Strong gravitational lensing by groups or clusters of galaxies provides a powerful technique to measure the dark matter properties of individual lens galaxies. We study in detail the mass ...distribution of the satellite lens galaxy in the group-scale lens SL2S J08544−0121 by modelling simultaneously the spatially extended surface brightness distribution of the source galaxy and the lens mass distribution using Markov chain Monte Carlo methods. In particular, we measure the dark matter halo size of the satellite lens galaxy to be $\rtmarg$ 6. 0 -2.0 + 2.9 kpc with a fiducial velocity dispersion of $\sigmarg$127-12+21 kms-1. This is the first time the size of an individual galaxy halo in a galaxy group has been measured using strong gravitational lensing without assumptions of mass following light. We verify the robustness of our halo size measurement using mock data resembling our lens system. Our measurement of the halo size is compatible with the estimated tidal radius of the satellite galaxy, suggesting that halos of galaxies in groups experience significant tidal stripping, a process that has been previously observed on galaxies in clusters. Our mass model of the satellite galaxy is elliptical with its major axis misaligned with that of the light by ~50deg. The major axis of the total matter distribution is oriented more towards the centre of the host halo, exhibiting the radial alignment found in N-body simulations and observational studies of satellite galaxies. This misalignment between mass and light poses a significant challenge to modified Newtonian dynamics.
Abstract
We present a blind time-delay strong lensing (TDSL) cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 . We combine the relative time delay between the quasar images, Hubble ...Space Telescope imaging, the Keck stellar velocity dispersion of the lensing galaxy, and wide-field photometric and spectroscopic data of the field to constrain two angular diameter distance relations. The combined analysis is performed by forward modelling the individual data sets through a Bayesian hierarchical framework, and it is kept blind until the very end to prevent experimenter bias. After unblinding, the inferred distances imply a Hubble constant H0 = 68.8$^{+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.
Abstract
The time delays between the multiple images of a strong lens system, together with a model of the lens mass distribution, allow a one-step measurement of a cosmological distance, namely, the ...'time-delay distance' of the lens (D
Δt
) that encodes cosmological information. The time-delay distance depends sensitively on the radial profile slope of the lens mass distribution; consequently, the lens slope must be accurately constrained for cosmological studies. We show that the slope cannot be constrained in two-image systems with single-component compact sources, whereas it can be constrained in systems with two-component sources provided that the separation between the image components can be measured with milliarcsecond precisions, which is not feasible in most systems. In contrast, we demonstrate that spatially extended images of the source galaxy in two-image systems break the radial slope degeneracy and allow D
Δt
to be measured with uncertainties of a few per cent. Deep and high-resolution imaging of the lens systems are needed to reveal the extended arcs, and stable point spread functions are required for our lens modelling technique. Two-image systems, no longer plagued by the radial profile slope degeneracy, would augment the sample of useful time-delay lenses by a factor of ∼6, providing substantial advances for cosmological studies.
Strong gravitational lens systems with measured time delays between the multiple images provide a method for measuring the 'time-delay distance' to the lens, and thus the Hubble constant. We present ...a Bayesian analysis of the strong gravitational lens system B1608+656, incorporating (1) new, deep Hubble Space Telescope (HST) observations, (2) a new velocity-dispersion measurement of 260 +- 15 km s{sup -1} for the primary lens galaxy, and (3) an updated study of the lens' environment. Our analysis of the HST images takes into account the extended source surface brightness, and the dust extinction and optical emission by the interacting lens galaxies. When modeling the stellar dynamics of the primary lens galaxy, the lensing effect, and the environment of the lens, we explicitly include the total mass distribution profile logarithmic slope gamma' and the external convergence kappa{sub ext}; we marginalize over these parameters, assigning well-motivated priors for them, and so turn the major systematic errors into statistical ones. The HST images provide one such prior, constraining the lens mass density profile logarithmic slope to be gamma' = 2.08 +- 0.03; a combination of numerical simulations and photometric observations of the B1608+656 field provides an estimate of the prior for kappa{sub ext}: 0.10{sup +0.08}{sub -0.05}. This latter distribution dominates the final uncertainty on H{sub 0}. Fixing the cosmological parameters at OMEGA{sub m} = 0.3, OMEGA{sub L}AMBDA = 0.7, and w = -1 in order to compare with previous work on this system, we find H{sub 0} = 70.6{sup +3.1}{sub -3.1} km s{sup -1} Mpc{sup -1}. The new data provide an increase in precision of more than a factor of 2, even including the marginalization over kappa{sub ext}. Relaxing the prior probability density function for the cosmological parameters to that derived from the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data set, we find that the B1608+656 data set breaks the degeneracy between OMEGA{sub m} and OMEGA{sub L}AMBDA at w = -1 and constrains the curvature parameter to be -0.031 < OMEGA{sub k} < 0.009 (95% CL), a level of precision comparable to that afforded by the current Type Ia SNe sample. Asserting a flat spatial geometry, we find that, in combination with WMAP, H{sub 0} = 69.7{sup +4.9}{sub -5.0} km s{sup -1} Mpc{sup -1} and w = -0.94{sup +0.17}{sub -0.19} (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as the current Baryon Acoustic Oscillation data do.
Realizing Refsdal's original idea from 1964, we present estimates of the Hubble constant that are complementary to, and potentially competitive with, those of other cosmological probes. We use the ...observed positions of 89 multiple images, with extensive spectroscopic information, from 28 background sources and the measured time delays between the images S1-S4 and SX of supernova "Refsdal" (z = 1.489), which were obtained thanks to Hubble Space Telescope deep imaging and Multi Unit Spectroscopic Explorer data. We extend the strong-lensing modeling of the Hubble Frontier Fields galaxy cluster MACS J1149.5+2223 (z = 0.542), published by Grillo et al. (2016), and explore different ΛCDM models. Taking advantage of the lensing information associated to the presence of very close pairs of multiple images at various redshifts, and to the extended surface brightness distribution of the SN Refsdal host, we can reconstruct the total mass-density profile of the cluster very precisely. The combined dependence of the multiple-image positions and time delays on the cosmological parameters allows us to infer the values of H0 and m with relative (1 ) statistical errors of, respectively, 6% (7%) and 31% (26%) in flat (general) cosmological models, assuming a conservative 3% uncertainty on the final time delay of image SX and, remarkably, no priors from other cosmological experiments. Our best estimate of H0, based on the model described in this work, will be presented when the final time-delay measurement becomes available. Our results show that it is possible to utilize time delays in lens galaxy clusters as an important alternative tool for measuring the expansion rate and the geometry of the universe.
We present new measurements of the values of the Hubble constant, matter density, dark energy density, and dark energy density equation-of-state (EoS) parameters. These results have been obtained ...from a full strong-lensing analysis of the observed positions of 89 multiple images and 4 measured time delays of the supernova (SN) Refsdal in the Hubble Frontier Fields galaxy cluster MACS J1149.5+2223. By strictly following the identical modelling methodology (as done in our previous work undertaken before time delays were available), our cosmographic measurements are essentially blind, based on the frozen procedure. Without using any priors from other cosmological experiments, in an open w CDM cosmological model and via our reference cluster mass model, we measure the following values: H 0 = 65.1 −3.4 +3.5 km s −1 Mpc −1 , Ω DE = 0.76 −0.10 +0.15 , and w = −0.92 −0.21 +0.15 (at the 68.3% confidence level). No other single cosmological probe has been able to simultaneously measure all these parameters. Remarkably, our estimated values of the cosmological parameters, in particular that of H 0 , are very robust and do not significantly depend on the assumed cosmological model or the cluster mass modelling details. The latter aspect introduces systematic uncertainties on the values of H 0 and w , which are found to be largely subdominant compared to the statistical errors. The results of this study demonstrate that the combination of time delays in lens galaxy clusters with extensive photometric and spectroscopic information offers a novel and competitive cosmological tool.
Stars and dark matter account for most of the mass of early-type galaxies, but uncertainties in the stellar population and the dark matter profile make it challenging to distinguish between the two ...components. Nevertheless, precise observations of stellar and dark matter are extremely valuable for testing the many models of structure formation and evolution. We present a measurement of the stellar mass and inner slope of the dark matter halo of a massive early-type galaxy at z = 0.222. The galaxy is the foreground deflector of the double Einstein ring gravitational lens system SDSSJ0946+1006, also known as the "Jackpot." By combining the tools of lensing and dynamics we first constrain the mean slope of the total mass density profile (rho sub(tot) is proportional to r super(- gamma ')) within the radius of the outer ring to be gamma ' = 1.98 + or - 0.02 + or - 0.01. Then we obtain a bulge-halo decomposition, assuming a power-law form for the dark matter halo. Our analysis yields = 1.7 + or -0.2 for the inner slope of the dark matter profile, in agreement with theoretical findings on the distribution of dark matter in ellipticals, and a stellar mass from lensing and dynamics M super(LD) sub(*) = 5.5 super(+0.4) sub(-1.3) x 10 super(11) M sub(middot in circle). By comparing this measurement with stellar masses inferred from stellar population synthesis fitting we find that a Salpeter initial mass function (IMF) provides a good description of the stellar population of the lens while the probability of the IMF being heavier than Chabrier is 95%. Our data suggest that growth by accretion of small systems from a compact red nugget is a plausible formation scenario for this object.
The upcoming Large Synoptic Survey Telescope (LSST) will detect many strongly lensed Type Ia supernovae (LSNe Ia) for time-delay cosmography. This will provide an independent and direct way for ...measuring the Hubble constant H0, which is necessary to address the current 4.4σ tension in H0 between the local distance ladder and the early Universe measurements. We present a detailed analysis of different observing strategies (also referred to as cadence strategy) for the LSST, and quantify their impact on time-delay measurement between multiple images of LSNe Ia. For this, we simulated observations by using mock LSNe Ia for which we produced mock-LSST light curves that account for microlensing. Furthermore, we used the free-knot splines estimator from the software PyCS to measure the time delay from the simulated observations. We find that using only LSST data for time-delay cosmography is not ideal. Instead, we advocate using LSST as a discovery machine for LSNe Ia, enabling time delay measurements from follow-up observations from other instruments in order to increase the number of systems by a factor of 2–16 depending on the observing strategy. Furthermore, we find that LSST observing strategies, which provide a good sampling frequency (the mean inter-night gap is around two days) and high cumulative season length (ten seasons with a season length of around 170 days per season), are favored. Rolling cadences subdivide the survey and focus on different parts in different years; these observing strategies trade the number of seasons for better sampling frequency. In our investigation, this leads to half the number of systems in comparison to the best observing strategy. Therefore rolling cadences are disfavored because the gain from the increased sampling frequency cannot compensate for the shortened cumulative season length. We anticipate that the sample of lensed SNe Ia from our preferred LSST cadence strategies with rapid follow-up observations would yield an independent percent-level constraint on H0.
We study possible systematic effects on the values of the cosmological parameters measured through strong lensing analyses of the Hubble Frontier Field galaxy cluster MACS J1149.5+2223. We use the ...observed positions of a large set of spectroscopically selected multiple images, including those of supernova "Refsdal" with their published time delays. Starting from our reference model in a flat ΛCDM cosmology, published in Grillo et al. (2018), we confirm the relevance of the longest measurable time delay, between SX and S1, and an approximately linear relation between its value and that of H0. We perform true blind tests by considering a range of time delays around its original estimate of 345 10 days, as an accurate measurement of this time delay is still not known at the time of analysis and writing. We investigate separately the impact of a constant sheet of mass at the cluster redshift, of a power-law profile for the mass density of the cluster main halo and of some scatter in the cluster member scaling relations. Remarkably, we find that these systematic effects do not introduce a significant bias on the inferred values of H0 and m and that the statistical uncertainties dominate the total error budget: a 3% uncertainty on the time delay of image SX translates into approximately 6% and 40% (including both statistical and systematic 1 ) uncertainties for H0 and m, respectively. Furthermore, our model accurately reproduces the extended surface brightness distribution of the supernova host. We also present the interesting possibility of measuring the value of the equation-of-state parameter w of the dark energy density, currently with a 30% uncertainty.
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.
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