Lens modelling and estimate ofH₀in quadruply lensed systems

Abstract

We present a numerical method to estimate the lensing parameters and the Hubble constant H 0 from quadruply imaged gravitational lens systems. The lens galaxy is modelled using both separable deflection potentials and constant mass-to-light ratio profiles, while possible external perturbations have been taken into account by introducing an external shear. The model parameters are recovered by inverting the lens and the time-delay ratio equations and imposing a set of physically motivated selection criteria. We investigate correlations among the model parameters and the Hubble constant. Finally, we apply the codes to the real lensed quasars PG 1115+080 and RX J0911+0551, and combine the results from these two systems to get H 0 = 56 ± 23 km s −1 Mpc −1 . In addition, we are able to fit to the single systems a general elliptical potential with a non-fixed angular part, and then we model the two-lens systems with the same potential and a shared H 0 : in this last case, we estimate H 0 = 49 +6 −11 km s −1 Mpc −1 .

Dynamical and gravitational lensing properties of a new phenomenological model of elliptical galaxies

“…Given their easy manageability, they have been widely used in literature. For semianalytical and/or numerical treatments in modeling lensed quasars see, e.g., Cardone et al (2001Cardone et al ( , 2002, Tortora et al (2004). In addition, considering that κ ∝ R ν−2 and following the previous Sec., power law with 0 < ν < 1 (1 < ν < 2) have strong (weak) cusp.…”

“…A first qualitative result can be obtained considering the index of the surface mass density defined as indκ(r) = d ln κ/d ln r. In order to shape lensing events with their model independent analysis, Williams & Saha (2000) have used as a constraint on the chosen lens model the condition indκ(r) ≤ −0.5 for values of r close to the images positions in strongly lensed quasars (see also Tortora et al 2004). Such a condition ensures that the image magnification is less than ∼ 2 which is a quite plausible constraint well satisfied in some real lenses.…”

Gerlumph Data Release 2:2.5 Billion Simulated Microlensing Light Curves

“…This has been performed in at least 24 multiply imaged systems (see Tortora et al 2004;Paraficz & Hjorth 2010;Eulaers & Magain 2011;Rathna Kumar et al 2014, and references therein) to yield values in the range 50-100 km s −1 Mpc −1 . The wide range of values, which is less accurate than results obtained from other methods (e.g., Cepheid variability; Riess et al 2011;Freedman et al 2012), is due to uncertainties and degeneracies of the lens potential (Kochanek 2002;Kochanek & Schechter 2004;Oguri 2007;Schneider & Sluse 2013;Suyu et al 2014).…”

“…Another experiment that can be performed using gravitationally lensed quasars is measuring the value of Hubble's constant, H 0 (Refsdal 1964). This has been performed in at least 24 multiply imaged systems (see Tortora et al 2004;Paraficz & Hjorth 2010;Eulaers & Magain 2011;Rathna Kumar et al 2014, and references therein) to yield values in the range 50 − 100 km s −1 Mpc −1 . The wide range of values, which is less accurate than results obtained from other methods (e.g.…”