scholarly journals Systematic errors induced by the elliptical power-law model in galaxy-galaxy strong lens modeling

2021 ◽  
Author(s):  
Xiaoyue Cao ◽  
Ran Li ◽  
James Nightingale ◽  
Richard Massey ◽  
Andrew Robertson ◽  
...  
Keyword(s):  
Power Law ◽  
Gravitational Lensing ◽  
Time Delays ◽  
Hubble Space Telescope ◽  
Stellar Dynamics ◽  
Hubble Constant ◽  
Power Law Model ◽  
Mass Model ◽  
Mass Distributions ◽  
Model Mismatch

Abstract The elliptical power-law (EPL) mass model of the mass in a galaxy is widely used in strong gravitational lensing analyses. However, the distribution of mass in real galaxies is more complex. We quantify the biases due to this model mismatch by simulating and then analysing mock {\it Hubble Space Telescope} imaging of lenses with mass distributions inferred from SDSS-MaNGA stellar dynamics data. We find accurate recovery of source galaxy morphology, except for a slight tendency to infer sources to be more compact than their true size. The Einstein radius of the lens is also robustly recovered with 0.1\% accuracy, as is the global density slope, with 2.5\% relative systematic error, compared to the 3.4\% intrinsic dispersion. However, asymmetry in real lenses also leads to a spurious fitted `external shear' with typical strength, $\gamma_{\rm ext}=0.015$. Furthermore, time delays inferred from lens modelling without measurements of stellar dynamics are typically underestimated by $\sim$5\%. Using such measurements from a sub-sample of 37 lenses would bias measurements of the Hubble constant $H_0$ by $\sim$9\%. The next generation cosmography must use more complex lens mass models.

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 Galaxy mass profiles from strong lensing III: The two-dimensional broken power-law model

2020 ◽  
Author(s):  
C M O’Riordan ◽  
S J Warren ◽  
D J Mortlock
Keyword(s):  
Power Law ◽  
Surface Density ◽  
Time Delays ◽  
Deflection Angle ◽  
Hubble Constant ◽  
Two Dimensional ◽  
Gravitational Lenses ◽  
Power Law Model ◽  
Multiple Images ◽  
Mass Profile

Abstract When modelling strong gravitational lenses, i.e., where there are multiple images of the same source, the most widely used parameterisation for the mass profile in the lens galaxy is the singular power-law model ρ(r)∝r−γ. This model may be insufficiently flexible for very accurate work, for example measuring the Hubble constant based on time delays between multiple images. Here we derive the lensing properties – deflection angle, shear, and magnification – of a more adaptable model where the projected mass surface density is parameterised as a continuous two-dimensional broken power-law (2DBPL). This elliptical 2DBPL model is characterised by power-law slopes t1, t2 either side of the break radius θB. The key to the 2DBPL model is the derivation of the lensing properties of the truncated power law (TPL) model, where the surface density is a power law out to the truncation radius θT and zero beyond. This TPL model is also useful by itself. We create mock observations of lensing by a TPL profile where the images form outside the truncation radius, so there is no mass in the annulus covered by the images. We then show that the slope of the profile interior to the images may be accurately recovered for lenses of moderate ellipticity. This demonstrates that the widely-held notion that lensing measures the slope of the mass profile in the annulus of the images, and is insensitive to the mass distribution at radii interior to the images, is incorrect.

scholarly journals Lens galaxies in the Illustris simulation: power-law models and the bias of the Hubble constant from time delays

2015 ◽  
Vol 456 (1) ◽  
pp. 739-755 ◽  
Author(s):  
Dandan Xu ◽  
Dominique Sluse ◽  
Peter Schneider ◽  
Volker Springel ◽  
Mark Vogelsberger ◽  
...  
Keyword(s):  
Power Law ◽  
Time Delays ◽  
Hubble Constant ◽  
Lens Galaxies

scholarly journals Gravitational Lensing by Power‐Law Mass Distributions: A Fast and Exact Series Approach

1998 ◽  
Vol 506 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Kyu‐Hyun Chae ◽  
Valery K. Khersonsky ◽  
David A. Turnshek
Keyword(s):  
Power Law ◽  
Gravitational Lensing ◽  
Mass Distributions

scholarly journals Magnification, dust and time-delay constraints from the first resolved strongly lensed Type Ia supernova iPTF16geu

2019 ◽  
Author(s):  
S Dhawan ◽  
J Johansson ◽  
A Goobar ◽  
R Amanullah ◽  
E Mörtsell ◽  
...  
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
Time Delays ◽  
Large Scale ◽  
Hubble Space Telescope ◽  
Type Ia Supernova ◽  
Model Predictions ◽  
Type Ia ◽  
Reference Images ◽  
Short Time

Abstract We report lensing magnifications, extinction, and time-delay estimates for the first resolved, multiply-imaged Type Ia supernova iPTF16geu, at z = 0.409, using Hubble Space Telescope (HST) observations in combination with supporting ground-based data. Multi-band photometry of the resolved images provides unique information about the differential dimming due to dust in the lensing galaxy. Using HST and Keck AO reference images taken after the SN faded, we obtain a total lensing magnification for iPTF16geu of $\mu = 67.8^{+2.6}_{-2.9}$, accounting for extinction in the host and lensing galaxy. As expected from the symmetry of the system, we measure very short time-delays for the three fainter images with respect to the brightest one: -0.23 ± 0.99, -1.43 ± 0.74 and 1.36 ± 1.07 days. Interestingly, we find large differences between the magnifications of the four supernova images, even after accounting for uncertainties in the extinction corrections: $\Delta m_1 = -3.88^{+0.07}_{-0.06}$, $\Delta m_2 = -2.99^{+0.09}_{-0.08}$, $\Delta m_3 = -2.19^{+0.14}_{-0.15}$ and $\Delta m_4 = -2.40^{+0.14}_{-0.12}$ mag, discrepant with model predictions suggesting similar image brightnesses. A possible explanation for the large differences is gravitational lensing by substructures, micro- or millilensing, in addition to the large scale lens causing the image separations. We find that the inferred magnification is insensitive to the assumptions about the dust properties in the host and lens galaxy.

scholarly journals Do Lensing Statistics Rule out a Cosmological Constant?

1999 ◽  
Vol 183 ◽  
pp. 65-65
Author(s):  
M. Chiba ◽  
Y. Yoshii
Keyword(s):  
Gravitational Lensing ◽  
Globular Clusters ◽  
Luminosity Function ◽  
Velocity Dispersion ◽  
Hubble Space Telescope ◽  
High Redshift ◽  
Hubble Constant ◽  
S0 Galaxies ◽  
Internal Velocity ◽  
Rule Out

We present new calculations of the gravitational lensing statistics following recent revised knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies which work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast with the earlier statistics supporting an Ω0 = 1 universe, the reported small lensing probability from the Hubble Space Telescope (HST) snapshot lens survey is in best agreement with a low-density, flat universe with Ω0 ≃ 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value of the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way (ApJ, 1997, Vol. 489, in press).

scholarly journals H0LiCOW XII. Lens mass model of WFI2033 − 4723 and blind measurement of its time-delay distance and H0

2019 ◽  
Vol 498 (1) ◽  
pp. 1440-1468 ◽  
Author(s):  
Cristian E Rusu ◽  
Kenneth C Wong ◽  
Vivien Bonvin ◽  
Dominique Sluse ◽  
Sherry H Suyu ◽  
...  
Keyword(s):  
Time Delay ◽  
Hubble Space Telescope ◽  
Hubble Constant ◽  
Companion Paper ◽  
Wide Field ◽  
Full Time ◽  
Gravitational Lenses ◽  
Mass Model ◽  
Imaging And Spectroscopy ◽  
Field Imaging

ABSTRACT We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033 − 4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 yr of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution Hubble Space Telescope imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average precision of $6.6{{\ \rm per\ cent}}$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat ΛCDM cosmology with a uniform prior on Ωm in the range [0.05, 0.5]. This work is part of the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII).

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.

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