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In a new paper submitted to MNRAS, our group introduces BayeSN-TD, a sophisticated probabilistic model for measuring cosmic distances using gravitationally lensed supernovae (2510.11719). This work, led by M. Grayling, tackles one of the most pressing challenges in modern cosmology: the “Hubble tension,” the persistent discrepancy between measurements of the Universe’s expansion rate ($H_0$) from the early Universe (10.1051/0004-6361/201833910) and the local Universe (10.3847/2041-8213/ac5c5b). Gravitationally lensed supernovae, whose multiple images arrive at our telescopes at different times, offer a powerful, independent way to measure $H_0$, an idea first proposed nearly sixty years ago (10.1093/mnras/128.4.307). Our new tool is designed to maximize the potential of these cosmic laboratories.

The Challenge of Microlensing

Extracting a precise time delay from a lensed supernova is complicated by microlensing—the gravitational influence of individual stars within the lensing galaxy. As the supernova’s expanding photosphere moves behind this field of stars, it experiences time-varying magnification, which can distort the observed light curves and significantly bias the inferred time delays (10.3847/1538-4357/aaa975). Naively fitting these light curves with standard supernova models can lead to inaccurate results and underestimated uncertainties. A robust analysis must account for these complex, time-dependent deviations.

A Flexible Bayesian Solution: BayeSN-TD

BayeSN-TD addresses this challenge head-on. It enhances our group’s hierarchical Bayesian model for Type Ia supernovae (SNe Ia), BayeSN, by integrating a flexible, non-parametric treatment of microlensing. Key features of the new model include:

  • Joint Inference: BayeSN-TD simultaneously infers the supernova’s intrinsic properties (like its light-curve shape), the time delays between images, the magnification of each image, and the unique microlensing signature affecting each light path.
  • Gaussian Process Modeling: We model the time-varying microlensing effect as a Gaussian Process (GP). This allows the model to learn the shape of the magnification curve from the data without imposing a rigid physical model. Specifically, we use a non-stationary Gibbs kernel, which is adept at capturing the rapid changes expected as the supernova crosses a stellar caustic.
  • Marginalization of Nuisances: By treating microlensing within a probabilistic framework, we can robustly marginalize over its effects, ensuring that the uncertainties on the time delay and $H_0$ properly account for this physical nuisance.

We rigorously tested BayeSN-TD on large suites of simulated lensed supernovae, including realistic mock observations for the upcoming Vera C. Rubin Observatory’s LSST (10.1093/mnras/stae1356). Our method proved remarkably robust, delivering well-calibrated time-delay uncertainties even when the simulations were generated with a different supernova model (SALT) and included chromatic microlensing—a wavelength-dependent effect that our current achromatic model averages over.

Application to SN H0pe and the Hubble Constant

We applied BayeSN-TD to the publicly available photometric data for SN H0pe, the first lensed SN Ia with time delays long enough for a competitive $H_0$ measurement (10.3847/1538-4357/ad3c43). Our analysis yielded time delays of $\Delta T_{BA}=121.9^{+9.5}{-7.5}$ days and $\Delta T{BC}=63.2^{+3.2}{-3.3}$ days. By combining these measurements with existing lens models of the galaxy cluster system (10.3847/1538-4357/ad9928), we derive a constraint on the Hubble constant of $H_0=69.3^{+12.6}{-7.8}$ km s$^{-1}$ Mpc$^{-1}$.

While this measurement is not yet precise enough to definitively arbitrate the Hubble tension, it demonstrates the power of our methodology. The development of BayeSN-TD provides a vital tool for the coming era of time-domain astronomy. With the anticipated discovery of dozens of lensed supernovae by LSST, robust and principled analysis tools like this will be essential for realizing the full potential of time-delay cosmography and unlocking new insights into the fundamental properties of our Universe.

M. Grayling

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