TDCOSMO. VIII. A key test of systematics in the hierarchical method of time-delay cosmography

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of H₀. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the H₀ bias associated with model choice to find H₀ within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower z, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of H₀ which is both more precise (σ ∼ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of H₀ via their kinematic constraints, assuming they come from the same global population as the time-delay set.