  We examine the temporal and spectral properties of nine Fe-Ka bright
molecular clouds within about 30 pc of Sgr A*, in order to understand and
constrain the primary energising source of the Fe fluorescence. Significant
Fe-Ka variability was detected, with a spatial and temporal pattern consistent
with that reported in previous studies. The main breakthrough that sets our
paper apart from earlier contributions on this topic is the direct measurement
of the column density and the Fe abundance of the MCs in our sample. We used
the EW measurements to infer the average Fe abundance within the clouds to be
1.6$\pm$0.1 times solar. The cloud column densities derived from the spectral
analysis were typically of the order of 10$^{23}$ cm$^{-2}$, which is
significantly higher than previous estimates. This in turn has a significant
impact on the inferred geometry and time delays within the cloud system. Past
X-ray activity of Sgr A* is the most likely source of ionisation within the
molecular clouds in the innermost 30 pc of the Galaxy. In this scenario, the
X-ray luminosity required to excite these reflection nebulae is of the order of
10$^{37}-10^{38}$ erg s$^{-1}$, significantly lower than that estimated for the
Sgr B2 molecular cloud. Moreover, the inferred Sgr A* lightcurve over the past
150 years shows a long-term downwards trend punctuated by occasional
counter-trend brightening episodes of at least 5 years duration. Finally, we
found that contributions to the Fe fluorescence by X-ray transient binaries and
cosmic-ray bombardment are very likely, and suggest possible ways to study this
latter phenomenon in the near future.
