The centre of our Galaxy harbours a 4 million solar mass black hole that is unusually quiet: its present X-ray luminosity is more than 10 orders of magnitude less than its Eddington luminosity. The observation of iron fluorescence and hard X-ray emission from some of the massive molecular clouds surrounding the Galactic Centre has been interpreted as an echo of a past flare. Alternatively, low-energy cosmic rays propagating inside the clouds might account for the observed emission, through inverse bremsstrahlung of low energy ions or bremsstrahlung emission of low energy electrons. Here we report the observation of a clear decay of the hard X-ray emission from the molecular cloud Sgr B2 during the past 7 years thanks to more than 20 Ms of INTEGRAL exposure. The measured decay time is compatible with the light crossing time of the molecular cloud core . Such a short timescale rules out inverse bremsstrahlung by cosmic-ray ions as the origin of the X ray emission. We also obtained 2-100 keV broadband X-ray spectra by combining INTEGRAL and XMM-Newton data and compared them with detailed models of X-ray emission due to irradiation of molecular gas by (i) low-energy cosmic-ray electrons and (ii) hard X-rays. Both models can reproduce the data equally well, but the time variability constraints and the huge cosmic ray electron luminosity required to explain the observed hard X-ray emission strongly favor the scenario in which the diffuse emission of Sgr B2 is scattered and reprocessed radiation emitted in the past by Sgr A*. Using recent parallax measurements that place Sgr B2 in front of Sgr A*, we find that the period of intense activity of Sgr A* ended between 75 and 155 years ago.
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