More than softer-when-brighter: the X-Ray powerlaw spectral variability in NGC 4051

Abstract

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.