A Novel Lensed Point Source Modeling Pipeline using GIGA-Lens with Application to SN Zwicky and SN iPTF16geu

TL;DR

This work tackles the Hubble constant tension by modeling strongly lensed point sources (e.g., SNe Ia) with a novel forward-modeling pipeline based on GIGA-Lens. It introduces a differentiable Bayesian framework built on the EPL mass model, employing a three-term, fully differentiable loss that integrates delensed source-plane distances, flux constraints, and time-delay information to recover lens parameters and $H_0$ from image positions, fluxes, and delays alone. The method demonstrates robust recovery across simulated archetypes, yields a $3.6\%$ uncertainty on $H_0$ from a single system, and successfully analyzes real systems SN iPTF16geu and SN Zwicky, providing competitive mass-profile constraints without requiring host-galaxy modeling or velocity-dispersion data. This approach offers a fast, convergent, and unbiased pathway to utilize rare lensed point-source events for precision cosmology and mass-profile studies, with clear avenues for extension to include host galaxies and dynamics.

Abstract

We introduce a novel modeling pipeline for strongly lensed point sources, using the GIGA-Lens framework, running on four A100 GPUs via the JAX platform. Using simulations, we demonstrate accurate and precise recovery of image positions, fluxes, and time delays, together with inference of complex lens mass distributions -- including the mass density slope, $γ$ -- from images of lensed point sources alone. We further show that we can achieve statistical uncertainty of $\sim 3.6\%$ ($\sim 2.5\, \mathrm{km\, s^{-1}/Mpc}$) on $H_0$ from a single system, with full forward modeling, i.e., simultaneous inference of all lens model parameters together with $H_0$. We apply our pipeline to two well-studied lensed SNe Ia, Zwicky and iPTF16geu. For SN iPTF16geu, unlike previous modeling efforts, we model only the images of the lensed point source (the SN) and do not use the lensed images of the extended host-galaxy. Nevertheless, we are able to infer all of the mass parameters modeled in earlier studies, and our best-fit values, including $γ$, are fully consistent with published results. In the case of SN Zwicky, taking the same approach, however, we obtain an alternative best-fit model compared to published results, underscoring the importance of fully exploring the model parameter space.

Figures (10)

• Figure 2: Modeling results for the cross configuration. The sampling converges with $\hat{R}\xspace_{max} = 1.004$ and ESS $= 6366-134623$, within 23 min. and 19 sec. of modeling time. Notice the banana-shaped marginals for some parameter combinations, indicating non-Gaussianity.
• Figure 3: Modeling results for the long-cusp configuration. The sampling achieves $\hat{R}\xspace_{max} = 1.005$ and ESS $= 1834-19525$, with a total modeling time of 5 min. and 25 sec.
• Figure 4: Modeling results for the short-cusp configuration. The sampling achieves $\hat{R}\xspace_{max} = 1.004$ and ESS $= 4691-7132$, within 2 min. and 1 sec. of modeling time. Notice the presence of an inner critical curve and caustic due to $\gamma < 2$.
• Figure 5: Modeling results for the fold configuration. The sampling results yield $\hat{R}\xspace_{max} = 1.002$ and ESS $= 2546-11008$, for a modeling time of 22 min. and 14 sec.
• Figure 6: Modeling results for the double configuration. The best-fit model shows decent predictions for flux and time delay but notably less accurate positions compared to other configurations. Regardless, the sampling notably achieves $\hat{R}\xspace_{max} = 1.015$ and ESS $= 943-15132$, after 20 min. and 50 sec. of modeling time.