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

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

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

HST observations of gravitationally lensed QSOs

Thanks to its sharp view, HST has significantly improved our knowledge of tens of gravitationally lensed quasars in four different respects: (1) confirming their lensed nature; (2) detecting the lensing galaxy responsible for the image splitting; (3) improving the astrometric accuracy on the positions of the unresolved QSO images and of the lens; (4) resolving extended lensed structures from the QSO hosts into faint NIR or optical rings or arcs. These observations have helped to break some degeneracies on the lens potential, to probe the galaxy evolution and to reconstruct the true shape of the QSO host with an increased angular resolution

Observations of radio-quiet quasars at 10mas resolution by use of gravitational lensing

We present VLA detections of radio emission in four four-image gravitational lens systems with quasar sources: HS0810+2554, RXJ0911+0511, HE0435$-$1223 and SDSSJ0924+0219, and e-MERLIN observations of two of the systems. The first three are detected at a high level of significance, and SDSS J0924+0219 is detected. HS0810+2554 is resolved, allowing us for the first time to achieve 10-mas resolution of the source frame in the structure of a radio quiet quasar. The others are unresolved or marginally resolved. All four objects are among the faintest radio sources yet detected, with intrinsic flux densities in the range 1-5$\mu$Jy; such radio objects, if unlensed, will only be observable routinely with the Square Kilometre Array. The observations of HS0810+2554, which is also detected with e-MERLIN, strongly suggest the presence of a mini-AGN, with a radio core and milliarcsecond scale jet. The flux densities of the lensed images in all but HE0435-1223 are consistent with smooth galaxy lens models without the requirement for smaller-scale substructure in the model, although some interesting anomalies are seen between optical and radio flux densities. These are probably due to microlensing effects in the optical.Comment: Accepted by MNRA

Testing the Evolution of the Correlations between Supermassive Black Holes and their Host Galaxies using Eight Strongly Lensed Quasars

One of the main challenges in using high redshift active galactic nuclei to study the correlations between the mass of the supermassive Black Hole (MBH) and the properties of their active host galaxies is instrumental resolution. Strong lensing magnification effectively increases instrumental resolution and thus helps to address this challenge. In this work, we study eight strongly lensed active galactic nuclei (AGN) with deep Hubble Space Telescope imaging, using the lens modelling code Lenstronomy to reconstruct the image of the source. Using the reconstructed brightness of the host galaxy, we infer the host galaxy stellar mass based on stellar population models. MBH are estimated from broad emission lines using standard methods. Our results are in good agreement with recent work based on non-lensed AGN, demonstrating the potential of using strongly lensed AGNs to extend the study of the correlations to higher redshifts. At the moment, the sample size of lensed AGN is small and thus they provide mostly a consistency check on systematic errors related to resolution for the non-lensed AGN. However, the number of known lensed AGN is expected to increase dramatically in the next few years, through dedicated searches in ground and space based wide field surveys, and they may become a key diagnostic of black hole and galaxy co-evolution.Comment: 12 pages, 4 figures, 3 tables. MNRAS in press. Comments welcom

H0LiCOW III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts

Based on spectroscopy and multiband wide-field observations of the gravitationally lensed quasar HE 0435-1223, we determine the probability distribution function of the external convergence $\kappa_\mathrm{ext}$ for this system. We measure the under/overdensity of the line of sight towards the lens system and compare it to the average line of sight throughout the universe, determined by using the CFHTLenS as a control field. Aiming to constrain $\kappa_\mathrm{ext}$ as tightly as possible, we determine under/overdensities using various combinations of relevant informative weighing schemes for the galaxy counts, such as projected distance to the lens, redshift, and stellar mass. We then convert the measured under/overdensities into a $\kappa_\mathrm{ext}$ distribution, using ray-tracing through the Millennium Simulation. We explore several limiting magnitudes and apertures, and account for systematic and statistical uncertainties relevant to the quality of the observational data, which we further test through simulations. Our most robust estimate of $\kappa_\mathrm{ext}$ has a median value $\kappa^\mathrm{med}_\mathrm{ext} = 0.004$ and a standard deviation of $\sigma_\kappa = 0.025$. The measured $\sigma_\kappa$ corresponds to $2.5\%$ uncertainty on the time delay distance, and hence the Hubble constant $H_0$ inference from this system. The median $\kappa^\mathrm{med}_\mathrm{ext}$ value is robust to $\sim0.005$ (i.e. $\sim0.5\%$ on $H_0$) regardless of the adopted aperture radius, limiting magnitude and weighting scheme, as long as the latter incorporates galaxy number counts, the projected distance to the main lens, and a prior on the external shear obtained from mass modeling. The availability of a well-constrained $\kappa_\mathrm{ext}$ makes \hequad\ a valuable system for measuring cosmological parameters using strong gravitational lens time delays.Comment: 24 pages, 17 figures, 6 tables. Submitted to MNRA

Zooming into the broad line region of the gravitationally lensed quasar Q2237+0305 = the Einstein Cross: III. Determination of the size and structure of the CIV and CIII] emitting regions using microlensing

Aims: We aim to use microlensing taking place in the lensed quasar Q2237+0305 to study the structure of the broad line region and measure the size of the region emitting the CIV and CIII] lines. Methods: Based on 39 spectrophotometric monitoring data points obtained between Oct. 2004 and Dec. 2007, we derive lightcurves for the CIV and CIII] emission lines. We use three different techniques to analyse the microlensing signal. Different components of the lines (narrow, broad and very broad) are identified and studied. We build a library of simulated microlensing lightcurves which reproduce the signal observed in the continuum and in the lines provided only the source size is changed. A Bayesian analysis scheme is then developed to derive the size of the various components of the BLR. Results: 1. The half-light radius of the region emitting the CIV line is found to be R_CIV ~ 66^{+110}_{-46} lt-days = 0.06^{+0.09}_{-0.04} pc = 1.7^{+2.8}_{-1.1} 10^17 cm (at 68.3% CI). Similar values are obtained for CIII]. Relative sizes of the V-band continuum and of the carbon line emitting regions are also derived with median values of R(line)/R(cont) in the range [4,29], depending of the FWHM of the line component. 2. The size of the CIV emitting region agrees with the Radius-Luminosity relationship derived from reverberation mapping. Using the virial theorem we derive the mass of the black hole in Q2237+0305 to be M_BH ~ 10^{8.3+/-0.3} M_sun. 3. We find that the CIV and CIII] lines are produced in at least 2 spatially distinct regions, the most compact one giving rise to the broadest component of the line. The broad and narrow line profiles are slightly different for CIV and CIII]. 4. Our analysis suggests a different structure of the CIV and FeII+III emitting regions, with the latter being produced in the inner part of the BLR or in a less extended emitting region than CIV.Peer reviewe