Detection of a Taylor-like Plasma Relaxation Process in the Sun and its Implication for Coronal Heating

The relaxation dynamics of a magnetized plasma system is a subject of fundamental importance in MHD – with applications ranging from laboratory plasma devices like the Toroidal Field Pinch and Spheromaks to astrophysical plasmas, stellar flaring activity and coronal heating. Taylor in 1974 proposed that the magnetic field in a plasma (of small but finite resistivity) relaxes to a minimum energy state, subject to the constraint that its total magnetic helicity is conserved (Woltjer 1958), such that the final magnetic field configuration is a constant α (linear) force-free field – where α is a quantity describing the twist in magnetic field lines. However, a clear signature of this mechanism in astrophysical plasmas remained undetected. Here we report observational detection of a relaxation process, similar to what Taylor (1974, 1986) envisaged, in the magnetic fields of flare-productive solar active regions. The implications of this result for magnetic reconnection and the coronal heating problem are discussed. 1. Summary of Main Results In astrophysical and laboratory plasma systems where the plasma-β parameter (the ratio of the gas to magnetic pressure) is low (< 1), the magnetic stresses in the field lines permeating the plasma become unbalanced and the magnetic field evolves in a selforganized manner to remove these stresses. The lower solar corona is a low β plasma and its magnetic field is believed to be nearly force-free. Coronal magnetic fields or loops are associated with solar active regions (ARs) with their foot points anchored slightly beneath the photosphere. The kinetic energy of the foot point motions (due to convective turbulent flows) can be transmitted into overlying tangled magnetic loops, the subsequent reconnection (and flaring activity) of which would be able to heat and maintain the solar corona by a Taylor-like relaxation process towards a linear force-free field configuration (Parker 1983; Heyvaerts and Priest 1984). We did a statistical study of the evolution of twists (quantified by the parameter αZ(x, y) as measured from Haleakala Stokes Polarimeter vector magnetograms) in a sample of flare-productive solar ARs (which had flare X-ray flux measurements from the GOES satellite) to seek possible signatures of relaxation towards a Taylor-like state (Nandy et al. 2003). As shown in Figure 1 (left), the variance in the αZ(x, y) distribution shows a statistically significant decrease over the flaring period for highly flare-productive solar ARs (at a confidence level of 98.95 %). Note that the variance indicates how nonuniform is the value of αZ(x, y) over the AR flux system and a decrease in this quantity implies an evolution towards a more uniform state. Therefore we find that AR flux systems (which were highly flare-productive, i.e., showing a high value of the integrated flare energy flux Ef ) tend to evolve towards a linear force-free state. However, they never