2017ApJ...849..161F

We present our observations of the optical intra-day variability (IDV) in γ-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 of Δm=0.03±0.005_stat±0.007_sys mag, a darkening timescale of τ_d=26.7 minutes, and an amplitude of IDV Amp=2.9 % ±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 τ_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 Δt_{min}^ob=0.89 hr gives M_• 10^9.20M_☉, which is consistent with measurements reported in the literature. This agreement indicates that the hypothesis about M_• and Δt_{min}^ob is consistent with the measurements/data.