We study the role of rotating sunspots in relation to the evolution of various physical parameters characterizing the non-potentiality of the active region (AR) NOAA 11158 and its eruptive events using the magnetic field data from the Helioseismic and Magnetic Imager (HMI) and multi-wavelength observations from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. From the evolutionary study of HMI intensity and AIA channels, it is observed that the AR consists of two major rotating sunspots, one connected to a flare-prone region and another with coronal mass ejection (CME). The constructed space-time intensity maps reveal that the sunspots exhibited peak rotation rates coinciding with the occurrence of major eruptive events. Further, temporal profiles of twist parameters, namely, average shear angle, α av , α best , derived from HMI vector magnetograms, and the rate of helicity injection, obtained from the horizontal flux motions of HMI line-of-sight magnetograms, correspond well with the rotational profile of the sunspot in the CME-prone region, giving predominant evidence of rotational motion causing magnetic non-potentiality. Moreover, the mean value of free energy from the virial theorem calculated at the photospheric level shows a clear step-down decrease at the onset time of the flares revealing unambiguous evidence of energy release intermittently that is stored by flux emergence and/or motions in pre-flare phases. Additionally, distribution of helicity injection is homogeneous in the CME-prone region while in the flare-prone region it is not and often changes sign. This study provides a clear picture that both proper and rotational motions of the observed fluxes played significant roles in enhancing the magnetic non-potentiality of the AR by injecting helicity, twisting the magnetic fields and thereby increasing the free energy, leading to favorable conditions for the observed transient activity.

An investigation of helicity injection by photospheric shear motions is carried out for two active regions(ARs), NOAA 11158 and 11166, using line-of-sight magnetic field observations obtained from the Helioseismic and Magnetic Imager on-board Solar Dynamics Observatory. We derived the horizontal velocities in the active regions from the Differential Affine Velocity Estimator(DAVE) technique. Persistent strong shear motions at the maximum velocities in the range of 0.6-0.9km/s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed in the two active regions. The helicities injected in NOAA 11158 and 11166 during their six days' evolution period were estimated as 14.16 × 10 42 Mx 2 and 9.5 × 10 42 Mx 2 , respectively. The estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min, and increased up to 9% by decreasing the DAVE window size from 21 × 18 to 9 × 6 pixel 2 , resulting in 10% variation in the accumulated helicity. In both ARs, the flare prone regions (R2) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of CME prone regions had almost homogeneous distribution of helicity flux dominated by single sign. The temporal profiles of helicity injection showed impulsive variations during some flares/CMEs due to negative helicity injection into the dominant region of positive helicity flux. A quantitative analysis reveals a marginally significant association of helicity flux with CMEs but not flares in AR 11158, while for the AR 11166, we found marginally significant association of helicity flux with flares but not CMEs, providing evidences of the role of helicity injection at localized sites of the events. These short-term variations of helicity flux are further discussed in view of possible flare-related effects. This study suggests that flux motions and spatial distribution of helicity injection are important to understand the complex nature of magnetic flux system of the active region leading to conditions favorable for eruptive events.

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