TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles (2007.02941v3)

Abstract: The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars 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 flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by stellar kinematics. The approach is validated on hydrodynamically simulated lenses. We apply the method to the TDCOSMO sample of 7 lenses (6 from H0LiCOW) and measure $H_0=74.5^{+5.6}_{-6.1}$ km s$^{-1}{\rm Mpc}^{-1}$. In order to further constrain the deflector mass profiles, we then add imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample. For 9 of the SLAC lenses we use resolved kinematics to constrain the stellar anisotropy. From the joint analysis of the TDCOSMO+SLACS sample, we measure $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{\rm Mpc}^{-1}$, assuming 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. While our new analysis does not statistically invalidate the mass profile assumptions by H0LiCOW, and thus their $H_0$ measurement relying on those, 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, chiefly spatially resolved kinematics of lens galaxies.

• The paper introduces a hierarchical Bayesian method to jointly estimate the Hubble constant and galaxy density profiles from strong gravitational lensing time delays.
• It mitigates the mass-sheet transform degeneracy by integrating flexible mass models with stellar kinematics and SLACS data, achieving about 5% precision in H0 measurements.
• The approach is validated with hydrodynamic simulations, paving the way for enhanced precision cosmology in upcoming surveys like Euclid and LSST.

Hierarchical Time-Delay Cosmography: Joint Inference of the Hubble Constant and Galaxy Density Profiles

The paper "TDCOSMO IV: Hierarchical time-delay cosmography - joint inference of the Hubble constant and galaxy density profiles" presents a methodological advancement in the field of cosmology, specifically focusing on improving the precision and accuracy of Hubble constant ($H_0$) measurements using strong gravitational lensing time delays. This work addresses a critical challenge in cosmology: the discrepancy in $H_0$ values inferred from early and late universe observations, known as the Hubble tension.

Key Contributions and Methodology

1. Addressing the Mass-Sheet Transform (MST) Degeneracy: The authors tackle the MST, a well-known degeneracy in lens modeling that allows for a range of equally valid mass distributions to describe the same lensing observables. This degeneracy significantly impacts $H_0$ determination. The paper employs a hierarchical Bayesian framework to quantitatively assess the effect of the MST, constrained by stellar kinematics.
2. Hierarchical Bayesian Approach: A novel aspect of the paper is the application of a hierarchical Bayesian model to jointly infer $H_0$ and galaxy density profiles. By utilizing a flexible family of mass models, the authors aim to minimize MST-induced uncertainties, integrating kinematic data to robustly constrain galaxy mass profiles. This approach blends cosmology with galactic dynamics, providing a more comprehensive modeling technique.
3. Comparative Analysis with SLACS Sample: To enhance constraints on the deflector mass density profiles, the paper incorporates imaging and spectroscopy from the Sloan Lens ACS (SLACS) sample alongside the TDCOSMO sample. This joint analysis yields an $H_0$ measurement with approximately 5% precision, showcasing statistical consistency between various blind analyses (H0LiCOW, TDCOSMO-only, and TDCOSMO+SLACS).
4. Validation and Robustness: The methodology is validated using mock lenses from hydrodynamic simulations, underscoring the framework's reliability. Notably, the findings do not statistically invalidate the original mass profile assumptions by the H0LiCOW collaboration, maintaining credibility while highlighting the importance of understanding elliptical galaxy mass distributions.

Results and Implications

The hierarchical analysis with the TDCOSMO and SLACS data sets results in an $H_0$ measurement that remains within previously reported estimates, albeit with a slightly lower inferred value when SLACS is included. The paper underscores the potential systematic effects due to MST and the necessity of addressing them through robust hierarchical modeling.

Future Directions

The research outlines a roadmap for future improvements, suggesting that further constraining $H_0$ with higher precision will require:

• More high-resolution imaging and extensive spectroscopic data to delineate mass profiles and dynamics.
• Refined kinematic models to address the mass-anisotropy degeneracy.
• An expanded sample of lenses, particularly with precise time delay measurements.

This hierarchical framework, when applied to upcoming large-scale surveys (e.g., Euclid, LSST), could significantly sharpen $H_0$ constraints, contributing to resolving the Hubble tension and refining the standard cosmological model.

In conclusion, this work represents a methodical advancement in cosmographically derived $H_0$ measurements, providing both a toolset and a benchmark for future cosmological analyses in the era of precision cosmology.