Revisiting Studies of the Statistical Property of a Strong Gravitational
  Lens System and Model-independent Constraint on the Curvature of the Universe
  In this paper we use a recently compiled data set, which comprises 118
galactic-scale strong gravitational lensing (SGL) systems to constrain the
statistic property of SGL system, as well as the curvature of universe without
assuming any fiducial cosmological model. Based on the singular isothermal
ellipsoid (SIE) model of SGL system, we obtain that the constrained curvature
parameter $\Omega_{\rm k}$ is close to zero from the SGL data, which is
consistent with the latest result of planck measurement. More interestingly, we
find that the parameter $f$ in the SIE model is strongly correlated with the
curvature $\Omega_{\rm k}$. Neglecting this correlation in the analysis will
significantly overestimate the constraining power of SGL data on the curvature.
Furthermore, the obtained constraint on $f$ is different from previous results:
$f=1.105\pm0.030$ ($68\%$ C.L.), which means that the standard singular
isothermal sphere (SIS) model ($f=1$) is disfavored by the current SGL data at
more than $3\sigma$ confidence level. We also divide the whole SGL data into
two parts according to the centric stellar velocity dispersion $\sigma_{\rm c}$
and find that the larger value of $\sigma_{\rm c}$ the subsample has, the more
favored the standard SIS model is. Finally, we extend the SIE model by assuming
the power-law density profiles for the total mass density,
$\rho=\rho_0(r/r_0)^{-\alpha}$, and luminosity density,
$\nu=\nu_0(r/r_0)^{-\delta}$, and obtain the constraints on the power-law
indexes: $\alpha=1.95\pm0.04$ and $\delta=2.40\pm0.13$ at 68\% confidence
level. When assuming the power-law index $\alpha=\delta=\gamma$, this scenario
is totally disfavored by the current SGL data, $\chi^2_{\rm min,\gamma} -
\chi^2_{\rm min,SIE} \simeq 53$.
