The Case for Space: Estimating Precise Time Delays from Ground- and Space-Based Observations of Lensed Supernovae with Glimpse

TL;DR

We address time-delay cosmography with ground- and space-based observations of lensed supernovae by developing the Glimpse model, a Bayesian Gaussian-process framework that jointly fits resolved and unresolved light curves while marginalizing chromatic microlensing and differential dust extinction. Glimpse uses a SALT3/SN template as the mean function and a 2D Gaussian-process microlensing treatment, enabling consistent inference across data with different resolutions and wavelengths; simulations quantify how follow-up with HST, JWST, and deep ground-based facilities improves time-delay and absolute-magnification constraints. The results indicate that for 22–24 mag glSNe, time delays can be recovered with 0.5–0.8 day precision when supplemented with multiple epochs of space-based and/or deep ground-based follow-up, and brighter, resolved systems can reach sub-5% precision; absolute magnifications can also be constrained to ~0.1 mag, helping to mitigate the mass-sheet degeneracy. These findings provide practical, data-driven guidance for follow-up strategies in the Rubin-LSST era and demonstrate the potential of glSNe as competitive probes of $H_{0}$, with extensions to core-collapse SNe and opportunities for deblending-era improvements.

Abstract

The delay in arrival time of the multiple images of gravitationally lensed supernovae (glSNe) can be related to the present-day expansion rate of the universe, $H_{0}$. Despite their rarity, Rubin Observatory's Legacy Survey of Space and Time (Rubin-LSST) is expected to discover tens of galaxy-scale glSNe per year, many of which will not be resolved due to their compact nature. Follow-up from ground- and space-based telescopes will be necessary to estimate time delays to sufficient precision for meaningful $H_{0}$ constraints. We present the Glimpse model (GausSN Light curve Inference of Magnifications and Phase Shifts, Extended) that estimates time delays with resolved and unresolved observations together for the first time, while simultaneously accounting for dust and microlensing effects. With this method, we explore best follow-up strategies for glSNe observed by Rubin-LSST. For unresolved systems on the dimmest end of detectability by Rubin-LSST, having peak i-band magnitudes of 22-24 mag, the time delays are measured to as low as 0.7 day uncertainty with 6-8 epochs of resolved space-based observations in each of 4-6 optical and NIR filters. For systems of similar brightness that are resolved by ground-based facilities, time delays are consistently constrained to 0.5-0.8 day precision with 6 epochs in 4 optical and NIR filters of space-based observations or 8 epochs in 4 optical filters of deep ground-based observations. This work improves on previous time-delay estimation methods and demonstrates that glSNe time delays of $\sim10-20$ days can be measured to sufficient precision for competitive $H_{0}$ estimates in the Rubin-LSST era.

Figures (13)

• Figure 1: The fitted microlensing surface described by a 2D GP in time and wavelength for a simulated doubly-imaged glSN Ia from Arendse_2024. The simulated object is observed in the Rubin-LSST $ugrizy$ filters, is assumed to be resolved by Rubin-LSST, and includes a realistic chromatic microlensing treatment. The light curve is very densely sampled and with very good signal-to-noise, which is how a strong constraint on the microlensing surface is obtained. While there is not a significant microlensing contribution affecting image 1, the significant microlensing affecting image 2 is well-captured by the GP. Left: The mean microlensing surface averaged over ten realizations of the fitted GP model. For each realization, we sample the posterior to get the light curve template and GP hyperparameters, divide out the fitted template from the observed data, and condition the GP on the data residuals. Right: Ten samples of the GP microlensing surface sliced at the mean effective wavelength of each filter compared to the true microlensing applied to the light curve in simulations. The Glimpse microlensing realisations generally match the truth very well. We attribute the offset in the recovered microlensing for image 2 in the $g$-band to a poor recovery of dust extinction from the Milky Way, which we fit as a free parameter for this object. The input amount of Milky Way extinction is not available from the simulations, so we cannot correct for this effect before fitting as one would using Milky Way extinction maps for real data. That the shape of the microlensing realisations is broadly correct demonstrates the robustness of this method.
• Figure 2: Corner plot for the source redshift, $z_{\text{source}}$, lens redshift, $z_{\text{lens}}$, time delay, $\Delta$, and the total (summed across all images) absolute magnification in magnitude space, $\mu$, for 500 randomly selected objects from the catalogue of simulated glSNe from Wojtak_2019. The time delay and absolute magnification are computed once for each draw of source redshift, lens redshift, and Einstein radius with one unique random realisations of the lens mass model and source position parameters. The solid red stars (joint distributions) and solid red lines (marginal distributions) indicate the parameters of the base objects used in this work, as tabulated in Table \ref{['tab:base-objects']}.
• Figure 3: Dates of observation by band for each location in space and time in the Rubin-LSST survey considered in this analysis. For each base object given in Table \ref{['tab:base-objects']}, we simulate the observed light curve in each of these eight locations.
• Figure 4: Example light curve for system B at spatiotemporal location 1 under dust configuration b with six epochs of HST follow-up in the F625W, F814W, F110W, and F160W filters. Some images show fewer than six observations per filter if the image is too faint to be observed at some point in time (a "non-detection"). In this realisation of the system, the Rubin-LSST data is assumed to be unresolved. The top row shows the unresolved Rubin-LSST light curves, the middle row shows the resolved image 1 light curves from HST, and the bottom row shows the resolved image 2 light curves from HST. We show 20 realisations of the Glimpse fit to the data, with the time-vary micro-magnification ($\epsilon(t)$) contributions to the fit shown in the panel below the data. Consistent with the ground truth of no microlensing contributions, the Glimpse model does not find any significant time- or wavelength-dependent deviations from the assumed template.
• Figure 5: Uncertainty on the time delay as a function of observing strategy, assuming unresolved data from Rubin-LSST. Each sub-panel corresponds to a doubly-imaged lensing system as described in Table \ref{['tab:base-objects']}. The colours correspond to brightness of the images, with the edge colour representing the peak $i$-band magnitude of the brighter image and the face colour representing the peak $i$-band magnitude of the dimmer image. The circle marker indicates that the glSN is in a WFD rolling active region (Locations 1 and 2 in Table \ref{['tab:locations']}), the square marker indicates a WFD passive active region (Location 3), and the diamond marker indicates a WFD non-rolling region (Location 4). The solid and dashed gray lines indicate a 10% and 5% precision estimate of the time delay, respectively, given the time delay of each system. We focus on time delay uncertainties of less than 3 days in this plot, though there are a significant number of systems which have time delay uncertainties of longer than 3 days in the case of little to no follow-up.