  A solar active region (AR) that produces at least one M- or X-class major
flare tends to produce multiple flares during its passage across the solar
disk. It will be interesting if we can estimate how flare-productive a given
major flaring AR is for a time interval of several days, by investigating time
series of its photospheric magnetic field properties. For this, we studied 93
major flaring ARs observed from 2010 to 2016 by the Helioseismic and Magnetic
Imager (HMI) on board the Solar Dynamics Observatory (SDO). More specifically,
for each AR under study, the mean and fluctuation were calculated from an 8-day
time series of each of 18 photospheric magnetic parameters extracted from the
Space-weather HMI Active Region Patch (SHARP) vector magnetogram products at
12-min cadence. We then compared these with the AR's 8-day flare index, which
is defined as the sum of soft X-ray peak fluxes of flares produced in the AR
during the same interval of the 8-day SHARP parameter time series. As a result,
it is found that the 8-day flare index is well correlated with the mean and/or
fluctuation values of some magnetic parameters (with correlation coefficients
of 0.6-0.7 in log-log space). Interestingly, the 8-day flare index shows a
slightly better correlation with the fluctuation than the mean for the SHARP
parameters associated with the surface integral of photospheric magnetic free
energy density. We also discuss how the correlation varies if the 8-day flare
index is compared with the mean or fluctuation calculated from an initial
portion of the SHARP parameter time series.
