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Iron Snow in Planetary Cores

Dr Chris Davies (SEE), Dr Andrew Walker (SEE)

Contact email: c.davies@leeds.ac.uk

Summary

Planetary magnetic fields exhibit remarkable variability in their intensity and spatio-temporal properties. These fields are generated in metallic cores and thus provide a unique probe into the dynamics and evolution of planetary interiors. Earth’s liquid core is currently freezing from the bottom upwards as the planet cools, releasing the heat and light material that power the geomagnetic field. In contrast, recent mineralogical studies suggest that the cores of the smaller terrestrial bodies Mercury, Mars and Ganymede freeze from the top down with solid iron particles “snowing” into the deeper core. It has even been suggested that the top of Earth’s core may have once entered a crystallizing regime. The evolution and dynamics of bodies in this “iron snow” regime will be profoundly different to those of present-day Earth; however, the ramifications are presently unknown. Since the iron snow regime is a recent discovery, fundamental questions remain: can iron snow generate a global magnetic field? If so, is the generated field compatible with available observations? Will planets in the iron snow regime ever grow a solid inner core like Earth?  

We have recently developed the first self-consistent thermodynamic model for studying the long-term evolution of snow zones based on the theory of slurries, i.e. liquid mixtures that contain a suspension of solid particles. There are two key advantages of this slurry evolution model (SEM) over previous studies: 1) the viability of dynamo action is calculated in a thermodynamically self-consistent manner, rather than empirically using scaling laws; 2) the equations are derived directly from the general theory for a two-phase two-component liquid mixture. 

In this project you will relax existing assumptions so that the SEM can be applied to the cores of Mercury, Mars and Ganymede to evaluate, for the first time, whether iron snow can generate the magnetism observed on these bodies. The analysis will make new predictions regarding the interior structure and evolution of these bodies, constrained by and informing existing and forthcoming observational data. The results will also likely improve our understanding of the possibility and nature of top-down crystallization in Earth. 

The present SEM describes the long-term evolution (i.e. the past 4.5 billion years) of an iron-sulphur snow zone in two dimensions: radius and time. The SEM is a `parameterised model’: the fluid dynamical behaviour of the snow zone is described by a small number of parameters rather than obtained by a forward solution of the fluid dynamical (e.g. Navier-Stokes) equations. This approach has the significant benefits that it is fast and efficient, allowing many solutions to be obtained that span uncertainties in the input parameters. However, the parameterisation is only as good as our understanding of the underlying physics, which comes from laboratory experiments and numerical simulations of the forward problem.  

You will develop and use numerical simulations to investigate the fluid dynamics of iron snow. In particular, you will investigate whether snow zones are stably stratified (i.e. non-convecting, with heavy material below light material) or unstably stratified (i.e. convecting). Such a distinction is crucial because convecting and non-convecting systems behave very differently in terms of how they transfer mass, momentum and energy. The behaviour of slurry systems can be very different to standard thermal convection systems. Indeed, while increasing the temperature difference across a fluid usually tends to promote convection, in slurries it can have the opposite effect! The stability of snow zones in planetary cores has received little attention and so this investigation is both important and timely given the recent interest in these systems. You will conduct a wide range of simulations and elucidate the physical conditions that give rise to stable and unstable snow zones. 

From these simulations the parameters needed by the SEM (e.g. mean temperature, composition and solid profiles) will be obtained and applied to Mercury, Mars and Ganymede. Your new SEM model will predict the time-dependent evolution of the snow zone, including its thickness and thermo-chemical properties, which can be tested using present and future observations. The model also predicts the viability of dynamo action, which provides new constraints on the magnetic history of these bodies.  From this the present-day dipole moment can be obtained using scaling laws and compared to observations. 

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Related undergraduate subjects:

  • Applied mathematics
  • Earth science
  • Geophysics
  • Mathematics
  • Natural sciences
  • Physics