Magnetic Tension of Sunspot Fine Structures

Abstract: The equilibrium structure of sunspots depends critically on its magnetic topology and is dominated by magnetic forces. Tension force is one component of the Lorentz force which balances the gradient of magnetic pressure in force-free configurations. We employ the tension term of the Lorentz force to clarify the structure of sunspot features like penumbral filaments, umbral light bridges and outer penumbral fine structures. We compute vertical component of tension term of Lorentz force over two active regions namely NOAA AR 10933 and NOAA AR 10930 observed on 05 January 2007 and 12 December 2006 respectively. The former is a simple while latter is a complex active region with highly sheared polarity inversion line (PIL). The vector magnetograms used are obtained from Hinode(SOT/SP). We find an inhomogeneous distribution of tension with both positive and negative signs in various features of the sunspots. The existence of positive tension at locations of lower field strength and higher inclination is compatible with the uncombed model of the penumbral structure. Positive tension is also seen in umbral light bridges which could be indication of uncombed structure of the light bridge. Likewise, the upward directed tension associated with bipolar regions in the penumbra could be a direct confirmation of the sea serpent model of penumbral structures. Upward directed tension at the PIL of AR 10930 seems to be related to flux emergence. The magnitude of the tension force is greater than the force of gravity in some places, implying a nearly force-free configuration for these sunspot features. From our study, magnetic tension emerges as a useful diagnostic of the local equilibrium of the sunspot fine structures.