# €2.5m grant awarded for novel approach for modelling solar magnetic activity

A new research project will use Direct Statistical Simulation to investigate the Sun's magnetic field.

The European Research Council (ERC) has awarded an advanced grant of €2.5 million (£2.2m) for University of Leeds Professor of Applied Mathematics Steve Tobias to spearhead a new research project, *Direct Statistical Simulation of the Sun and Stars *(D5S).

The proposal aims to address a key problem of astrophysics – the origin of magnetic activity in the Sun and solar-type stars. While it is known that the Sun’s variable magnetic field is generated by an interaction between its rotation and magnetohydrodynamic (MHD) turbulence, there is currently no realistic model for this dynamo action.

The D5S project will take advantage of two significant recent breakthroughs in order to build a useful predictive model for solar magnetic activity. The first is a new approach, known as Direct Statistical Simulation (DSS), which allows the statistics of astrophysical flows to be solved for directly: solving for the dynamics is simply beyond the capability even of the largest supercomputers.

The second is a better understanding of the physics of MHD turbulence at the extreme parameters relevant to solar interiors, as detailed by Professor Tobias in an article published in Nature. Combining these approaches gives the potential for a paradigm shift in theories for solar (and other astrophysical) magnetic activity.

### Why is predicting solar activity important?

Sunspots, solar flares and coronal mass ejections may seem far removed from life on this planet, but in fact they can have profound and dangerous consequences. When a coronal mass ejection is directed towards Earth, its arrival may bring a geomagnetic storm.

The effects of such a storm can be benign (for example, the Northern Lights), but they can also disrupt radios and GPS, damage power lines and transformers, threaten aeroplanes and in some cases can even disrupt satellites.

While there’s not much we can do to stop these ill-tempered outbursts from our Sun, being able to predict events like this helps authorities to prepare for them and mitigate any damage caused. It will also help scientists to further our understanding of the Sun and other stars by timing research activities to solar phenomena.

By Daniel Hershman from Federal Way, US (heart shaped sunspot) [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

Sunspots are (relatively) cool dark patches on the solar surface which are a manifestation of the sun’s magnetic field. These have been observed systematically since at least the time of Galileo. Since 1843, it has been known that the Sun follows a regular cycle of activity, during which the number of sunspots and other phenomena increases and decreases roughly every 11 years.

### Why use Direct Statistical Simulation?

The equations necessary for a truly predictive model of a solar magnetic field are far beyond even the most advanced supercomputers of today, and it may be decades before we develop the hardware necessary to solve them computationally. Current models are limited by the enormous range of spatial and temporal scales that must be resolved before the dynamics can be accurately described.

The major innovation in the D5S project is to instead approach the problem from a statistical viewpoint. Direct Statistical Simulation – described by mathematician and chaos theory pioneer Edward Lorenz as “deriving a new system of equations whose unknowns are the statistics themselves” - uses techniques from non-equilibrium statistical mechanics to derive the equations described by the statistics of fluid flows. This may dramatically reduce the time and resources required for a simulation, while still providing accurate results about the statistics of the flow.

As an example, imagine simulating the movement of air in a room. You could map the position, direction and speed of every single air molecule in your simulation, which would take a long time and consume an enormous amount of processing power. Alternatively, you could develop statistical mechanics to find the relatively simple laws known to underpin the movement of gases, and use them for your simulation.

As well as astrophysical bodies, Direct Statistical Simulation is being investigated as a potentially useful tool for climate modelling. As noted in quote attributed to Mark Twain: “Climate is what we expect, weather is what we get”.

### Partners and research opportunities

The five-year D5S project, which is due to begin in October 2018, will be coordinated by Professor Tobias and will involve a number of academic partners, including:

- The University of Chicago
- Brown University
- The University of Colorado
- Bates College
- MIT
- The University of Sydney

It is expected that the grant will fund PhD projects and postdoctoral research at the University of Leeds and these partner institutions.

### Further reading

cordis.europa.eu – Direct Statistical Simulation of the Sun and Stars

*(Title image courtesy of SOHO (ESA & NASA))*