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 _ { 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 _ { 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 \pm 0.030 ( 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 _ { c } and find that the larger value of \sigma _ { 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 \pm 0.04 and \delta = 2.40 \pm 0.13 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 } _ { min, \gamma } - \chi ^ { 2 } _ { min,SIE } \simeq 53 .