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 statistical property of the SGL system as well as the curvature of the universe without assuming any fiducial cosmological model. Based on the singular isothermal ellipsoid (SIE) model of the 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 Wk. 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 +/- 0.030 (68% confidence level [ C.L.]), which means that the standard singular isothermal sphere (SIS) model (f = 1) is disfavored by the current SGL data at more than a 3 sigma C.L. We also divide all of the SGL data into two parts according to the centric stellar velocity dispersion sigma(c) and find that the larger the value of sc for the subsample, 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, v = v(0)(r/r(0))(-delta), and obtain the constraints on the power-law indices: alpha = 1.95 +/- 0.04 and delta = 2.40 +/- 0.13 at a 68% C.L. 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) similar or equal to 53.