Search for intra-day optical variability in Mrk 501
  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 $\Delta m = 0.03 \pm 0.005_{\rm{stat}} \pm
0.007_{\rm{sys}}$ mag, \textbf{a darkening timescale of $\tau_{\rm{d}}=$ 26.7
minutes}, and an amplitude of IDV $Amp=2.9\% \pm0.7\%$. A decline
\textbf{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, \textbf{and that the flare duration,
being two times $\tau_{\rm{d}}$, 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 $\Delta
t_{\rm{min}}^{\rm{ob}}=$ 0.89 hours gives $M_{\bullet}\la 10^{9.20} M_{\odot}$,
which is consistent with measurements reported in the literature. This
agreement indicates that the hypothesis about $M_{\bullet}$ and $\Delta
t_{\rm{min}}^{\rm{ob}}$ is consistent with the measurements/data.
