Lens modelling of the strongly lensed Type Ia supernova iPTF16geu
  In 2016, the first strongly lensed Type Ia supernova, iPTF16geu at redshift
$z=0.409$ with four resolved images arranged symmetrically around the lens
galaxy at $z=0.2163$, was discovered. Here, refined observations of iPTF16geu,
including the time delay between images, are used to decrease uncertainties in
the lens model, including the the slope of the projected surface density of the
lens galaxy, $\Sigma\propto r^{1-\eta}$, and to constrain the universal
expansion rate $H_0$. Imaging with HST provides an upper limit on the slope
$\eta$, in slight tension with the steeper density profiles indicated by
imaging with Keck after iPTF16geu had faded, potentially due to dust extinction
not corrected for in host galaxy imaging. Since smaller $\eta$ implies larger
magnifications, we take advantage of the standard candle nature of Type Ia
supernovae constraining the image magnifications, to obtain an independent
constraint of the slope. We find that a smooth lens density fails to explain
the iPTF16geu fluxes, regardless of the slope, and additional sub-structure
lensing is needed. The total probability for the smooth halo model combined
with star microlensing to explain the iPTF16geu image fluxes is maximized at
$12\,\%$ for $\eta\sim 1.8$, in excellent agreement with Keck high spatial
resolution data, and flatter than an isothermal halo. It also agrees perfectly
with independent constraints on the slope from lens velocity dispersion
measurements. Combining with the observed time delays between the images, we
infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\,{\rm km \ s^{-1}
Mpc^{-1}}$ at $68.3\,\%$ confidence level.
