Probing the structure of lensing galaxies with quadruple lenses: the effect of 'external' shear

Abstract

We study a general elliptical potential of the form ψ(x 2 + y 2 /q 2 ) (0 < q ≤ 1) plus an additional shear (with an arbitrary direction) as models for the observed quadruple lenses. It is shown that a minimum additional shear is needed even just to reproduce the observed positions alone. We also obtain the dependence of the axial ratio, q, on the orientation of the major axis of potential. A general relation also exists between the shear, the position angle and axial ratio of the lensing galaxy. The relation shows a generic degeneracy in modelling quadruple lenses. In particular, it shows that only the ratio of the ellipticity, ǫ ≡ (1−q 2 )/(1+q 2 ), to the magnitude of shear, γ can be determined.All these results are valid regardless of the radial profile of the potential. Our formalism applies when the galaxy position is observed, which is the case for seven of the eight known quadruple lenses. Application to these seven cases reveals two quadruple lenses CLASS 1608+656 and HST 12531-2914, requiring highly significant shear with magnitude ≈ 0.2. For HST 12531-2914, there must be a misalignment between the major axis of light and the major axis of potential (mass). We conclude that detailed modelling of quadruple lenses can yield valuable quantitative information about the shape of lensing galaxies and their dark matter halos.

Investigation of Gravitational Lens Mass Models

“…This shear could be due to a nearby galaxy or by dropping the requirement that the mass of the lens be aligned with the light. Since there does not appear to be a galaxy at the required angle of approximately [26¡, we agree with the Ðndings of Witt & Mao (1997), who concluded that the shear was due to a misalignment of mass and light. In fact, the lens system was well Ðtted by allowing the mass to be rotated by approximately [15¡.…”

“…In the case of 12531[2914, we Ðnd that a shear of B0.14 is required to Ðt the observed conÐguration. This value is slightly less than the value of B0.20 found by Witt & Mao (1997). This shear could be due to a nearby galaxy or by dropping the requirement that the mass of the lens be aligned with the light.…”

Gravitational Lensing Magnification without Multiple Imaging

“…Gravitational tidal shear, produced by objects near the main lens halo or projected along the line of sight, can increase the probability of high magnifications. Shear is expected to be common, on the basis of both analytic estimates and numerical simulations (e.g., Keeton et al 1997;Holder & Schechter 2003), and it is generally required for fitting observed galaxy-mass (M $ 10 12 M ) strong-lens systems (e.g., Keeton et al 1997;Witt & Mao 1997). The lens potential associated with shear is…”

“…Shears of $ 0:05-0.1 are common for galaxy-mass lenses, and shears of $ 0:2-0.3 are possible for lens galaxies lying in dense environments (e.g., Keeton et al 1997;Witt & Mao 1997;Kundić et al 1997aKundić et al , 1997bFischer et al 1998;Kneib et al 2000;Holder & Schechter 2003).…”

Gravitational lensing potential reconstruction in quadruply imaged systems

“…The degeneracy of the results is often not fully explored since a large parameter space should be analyzed using a huge amount of computer time. Previously, several authors have often restricted V. F. Cardone et al: Lensing potential reconstruction 73 their studies to isothermal or power-law spherical models (Evans & Wilkinson 1998), elliptical models (Witt & Mao 1997) and other simple models (Kassiola & Kovner 1993, 1995 with or without external shear. The fully general non-parametric method, e.g.…”