We present our observations of the optical intra-day variability ( IDV ) in \gamma -ray BL Lac object Mrk 501 .
The observations were run with the 1.02 m and 2.4 m optical telescopes at Yunnan Observatories from 2005 April to 2012 May .
The light curve at the R band on 2010 May 15 passes both variability tests ( the F test and the ANOVA test ) .
A flare within the light curve on 2010 May 15 has a magnitude change \Delta m = 0.03 \pm 0.005 _ { stat } \pm 0.007 _ { sys } mag , a darkening timescale of \tau _ { d } = 26.7 minutes , and an amplitude of IDV Amp = 2.9 \% \pm 0.7 \% .
A decline described by 11 consecutive flux measurements within the flare can be fitted linearly with a Pearson ’ s correlation coefficient r = 0.945 at the confidence level of > 99.99 \% .
Under the assumptions that the IDV is tightly connected to the mass of the black hole , and that the flare duration , being two times \tau _ { d } , is representative of the minimum characteristic timescale , we can derive upper bounds to the mass of the black hole .
In the case of the Kerr black hole , the timescale of \Delta t _ { min } ^ { ob } = 0.89 hours gives M _ { \bullet } \lesssim 10 ^ { 9.20 } M _ { \odot } , which is consistent with measurements reported in the literature .
This agreement indicates that the hypothesis about M _ { \bullet } and \Delta t _ { min } ^ { ob } is consistent with the measurements/data .