We present accurate time delays for the quadruply imaged quasar HE 0435-1223. The delays were measured from 575 independent photometric points obtained in the R-band between January 2004 and March 2010. With seven years of data, we clearly show that quasar image A is affected by strong microlensing variations and that the time delays are best expressed relative to quasar image B. We measured Δt BC = 7.8 ± 0.8 days, Δt BD = −6.5 ± 0.7 days and Δt CD = −14.3 ± 0.8 days. We spacially deconvolved HST NICMOS2 F160W images to derive accurate astrometry of the quasar images and to infer the light profile of the lensing galaxy. We combined these images with a stellar population fitting of a deep VLT spectrum of the lensing galaxy to estimate the baryonic fraction, f b , in the Einstein radius. We measured f b = 0.65 The spectrum also allowed us to estimate the velocity dispersion of the lensing galaxy, σ ap = 222 ± 34 km s −1 . We used f b and σ ap to constrain an analytical model of the lensing galaxy composed of an Hernquist plus generalized NFW profile. We solved the Jeans equations numerically for the model and explored the parameter space under the additional requirement that the model must predict the correct astrometry for the quasar images. Given the current error bars on f b and σ ap , we did not constrain H 0 yet with high accuracy, i.e., we found a broad range of models with χ 2 < 1. However, narrowing this range is possible, provided a better velocity dispersion measurement becomes available. In addition, increasing the depth of the current HST imaging data of HE 0435-1223 will allow us to combine our constraints with lens reconstruction techniques that make use of the full Einstein ring that is visible in this object. Key words. cosmological parameters -gravitational lensing: strong Based on observations made with the 1.2 m Euler Swiss Telescope, the 1.5 m telescope of Maidanak Observatory in Uzbekistan, and with the 1.2 m Mercator Telescope, operated on the island of La Palma by the Flemish Community, at the Spanish Observatorio del Roque de los
We present a simultaneous analysis of 10 galaxy lenses having time delay measurements. For each lens, we derive a detailed free-form mass map, with uncertainties, and with the additional requirement of a shared value of the Hubble parameter across all the lenses. We test the prior involved in the lens reconstruction against a galaxy-formation simulation. Assuming a concordance cosmology, we obtain .
Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H 0 by measuring the time delays between the quasar images. Here we report the measurement of two independent time delays in the quadruply imaged quasar WFI J2033−4723 (z = 1.66). Our data consist of R-band images obtained with the Swiss 1.2 m EULER telescope located at La Silla and with the 1.3 m SMARTS telescope located at Cerro Tololo. The light curves have 218 independent epochs spanning 3 full years of monitoring between March 2004 and May 2007, with a mean temporal sampling of one observation every 4th day. We measure the time delays using three different techniques, and we obtain Δt B−A = 35.5 ± 1.4 days (3.8%) and Δt B−C = 62.6 + 4.1 − 2.3 days ( + 6.5% − 3.7% ), where A is a composite of the close, merging image pair. After correcting for the time delays, we find R-band flux ratios of F A /F B = 2.88 ± 0.04, F A /F C = 3.38 ± 0.06, and F A1 /F A2 = 1.37 ± 0.05 with no evidence for microlensing variability over a time scale of three years. However, these flux ratios do not agree with those measured in the quasar emission lines, suggesting that longer term microlensing is present. Our estimate of H 0 agrees with the concordance value: non-parametric modeling of the lensing galaxy predicts H 0 = 67 (68% confidence level). More complex lens models using a composite de Vaucouleurs plus NFW galaxy mass profile show twisting of the mass isocontours in the lensing galaxy, as do the non-parametric models. As all models also require a significant external shear, this suggests that the lens is a member of the group of galaxies seen in field of view of WFI J2033−4723.
This paper examines free-form modeling of gravitational lenses using Bayesian ensembles of pixelated mass maps. The priors and algorithms from previous work are clarified and significant technical improvements are made. Lens reconstruction and Hubble Time recovery are tested using mock data from simple analytic models and recent galaxy-formation simulations. Finally, using published data, the Hubble Time is inferred through the simultaneous reconstruction of eleven time-delay lenses. The result is H −1 0 = 13.7 +1.8 −1.0 Gyr (H 0 = 71 +6 −8 km s −1 Mpc −1 ).
We use a new non-parametric gravitational modelling tool -Glass -to determine what quality of data (strong lensing, stellar kinematics, and/or stellar masses) are required to measure the circularly averaged mass profile of a lens and its shape. Glass uses an under-constrained adaptive grid of mass pixels to model the lens, searching through thousands of models to marginalise over model uncertainties. Our key findings are as follows: (i) for pure lens data, multiple sources with wide redshift separation give the strongest constraints as this breaks the well-known mass-sheet or steepness degeneracy; (ii) a single quad with time delays also performs well, giving a good recovery of both the mass profile and its shape; (iii) stellar masses -for lenses where the stars dominate the central potential -can also break the steepness degeneracy, giving a recovery for doubles almost as good as having a quad with time delay data, or multiple source redshifts; (iv) stellar kinematics provide a robust measure of the mass at the half light radius of the stars r 1/2 that can also break the steepness degeneracy if the Einstein radius r E = r 1/2 ; and (v) if r E ∼ r 1/2 , then stellar kinematic data can be used to probe the stellar velocity anisotropy β -an interesting quantity in its own right. Where information on the mass distribution from lensing and/or other probes becomes redundant, this opens up the possibility of using strong lensing to constrain cosmological models.
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