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 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 Astrometric requirements for strong lensing time-delay cosmography

2019 ◽  
Vol 489 (2) ◽  
pp. 2097-2103 ◽  
Author(s):  
Simon Birrer ◽  
Tommaso Treu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Direct Estimate ◽  
Strong Lensing ◽  
Image Separation ◽  
Modelling Techniques ◽  
Precision Time ◽  
Image Position

ABSTRACT The time-delay between the arrival of photons of multiple images of time-variable sources can be used to constrain absolute distances in the Universe, and in turn obtain a direct estimate of the Hubble constant and other cosmological parameters. To convert the time-delay into distances, it is well known that the gravitational potential of the main deflector and the contribution of the matter along the line of sight need to be known to a sufficient level of precision. In this paper, we discuss a new astrometric requirement that is becoming important, as time-delay cosmography improves in precision and accuracy with larger samples, and better data and modelling techniques. We derive an analytic expression for the propagation of astrometric uncertainties on the multiple image positions into the inference of the Hubble constant and derive requirements depending on image separation and relative time-delay. We note that this requirement applies equally to the image position measurements and to the accuracy of the model in reproducing them. To illustrate the requirement, we discuss some example lensing configurations and highlight that, especially for time-delays of order 10 d or shorter, the relative astrometric requirement is of order milliarcseconds, setting a tight requirement on both measurements and models. With current optical infrared technology, astrometric uncertainties may be the dominant limitation for strong lensing cosmography in the small image-separation regime when high-precision time-delays become accessible.

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 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 Strongly Lensed Supernovae in Well-Studied Galaxy Clusters with the Vera C. Rubin Observatory

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1966
Author(s):  
Tanja Petrushevska
Keyword(s):  
Galaxy Clusters ◽  
High Redshift ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Multiple Images ◽  
Strong Lensing ◽  
Type Ia ◽  
Ia Supernovae ◽  
Massive Galaxy

Strong lensing by galaxy clusters can be used to significantly expand the survey reach, thus allowing observation of magnified high-redshift supernovae that otherwise would remain undetected. Strong lensing can also provide multiple images of the galaxies that lie behind the clusters. Detection of strongly lensed Type Ia supernovae (SNe Ia) is especially useful because of their standardizable brightness, as they can be used to improve either cluster lensing models or independent measurements of cosmological parameters. The cosmological parameter, the Hubble constant, is of particular interest given the discrepancy regarding its value from measurements with different approaches. Here, we explore the feasibility of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) of detecting strongly lensed SNe in the field of five galaxy clusters (Abell 1689 and Hubble Frontier Fields clusters) that have well-studied lensing models. Considering the 88 systems composed of 268 individual multiple images in the five cluster fields, we find that the LSST will be sensitive to SNe Ia (SNe IIP) exploding in 41 (23) galaxy images. The range of redshift of these galaxies is between 1.01<z<3.05. During its 10 years of operation, LSST is expected to detect 0.2±0.1 SN Ia and 0.9±0.3 core collapse SNe. However, as LSST will observe many more massive galaxy clusters, it is likely that the expectations are higher. We stress the importance of having an additional observing program for photometric and spectroscopic follow-up of the strongly lensed SNe detected by LSST.

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.

scholarly journals H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes

2019 ◽  
Vol 498 (1) ◽  
pp. 1420-1439 ◽  
Author(s):  
Kenneth C Wong ◽  
Sherry H Suyu ◽  
Geoff C-F Chen ◽  
Cristian E Rusu ◽  
Martin Millon ◽  
...  
Keyword(s):  
Time Delay ◽  
Cold Dark Matter ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Joint Analysis ◽  
Type Ia Supernovae ◽  
Acoustic Oscillations ◽  
Type Ia ◽  
Measured Time ◽  
Ia Supernovae

ABSTRACT We present a measurement of the Hubble constant (H0) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analysed blindly with respect to the cosmological parameters. In a flat Λ cold dark matter (ΛCDM) cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$, a $2.4{{\ \rm per\ cent}}$ precision measurement, in agreement with local measurements of H0 from type Ia supernovae calibrated by the distance ladder, but in 3.1σ tension with Planck observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in 5.3σ tension with Planck CMB determinations of H0 in flat ΛCDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat ΛCDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from Planck, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with Planck. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our H0 inference to cosmological model assumptions. For six different cosmological models, our combined inference on H0 ranges from ∼73 to 78 km s−1 Mpc−1, which is consistent with the local distance ladder constraints.

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.

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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