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A Rapid X-ray Flare from Markarian 501

We present X-ray observations of the BL Lacertae (BL Lac) object Markarian 501 (Mrk 501), taken with the Rossi X-ray Timing Explorer in 1998 May as part of a multi-wavelength campaign. The X-ray light curve shows a very rapid flare in which the 2-10 keV flux increased by ~60% in <200 seconds. This rapid rise is followed by a drop-off in the 2-10 keV flux of ~40% in <600 seconds. The 10-15 keV variation in this flare is roughly a factor of two on similar time-scales. During the rise of the flare, the 3-15 keV spectral index hardened from 2.02 +/- 0.03 to 1.87 +/- 0.04, where it remained during the decay of the flare. This is the fastest variation ever seen in X-rays from Mrk 501 and among the fastest seen at any wavelength for this object. The shift in the energy at which the spectral power peaks (from <3 keV before the flare to >30 keV during the flare) is also among the most rapid shifts seen from this object. This flare occurs during an emission state (2-10 keV flux approximately 1.2e-10 erg cm^-2 s^-1) that is approximately 25% of the peak flux observed in 1997 April from this object but which is still high compared to its historical average X-ray flux. The variations in the hardness ratio are consistent with the low energy variations leading those at high energies during the development and decay of the flare. This pattern is rare among high frequency peaked BL Lac objects like Mrk 501, but has been seen recently in two other TeV emitting BL Lacs, Mrk 421 and PKS 2155-304. The hard lag is consistent with a flare dominated by the acceleration time-scale for a simple relativistic shock model of flaring.