SHARP VIII: J0924+0219 lens mass distribution and time-delay prediction
  through adaptive-optics imaging
  Strongly lensed quasars can provide measurements of the Hubble constant
($H_{0}$) independent of any other methods. One of the key ingredients is
exquisite high-resolution imaging data, such as Hubble Space Telescope (HST)
imaging and adaptive-optics (AO) imaging from ground-based telescopes, which
provide strong constraints on the mass distribution of the lensing galaxy. In
this work, we expand on the previous analysis of three time-delay lenses with
AO imaging (RXJ1131-1231, HE0435-1223, and PG1115+080), and perform a joint
analysis of J0924+0219 by using AO imaging from the Keck Telescope, obtained as
part of the SHARP (Strong lensing at High Angular Resolution Program) AO
effort, with HST imaging to constrain the mass distribution of the lensing
galaxy. Under the assumption of a flat $\Lambda$CDM model with fixed
$\Omega_{\rm m}=0.3$, we show that by marginalizing over two different kinds of
mass models (power-law and composite models) and their transformed mass
profiles via a mass-sheet transformation, we obtain $\Delta t_{\rm
BA}h\hat{\sigma}_{v}^{-2}=6.89\substack{+0.8\\-0.7}$ days, $\Delta t_{\rm
CA}h\hat{\sigma}_{v}^{-2}=10.7\substack{+1.6\\-1.2}$ days, and $\Delta t_{\rm
DA}h\hat{\sigma}_{v}^{-2}=7.70\substack{+1.0\\-0.9}$ days, where
$h=H_{0}/100~\rm km\,s^{-1}\,Mpc^{-1}$ is the dimensionless Hubble constant and
$\hat{\sigma}_{v}=\sigma^{\rm ob}_{v}/(280~\rm km\,s^{-1})$ is the scaled
dimensionless velocity dispersion. Future measurements of time delays with 10%
uncertainty and velocity dispersion with 5% uncertainty would yield a $H_0$
constraint of $\sim15$% precision.
