More than softer-when-brighter: the X-Ray powerlaw spectral variability
  in NGC 4051
  The powerlaw X-ray spectra of active galactic nuclei at moderate to high
accretion rates normally appear softer when they brighten, for which the
underlying mechanisms are yet unclear. Utilizing XMM-Newton observations and
excluding photons $<$ 2 keV to avoid contamination from the soft excess, in
this work we scrutinize the powerlaw spectral variability of NCG 4051 from two
new aspects. We first find that a best-fit "softer-when-brighter" relation is
statistically insufficient to explain the observed spectral variabilities, and
intervals deviated from the empirical relation are clearly visible in the light
curve of 2 -- 4 keV/4 -- 10 keV count rate ratio. The deviations are seen not
only between but also within individual XMM-Newton exposures, consistent with
random variations of the corona geometry or inner structure (with timescales as
short as $\sim$ 1 ks), in addition to those behind the smooth
"softer-when-brighter" trend. We further find the "softer-when-brighter" trend
gradually weakens with the decreasing timescale (from $\sim$ 100 ks down to 0.5
ks). These findings indicate that the powerlaw spectral slope is not solely
determined by its brightness. We propose a two-tier geometry, including
flares/nano-flares on top of the inner disc and an embedding extended corona
(heated by the flares, in analogy to solar corona) to explain the observations
together with other observational clues in literature. Rapid spectral
variabilities could be due to individual flares/nano-flares, while slow ones
are driven by the variations in the global activity of inner disc region (akin
to the variation of solar activity, but not the accretion rate) accompanied
with heating/cooling and inflation/contraction of the extended corona.
