我们提出了我们的观测$γ$射线BL Lac对象Mrk 501的光学日内变化（IDV）。2005年4月至2012年5月，在云南天文台使用1.02 m和2.4 m光学望远镜进行了观测。2010年5月15日$R$条带的光变曲线通过了两项变异性检验（$F$检验和ANOVA检验）。在2010年5月15日的光变曲线中，耀斑的星等变化为$Δm = 0.03 \pm 0.005_{\rm{stat}} \pm 0.007_{\rm{sys}}$等，\textbf{a darkening timescale of $τ_{\rm{d}}=$ 26.7 minutes}，振幅为IDV $Amp=2.9\% \pm0.7\%$。耀斑内的下降\textbf{described by 11 consecutive flux measurements}可以在$> 99.99\%$的置信水平下与Pearson相关系数$r = 0.945$线性拟合。在假设IDV与黑洞的质量紧密相连的情况下，\textbf{and that the flare duration, being two times $τ_{\rm{d}}$, is representative of the minimum characteristic timescale, we can derive upper bounds to the mass of the black hole}。在克尔黑洞的情况下，$Δt_{\rm{min}}^{\rm{ob}}=$ 0.89小时的时间尺度给出了$M_{\bullet}\la 10^{9.20} M_{\odot}$，这与文献中报道的测量结果一致。该一致性表明，关于$M_{\bullet}$和$Δt_{\rm{min}}^{\rm{ob}}$的假设与测量值/数据一致。
英文摘要：
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 $Δm = 0.03 \pm 0.005_{\rm{stat}} \pm 0.007_{\rm{sys}}$ mag, \textbf{a darkening timescale of $τ_{\rm{d}}=$ 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 $τ_{\rm{d}}$, 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 $Δt_{\rm{min}}^{\rm{ob}}=$ 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 $Δt_{\rm{min}}^{\rm{ob}}$ is consistent with the measurements/data.
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