Abstract
We present a blind time-delay strong lensing (TDSL) cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 . We combine the relative time delay between the quasar images, Hubble ...Space Telescope imaging, the Keck stellar velocity dispersion of the lensing galaxy, and wide-field photometric and spectroscopic data of the field to constrain two angular diameter distance relations. The combined analysis is performed by forward modelling the individual data sets through a Bayesian hierarchical framework, and it is kept blind until the very end to prevent experimenter bias. After unblinding, the inferred distances imply a Hubble constant H0 = 68.8$^{+5.4}_{-5.1}$ km s−1 Mpc−1, assuming a flat Λ cold dark matter cosmology with uniform prior on Ωm in 0.05, 0.5. The precision of our cosmographic measurement with the doubly imaged quasar SDSS 1206+4332 is comparable with those of quadruply imaged quasars and opens the path to perform on selected doubles the same analysis as anticipated for quads. Our analysis is based on a completely independent lensing code than our previous three H0LiCOW systems and the new measurement is fully consistent with those. We provide the analysis scripts paired with the publicly available software to facilitate independent analysis (footnote with link to www.h0licow.org). The consistency between blind measurements with independent codes provides an important sanity check on lens modelling systematics. By combining the likelihoods of the four systems under the same prior, we obtain H0 = 72.5$^{+2.1}_{-2.3}$ km s−1 Mpc−1. This measurement is independent of the distance ladder and other cosmological probes.
Context. The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constant H0, is one of the most pressing challenges in modern cosmology. Assuming ...flat ΛCDM, H0 inference at high redshift using cosmic microwave background data from Planck disagrees at the 4.4σ level with measurements based on the local distance ladder made up of parallaxes, Cepheids, and Type Ia supernovae (SNe Ia), often referred to as Hubble tension. Independent cosmological-model-insensitive ways to infer H0 are of critical importance. Aims. We apply an inverse distance ladder approach, combining strong-lensing time-delay distance measurements with SN Ia data. By themselves, SNe Ia are merely good indicators of relative distance, but by anchoring them to strong gravitational lenses we can obtain an H0 measurement that is relatively insensitive to other cosmological parameters. Methods. A cosmological parameter estimate was performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets. Results. The cosmological-model dependence of strong-lensing H0 measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferred H0 consistently lies around 73–74 km s−1 Mpc−1, regardless of the assumed cosmological background model. Our results agree closely with those from the local distance ladder, but there is a > 2σ tension with Planck results, and a ∼1.5σ discrepancy with results from an inverse distance ladder including Planck, baryon acoustic oscillations, and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties in H0 from our inverse distance ladder.
Multiply lensed images of a same source experience a relative time delay in the arrival of photons due to the path length difference and the different gravitational potentials the photons travel ...through. This effect can be used to measure absolute distances and the Hubble constant (
H
0
) and is known as time-delay cosmography. The method is independent of the local distance ladder and early-universe physics and provides a precise and competitive measurement of
H
0
. With upcoming observatories, time-delay cosmography can provide a 1% precision measurement of
H
0
and can decisively shed light on the current reported ‘Hubble tension’. This manuscript details the general methodology developed over the past decades in time-delay cosmography, discusses recent advances and results, and, foremost, provides a foundation and outlook for the next decade in providing accurate and ever more precise measurements with increased sample size and improved observational techniques.
ABSTRACT
We demonstrate an efficient method to compute the strong-gravitational-lensing deflection angle and magnification for any elliptical surface density profile. This method solves a numerical ...hurdle in lens modelling that has lacked a general solution for nearly three decades. The hurdle emerges because it is prohibitive to derive analytic expressions of the lensing quantities for most elliptical mass profiles. In our method, we first decompose an elliptical mass profile into concentric Gaussian components. We introduce an integral transform that provides us with a fast and accurate algorithm for this Gaussian decomposition. We derive analytic expressions of the lensing quantities for a Gaussian component. As a result, we can compute these quantities for the total mass profile by adding up the contributions from the individual components. This lensing analysis self-consistently completes the kinematic description in terms of Gaussian components presented by Cappellari (2008). Our method is general without extra computational burden unlike other methods currently in use.
ABSTRACT
We investigate the internal structure of elliptical galaxies at z ∼ 0.2 from a joint lensing–dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy–galaxy lenses ...selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median 2.08c ± 0.03 and intrinsic scatter 0.13 ± 0.02, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) haloes. We find that the DM haloes are well described by a standard Navarro–Frenk–White halo with no contraction on average for both of a constant stellar mass-to-light ratio (M/L) model and a stellar M/L gradient model. For the M/L gradient model, we find that most galaxies are consistent with no M/L gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM haloes.
Abstract
Strongly gravitational lensed quasars can be used to measure the so-called time-delay distance DΔt, and thus the Hubble constant H0 and other cosmological parameters. Stellar kinematics of ...the deflector galaxy play an essential role in this measurement by: (i) helping break the mass-sheet degeneracy; (ii) determining in principle the angular diameter distance Dd to the deflector and thus further improving the cosmological constraints. In this paper we simulate observations of lensed quasars with integral field spectrographs and show that spatially resolved kinematics of the deflector enables
further progress by helping break the mass-anisotropy degeneracy. Furthermore, we use our simulations to obtain realistic error estimates with current/upcoming instruments like OSIRIS on Keck and NIRSPEC on the James Webb Space Telescope for both distances (typically ∼6 per cent on DΔt and ∼10 per cent on Dd). We use the error estimates to compute cosmological forecasts for the sample of nine lenses that currently have well-measured time delays and deep Hubble Space Telescope images and for a sample of 40 lenses that is projected to be available in a few years through follow-up of candidates found in ongoing wide field surveys. We find that H0 can be measured with 2 per cent (1 per cent) precision from nine (40) lenses in a flat Λcold dark matter
cosmology. We study several other cosmological models beyond the flat Λcold dark matter model and find that time-delay lenses with spatially resolved kinematics can greatly improve the precision of the cosmological parameters measured by cosmic microwave background data.
Abstract
The dominant uncertainty in the current measurement of the Hubble constant (
H
0
) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the ...main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a data set of SNe that are not strongly lensed and a data set of strongly lensed SNe with measured time delays. We jointly constrain (i)
H
0
using the time delays as an absolute distance indicator, (ii) the lens model profiles using the magnification ratio of lensed and unlensed fluxes on the population level, and (iii) the unlensed apparent magnitude distribution of the SN population and the redshift–luminosity relation of the relative expansion history of the universe. We apply our joint inference framework on a future expected data set of glSNe and forecast that a sample of 144 glSNe of Type Ia with well-measured time series and imaging data will measure
H
0
to 1.5%. We discuss strategies to mitigate systematics associated with using absolute flux measurements of glSNe to constrain the mass density profiles. Using the magnification of SN images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and Roman observatories, will be able to discover the necessary number of glSNe, and with additional follow-up observations, this methodology will provide precise constraints on mass profiles and
H
0
.
Abstract
We present the discovery of three quasar lenses in the Sloan Digital Sky Survey, selected using two novel photometry-based selection techniques. The J0941+0518 system, with two point sources ...separated by 5.46 arcsec on either side of a galaxy, has source and lens redshifts 1.54 and 0.343. Images of J2257+2349 show two point sources separated by 1.67 arcsec on either side of an E/S0 galaxy. The extracted spectra show two images of the same quasar at zs = 2.10. SDSS J1640+1045 has two quasar spectra at zs = 1.70 and fits to the SDSS and Pan-STARRS images confirm the presence of a galaxy between the two point sources. We observed 56 photometrically selected lens candidates in this follow-up campaign, confirming three new lenses, re-discovering one known lens, and ruling out 36 candidates, with 16 still inconclusive. This initial campaign demonstrates the power of purely photometric selection techniques in finding lensed quasars.
Time delay lens modelling challenge Ding, X; Treu, T; Birrer, S ...
Monthly notices of the Royal Astronomical Society,
05/2021, Volume:
503, Issue:
1
Journal Article, Web Resource
Peer reviewed
Open access
ABSTRACT
In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant H0. However, published ...state-of-the-art analyses require of order 1 yr of expert investigator time and up to a million hours of computing time per system. Furthermore, as precision improves, it is crucial to identify and mitigate systematic uncertainties. With this time delay lens modelling challenge, we aim to assess the level of precision and accuracy of the modelling techniques that are currently fast enough to handle of order 50 lenses, via the blind analysis of simulated data sets. The results in Rungs 1 and 2 show that methods that use only the point source positions tend to have lower precision ($10\!-\!20{{\ \rm per\ cent}}$) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic data sets can recover H0 within the target accuracy (|A| < 2 per cent) and precision (<6 per cent per system), even in the presence of a poorly known point spread function and complex source morphology. A post-unblinding analysis of Rung 3 showed the numerical precision of the ray-traced cosmological simulations to be insufficient to test lens modelling methodology at the percent level, making the results difficult to interpret. A new challenge with improved simulations is needed to make further progress in the investigation of systematic uncertainties. For completeness, we present the Rung 3 results in an appendix and use them to discuss various approaches to mitigating against similar subtle data generation effects in future blind challenges.
TDCOSMO Birrer, S.; Shajib, A. J.; Galan, A. ...
Astronomy and astrophysics (Berlin),
11/2020, Volume:
643
Journal Article, Web Resource
Peer reviewed
Open access
The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of
H
0
= 73.3
−1.8
+1.7
km s
−1
Mpc
−1
, describing deflector mass density profiles by either a ...power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in
H
0
. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with
H
0
. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured
H
0
= 74.5
−6.1
+5.6
km s
−1
Mpc
−1
. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured
H
0
= 67.4
−3.2
+4.1
km s
−1
Mpc
−1
. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of
H
0
. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the
H
0
measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on
H
0
derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.
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