scholarly journals Ambiguities in gravitational lens models: impact on time delays of the source position transformation

2018 ◽  
Vol 617 ◽  
pp. A140 ◽  
Author(s):  
Olivier Wertz ◽  
Bastian Orthen ◽  
Peter Schneider
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Hubble Constant ◽  
Companion Paper ◽  
Gravitational Lens ◽  
Source Position ◽  
Double Image ◽  
Validity Criterion ◽  
Mass Profile ◽  
Image Pairs

The central ambition of the modern time delay cosmography consists in determining the Hubble constant H0 with a competitive precision. However, the tension with H0 obtained from the Planck satellite for a spatially flat ΛCDM cosmology suggests that systematic errors may have been underestimated. The most critical of these errors probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which contains the MST as a special case, may affect the time delays predicted by a model. To this aim, we have used pySPT, a new open-source python package fully dedicated to the SPT that we present in a companion paper. For axisymmetric lenses, we find that the time delay ratios between a model and its SPT-modified counterpart simply scale like the corresponding source position ratios, Δtˆ/Δt ≈ βˆ/β, regardless of the mass profile and the isotropic SPT. Similar behavior (almost) holds for nonaxisymmetric lenses in the double image regime and for opposite image pairs in the quadruple image regime. In the latter regime, we also confirm that the time delay ratios are not conserved. In addition to the MST effects, the SPT-modified time delays deviate in general no more than a few percent for particular image pairs, suggesting that its impact on time delay cosmography seems not be as crucial as initially suspected. We also reflected upon the relevance of the SPT validity criterion and present arguments suggesting that it should be reconsidered. Even though a new validity criterion would affect the time delays in a different way, we expect from numerical simulations that our conclusions will remain unchanged.

scholarly journals A dedicated source-position transformation package: pySPT

2018 ◽  
Vol 619 ◽  
pp. A117 ◽  
Author(s):  
Olivier Wertz ◽  
Bastian Orthen
Keyword(s):  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Companion Paper ◽  
Source Position ◽  
Development Platform ◽  
Lens Modeling ◽  
A Minor ◽  
Modeling Code ◽  
The Impact

Modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimates of the Hubble constant. The source position transformation (SPT), which covers the well-known mass-sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. The pySPT program also comes with a subpackage dedicated to simple lens modeling. This can be used to generate lensing related quantities for a wide variety of lens models independent of any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in a previous work between a softened power law and composite (baryons + dark matter) lenses. We find that the large deviations previously predicted have been overestimated because of a minor bug in the public lens modeling code lensmodel (v1.99), which is now fixed. We conclude that the predictions for the Hubble constant deviate by ∼7%, first and foremost as a consequence of an MST. The latest version of pySPT is available on Github, a software development platform, along with some tutorials to describe in detail how making the best use of pySPT.

scholarly journals Accurate cosmology from gravitational-lens time delays

2012 ◽  
Vol 8 (S289) ◽  
pp. 331-338
Author(s):  
S. H. Suyu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Current Status ◽  
Gravitational Lenses ◽  
Distance Measurements ◽  
One Step

AbstractThe time delays between the multiple images of a strong gravitational-lens system, together with a model of the lens-mass distribution, provide a one-step determination of the time-delay distance, and thus a measure of cosmological parameters, particularly the Hubble constant, H0. I review the recent advances in measuring time-delay distances, and present the current status of cosmological constraints based on gravitational-lens time delays. In particular, I report the time-delay distance measurements of two gravitational lenses and their implication for cosmology from a recent study by Suyuet al.

scholarly journals Limits between the Cosmological Parameters from Strong Lensing Observations for Generalized Isothermal Models

2009 ◽  
Vol 6 (2) ◽  
pp. 394-400
Author(s):  
Baghdad Science Journal
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Angular Structure ◽  
Density Distributions ◽  
General Family ◽  
Strong Lensing ◽  
Elegant Form

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time delay and by using the models of distances.

scholarly journals The Hubble Constant from (CLASS) Gravitational Lenses

2001 ◽  
Vol 18 (2) ◽  
pp. 179-181 ◽  
Author(s):  
L. V. E. Koopmans ◽  
The CLASS Collaboration
Keyword(s):  
Time Delays ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Gravitational Lenses ◽  
Monitoring Programs ◽  
Systematic Uncertainties ◽  
Sky Survey ◽  
Image Pairs ◽  
Near Future

AbstractOne of the main objectives of the Cosmic Lens All-Sky Survey (CLASS) collaboration has been to find gravitational lens (GL) systems at radio wavelengths that are suitable for the determination of time delays between image pairs. The survey is now near completion and at least 18 GL systems have been found. Here, I will discuss our efforts to measure time delays from several of these systems with the ultimate aim of constraining the Hubble Constant (H0). Thus far three CLASS GL systems (B0218+357, B1600+434 and B1608+656) have yielded measurements of time delays, from which values of H0 ≈ 60–70 km s−1 Mpc−1 have been estimated. Although most GL systems give similar values of H0, statistical and systematic uncertainties are still considerable. To reduce these uncertainties, I will mention two monitoring programs that we are undertaking to (re)measure time delays in 14 CLASS GL systems and address several important issues for the near future.

scholarly journals A SHARP view of H0LiCOW: H0 from three time-delay gravitational lens systems with adaptive optics imaging

2019 ◽  
Vol 490 (2) ◽  
pp. 1743-1773 ◽  
Author(s):  
Geoff C-F Chen ◽  
Christopher D Fassnacht ◽  
Sherry H Suyu ◽  
Cristian E Rusu ◽  
James H H Chan ◽  
...  
Keyword(s):  
Time Delay ◽  
Adaptive Optics ◽  
Cold Dark Matter ◽  
Hubble Space Telescope ◽  
Hubble Constant ◽  
Companion Paper ◽  
Gravitational Lens ◽  
High Angular Resolution ◽  
Full Time ◽  
Mass Model

ABSTRACT We present the measurement of the Hubble constant, H0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H0. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rm km\, s^{-1}\, Mpc^{-1}$ for PG 1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$ for HE 0435−1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$ for RXJ 1131−1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\, s^{-1}\, Mpc^{-1}$. The joint result of the AO + HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rm km\, s^{-1}\, Mpc^{-1}$. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ωm in [0.05, 0.5] and H0 in [0, 150] $\rm km\, s^{-1}\, Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H0. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper.

scholarly journals The Gravitational Lens System B1030+074. Discovery and Follow-up

1999 ◽  
Vol 194 ◽  
pp. 373-378
Author(s):  
E. Xanthopoulos ◽  
I. W. A. Browne ◽  
L. J. King ◽  
N. J. Jackson ◽  
D. R. Marlow ◽  
...  
Keyword(s):  
Time Delay ◽  
Flux Density ◽  
Density Ratio ◽  
Hubble Constant ◽  
Time Variable ◽  
Gravitational Lens ◽  
Lens System ◽  
Double Image ◽  
The Galaxy

We report the discovery of a new double image gravitational lens system B1030+074 which was found during the Jodrell Bank - VLA Astrometric Survey (JVAS). We have collected extensive radio data on the system using the VLA, MERLIN, the EVN and the VLBA as well as HST WFPC2 and NICMOS observations. The lensed images are separated by 1.56 arcseconds and their flux density ratio at centimetric wavelengths is approximately 14:1 although the ratio is slightly frequency dependent and the images appear to be time variable. The HST pictures show both the lensed images and the lensing galaxy close to the weaker image. The lensing galaxy has substructure which could be either part of the galaxy or a companion object. We have modeled B1030+074 using a Singular Isothermal Ellipsoid that yielded a time delay of 156/h50 days. This lens is likely to be suitable for the measurement of the Hubble constant.

scholarly journals TDCOSMO

2020 ◽  
Vol 642 ◽  
pp. A194 ◽  
Author(s):  
D. Gilman ◽  
S. Birrer ◽  
T. Treu
Keyword(s):  
Dark Matter ◽  
Time Delay ◽  
Time Delays ◽  
Arrival Time ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Line Of Sight ◽  
Gravitational Lenses ◽  
Additional Source ◽  
Precision Limit

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant H0. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer H0. We base the mock lenses on six quadruply imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of H0. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of H0 that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.7 − 2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and it sets a precision limit on inferences from single lenses.

scholarly journals Overconstrained gravitational lens models and the Hubble constant

2020 ◽  
Vol 493 (2) ◽  
pp. 1725-1735 ◽  
Author(s):  
C S Kochanek
Keyword(s):  
Power Law ◽  
Time Delays ◽  
Degrees Of Freedom ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Dark Matter Halo ◽  
Power Law Model ◽  
Dimensionless Quantity ◽  
Mean Convergence ◽  
The Mean

ABSTRACT It is well known that measurements of H0 from gravitational lens time delays scale as H0 ∝ 1 − κE, where κE is the mean convergence at the Einstein radius RE but that all available lens data other than the delays provide no direct constraints on κE. The properties of the radial mass distribution constrained by lens data are RE and the dimensionless quantity ξ = REα″(RE)/(1 − κE), where α″(RE) is the second derivative of the deflection profile at RE. Lens models with too few degrees of freedom, like power-law models with densities ρ ∝ r−n, have a one-to-one correspondence between ξ and κE (for a power-law model, ξ = 2(n − 2) and κE = (3 − n)/2 = (2 − ξ)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of κE and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ${\sim} 10{{\ \rm per\ cent}}$, regardless of the reported precision.

Time Delays in the Gravitational Lens CLASS B1608+656: Results from Second and Third Seasons of VLA Monitoring

2005 ◽  
Vol 201 ◽  
pp. 455-456
Author(s):  
Christopher. Fassnacht ◽  
Emily. Xanthopoulos ◽  
David. Rusin ◽  
Leon. Koopmans
Keyword(s):  
Time Delay ◽  
Flux Density ◽  
Time Delays ◽  
Optical Emission ◽  
Gravitational Lens ◽  
Delay Analysis ◽  
Constrained Model

The gravitational lens CLASS B1608+656 is one of the most promising lens systems for the measurement of H0 on cosmological scales. The three independent time delays between the four lensed images have been measured, and the extended lensed optical emission holds the promise for a very well-constrained model. The published time delay measurements are based on the first season of VLA monitoring, in which the background source varied by only 5% in flux density. The small level of variation leads to relatively large uncertainties in the determination of the time delays (10-20%). Two more seasons of monitoring have now been completed and the source flux density has changed by ˜25% during that time. We present the results of the continued VLA monitoring and the resulting time-delay analysis. The new data have significantly reduced the uncertainties on the time delays and, hence, reduced the uncertainties on the resulting determination of H0 from this system.

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