Durham mathematicians help develop a new method for studying solar knots

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The release of solar energy and how it causes space weather events has long been debated. But now, researchers from Durham University, the University of Glasgow, and INAF-Osservatorio Astrofisico di Catania have come up with a new way to measure the entanglement of the magnetic field of the Sun. These twisted magnetic fields rise to the convection zone of the Sun and cause solar flares.

Dr Christopher Prior of Durham University’s Department of Mathematical Sciences led Durham’s involvement in the research. Prior presented the research at the Royal Astronomical Society’s virtual National Astronomy Meeting 2021 held from 19th – 23rd July.

The team’s novel approach to measuring the entanglement of the magnetic field involved tracking the rotation of the field lines at the points where they intersect the photosphere, the innermost layer of the Sun’s atmosphere. This is known as magnetic winding and is a valuable tool in gaining information on the magnetic topology of the Sun.

Topology is a branch of mathematics that studies the geometric properties of an object that are preserved under deformations such as stretching, twisting, and bending. Magnetic topology relates these properties to magnetic fields.

The researchers looked at magnetic winding, a topological quantity that measures the entanglement of these magnetic field lines. It is also key for quantifying other topological properties of the field lines, such as how much they are linked, twisted, or knotted, collectively known as magnetic helicity.

The team’s research predicted that pre-twisted magnetic structures from the Sun’s convection zone rise up into the photosphere. This is one of two dominant theories for how the field lines become tangled. The other theory suggests they form above the photosphere due to photospheric motions.

In the research paper presenting their findings, the team argues that a “twist allows a flux tube to suffer less deformation in the convection zone compared to untwisted tubes, thus allowing it to survive and reach the photosphere to emerge”.

The researchers provide direct evidence that large twisted magnetic flux tubes cause active regions of the Sun

Before this research, there had been no direct observations of pre-twisted magnetic flux tubes from the photosphere. The researchers also provide direct evidence that large twisted magnetic flux tubes do cause active regions of the Sun.

They studied ten such regions and compared them to simulations they had run previously. Using the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory, the team found that the emergence of pre-twisted field line structures dominated those that became twisted into a braid-like structure whilst in the photosphere. The new tool the researchers developed, magnetic winding, is able to detect the emergence of these pre-twisted structures where magnetic helicity observations are unable to.

The team only investigated twisted flux tubes, but says “it is likely that other magnetic topologies also emerge to create active regions”. They hope that magnetic winding will play an important role in future observations of other causes of the Sun’s active regions.

Image: with VQGAN+CLIP

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