Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of $H_0$ from the Planck satellite for a spatially flat six-parameters $\Lambda CDM$ cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analytical arguments and numerical experiments reveal that mass-sheet like transformations yield significant freedom in choosing the mass profile, even when exquisite Einstein rings are observed. Furthermore, the characterization of the environment of the lens does not break that degeneracy which is not physically linked to extrinsic convergence. We present an illustrative example where the multiple imaging properties of a composite (baryons + dark matter) lens can be extremely well reproduced by a power-law model having the same velocity dispersion, but with predictions for the Hubble constant that deviate by $\sim 20$. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current $H_0$ measurements from lensing, and need to be carefully reconsidered.Comment: Accepted for publication in Astronomy and Astrophysics. Discussion expanded (MSD and velocity dispersion, MSD and free form lens models, MSD and multiple source redshifts

Source-position transformation -- an approximate invariance in strong gravitational lensing

The main obstacle for gravitational lensing to determine accurate masses of deflectors, or to determine precise estimates for the Hubble constant, is the degeneracy of lensing observables with respect to the mass-sheet transformation (MST). The MST is a global modification of the mass distribution which leaves all image positions, shapes and flux ratios invariant, but which changes the time delay. Here we show that another global transformation of lensing mass distributions exists which almost leaves image positions and flux ratios invariant, and of which the MST is a special case. Whereas for axi-symmetric lenses this source position transformation exactly reproduces all strong lensing observables, it does so only approximately for more general lens situations. We provide crude estimates for the accuracy with which the transformed mass distribution can reproduce the same image positions as the original lens model, and present an illustrative example of its performance. This new invariance transformation most likely is the reason why the same strong lensing information can be accounted for with rather different mass models.Comment: Submitted to Astronomy and Astrophysics. Comments welcome. 9 page

Imprints of the quasar structure in time-delay light curves: Microlensing-aided reverberation mapping

Owing to the advent of large area photometric surveys, the possibility to use broad band photometric data, instead of spectra, to measure the size of the broad line region of active galactic nuclei, has raised a large interest. We describe here a new method using time-delay lensed quasars where one or several images are affected by microlensing due to stars in the lensing galaxy. Because microlensing decreases (or increases) the flux of the continuum compared to the broad line region, it changes the contrast between these two emission components. We show that this effect can be used to effectively disentangle the intrinsic variability of those two regions, offering the opportunity to perform reverberation mapping based on single band photometric data. Based on simulated light curves generated using a damped random walk model of quasar variability, we show that measurement of the size of the broad line region can be achieved using this method, provided one spectrum has been obtained independently during the monitoring. This method is complementary to photometric reverberation mapping and could also be extended to multi-band data. Because the effect described above produces a variability pattern in difference light curves between pairs of lensed images which is correlated with the time-lagged continuum variability, it can potentially produce systematic errors in measurement of time delays between pairs of lensed images. Simple simulations indicate that time-delay measurement techniques which use a sufficiently flexible model for the extrinsic variability are not affected by this effect and produce accurate time delays.Comment: Accepted for publication in Astronomy and Astrophysic

Optical linear polarization measurements of quasars obtained with the 3.6m telescope at the La Silla Observatory

We report 192 previously unpublished optical linear polarization measurements of quasars obtained in April 2003, April 2007, and October 2007 with the European Southern Observatory Faint Object Spectrograph and Camera (EFOSC2) instrument attached to the 3.6m telescope at the La Silla Observatory. Each quasar was observed once. Among the 192 quasars, 89 have a polarization degree $p \geq 0.6\%$, 18 have $p \geq 2\%$, and two have $p \geq 10\%$.Comment: Accepted for publication in A&

Alignment of quasar polarizations with large-scale structures

We have measured the optical linear polarization of quasars belonging to Gpc-scale quasar groups at redshift z ~ 1.3. Out of 93 quasars observed, 19 are significantly polarized. We found that quasar polarization vectors are either parallel or perpendicular to the directions of the large-scale structures to which they belong. Statistical tests indicate that the probability that this effect can be attributed to randomly oriented polarization vectors is of the order of 1%. We also found that quasars with polarization perpendicular to the host structure preferentially have large emission line widths while objects with polarization parallel to the host structure preferentially have small emission line widths. Considering that quasar polarization is usually either parallel or perpendicular to the accretion disk axis depending on the inclination with respect to the line of sight, and that broader emission lines originate from quasars seen at higher inclinations, we conclude that quasar spin axes are likely parallel to their host large-scale structures.Comment: Accepted for publication in Astronomy and Astrophysic

The different origins of high- and low-ionization broad emission lines revealed by gravitational microlensing in the Einstein cross

We investigate the kinematics and ionization structure of the broad emission line region of the gravitationally lensed quasar QSO2237+0305 (the Einstein cross) using differential microlensing in the high- and low-ionization broad emission lines. We combine visible and near-infrared spectra of the four images of the lensed quasar and detect a large-amplitude microlensing effect distorting the high-ionization CIV and low-ionization H$\alpha$ line profiles in image A. While microlensing only magnifies the red wing of the Balmer line, it symmetrically magnifies the wings of the CIV emission line. Given that the same microlensing pattern magnifies both the high- and low-ionization broad emission line regions, these dissimilar distortions of the line profiles suggest that the high- and low-ionization regions are governed by different kinematics. Since this quasar is likely viewed at intermediate inclination, we argue that the differential magnification of the blue and red wings of H$\alpha$ favors a flattened, virialized, low-ionization region whereas the symmetric microlensing effect measured in CIV can be reproduced by an emission line formed in a polar wind, without the need of fine-tuned caustic configurations.Comment: 11 pages, 4 figures, A&

Large scale correlations of quasar polarisation vectors: Hints of extreme scale structures?

A survey measuring quasar polarization vectors has been started in two regions towards the North and South Galactic Poles. Here, We review the discovery of significant correlations of orientations of polarization vectors over huge angular distances. We report new results including a larger sample of the quasars confirming the existence of coherent orientations at redshifts z>1.Comment: Proc. of Astronomical Polarimetry - Current Status and Future Directions March 15-19, 2004. Waikoloa Beach Marriott, Hawaii. 5 pages, 3 figure

Mid-infrared microlensing of accretion disc and dusty torus in quasars: effects on flux ratio anomalies

Multiply-imaged quasars and AGNs observed in the mid-infrared (MIR) range are commonly assumed to be unaffected by the microlensing produced by the stars in their lensing galaxy. In this paper, we investigate the validity domain of this assumption. Indeed, that premise disregards microlensing of the accretion disc in the MIR range, and does not account for recent progress in our knowledge of the dusty torus. To simulate microlensing, we first built a simplified image of the quasar composed of an accretion disc, and of a larger ring-like torus. The mock quasars are then microlensed using an inverse ray-shooting code. We simulated the wavelength and size dependence of microlensing for different lensed image types and fraction of compact objects projected in the lens. This allows us to derive magnification probabilities as a function of wavelength, as well as to calculate the microlensing-induced deformation of the spectral energy distribution of the lensed images. We find that microlensing variations as large as 0.1 mag are very common at 11 microns (observer-frame). The main signal comes from microlensing of the accretion disc, which may be significant even when the fraction of flux from the disc is as small as 5 % of the total flux. We also show that the torus of sources with Lbol <~ 10^45 erg/s is expected to be noticeably microlensed. Microlensing may thus be used to get insight into the rest near-infrared inner structure of AGNs. Finally, we investigate whether microlensing in the mid-infrared can alter the so-called Rcusp relation that links the fluxes of the lensed images triplet produced when the source lies close to a cusp macro-caustic. This relation is commonly used to identify massive (dark-matter) substructures in lensing galaxies. We find that significant deviations from Rcusp may be expected, which means that microlensing can explain part of the flux ratio problem.Comment: Updated to match the version published in Astronomy and Astrophysics. 12 pages. Abridged version of the abstract. Microlensing maps and source profiles used in the simulations are available via CDS - http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/553/A5