Determining the Transport of Magnetic Helicity in the Sun's Atmosphere

A critically important factor determining solar coronal activity is the constraint of magnetic helicity conservation. Direct measurement of the magnetic helicity in the coronal volume is difficult, but its value may be estimated from measurements of the helicity transport rates through the photosphere. We examine this transport for a topologically open system such as the corona, in which the magnetic field has a nonzero normal component at the boundaries, and derive a new formula for the helicity transport rate at the boundaries. In addition, we derive new expressions for helicity transport due to flux emergence/submergence versus photospheric horizontal motions. The key new feature of our formulas is that they are manifestly gauge invariant. We discuss the physical interpretation of our results and their implications for using photospheric vector magnetic and velocity field measurements to derive the solar coronal helicity, which can then be used to constrain and drive models for coronal activity.

This work was supported by the NASA LWS Program.