We present XMM-Newton and Chandra observations of 1E 1048.1-5937, being the first to show evidence for a significant variation in the X-ray luminosity of this anomalous X-ray pulsar (AXP). While during the first XMM-Newton (2000 December) and Chandra (2001 July) observations the source had a flux consistent with that measured on previous occasions (~5×10-12 ergs cm-2 s-1), two more recent observations found it at a considerably higher flux level of 2×10-11 ergs cm-2 s-1 (2002 August; Chandra) and 10-11 ergs cm-2 s-1 (2003 June; XMM-Newton). All the spectra are fit by the sum of a blackbody with kT~0.6 keV and a power law with photon index ~3. No significant changes were seen in the spectral parameters, while the pulsed fraction in the 0.6-10 keV energy range decreased from ~90% in 2000 to ~53% in 2003. The spectral invariance does not support the presence of two physically distinct components in the AXP emission. The sparse coverage of the data does not permit us to unambiguously relate the observed variations to the two bursts seen from this source in the fall of 2001.
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