An Improved Virial Estimate of Solar Active Region Energy

The MHD virial theorem may be used to estimate the magnetic energy of active regions based on vector magnetic fields measured at the photosphere or chromosphere. However, the virial estimate depends on the measured vector magnetic field being force-free. Departure from force-freeness leads to an unknown systematic error in the virial energy estimate, and an origin dependence of the result. We present a method for estimating the systematic error by assuming that magnetic forces are confined to a thin layer near the photosphere. If vector magnetic field measurements are available at two levels in the low atmosphere (e.g. the photosphere and the chromosphere), the systematic error may be directly calculated using the observed horizontal and vertical field gradients, resulting in an energy estimate which is independent of the choice of origin. If (as is generally the case) measurements are available at only one level, the systematic error may be approximated using the observed horizontal field gradients together with a simple linear force-free model for the vertical field gradients. The resulting `improved' virial energy estimate is independent of the choice of origin, but depends on the choice of the model for the vertical field gradients, i.e. the value of the linear force-free parameter $\alpha$. This procedure is demonstrated for five vector magnetograms, including a chromospheric magnetogram.Comment: 17 pages, 1 figur

Dynamic topology and flux rope evolution during non-linear tearing of 3D null point current sheets

In this work, the dynamic magnetic field within a tearing-unstable three-dimensional current sheet about a magnetic null point is described in detail. We focus on the evolution of the magnetic null points and flux ropes that are formed during the tearing process. Generally, we find that both magnetic structures are created prolifically within the layer and are non-trivially related. We examine how nulls are created and annihilated during bifurcation processes, and describe how they evolve within the current layer. The type of null bifurcation first observed is associated with the formation of pairs of flux ropes within the current layer. We also find that new nulls form within these flux ropes, both following internal reconnection and as adjacent flux ropes interact. The flux ropes exhibit a complex evolution, driven by a combination of ideal kinking and their interaction with the outflow jets from the main layer. The finite size of the unstable layer also allows us to consider the wider effects of flux rope generation. We find that the unstable current layer acts as a source of torsional magnetohydrodynamic waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed