. This turbulence excites a vast spectrum of global modes of vibration, which may be detected by analysis of the solar surface. Decomposition of the spectrum into a superposition of eigenmodes then allows an accurate reconstruction of the interior, including the small differential rotation. The contours of constant rotation velocity are seen in the above diagram. This shows a meridional slice of the Sun. The black lines are the isorotation contours; in 3D they are surfaces of rotation about the vertical (rotation) axis of this figure. The topmost black contour near the pole represents an angular rotation frequency of 330 nanohertz, the most equatorial contour some 460 nanohertz. The white lines show the results of an analytic solution of the a fundamental fluid equation, the vorticity equation. The analytic theory is meant to apply only to the bulk of the interior, not to the boundary layers. The blue line marks the boundary between the interior radiative zone (RZ) and the exterior convective zone (CZ). Several points will be noted:
i.) Differential rotation is predominantly restricted to the CZ.
ii) The RZ is nearly, but not quite, in a state of uniform rotation. The outer RZ edge is markedly diferentially rotating.
iii.) The analytic theory works very well where it is intended to work, but breaks down completely in the outer layers of the Sun and in the boundary between the RZ and CZ (known as the tachocline).
iv.) The Sun rotates more rapidly at the equator than at the poles.
The analytic theory takes as its starting point the Sun’s angular velocity at a particular location near the surface (but not in the outer boundary layer itself). While it reproduces the the contours wellthey are in fact the characteristics of a first order partial differential equationthe theory does not explain why, for example, the Sun rotates more rapidly at the equator.
Preliminary theoretical ideas that will serve as our starting point may be found in Balbus, S. A. & Schaan, E. 2012, MNRAS, in press; http://adsabs.harvard.edu/abs/2012arXiv1207.3810B and references therein. In particular, it appears that local conditions near the radius at which the entropy gradient passes through zero are important for establishing the global nature of the Sun’s rotation. If so, an exciting possibility that could emerge from this work is a theory for how different internal stellar convection profiles might lead to different internal rotation profiles. Understanding the Sun may thus be key to understanding stellar rotation more generally.
In this PhD project, I would like to develop a much deeper understanding, not only for why the Sun’s overall pattern is what it is, but what is happening in the inner and outer boundary layers as well. Depending upon the interests of the student, the approach we use can either be predominantly numerical or predominantly analytic. The student will be expected to contribute to interactive discussions within a larger group working on problems in astrophysical fluid dynamics.
Extracting science from surveys of our Galaxy
James Binney
We are involved in big international surveys to reveal the structure, dynamics and history of our Galaxy. This series of surveys will culminate in ESA's Cornerstone Mission Gaia, to be launch in 2nd half of 2013. Sophisticated dynamical models are key to inferring from massive surveys what is the distribution of the Galaxy's dark matter, and how the Galaxy was assembled.
Project 1: What's the most effective way of comparing a model with an analytic distribution function to (a) real survey data, and (b) a model galaxy that is the endpoint of a numerical simulation of galaxy formation? How best to detect systematic deviations between the analytic model and the data? How to infer from these deviations how the model needs to be changed?
Project 2: Our galaxy is barred and our models are for the moment axisymmetric. What is the most effective way to progress to barred models?
Project 3: What are the signatures of spiral structure in groundbased & Gaia data, & how can we best exploit these signatures to assess the magnitude of nonaxisymmetric perturbations to the potential and the impact these will have on the chemodynamical evolution of the Galaxy?
Plasma astrophysics of galaxy clusters
A. Schekochihin
Any astrophysical plasma is a multiscale system, where largescale ("global") dynamics erupts into a sea of microscale fluctuations (turbulence), which then respond by modifying, in the mean, the properties of the large scales. The global dynamics, which are what is usually accessible to us observationally, cannot really be understood or successfully modelled without a good theory of the mean effect of the small scales (think of this as an effective mean field theory for the global behaviour of the plasma). Galaxy clusters are such mutiscale systems (they also happen to be the largest structured chunks of luminous matter in the Universe)  and we understand neither their global structure nor the nature of the turbulent tangle of motions and magnetic fields that underlies it.
Some of the key questions/topics are
magnetogenesis, i.e. the physical origin and the implied structure of the magnetic fields in galaxy clusters; the fields are observable via radio telescopes, so theories of their origin are falsifiable if they predict the characteristics of the field as it exists today
the structure of the magnetised plasma turbulence (how is energy transferred and distributed between different scales and different types of energy: magnetic, kinetic, etc); observationally, ideas can be tested by looking at the measurements of plasma turbulence in the solar wind  a nearby plasma, which is not hugely different from other hot astrophysical plasmas, but which is readily accessible to detailed in situ exploration
heating of intracluster plasmas via turbulence and their thermal stability ("the cooling catastrophe" problem  from what we know about largescale dynamics of galaxy clusters, their cores should collapse to low temperatures, but they don't!); ways in which the heating and transport properties of the intracluster medium are determined by plasma instabilities driven by pressure anisotropies spontaneously arising in highbeta plasmas;
thermal conduction in tangled magnetic fields (the general physical problem and application to intracluster plasma, where there is a multitude of phenomena that would be impossible if heat could be easily transported: cold filaments, hot bubbles, sharp fronts etc.);
The projects will involve kinetic theory and/or numerical simulations of magnetised plasmas, as well as, should the student be so inclined, data analysis. Interested candidates are invited to contact Dr A. Schekochihin for further information (a.schekochihin1@physics.ox.ac.uk). Some of these topics may be pursued in collaboration with Dr J. Devriendt and Dr A. Slyz.
Hydrodynamical Modelling of CommonEnvelope Evolution and Stellar Mergers
Philipp Podsiadlowski
Commonenvelope evolution, where two two stars spiral towards each other inside a surrounding gaseous envelope, is one of the most important, but also one of the least understood phases of binary evolution. The objective of this project is to model this phase using different complementary approaches (combining 1d stellar hydro calculations with realistic input physics and more approximate 3d SPH simulations) and to assess the importance of various physical processes (e.g. recombination energy, accretion energy). The goal is to develop realistic physical criteria for the ejection of common envelopes and the merging of the stars with applications to gammaray bursts, planetary nebulae and supernova progenitors.
The Fireworks Initiative: Understanding Cosmic Explosions
Philipp Podsiadlowski
This project is part of an international collaboration trying to understand the diversity of cosmic explosions, such as supernovae of various types, hypernovae and gammaray bursts, and their implications for the evolution of galaxies and the chemical evolution of the Universe. As part of this project, the student will explore theoretically how various progenitor channels can account for the observed diversity, examining the role of rotation, binary evolution and metallicity. This will involve performing stellar and binary evolution calculations and possibly simulations of whole stellar populations. One of the objectives is to develop observational predictions that can be tested within the framework of the fireworks project.
Reshaping galaxies with outflows
Julien Devriendt, Andrew Pontzen and Adrianne Slyz
The past few years have seen a seismic shift in the way we think about the role of baryons in galaxies. While it has long been understood that gas flows into dark matter halos and cools to form stars, observations and stateoftheart numerical simulations now provide compelling evidence that a large fraction of gas is subsequently reejected in "outflows".
We are starting to realize that these outflows radically change the nature of the galaxies that they leave behind. However there is little agreement on the exact fraction of gas involved, the speed and size of the outflows, or even the physics leading to the gas expulsion. The observational evidence requires comparison with numerical and physical models before this situation can be clarified.
This project is suitable for a strong D.Phil. student and will involve running and analysing cuttingedge numerical simulations (AMR and, through an international collaboration, SPH). There is scope for analytic modelling and for direct comparison to observational datasets. The result will be a timely thesis and a broad skillset covering computational, theoretical and observational methods.
Super Massive Black Holes, Magnetic Fields and their impact on Galaxy Evolution
Supervisors: Julien Devriendt and Adrianne Slyz
In the past decade or so, a substantial amount of observational evidence has accumulated about the major role played by super massive black holes in driving the evolution of galaxies. However, the way to model how they accrete gas and inject energy back into the interstellar and intergalactic medium its still in its infancy. Perhaps the most obvious example is that the strong magnetic fields they are known to generate are purely and simply ignored. This project is therefore geared towards making a step change in numerical simulations of the coeval evolution of super massive black holes and their host galaxies in an explicit cosmological context. We expect it will attract students with a strong theoretical background and real motivation to do heavy duty numerical work.
https://www2.physics.ox.ac.uk/studyhere/postgraduates/astrophysics/dphilprojectsfor2013/theoreticalastrophysics

