Correcting for selection biases in the determination of the hubble constant from time-delay cosmography

The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred H₀. The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred H₀ by 8 per cent. Here, we test the assumption that the density profiles of galaxy–galaxy and galaxy–quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy–galaxy and galaxy–quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy–galaxy lenses have systematically higher mass-sheet components than galaxy– quasar lenses. For individual systems, λ_int correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO hierarchical inference code, we find that H₀ is lowered by a further ∼3 per cent. Using a more recent measurement of velocity dispersions and our fiducial model for selection biases, we infer H₀ = 66 ± 4 (stat) ± 1 (model sys) ± 2 (measurement sys) km s⁻¹ Mpc⁻¹ for the TDCOSMO plus SLACS data set. The first residualsystematic error is due to plausible alternative choicesin modelling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.