Analytic Time Delays andH₀Estimates for Gravitational Lenses

Abstract

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H 0 ; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H 0 , although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.

An Optical Time Delay Estimate for the Double Gravitational Lens System B1600+434

“…Finally, as pointed out by Romanowsky & Kochanek (1999) and Witt et al (2000), the time delay depends on the density proÐle of the lens galaxy. Hence, if the real density proÐle of the spiral galaxy is di †erent from our models, the errors in will increase.…”

“…For comparison, we also estimate using a simple ana-H 0 lytical generalized isothermal galaxy model, as described by Witt, Mao, & Keeton (2000). This method depends only on the time delay and the observed images positions.…”

Meso‐Structure in Three Strong‐lensing Systems

“…The ratios vary across the ensemble, but images 2Y4 consistently have their inverse radial magnifications in decreasing order. This is of interest because the generalized isothermal potentials ( Witt et al 2000) widely used in parametric models of galaxy lenses predict that the radial magnification should be equal for all images. Could the total lens potential here consist of a generalized isothermal for the main lens, plus a small perturbation from galaxy X?…”

Cosmological constraints from the double source plane lens SDSSJ0946+1006

“…Strong gravitational lensing is potentially a powerful tool to test cosmological models (Witt, Mao, & Keeton 2000;Kochanek 2002;Saha & Williams 2003;Schechter 2005;Oguri 2007;Oguri et al 2012;Suyu et al 2010Suyu et al , 2013Gavazzi et al 2008;Collett et al 2012), due to its sensitivity on the distances between components of the lens system (e.g., the observer, the foreground massive lensing object, and any background lensed sources).…”