Motivated by the recent discovery of a hierarchical X-ray flaring phenomenon in Mrk 421, we conducted a systematic search for X-ray flares from Mrk 501, another well-known TeV blazar, by making use of the rich RXTE archival database. We detected flares over a wide range of timescales, from months down to minutes, as in the case of Mrk 421. However, the flares do not seem to occur nearly as frequently in Mrk 501 as in Mrk 421 on any of the timescales. The flaring hierarchy also seems apparent in Mrk 501, suggesting that it might be common among TeV blazars. The results seem to imply a scale-invariant physical origin of the flares (large or small). The X-ray spectrum of the source shows a general trend of hardening toward the peak of long-duration flares, with indication of spectral hysteresis, which is often seen in TeV blazars. However, the data are not of sufficient quality to allow us to draw definitive conclusions about spectral variability associated with more rapid but weaker flares. We critically examine a reported subhour X-ray flare from Mrk 501, in light of intense background-flaring activity at the time of the observation, and concluded that the flare is likely an artifact. On the other hand, we did identify a rapid X-ray flare that appears to be real. It lasted only for about 15 minutes, during which the flux of the source varied by about 30%. Substructures are apparent in its profile, implying variabilities on even shorter timescales. Such rapid variabilities of Mrk 501 place severe constraints on the physical properties of the flaring region in the jet, and the constraints have serious implications for the emission models proposed for TeV blazars.
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