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 $H_0$. 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.