On 2009 January 22 numerous strong bursts were detected from the anomalous X-ray pulsar 1E 1547.0-5408. Swift/XRT and XMM-Newton/EPIC observations carried out in the following two weeks led to the discovery of three X-ray rings centered on this source. The ring radii increased with time following the expansion law expected for a short impulse of X-rays scattered by three dust clouds. Assuming different models for the dust composition and grain size distribution, we fit the intensity decay of each ring as a function of time at different energies, obtaining tight constraints on the distance of the X-ray source. Although the distance strongly depends on the adopted dust model, we find that some models are incompatible with our X-ray data, restricting to 4-8 kpc the range of possible distances for 1E 1547.0-5408. The best-fitting dust model provides a source distance of 3.91 ± 0.07 kpc, which is compatible with the proposed association with the supernova remnant G327.24-0.13, and implies distances of 2.2 kpc, 2.6 kpc and 3.4 kpc for the dust clouds, in good agreement with the dust distribution inferred by CO line observations toward 1E 1547.0-5408. However, dust distances in agreement with CO data are also obtained for a set of similarly well-fitting models that imply a source distance of ~5 kpc. A distance of ~4-5 kpc is also favored by the fact that these dust models are already known to provide good fits to the dust-scattering halos of bright X-ray binaries. Assuming N H = 1022 cm-2 in the dust cloud responsible for the brightest ring and a bremsstrahlung spectrum with kT = 100 keV, we estimate that the burst producing the X-ray ring released an energy of 1044-1045 erg in the 1-100 keV band, suggesting that this burst was the brightest flare without any long-lasting pulsating tail ever detected from a magnetar.
