Topology and Connectivity Changes in AR 8210

Using a time series of 15 averaged vector magnetograms and their associated 3D coronal nonlinear force-free fields, we study the evolution in time of the active region 8210. In particular we focus our study on the changes in connectivity associated with photospheric motions as the sunspot rotation and a moving emerging polarity. Relevance of photospheric motions is shown by studying the energetics of the active region and the injection of energy by transverse photospheric motions.


Evolution of the Connectivity and Separatrix Surfaces

We study the evolution of the nonlinear force-free fields (nlff) of 15 averaged vector magnetograms in AR 8210. Two characteristic features are detailed here: the rotation of the sunspot and a moving emerging polarity.

The clockwise sunspot rotation creates sheared arcades. In Fig.1, the magnetic configuration at the location of strong photospheric motions due to the rotation is plotted. This configuration evidences a separatrix surfaces (black line) separating two connectivity domains (A south domain, B north domain). The field lines anchored in domain A are moving towards the north and when they reach the separatrix surface a reconnection occurs and new field lines are connected in the domain B.

In Fig.2, we plot the magnetic configuration above a moving negative polarity. A separatrix surface (black line) separates two connectivity domains above this polarity (A east domain, B west domain). The polarity is moving toward the south-west. The field lines connecting the polarity in domain A are touching the separatrix surface when the polarity is moving. Then a reconnection process occurs and new field lines appear to be connected in domain B. At the end of the time series few field lines are still connected at the negative polarity in domain A. The reconnection process does not change the topology.
Fig. 1 (click to enlarge): magnetic field configuration of AR 8210 restricted to the location of high shear (where the sunspot rotation is the strongest). A separatrix surfaces is plotted showing two different connectivity domains.
Fig. 2 (click to enlarge): magnetic field configuration around a moving emerging negative polarity. The plotted separatrix surface is above the moving polarity.

Transverse Motions and Energetics

In terms of energetics in the AR 8210, we can estimated the free magnetic energy budget which is defined by the difference of the nlff magnetic energy and the potential magnetic energy in the volume above the photosphere. We can also estimate the energy rate due to transverse motions by determining the horizontal velocity field using the MEF (Minimum Energy Fits, Longcope & Klapper 2003).

In Fig.3, we plot the X-ray flux observed by GOES-8 in the wavelength range 0.5-4 A to know where the flaring activity occurs in AR 8210. In Fig.4, we plot the two energy rates described below : free magnetic energy budget (solid line) and due to transverse motions (dashed line). This plot shows a strong correlation between the injection of energy into the corona by transverse motions and the occurance of flares.

Fig. 3 (click to enlarge): X-ray flux from GOES-8 stellite in the wavelength band 0.5-4 A. Gray areas show the flaring periods in AR 8210.
Fig. 4 (click to enlarge): Solid line: rate of change of the free magnetic energy (difference between nlff and potential magnetic energy. Dashed line: Rate of input of energy into the corona due to photospheric transverse motions, using the Mininum Energy Fit (MEF) method (Longcope and Regnier, in prepration). The dark and light gray areas refer to the rise and fall phases of the flare X-ray emission. Note two points: (1) the only times that the coronal energy is found to decrease by a significant amount are during flares. (2) The only times that the coronal energy is found to increase is in the period between 0 - 40 minutes before the flares.
Fig. 5 (click to enlarge): The time evolution of different helicities (see Berger 1999): the self helicity of the closed field (dotted-dashed line), the mutual helicity between closed field and potential field (dashed line), the self helicity of the potential field (dot-dot-dot-dashed line, nearly constant), and the relative magnetic helicity computed directly from the Finn-Antonsen (85) formula (solid line) and from the sum of the self and mutual helicity (stars). Note that there is something going on with the self helicity during the quiet period that we have to investigate.

MURI-MSU Nugget January 2004

Stéphane Régnier, Richard Canfield, Dana Longcope