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

TL;DR

This paper validates a hierarchical Bayesian method for time-delay cosmography, demonstrating it can accurately estimate the Hubble constant by combining lensing data with and without time delays, reducing systematic biases.

Contribution

It expands the validation of the hierarchical framework to a broader set of lens systems, including those without time delays, improving H0 measurement accuracy and precision.

Findings

Hierarchical framework corrects H0 bias within 1.5σ of true value

Combining time-delay and non-time-delay lenses yields 2% precision in H0

Method recovers H0 with 0.7% median offset, confirming robustness

Abstract

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 $H_0$. 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 on 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 generate 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 are also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allows us to correct the $H_0$ bias associated with model choice, finding $H_0$ within $1.5\sigma$ of the fiducial value. We then combine 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 successfully accounts for this effect, recovering a value of $H_0$ which is both more precise ($\sigma\sim2\%$) 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 $H_0$ via their kinematic constraints, assuming they come from the same global population as the time-delay set.