The X-ray lightcurve of Sagittarius A* over the past 150 years inferred from Fe-Kα line reverberation in Galactic centre molecular clouds

Context. The spatial distribution and variability of Fe-K alpha emission from molecular clouds in the Galactic centre region may provide an important key to the understanding of the recent history of Sgr A*. A very plausible interpretation is that this variability represents an echo in the reflected radiation from the clouds of a past episode of high activity in Sgr A*. Aims. We examine the temporal and spectral properties of nine Fe-K alpha bright molecular clouds (three of which newly studied) within about 30 pc of Sgr A*, in order to understand and constrain the primary energising source of the Fe fluorescence. Methods. We collected all the archival XMM-Newton observations targeted at Sgr A*. The variability of the Fe-K alpha line at 6.4-keV in specific cloud regions was investigated by spectrally fitting the data derived from the EPIC MOS cameras, after subtracting a modelled background. We have also studied the reflection imprints in time-averaged pn-spectra of each cloud. This involved measuring the equivalent width (EW) of the 6.4 keV line with respect to the underlying scattered continuum and the optical depth of the Fe-K absorption edge at 7.1 keV, superimposed on this same continuum. Finally we stacked the MOS spectra from two extended regions in order to quantify the east-west asymmetry apparent in the low-surface brightness diffuse Fe-K alpha line emission. Results. Significant Fe-K alpha 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. All the spectra were characterised by a high EW of the Fe-K alpha line and the presence of absorption at the Fe-K edge, both of which serve as tracers of X-ray illumination. We used the EW measurements to infer the average Fe abundance within the clouds to be 1.6 +/- 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. The measured cloud parameters were used to set constraints on the past activity of Sgr A* and to investigate whether a contribution to the Fe fluorescence by cosmic-ray bombardment is plausible. Conclusions. 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 a contribution 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.