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TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography

M. Millon, A. Galan, F. Courbin, T. Treu, S. H. Suyu, X. Ding, S. Birrer, G. C. -F. Chen, A. J. Shajib, D. Sluse, K. C. Wong, A. Agnello, M. W. Auger, E. J. Buckley-Geer, J. H. H. Chan, T. Collett, C. D. Fassnacht, S. Hilbert, L. V. E. Koopmans, V. Motta, S. Mukherjee, C. E. Rusu, A. Sonnenfeld, C. Spiniello, L. Van de Vyvere

Abstract

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 $74.0^{+1.7}_{-1.8}$ $km.s^{-1}.Mpc^{-1}$, while the power-law model yields $H_0=74.2^{+1.6}_{-1.6}$ $km.s^{-1}.Mpc^{-1}$. In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.

TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography

Abstract

Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, . 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 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 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, 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 , while the power-law model yields . In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.

Paper Structure

This paper contains 23 sections, 17 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Time-delay cosmography and the mass-sheet degeneracy
  4. Two-distance inference
  5. The current TDCOSMO model families
  6. Power-law model
  7. Composite model
  8. Inference procedure and limitations of toy models
  9. Influence of kinematics data on $H_0$ measurement
  10. The TDCOSMO analysis and its sensitivity to the measured velocity dispersion
  11. Sensitivity to kinematics of the different mass model families
  12. Search for correlations between $H_0$ and physically independent observables
  13. Dependency on the characteristic scale of the lens system and spectroscopic aperture.
  14. Dependency on intrinsic parameters of the deflector traced by the velocity dispersion
  15. Dependency on the external convergence and lens redshift
  16. ...and 8 more sections

Figures (9)

  • Figure 1: Sensitivity of the inferred Hubble constant as a function of fractional change in the measured lens velocity dispersion, $\sigma_v$ (see Eq. \ref{['eq:sensitivity']}). Each color corresponds to one of the seven strong lens systems of the current TDCOSMO sample. The dotted lines display the best linear fit to the data. The joint inference performed on the seven lenses is shown in black. The error bars correspond to the $16^{th}$ and $84^{th}$ percentile of the posterior distributions. The two bottom panels show the sensitivity of $H_0$ to a change in the measured lens velocity dispersion for power-law (left) and composite (right) models independently. The sensitivity of the joint inference, $\langle \xi \rangle$ is indicated on each panel.
  • Figure 2: Effective radius $\theta_\mathrm{eff}$, Einstein radius $\theta_\mathrm{E}$ and radius of the spectroscopic aperture $\theta_\mathrm{aperture}$ of the TDCOSMO lenses. We show the ratios of these three quantities and the corresponding $H_0$ value inferred for each system. We do not observe significant correlations between the characteristic sizes of the lens, the spectroscopic aperture and $H_0$. The horizontal lines indicate the latest H0LiCOW 2019 Wong2019 and Planck Planck2018 results along with the 1$\sigma$ uncertainties.
  • Figure 3: Hubble constant as a function of the measured velocity dispersion of the main lens. The horizontal lines indicate the latest H0LiCOW 2019 Wong2019 and Planck Planck2018 results along with the 1$\sigma$ uncertainties.
  • Figure 4: Measured Hubble constant, before (upper panel) and after (lower panel) correction for the mass along the line of sight as a function of the estimated external convergence. $H_0\xspace^\mathrm{uncorr}$ and $H_0\xspace^\mathrm{corr}$ are related according to Equation (\ref{['eq:H0_externalk']}). The dashed black lines show the best linear fit, and the shaded gray envelopes correspond to the 1$\sigma$ uncertainties. The dotted blue lines represent the relation expected from the theory between $H_0\xspace^\mathrm{uncorr}$, $H_0\xspace^\mathrm{corr}$ and $\kappa_\mathrm{ext}$.
  • Figure 5: $H_0$ constraints for the TDCOSMO lenses as a function of lens redshift before (top) and after (bottom) correction for the external convergence. The best linear fits and their 1$\sigma$ envelopes are shown in shaded gray. The tentative ($1.7\sigma$ significance) trend is not introduced by the LOS contribution as it is still visible before correcting for the external convergence.
  • ...and 4 more figures