# Lens modelling of the strongly lensed Type Ia supernova iPTF16geu

## TL;DR

This paper refines lens models of the strongly lensed Type Ia supernova iPTF16geu, constraining the lens density profile and the Hubble constant through detailed observations and analysis of fluxes, time delays, and sub-structure effects.

## Contribution

It provides a detailed lens model of iPTF16geu, incorporating sub-structure and microlensing, and offers independent constraints on the density slope and Hubble constant.

## Key findings

- Smooth lens models cannot fully explain the fluxes, indicating sub-structure is needed.
- The lens density slope is constrained to around 1.8, consistent with high-resolution imaging and velocity dispersion data.
- A lower bound on the Hubble constant is established at approximately 40 km/s/Mpc.

## Abstract

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.