What Do Gravitational Lens Time Delays Measure?

By C. Kochanek. 2002

151 citations recorded by the source corpus.

Gravitational lens time delays depend on the Hubble constant, the observed image positions, and the surface mass density of the lens in the annulus between the images. Simple time delay lenses like PG 1115+80, SBS 1520+530, B1600+434, PKS 1830-211, and HE 2149-2745 have H0 = A(1 - ⟨κ⟩) + B⟨κ⟩(η - 1), where the two coefficients A ≃ 90 km s-1 Mpc-1 and B ≃ 10 km s-1 Mpc-1 depend on the measured delays and the observed image positions, ⟨κ⟩ is the mean surface density in the annulus between the images, and there is a small correction from the logarithmic slope η ≃ 2 of the density profile, κ ∝ R1-η, in the annulus. These five systems are very homogeneous since for fixed H0 = 100 h km s-1 Mpc-1 they must have the same surface density, ⟨κ⟩ = 1.11 - 1.22 h ± 0.04, with an upper bound of σκ < 0.07 on any dispersion in ⟨κ⟩ beyond those due to the measurement errors. If the lenses have their expected dark halos, ⟨κ⟩ ≃ 0.5 and H0 ≃ 51 ± 5 km s-1 Mpc-1, while if they have constant mass-to-light ratios, ⟨κ⟩ ≃ 0.1-0.2 and H0 ≃ 73 ± 8 km s-1 Mpc-1. More complicated lenses with multiple components or strong perturbations from nearby clusters, like RX J0911+0551 and Q0957+561, are easily recognized because they have significantly different coefficients.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

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Citations in the corpus

H0LiCOW - IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology (2016, background): “Deep, high-resolution imaging is required to accurately model the lens using the extended source images, which is needed to break degeneracies between the mass profile and the underlying cosmology (e.g., Kochanek 2002; Warren & Dye 2003).”
TWO ACCURATE TIME-DELAY DISTANCES FROM STRONG LENSING: IMPLICATIONS FOR COSMOLOGY (2012, background): “…radial slope of the lens mass distribution and the timedelay distance both have direct influence on the observables: for a given time delay, a galaxy with a steep radial profile leads to a lower DΔt than that of a galaxy with a shallow profile (e.g., Witt et al. 2000; Wucknitz 2002; Kochanek 2002).”
Gravitational Lens Time Delays: A Statistical Assessment of Lens Model Dependences and Implications for the Global Hubble Constant (2006, methodology): “In particular, from the analysis of Kochanek (2002) we obtain N ¼ 2(1 h i) at the lowest order of expansion, where h i is the average surface density in the annulus bounded by the images.”
H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes (2019, background): “In addition, deep high-resolution imaging of the lens is required to observe the extended images of the quasar host galaxy, which is needed to break degeneracies in the lens modelling between the mass profile and the underlying cosmology (e.g. Kochanek 2002; Koopmans et al. 2003; Dye & Warren 2005).”
Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys (2010, background): “…between multiple images; these time delays contain rich information on the lens potentials as well as cosmology (e.g. Witt, Mao & Keeton 2000; Kochanek 2002; Saha & Williams 2003; Schechter 2005; Oguri 2007a; Congdon, Keeton & Nordgren 2008; Keeton & Moustakas 2009; Congdon, Keeton &…”
The Sloan Lens ACS Survey. II. Stellar Populations and Internal Structure of Early-Type Lens Galaxies (2005, background): “…of the Hubble Constant from gravitational time delays; note however that time delays are sensitive to the slope in the region of the images – Kochanek 2002 –, while here we are considering the average slope inside the largest of the effective and Einstein radii) as discussed in paper III.”
TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography (2019, background): “As noted by Kochanek (2002), the time delay is mainly determined by the mean convergence 〈κ〉 in an annulus between the multiple images.”
DISSECTING THE GRAVITATIONAL LENS B1608+656. II. PRECISION MEASUREMENTS OF THE HUBBLE CONSTANT, SPATIAL CURVATURE, AND THE DARK ENERGY EQUATION OF STATE (2009, background): “From Kochanek (2002), the relative Fermat potential depends only on the mean surface mass density enclosed in the annulus between the images, to first order in δR/〈R〉, where δR is the difference in the radial distance of the image locations from the effective center of the lens galaxies and 〈R〉 is…”
The Time Delays of Gravitational Lens HE 0435–1223: An Early-Type Galaxy with a Rising Rotation Curve (2005, methodology): “We also used an a priori constraint on the amplitude of the external shear ( ¼ 0:05 0:05) based on limits from the alignment between the major axes of lens models and observed lens galaxies (Kochanek 2002a).”
H0LiCOW - V. New COSMOGRAIL time delays of HE 0435-1223: H0 to 3.8 per cent precision from strong lensing in a flat ΛCDM model (2016, background): “Indeed, time-delay measurements alone can constrain only a combination of the time-delay distance and the surface density of the lens around the quasar images (Kochanek 2002).”
Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing (2013, methodology): “A measurement of the time delays between lensed images, assuming a value of H0 determined by other methods, can break this degeneracy since τ is mostly sensitive to the slope of the mass profile near the Einstein radius (Gorenstein et al. 1988; Kochanek 2002).”
TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles (2020, background): “This degeneracy is well known and frequently discussed in the literature (e.g., Gorenstein et al. 1988; Kochanek 2002, 2006, 2020a; Saha & Williams 2006; Read et al. 2007; Schneider & Sluse 2013, 2014; Coles et al. 2014; Xu et al. 2016; Birrer et al. 2016; Unruh et al. 2017; Sonnenfeld 2018; Wertz…”
A Determination of H0 with the CLASS Gravitational Lens B1608+656. III. A Significant Improvement in the Precision of the Time Delay Measurements (2002, methodology): “Recent attempts have been limited to samples consisting of five or fewer lenses, and have obtained global values ofH0 ranging from 50 to 75 km s 1 Mpc 1 (e.g., Paper II; Schechter 2000; Kochanek 2002a).”
The Evolution and Structure of Early-Type Field Galaxies: A Combined Statistical Analysis of Gravitational Lenses (2004, unknown): “With a known Hubble constant, time delays measure the surface mass density near the lensed images (Kochanek 2002), which would break the model degeneracies for individual lenses in the same manner as a velocity dispersion measurement.”
Time delay cosmography (2016, background): “profiles produce longer time delays leading to shorter inferred time delay distances, and thus larger inferred values of H0 (Wucknitz 2002; Kochanek 2002; Suyu 2012).”
Gravitational lensing (2010, background): “It turns out that the time delays between multiple images is essentially determined by the mean surface-mass density in an annulus around the lens centre bounded by the images [259].”
Quantitative Interpretation of Quasar Microlensing Light Curves (2003, background): “…time delay measurement provides a direct estimate of the total surface density near the lensed images (under the assumption that H0 is known, see Kochanek 2002), which can be compared to the estimates of the total or stellar surface density derived from analyzing the variability created by…”
H0LiCOW – I. H0 Lenses in COSMOGRAIL's wellspring: program overview (2016, background): “The time-delay distance is particularly sensitive to the radial profile of the lens galaxy mass distribution (e.g., Kochanek 2002; Wucknitz 2002; Wucknitz et al. 2004; Suyu 2012).”