Gravitational lensing potential reconstruction in quadruply imaged systems

Abstract

Abstract. We develop a semi-analytical method to reconstruct the lensing potential in quadruply imaged gravitational lens systems. Assuming that the potential belongs to a broad class of boxy non-elliptical models, we show how it is possible to write down a system of equations which can be numerically solved to recover the potential parameters directly from image positions and using physical constraints. We also describe a code developed to search for solutions of the system previously found and test it on simulated cases. Finally, we apply the method to the quadruple lens PG 1115+080 which allows us to get also an estimate of the Hubble constant H0 from the measured time delay as H0 = 56 +12 −11 km s −1 Mpc −1 .

A new method for the estimate of $\vec{H_0}$ from quadruply imaged gravitational lens systems

“…A direct comparison with the value of the slope α is not possible since they do not report the estimate for this latter parameter, but only three vales for what they call the effective power -law slope. In an our previous paper (Cardone et al 2001) we have presented a semianalytical technique to reconstruct a lensing potential as in Eq. (8) with F (θ) as in (20) using as constraints only the images positions.…”

“…On the other hand, introducing a general but parametric expression for F (θ), Zhao & Pronk (2001) were able to develop a semianalytical technique to reconstruct the lensing potential in quadruply imaged systems having assigned the boxiness parameter. Their work has been then generalized by Cardone et al (2001) which have implemented another semianalytical method which is able to recover all the lensing potential parameters without assigning ab initio any of them. More recently, Evans & Witt (2001; see also Hunter & Evans, 2001) have studied the gravitational lensing properties (i.e.…”

“…where β is a boxiness parameter, δ is a flattening indicator and θ p is the position angle of the lensing potential (see Zhao &Pronk, 2001 andCardone et al, 2001 for further details). Different choices of the three parameters (β, δ, θ p ) and of the slope α of the radial profile allows to generate different simulated systems provided that one have also fixed both the source coordinates (r s , θ s ) and the shear parameters (γ, θ γ ).…”

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.…”

Lens modelling and estimate ofH0in quadruply lensed systems

“…Here, we further improve the general method in Cardone et al (2001) (hereafter CCRP01) and CCRP02, implementing a set of mathematica codes to shape quadruple lens systems and obtain a better estimate of the Hubble constant. Such a method in fact allows us to manage a still wider class of lens models and to obtain useful information about lens parameters and H 0 , eliminating possible non‐physical solutions.…”