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1. TDCOSMO III: Dark matter substructure meets dark energy -- the effects of (sub)halos on strong-lensing measurements of H0

   Gilman, Daniel; Birrer, Simon; Treu, Tommaso (July 2020, Astronomy astrophysics)

   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 realistic 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 0.6−2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and sets a precision limit on inferences from single lenses. 

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2. TDCOSMO: XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

   https://doi.org/10.1051/0004-6361/202345878  

   Shajib, Anowar J.; Mozumdar, Pritom; Chen, Geoff C.-F.; Treu, Tommaso; Cappellari, Michele; Knabel, Shawn; Suyu, Sherry H.; Bennert, Vardha N.; Frieman, Joshua A.; Sluse, Dominique; et al (May 2023, Astronomy & Astrophysics)

   Strong-lensing time delays enable the measurement of the Hubble constant ( H 0 ) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H 0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H 0 , effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy D d  = 865 −81 +85 Mpc and the time-delay distance D Δt  = 2180 −271 +472 Mpc, giving H 0  = 77.1 −7.1 +7.3 km s −1 Mpc −1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ( H 0  = 78.3 −3.3 +3.4 km s −1 Mpc −1 ) and for seven lenses ( H 0  = 74.2 −1.6 +1.6 km s −1 Mpc −1 ), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H 0  = 73.3 −5.8 +5.8 km s −1 Mpc −1 ). This agreement corroborates the methodology of time-delay cosmography. 

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3. TDCOSMO: V. Strategies for precise and accurate measurements of the Hubble constant with strong lensing

   https://doi.org/10.1051/0004-6361/202039179  

   Birrer, Simon; Treu, Tommaso (May 2021, Astronomy & Astrophysics)

   null (Ed.)

   Strong lensing time delays can measure the Hubble constant H 0 independently of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2% precision has been achieved with seven Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H 0 from the cosmic microwave background. However, without assumptions on the radial mass density profile – and relying exclusively on stellar kinematics to break the mass-sheet degeneracy – the precision drops to 8% with the current data obtained using the seven TDCOSMO lenses, which is insufficient to resolve the H 0 tension. With the addition of external information from 33 Sloan Lens ACS (SLACS) lenses, the precision improves to 5% if the deflectors of TDCOSMO and SLACS lenses are drawn from the same population. We investigate the prospect of improving the precision of time-delay cosmography without relying on mass profile assumptions to break the mass-sheet degeneracy. Our forecasts are based on a previously published hierarchical framework. With existing samples and technology, 3.3% precision on H 0 can be reached by adding spatially resolved kinematics of the seven TDCOSMO lenses. The precision improves to 2.5% with the further addition of kinematics for 50 nontime-delay lenses from SLACS and the Strong Lensing Legacy Survey. Expanding the samples to 40 time-delay and 200 nontime-delay lenses will improve the precision to 1.5% and 1.2%, respectively. Time-delay cosmography can reach sufficient precision to resolve the Hubble tension at 3–5 σ , without assumptions on the radial mass profile of lens galaxies. By obtaining this precision with and without external datasets, we will test the consistency of the samples and enable further improvements based on even larger future samples of time-delay and nontime-delay lenses (e.g., from the Rubin , Euclid , and Roman Observatories). 

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4. TDCOSMO: I. An exploration of systematic uncertainties in the inference of H ₀ from time-delay cosmography

   https://doi.org/10.1051/0004-6361/201937351  

   Millon, M.; Galan, A.; Courbin, F.; Treu, T.; Suyu, S. H.; Ding, X.; Birrer, S.; Chen, G. C.-F.; Shajib, A. J.; Sluse, D.; et al (July 2020, Astronomy & Astrophysics)

   Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, H 0 . As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic change of 10% of measured velocity dispersion leads to only a 0.7% shift on H 0 from the seven lenses analyzed by TDCOSMO. Second, we find no bias to arise from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in H 0 values. However, the TDCOSMO procedures that model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the “bulge-halo” conspiracy, H 0 is recovered precisely and accurately by both models. If the two models disagree, as in the case of some pathological models illustrated here, the TDCOSMO procedure either discriminates between them through the goodness of fit, or it accounts for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of six of the TDCOSMO (real) lenses: the composite model yields H 0 = 74.0 −1.8 +1.7 km s −1 Mpc −1 , while the power-law model yields 74.2 −1.6 +1.6 km s −1 Mpc −1 . In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO. 

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5. Constraints on the mass-concentration relation of cold dark matter halos with 11 strong gravitational lenses

   https://doi.org/10.1093/mnrasl/slz173  

   Gilman, Daniel; Du, Xiaolong; Benson, Andrew; Birrer, Simon; Nierenberg, Anna; Treu, Tommaso (February 2020, Monthly Notices of the Royal Astronomical Society: Letters)

   Abstract The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios, and depends on fundamental quantities in cosmology such as the slope of the primordial matter power-spectrum. This relation is unconstrained by observations on sub-galactic scales. We derive the first measurement of the mass-concentration relation using the image positions and flux ratios from eleven quadruple-image strong gravitational lenses (quads) in the mass range 106 − 1010M⊙, assuming cold dark matter. We model both subhalos and line of sight halos, finite-size background sources, and marginalize over nuisance parameters describing the lens macromodel. We also marginalize over the the logarithmic slope and redshift evolution of the mass-concentration relation, using flat priors that encompass the range of theoretical uncertainty in the literature. At z = 0, we constrain the concentration of 108M⊙ halos $$c=12_{-5}^{+6}$$ at $$68 \%$$ CI, and $$c=12_{-9}^{+15}$$ at $$95 \%$$ CI. For a 107M⊙ halo, we obtain $$68 \%$$ ($$95 \%$$) constraints $$c=15_{-8}^{+9}$$ ($$c=15_{-11}^{+18}$$), while for 109M⊙ halos $$c=10_{-4}^{+7}$$ ($$c=10_{-7}^{+14}$$). These results are consistent with the theoretical predictions from mass-concentration relations in the literature, and establish strong lensing by galaxies as a powerful probe of halo concentrations on sub-galactic scales across cosmological distance. 

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