  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
$14.16\times10^{42}$Mx$^2$ and $9.5\times10^{42}$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 $21\times18$ to $9\times6$ 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.
