$R$-band host galaxy contamination of TeV $\gamma$-ray blazar Mrk 501:
  effects of the aperture size and seeing
  We simulated the $R$-band contribution of the host galaxy of TeV $\gamma$-ray
BL Lac object Mrk 501 in different aperture sizes and seeing conditions . The
intensive observations were run with the 1.02 m optical telescope at Yunnan
Observatories from 2010 May 15 to 18. Based on the host subtraction data
presented in Nilsson et al. (2007), the subtraction of host galaxy
contamination results in significant seeing-brightness correlations. These
correlations would lead to illusive large amplitude variations at short
timescales, which will mask the intrinsic micro variability, thus gives rise to
difficulty in detecting the intrinsic micro variability. Both aperture size and
seeing condition influence the flux measurements, but aperture size impact the
result more significantly. Based on the parameters of elliptical galaxy
provided in Nilsson et al. (1999), we simulated the host contributions of Mrk
501 in the different aperture sizes and seeing conditions. Our simulation data
of the host galaxy obviously weaken these significant seeing-brightness
correlations for the host-subtracted brightness of Mrk 501, and can help us
discover the intrinsic short timescale micro variability. The pure nuclear flux
is $\sim$ 8.0 $\rm{mJy}$ in \emph{R} band, i.e., AGN has a magnitude of
$R\sim13^{m}_{\cdot}96$.
