  Time series of photospheric magnetic parameters of solar active regions (ARs)
are used to answer whether scaling properties of fluctuations embedded in such
time series help to distinguish between flare-quiet and flaring ARs. We examine
a total of 118 flare-quiet and 118 flaring AR patches (called HARPs), which
were observed from 2010 to 2016 by the Helioseismic and Magnetic Imager (HMI)
on board the Solar Dynamics Observatory (SDO). Specifically, the scaling
exponent of fluctuations is derived applying the Detrended Fluctuation Analysis
(DFA) method to a dataset of 8-day time series of 18 photospheric magnetic
parameters at 12-min cadence for all HARPs under investigation. We first find a
statistically significant difference in the distribution of the scaling
exponent between the flare-quiet and flaring HARPs, in particular for some
space-averaged, signed parameters associated with magnetic field line twist,
electric current density, and current helicity. The flaring HARPs tend to show
higher values of the scaling exponent compared to those of the flare-quiet
ones, even though there is considerable overlap between their distributions. In
addition, for both the flare-quiet and flaring HARPs the DFA analysis indicates
that (1) time series of most of various magnetic parameters under consideration
are non-stationary, and (2) time series of the total unsigned magnetic flux and
the mean photospheric magnetic free energy density in general present a
non-stationary, persistent property, while the total unsigned flux near
magnetic polarity inversion lines and parameters related to current density
show a non-stationary, anti-persistent trend in their time series.
